%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP334-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:37 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP334-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:00:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(sk_c7_type, type, (
% 0.21/0.41 sk_c7: $i)).
% 0.21/0.41 tff(multiply_type, type, (
% 0.21/0.41 multiply: ( $i * $i ) > $i)).
% 0.21/0.41 tff(sk_c6_type, type, (
% 0.21/0.41 sk_c6: $i)).
% 0.21/0.41 tff(sk_c2_type, type, (
% 0.21/0.41 sk_c2: $i)).
% 0.21/0.41 tff(identity_type, type, (
% 0.21/0.41 identity: $i)).
% 0.21/0.41 tff(sk_c5_type, type, (
% 0.21/0.41 sk_c5: $i)).
% 0.21/0.41 tff(inverse_type, type, (
% 0.21/0.41 inverse: $i > $i)).
% 0.21/0.41 tff(sk_c1_type, type, (
% 0.21/0.41 sk_c1: $i)).
% 0.21/0.41 tff(sk_c3_type, type, (
% 0.21/0.41 sk_c3: $i)).
% 0.21/0.41 tff(sk_c4_type, type, (
% 0.21/0.41 sk_c4: $i)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(4,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.41 tff(6,plain,(
% 0.21/0.41 ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.41 inference(skolemize,[status(sab)],[5])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (multiply(identity, sk_c7) = sk_c7),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.41 tff(10,assumption,(~(inverse(sk_c7) = sk_c5)), introduced(assumption)).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c5) = sk_c6)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c5) = sk_c6))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (((multiply(sk_c2, sk_c5) = sk_c6) | (inverse(sk_c7) = sk_c5)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c5) = sk_c6))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(13,axiom,((multiply(sk_c2, sk_c5) = sk_c6) | (inverse(sk_c7) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_18')).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c5) = sk_c6)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c5) = sk_c6)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (multiply(sk_c2, sk_c5) = sk_c6),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[15, 10])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c7) = sk_c5)) <=> ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c7) = sk_c5))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(18,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c7) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_3')).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (multiply(sk_c1, sk_c6) = sk_c7),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[23, 10])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (((inverse(sk_c1) = sk_c6) | (inverse(sk_c7) = sk_c5)) <=> ((inverse(sk_c1) = sk_c6) | (inverse(sk_c7) = sk_c5))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(26,axiom,((inverse(sk_c1) = sk_c6) | (inverse(sk_c7) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_8')).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 ((inverse(sk_c1) = sk_c6) | (inverse(sk_c7) = sk_c5)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (inverse(sk_c1) = sk_c6),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[27, 10])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (((inverse(sk_c2) = sk_c6) | (inverse(sk_c7) = sk_c5)) <=> ((inverse(sk_c2) = sk_c6) | (inverse(sk_c7) = sk_c5))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(30,axiom,((inverse(sk_c2) = sk_c6) | (inverse(sk_c7) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_13')).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 ((inverse(sk_c2) = sk_c6) | (inverse(sk_c7) = sk_c5)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (inverse(sk_c2) = sk_c6),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[31, 10])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 ((multiply(sk_c6, sk_c7) = sk_c5) <=> (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(34,axiom,(multiply(sk_c6, sk_c7) = sk_c5), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_1')).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.41 tff(36,assumption,(multiply(sk_c1, sk_c6) = sk_c7), introduced(assumption)).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (sk_c7 = multiply(sk_c1, sk_c6)),
% 0.21/0.41 inference(symmetry,[status(thm)],[36])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c1, sk_c6))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.21/0.41 inference(symmetry,[status(thm)],[38])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(43,axiom,(![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','associativity')).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.41 tff(45,plain,(
% 0.21/0.41 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[44])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(sk_c6, multiply(sk_c1, sk_c6)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(sk_c6, multiply(sk_c1, sk_c6))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(52,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.41 tff(54,plain,(
% 0.21/0.41 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.41 inference(skolemize,[status(sab)],[53])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.21/0.42 tff(58,assumption,(inverse(sk_c1) = sk_c6), introduced(assumption)).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 (sk_c6 = inverse(sk_c1)),
% 0.21/0.42 inference(symmetry,[status(thm)],[58])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (multiply(sk_c6, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[59])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (multiply(sk_c6, sk_c1) = identity),
% 0.21/0.42 inference(transitivity,[status(thm)],[60, 57])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(identity, sk_c6)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[62])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c6) = sk_c6)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(65,plain,
% 0.21/0.42 (multiply(identity, sk_c6) = sk_c6),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[64, 7])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 (sk_c6 = multiply(identity, sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[65])).
% 0.21/0.42 tff(67,assumption,(inverse(sk_c2) = sk_c6), introduced(assumption)).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c2) = sk_c2)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (multiply(identity, sk_c2) = sk_c2),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[68, 7])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c6, sk_c1)),
% 0.21/0.42 inference(symmetry,[status(thm)],[60])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.42 inference(symmetry,[status(thm)],[57])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (identity = multiply(sk_c6, sk_c1)),
% 0.21/0.42 inference(transitivity,[status(thm)],[71, 70])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (multiply(identity, sk_c2) = multiply(multiply(sk_c6, sk_c1), sk_c2)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[72])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (multiply(multiply(sk_c6, sk_c1), sk_c2) = multiply(identity, sk_c2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[73])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c1), sk_c2) = multiply(sk_c6, multiply(sk_c1, sk_c2)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (multiply(multiply(sk_c6, sk_c1), sk_c2) = multiply(sk_c6, multiply(sk_c1, sk_c2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[75, 46])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (multiply(sk_c6, multiply(sk_c1, sk_c2)) = multiply(multiply(sk_c6, sk_c1), sk_c2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[76])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (sk_c6 = sk_c5),
% 0.21/0.42 inference(transitivity,[status(thm)],[66, 63, 48, 39, 35])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 (multiply(sk_c2, sk_c6) = multiply(sk_c2, sk_c5)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[78])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (multiply(sk_c2, sk_c5) = multiply(sk_c2, sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[79])).
% 0.21/0.42 tff(81,assumption,(multiply(sk_c2, sk_c5) = sk_c6), introduced(assumption)).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (sk_c6 = multiply(sk_c2, sk_c5)),
% 0.21/0.42 inference(symmetry,[status(thm)],[81])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (sk_c6 = multiply(sk_c2, sk_c6)),
% 0.21/0.42 inference(transitivity,[status(thm)],[82, 80])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (multiply(sk_c6, sk_c6) = multiply(sk_c6, multiply(sk_c2, sk_c6))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (multiply(sk_c6, multiply(sk_c2, sk_c6)) = multiply(sk_c6, sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[84])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c2), sk_c6) = multiply(sk_c6, multiply(sk_c2, sk_c6)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (multiply(multiply(sk_c6, sk_c2), sk_c6) = multiply(sk_c6, multiply(sk_c2, sk_c6))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[86, 46])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[88, 55])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (sk_c6 = inverse(sk_c2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[67])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (multiply(sk_c6, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (multiply(sk_c6, sk_c2) = multiply(sk_c6, sk_c1)),
% 0.21/0.42 inference(transitivity,[status(thm)],[91, 89, 71, 70])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (multiply(multiply(sk_c6, sk_c2), sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(multiply(sk_c6, sk_c2), sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[93])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (sk_c6 = multiply(sk_c6, sk_c6)),
% 0.21/0.42 inference(transitivity,[status(thm)],[66, 63, 94, 87, 85])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (multiply(sk_c6, multiply(sk_c1, sk_c2)) = multiply(multiply(sk_c6, sk_c6), multiply(sk_c1, sk_c2))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[95])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (multiply(multiply(sk_c6, sk_c6), multiply(sk_c1, sk_c2)) = multiply(sk_c6, multiply(sk_c1, sk_c2))),
% 0.21/0.42 inference(symmetry,[status(thm)],[96])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c6), multiply(sk_c1, sk_c2)) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c1, sk_c2))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (multiply(multiply(sk_c6, sk_c6), multiply(sk_c1, sk_c2)) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c1, sk_c2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[98, 46])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (multiply(sk_c6, multiply(sk_c6, multiply(sk_c1, sk_c2))) = multiply(multiply(sk_c6, sk_c6), multiply(sk_c1, sk_c2))),
% 0.21/0.42 inference(symmetry,[status(thm)],[99])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (multiply(sk_c6, multiply(sk_c1, sk_c2)) = sk_c2),
% 0.21/0.42 inference(transitivity,[status(thm)],[77, 74, 69])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (multiply(sk_c6, multiply(sk_c6, multiply(sk_c1, sk_c2))) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[90, 101])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c1, sk_c2)))),
% 0.21/0.42 inference(symmetry,[status(thm)],[102])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[89])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c7), sk_c7) = identity)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (multiply(inverse(sk_c7), sk_c7) = identity),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[105, 55])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c1, sk_c2), identity), sk_c6) = multiply(multiply(sk_c1, sk_c2), multiply(identity, sk_c6)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (multiply(multiply(multiply(sk_c1, sk_c2), identity), sk_c6) = multiply(multiply(sk_c1, sk_c2), multiply(identity, sk_c6))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[107, 46])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, sk_c2), multiply(identity, sk_c6)) = multiply(multiply(multiply(sk_c1, sk_c2), identity), sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[108])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, sk_c2), multiply(identity, sk_c6)) = multiply(multiply(sk_c1, sk_c2), sk_c6)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[65])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, sk_c2), sk_c6) = multiply(multiply(sk_c1, sk_c2), multiply(identity, sk_c6))),
% 0.21/0.42 inference(symmetry,[status(thm)],[110])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, sk_c2), sk_c6) = multiply(multiply(sk_c1, sk_c2), sk_c5)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[78])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, sk_c2), sk_c5) = multiply(multiply(sk_c1, sk_c2), sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[112])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c2), sk_c5) = multiply(sk_c1, multiply(sk_c2, sk_c5)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, sk_c2), sk_c5) = multiply(sk_c1, multiply(sk_c2, sk_c5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[114, 46])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (multiply(sk_c1, multiply(sk_c2, sk_c5)) = multiply(multiply(sk_c1, sk_c2), sk_c5)),
% 0.21/0.42 inference(symmetry,[status(thm)],[115])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (multiply(sk_c1, multiply(sk_c2, sk_c5)) = multiply(sk_c1, sk_c6)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (multiply(sk_c1, sk_c6) = multiply(sk_c1, multiply(sk_c2, sk_c5))),
% 0.21/0.42 inference(symmetry,[status(thm)],[117])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (sk_c7 = multiply(multiply(multiply(sk_c1, sk_c2), identity), sk_c6)),
% 0.21/0.42 inference(transitivity,[status(thm)],[37, 118, 116, 113, 111, 109])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (multiply(sk_c7, sk_c6) = multiply(multiply(multiply(multiply(sk_c1, sk_c2), identity), sk_c6), sk_c6)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[119])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (multiply(multiply(multiply(multiply(sk_c1, sk_c2), identity), sk_c6), sk_c6) = multiply(sk_c7, sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[120])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[48])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (sk_c5 = multiply(sk_c6, sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[35])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 (sk_c5 = sk_c6),
% 0.21/0.42 inference(transitivity,[status(thm)],[123, 38, 122, 62, 65])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (multiply(sk_c5, sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[124])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (multiply(sk_c6, sk_c7) = multiply(sk_c5, sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[125])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 (sk_c6 = multiply(sk_c5, sk_c7)),
% 0.21/0.42 inference(transitivity,[status(thm)],[66, 63, 48, 39, 126])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), sk_c6) = multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c5, sk_c7))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c5, sk_c7)) = multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[128])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c5, sk_c7)) = multiply(multiply(sk_c1, sk_c2), multiply(sk_c2, multiply(sk_c5, sk_c7))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c5, sk_c7)) = multiply(multiply(sk_c1, sk_c2), multiply(sk_c2, multiply(sk_c5, sk_c7)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[130, 46])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, sk_c2), multiply(sk_c2, multiply(sk_c5, sk_c7))) = multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c5, sk_c7))),
% 0.21/0.42 inference(symmetry,[status(thm)],[131])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 (multiply(multiply(sk_c2, sk_c5), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c5), sk_c7) = multiply(sk_c2, multiply(sk_c5, sk_c7)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 (multiply(multiply(sk_c2, sk_c5), sk_c7) = multiply(sk_c2, multiply(sk_c5, sk_c7))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[134, 46])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 (multiply(sk_c2, multiply(sk_c5, sk_c7)) = multiply(multiply(sk_c2, sk_c5), sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[135])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 (multiply(sk_c2, multiply(sk_c5, sk_c7)) = sk_c5),
% 0.21/0.42 inference(transitivity,[status(thm)],[136, 133, 35])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, sk_c2), multiply(sk_c2, multiply(sk_c5, sk_c7))) = multiply(multiply(sk_c1, sk_c2), sk_c5)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[137])).
% 0.21/0.42 tff(139,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, sk_c2), sk_c5) = multiply(multiply(sk_c1, sk_c2), multiply(sk_c2, multiply(sk_c5, sk_c7)))),
% 0.21/0.42 inference(symmetry,[status(thm)],[138])).
% 0.21/0.42 tff(140,plain,
% 0.21/0.42 (multiply(multiply(multiply(sk_c1, sk_c2), identity), sk_c6) = multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), sk_c6)),
% 0.21/0.42 inference(transitivity,[status(thm)],[108, 110, 112, 139, 132, 129])).
% 0.21/0.42 tff(141,plain,
% 0.21/0.42 (multiply(multiply(multiply(multiply(sk_c1, sk_c2), identity), sk_c6), sk_c6) = multiply(multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), sk_c6), sk_c6)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.42 tff(142,plain,
% 0.21/0.42 (multiply(multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), sk_c6), sk_c6) = multiply(multiply(multiply(multiply(sk_c1, sk_c2), identity), sk_c6), sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[141])).
% 0.21/0.42 tff(143,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), sk_c6), sk_c6) = multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c6, sk_c6)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(144,plain,
% 0.21/0.42 (multiply(multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), sk_c6), sk_c6) = multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c6, sk_c6))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[143, 46])).
% 0.21/0.42 tff(145,plain,
% 0.21/0.42 (multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c6, sk_c6)) = multiply(multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), sk_c6), sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[144])).
% 0.21/0.42 tff(146,plain,
% 0.21/0.42 (multiply(sk_c6, multiply(sk_c2, sk_c6)) = multiply(multiply(sk_c6, sk_c2), sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[87])).
% 0.21/0.42 tff(147,plain,
% 0.21/0.42 (multiply(sk_c6, sk_c6) = sk_c6),
% 0.21/0.42 inference(transitivity,[status(thm)],[84, 146, 93, 62, 65])).
% 0.21/0.42 tff(148,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c2), sk_c2) = multiply(sk_c1, multiply(sk_c2, sk_c2)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(149,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, sk_c2), sk_c2) = multiply(sk_c1, multiply(sk_c2, sk_c2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[148, 46])).
% 0.21/0.42 tff(150,plain,
% 0.21/0.42 (multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c6, sk_c6)) = multiply(multiply(sk_c1, multiply(sk_c2, sk_c2)), sk_c6)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[149, 147])).
% 0.21/0.42 tff(151,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, multiply(sk_c2, sk_c2)), sk_c6) = multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c6, sk_c6))),
% 0.21/0.42 inference(symmetry,[status(thm)],[150])).
% 0.21/0.42 tff(152,plain,
% 0.21/0.42 (multiply(sk_c1, multiply(sk_c2, sk_c2)) = multiply(multiply(sk_c1, sk_c2), sk_c2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[149])).
% 0.21/0.42 tff(153,plain,
% 0.21/0.42 (multiply(multiply(sk_c1, multiply(sk_c2, sk_c2)), sk_c6) = multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c5, sk_c7))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[152, 127])).
% 0.21/0.42 tff(154,plain,
% 0.21/0.42 (multiply(multiply(multiply(sk_c1, sk_c2), sk_c2), multiply(sk_c5, sk_c7)) = multiply(multiply(sk_c1, multiply(sk_c2, sk_c2)), sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[153])).
% 0.21/0.42 tff(155,plain,
% 0.21/0.42 (sk_c7 = multiply(sk_c7, sk_c6)),
% 0.21/0.42 inference(transitivity,[status(thm)],[37, 118, 116, 139, 132, 154, 151, 145, 142, 121])).
% 0.21/0.42 tff(156,plain,
% 0.21/0.42 (multiply(inverse(sk_c7), sk_c7) = multiply(inverse(sk_c7), multiply(sk_c7, sk_c6))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[155])).
% 0.21/0.42 tff(157,plain,
% 0.21/0.42 (multiply(inverse(sk_c7), multiply(sk_c7, sk_c6)) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[156])).
% 0.21/0.42 tff(158,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c7), sk_c7), sk_c6) = multiply(inverse(sk_c7), multiply(sk_c7, sk_c6)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 (multiply(multiply(inverse(sk_c7), sk_c7), sk_c6) = multiply(inverse(sk_c7), multiply(sk_c7, sk_c6))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[158, 46])).
% 0.21/0.43 tff(160,plain,
% 0.21/0.43 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c6, sk_c1)),
% 0.21/0.43 inference(transitivity,[status(thm)],[106, 71, 70])).
% 0.21/0.43 tff(161,plain,
% 0.21/0.43 (multiply(multiply(inverse(sk_c7), sk_c7), sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[160])).
% 0.21/0.43 tff(162,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(multiply(inverse(sk_c7), sk_c7), sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[161])).
% 0.21/0.43 tff(163,plain,
% 0.21/0.43 (sk_c6 = sk_c2),
% 0.21/0.43 inference(transitivity,[status(thm)],[66, 63, 162, 159, 157, 106, 104, 103, 100, 97, 77, 74, 69])).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 (inverse(sk_c6) = inverse(sk_c2)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[163])).
% 0.21/0.43 tff(165,plain,
% 0.21/0.43 (multiply(inverse(sk_c7), multiply(sk_c7, sk_c6)) = multiply(multiply(inverse(sk_c7), sk_c7), sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[159])).
% 0.21/0.43 tff(166,plain,
% 0.21/0.43 (identity = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[106])).
% 0.21/0.43 tff(167,plain,
% 0.21/0.43 (identity = sk_c6),
% 0.21/0.43 inference(transitivity,[status(thm)],[166, 156, 165, 161, 62, 65])).
% 0.21/0.43 tff(168,plain,
% 0.21/0.43 (multiply(identity, sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[167])).
% 0.21/0.43 tff(169,plain,
% 0.21/0.43 (sk_c7 = multiply(identity, sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[9])).
% 0.21/0.43 tff(170,plain,
% 0.21/0.43 (sk_c7 = sk_c6),
% 0.21/0.43 inference(transitivity,[status(thm)],[169, 168, 38, 122, 62, 65])).
% 0.21/0.43 tff(171,plain,
% 0.21/0.43 (inverse(sk_c7) = inverse(sk_c6)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[170])).
% 0.21/0.43 tff(172,plain,
% 0.21/0.43 (inverse(sk_c7) = sk_c5),
% 0.21/0.43 inference(transitivity,[status(thm)],[171, 164, 67, 66, 63, 48, 39, 35])).
% 0.21/0.43 tff(173,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[10, 172])).
% 0.21/0.43 tff(174,plain,((inverse(sk_c7) = sk_c5) | (~(inverse(sk_c2) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c2, sk_c5) = sk_c6))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(175,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[174, 32, 10, 28, 24, 16])).
% 0.21/0.43 tff(176,plain,(inverse(sk_c7) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(177,plain,
% 0.21/0.43 (sk_c5 = inverse(sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[176])).
% 0.21/0.43 tff(178,plain,
% 0.21/0.43 (multiply(sk_c5, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[177])).
% 0.21/0.43 tff(179,plain,
% 0.21/0.43 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c5, sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[178])).
% 0.21/0.43 tff(180,plain,
% 0.21/0.43 (identity = multiply(sk_c5, sk_c7)),
% 0.21/0.43 inference(transitivity,[status(thm)],[166, 179])).
% 0.21/0.43 tff(181,plain,
% 0.21/0.43 (multiply(identity, sk_c7) = multiply(multiply(sk_c5, sk_c7), sk_c7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[180])).
% 0.21/0.43 tff(182,plain,
% 0.21/0.43 (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[181])).
% 0.21/0.43 tff(183,plain,
% 0.21/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(184,plain,
% 0.21/0.43 (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[183, 46])).
% 0.21/0.43 tff(185,plain,
% 0.21/0.43 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c5, sk_c7), sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[184])).
% 0.21/0.43 tff(186,plain,
% 0.21/0.43 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = sk_c7),
% 0.21/0.43 inference(transitivity,[status(thm)],[185, 182, 9])).
% 0.21/0.43 tff(187,plain,
% 0.21/0.43 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c3), sk_c3) = identity)),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(188,plain,
% 0.21/0.43 (multiply(inverse(sk_c3), sk_c3) = identity),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[187, 55])).
% 0.21/0.43 tff(189,assumption,(~(multiply(sk_c2, sk_c5) = sk_c6)), introduced(assumption)).
% 0.21/0.43 tff(190,plain,
% 0.21/0.43 (((inverse(sk_c3) = sk_c6) | (multiply(sk_c2, sk_c5) = sk_c6)) <=> ((inverse(sk_c3) = sk_c6) | (multiply(sk_c2, sk_c5) = sk_c6))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(191,plain,
% 0.21/0.43 (((multiply(sk_c2, sk_c5) = sk_c6) | (inverse(sk_c3) = sk_c6)) <=> ((inverse(sk_c3) = sk_c6) | (multiply(sk_c2, sk_c5) = sk_c6))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(192,axiom,((multiply(sk_c2, sk_c5) = sk_c6) | (inverse(sk_c3) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_21')).
% 0.21/0.43 tff(193,plain,
% 0.21/0.43 ((inverse(sk_c3) = sk_c6) | (multiply(sk_c2, sk_c5) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.21/0.43 tff(194,plain,
% 0.21/0.43 ((inverse(sk_c3) = sk_c6) | (multiply(sk_c2, sk_c5) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[193, 190])).
% 0.21/0.43 tff(195,plain,
% 0.21/0.43 (inverse(sk_c3) = sk_c6),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[194, 189])).
% 0.21/0.43 tff(196,plain,
% 0.21/0.43 (sk_c6 = inverse(sk_c3)),
% 0.21/0.43 inference(symmetry,[status(thm)],[195])).
% 0.21/0.43 tff(197,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[196])).
% 0.21/0.43 tff(198,plain,
% 0.21/0.43 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c6, sk_c3)),
% 0.21/0.43 inference(symmetry,[status(thm)],[197])).
% 0.21/0.43 tff(199,plain,
% 0.21/0.43 (identity = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.43 inference(symmetry,[status(thm)],[188])).
% 0.21/0.43 tff(200,plain,
% 0.21/0.43 (identity = multiply(sk_c6, sk_c3)),
% 0.21/0.43 inference(transitivity,[status(thm)],[199, 198])).
% 0.21/0.43 tff(201,plain,
% 0.21/0.43 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[200])).
% 0.21/0.43 tff(202,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c3), sk_c6) = multiply(identity, sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[201])).
% 0.21/0.43 tff(203,plain,
% 0.21/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c3), sk_c6) = multiply(sk_c6, multiply(sk_c3, sk_c6)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(204,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c3), sk_c6) = multiply(sk_c6, multiply(sk_c3, sk_c6))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[203, 46])).
% 0.21/0.43 tff(205,plain,
% 0.21/0.43 (multiply(sk_c6, multiply(sk_c3, sk_c6)) = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[204])).
% 0.21/0.43 tff(206,assumption,(~(multiply(sk_c3, sk_c6) = sk_c4)), introduced(assumption)).
% 0.21/0.43 tff(207,plain,
% 0.21/0.43 (((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c4)) <=> ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c4))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(208,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_5')).
% 0.21/0.43 tff(209,plain,
% 0.21/0.43 ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c4)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.21/0.43 tff(210,plain,
% 0.21/0.43 (multiply(sk_c1, sk_c6) = sk_c7),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[209, 206])).
% 0.21/0.43 tff(211,plain,
% 0.21/0.43 (sk_c7 = multiply(sk_c1, sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[210])).
% 0.21/0.43 tff(212,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c1, sk_c6))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[211])).
% 0.21/0.43 tff(213,plain,
% 0.21/0.43 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[212])).
% 0.21/0.43 tff(214,plain,
% 0.21/0.43 (((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4)) <=> ((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(215,axiom,((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_10')).
% 0.21/0.43 tff(216,plain,
% 0.21/0.43 ((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.21/0.43 tff(217,plain,
% 0.21/0.43 (inverse(sk_c1) = sk_c6),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[216, 206])).
% 0.21/0.43 tff(218,plain,
% 0.21/0.43 (sk_c6 = inverse(sk_c1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[217])).
% 0.21/0.43 tff(219,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[218])).
% 0.21/0.43 tff(220,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c1) = identity),
% 0.21/0.43 inference(transitivity,[status(thm)],[219, 57])).
% 0.21/0.43 tff(221,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(identity, sk_c6)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[220])).
% 0.21/0.43 tff(222,plain,
% 0.21/0.43 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[221])).
% 0.21/0.43 tff(223,plain,
% 0.21/0.43 (((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4)) <=> ((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(224,axiom,((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_15')).
% 0.21/0.43 tff(225,plain,
% 0.21/0.43 ((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.21/0.43 tff(226,plain,
% 0.21/0.43 (inverse(sk_c2) = sk_c6),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[225, 206])).
% 0.21/0.43 tff(227,plain,
% 0.21/0.43 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c6, sk_c1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[219])).
% 0.21/0.43 tff(228,plain,
% 0.21/0.43 (identity = multiply(sk_c6, sk_c1)),
% 0.21/0.43 inference(transitivity,[status(thm)],[71, 227])).
% 0.21/0.43 tff(229,plain,
% 0.21/0.43 (multiply(identity, sk_c2) = multiply(multiply(sk_c6, sk_c1), sk_c2)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[228])).
% 0.21/0.43 tff(230,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c1), sk_c2) = multiply(identity, sk_c2)),
% 0.21/0.43 inference(symmetry,[status(thm)],[229])).
% 0.21/0.43 tff(231,plain,
% 0.21/0.43 (sk_c6 = sk_c5),
% 0.21/0.43 inference(transitivity,[status(thm)],[66, 222, 48, 213, 35])).
% 0.21/0.43 tff(232,plain,
% 0.21/0.43 (multiply(sk_c2, sk_c6) = multiply(sk_c2, sk_c5)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[231])).
% 0.21/0.43 tff(233,plain,
% 0.21/0.43 (multiply(sk_c2, sk_c5) = multiply(sk_c2, sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[232])).
% 0.21/0.43 tff(234,plain,
% 0.21/0.43 (((multiply(sk_c2, sk_c5) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4)) <=> ((multiply(sk_c2, sk_c5) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(235,axiom,((multiply(sk_c2, sk_c5) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_20')).
% 0.21/0.43 tff(236,plain,
% 0.21/0.43 ((multiply(sk_c2, sk_c5) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c4)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.21/0.43 tff(237,plain,
% 0.21/0.43 (multiply(sk_c2, sk_c5) = sk_c6),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[236, 206])).
% 0.21/0.43 tff(238,plain,
% 0.21/0.43 (sk_c6 = multiply(sk_c2, sk_c5)),
% 0.21/0.43 inference(symmetry,[status(thm)],[237])).
% 0.21/0.43 tff(239,plain,
% 0.21/0.43 (sk_c6 = multiply(sk_c2, sk_c6)),
% 0.21/0.43 inference(transitivity,[status(thm)],[238, 233])).
% 0.21/0.43 tff(240,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c6) = multiply(sk_c6, multiply(sk_c2, sk_c6))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[239])).
% 0.21/0.43 tff(241,plain,
% 0.21/0.43 (multiply(sk_c6, multiply(sk_c2, sk_c6)) = multiply(sk_c6, sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[240])).
% 0.21/0.43 tff(242,plain,
% 0.21/0.43 (sk_c6 = inverse(sk_c2)),
% 0.21/0.43 inference(symmetry,[status(thm)],[226])).
% 0.21/0.43 tff(243,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[242])).
% 0.21/0.43 tff(244,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c2) = multiply(sk_c6, sk_c1)),
% 0.21/0.43 inference(transitivity,[status(thm)],[243, 89, 71, 227])).
% 0.21/0.43 tff(245,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c2), sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[244])).
% 0.21/0.43 tff(246,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(multiply(sk_c6, sk_c2), sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[245])).
% 0.21/0.43 tff(247,plain,
% 0.21/0.43 (sk_c6 = multiply(sk_c6, sk_c6)),
% 0.21/0.43 inference(transitivity,[status(thm)],[66, 222, 246, 87, 241])).
% 0.21/0.43 tff(248,plain,
% 0.21/0.43 (multiply(sk_c6, multiply(sk_c1, sk_c2)) = multiply(multiply(sk_c6, sk_c6), multiply(sk_c1, sk_c2))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[247])).
% 0.21/0.44 tff(249,plain,
% 0.21/0.44 (multiply(multiply(sk_c6, sk_c6), multiply(sk_c1, sk_c2)) = multiply(sk_c6, multiply(sk_c1, sk_c2))),
% 0.21/0.44 inference(symmetry,[status(thm)],[248])).
% 0.21/0.44 tff(250,plain,
% 0.21/0.44 (multiply(sk_c6, multiply(sk_c1, sk_c2)) = sk_c2),
% 0.21/0.44 inference(transitivity,[status(thm)],[77, 230, 69])).
% 0.21/0.44 tff(251,plain,
% 0.21/0.44 (multiply(sk_c6, multiply(sk_c6, multiply(sk_c1, sk_c2))) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[242, 250])).
% 0.21/0.44 tff(252,plain,
% 0.21/0.44 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c1, sk_c2)))),
% 0.21/0.44 inference(symmetry,[status(thm)],[251])).
% 0.21/0.44 tff(253,plain,
% 0.21/0.44 (inverse(sk_c7) = sk_c5),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[174, 226, 217, 210, 237])).
% 0.21/0.44 tff(254,plain,
% 0.21/0.44 (inverse(sk_c7) = sk_c6),
% 0.21/0.44 inference(transitivity,[status(thm)],[253, 123, 212, 122, 221, 65])).
% 0.21/0.44 tff(255,plain,
% 0.21/0.44 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[254])).
% 0.21/0.44 tff(256,plain,
% 0.21/0.44 (multiply(sk_c6, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[255])).
% 0.21/0.44 tff(257,plain,
% 0.21/0.44 (sk_c6 = sk_c2),
% 0.21/0.44 inference(transitivity,[status(thm)],[66, 222, 48, 213, 256, 106, 104, 252, 100, 249, 77, 230, 69])).
% 0.21/0.44 tff(258,plain,
% 0.21/0.44 (inverse(sk_c6) = inverse(sk_c2)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[257])).
% 0.21/0.44 tff(259,plain,
% 0.21/0.44 (inverse(sk_c6) = sk_c5),
% 0.21/0.44 inference(transitivity,[status(thm)],[258, 226, 66, 222, 48, 213, 35])).
% 0.21/0.44 tff(260,plain,
% 0.21/0.44 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5),
% 0.21/0.44 inference(transitivity,[status(thm)],[213, 35])).
% 0.21/0.44 tff(261,plain,
% 0.21/0.44 (^[X4: $i, X3: $i, X2: $i] : refl(((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(262,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[261])).
% 0.21/0.44 tff(263,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(264,plain,
% 0.21/0.44 (^[X4: $i, X3: $i, X2: $i] : rewrite(((~(multiply(X3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(265,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X2: $i] : ((~(multiply(X3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[264])).
% 0.21/0.44 tff(266,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(X3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i] : ((~(multiply(X3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)))),
% 0.21/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.44 tff(267,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = X1)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(X3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)))),
% 0.21/0.44 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.44 tff(268,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = X1)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) <=> ![X4: $i, X3: $i, X2: $i] : ((~(multiply(X3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[267, 266])).
% 0.21/0.44 tff(269,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = X1)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) <=> ![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[268, 265])).
% 0.21/0.44 tff(270,plain,
% 0.21/0.44 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)))), (((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) <=> (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X4) = sk_c6))))), rewrite((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X4) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)))), (((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))))), ((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) <=> (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(multiply(X4, sk_c5) = sk_c6))))), rewrite((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(multiply(X4, sk_c5) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)))), ((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))))), (((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) <=> (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(sk_c6) = sk_c5))))), rewrite((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(sk_c6) = sk_c5))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)))), (((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))))), ((((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) <=> (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(sk_c7) = sk_c5))))), rewrite((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(sk_c7) = sk_c5))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)))), ((((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))))), (((((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c6, X1) = sk_c5))) <=> (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(multiply(sk_c6, X1) = sk_c5))))), rewrite((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(multiply(sk_c6, X1) = sk_c5))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)))), (((((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c6, X1) = sk_c5))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))))), ((((((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c6, X1) = sk_c5))) | (~(multiply(X2, sk_c6) = X1))) <=> (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = X1))))), rewrite((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = X1))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = X1)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)))), ((((((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c6, X1) = sk_c5))) | (~(multiply(X2, sk_c6) = X1))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = X1)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))))), (((((((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c6, X1) = sk_c5))) | (~(multiply(X2, sk_c6) = X1))) | (~(inverse(X2) = sk_c6))) <=> (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = X1)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))))), rewrite((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = X1)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = X1)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)))), (((((((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c6, X1) = sk_c5))) | (~(multiply(X2, sk_c6) = X1))) | (~(inverse(X2) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = X1)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(271,plain,
% 0.21/0.45 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c6, X1) = sk_c5))) | (~(multiply(X2, sk_c6) = X1))) | (~(inverse(X2) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = X1)) | (~(multiply(sk_c6, X1) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(inverse(X3) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[270])).
% 0.21/0.45 tff(272,plain,
% 0.21/0.45 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c6, X1) = sk_c5))) | (~(multiply(X2, sk_c6) = X1))) | (~(inverse(X2) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[271, 269])).
% 0.21/0.45 tff(273,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X3, sk_c6) = sk_c7))) | (~(inverse(X3) = sk_c6))) | (~(inverse(X4) = sk_c6))) | (~(multiply(X4, sk_c5) = sk_c6))) | (~(inverse(sk_c6) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c6, X1) = sk_c5))) | (~(multiply(X2, sk_c6) = X1))) | (~(inverse(X2) = sk_c6)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_22')).
% 0.21/0.46 tff(274,plain,
% 0.21/0.46 (![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.21/0.46 tff(275,plain,
% 0.21/0.46 (![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[274, 263])).
% 0.21/0.46 tff(276,plain,(
% 0.21/0.46 ![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[275])).
% 0.21/0.46 tff(277,plain,
% 0.21/0.46 (![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[276, 262])).
% 0.21/0.46 tff(278,plain,
% 0.21/0.46 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(279,plain,
% 0.21/0.46 (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c2, sk_c5) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(280,plain,
% 0.21/0.46 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c2, sk_c5) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[279])).
% 0.21/0.46 tff(281,plain,
% 0.21/0.46 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c2, sk_c5) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[280, 278])).
% 0.21/0.46 tff(282,plain,
% 0.21/0.46 ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c2, sk_c5) = sk_c6)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(283,plain,
% 0.21/0.46 ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.21/0.46 tff(284,plain,
% 0.21/0.46 ((~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[283, 35, 210, 217, 226, 237, 277])).
% 0.21/0.46 tff(285,plain,
% 0.21/0.46 (~(inverse(sk_c6) = sk_c5)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[284, 253, 260])).
% 0.21/0.46 tff(286,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[285, 259])).
% 0.21/0.46 tff(287,plain,(multiply(sk_c3, sk_c6) = sk_c4), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(288,plain,
% 0.21/0.46 (multiply(sk_c6, multiply(sk_c3, sk_c6)) = multiply(sk_c6, sk_c4)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[287])).
% 0.21/0.46 tff(289,plain,
% 0.21/0.46 (multiply(sk_c6, sk_c4) = multiply(sk_c6, multiply(sk_c3, sk_c6))),
% 0.21/0.46 inference(symmetry,[status(thm)],[288])).
% 0.21/0.46 tff(290,plain,
% 0.21/0.46 (((multiply(sk_c2, sk_c5) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5)) <=> ((multiply(sk_c2, sk_c5) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(291,axiom,((multiply(sk_c2, sk_c5) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_19')).
% 0.21/0.46 tff(292,plain,
% 0.21/0.46 ((multiply(sk_c2, sk_c5) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.21/0.46 tff(293,plain,
% 0.21/0.46 (multiply(sk_c6, sk_c4) = sk_c5),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[292, 189])).
% 0.21/0.46 tff(294,plain,
% 0.21/0.46 (sk_c5 = multiply(sk_c6, sk_c4)),
% 0.21/0.46 inference(symmetry,[status(thm)],[293])).
% 0.21/0.46 tff(295,plain,
% 0.21/0.46 (multiply(multiply(identity, sk_c6), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[65])).
% 0.21/0.46 tff(296,plain,
% 0.21/0.46 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c6), sk_c7) = multiply(identity, multiply(sk_c6, sk_c7)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(297,plain,
% 0.21/0.46 (multiply(multiply(identity, sk_c6), sk_c7) = multiply(identity, multiply(sk_c6, sk_c7))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[296, 46])).
% 0.21/0.46 tff(298,plain,
% 0.21/0.46 (multiply(identity, multiply(sk_c6, sk_c7)) = multiply(multiply(identity, sk_c6), sk_c7)),
% 0.21/0.46 inference(symmetry,[status(thm)],[297])).
% 0.21/0.46 tff(299,plain,
% 0.21/0.46 (sk_c6 = multiply(sk_c6, sk_c7)),
% 0.21/0.46 inference(transitivity,[status(thm)],[66, 201, 204, 288, 293, 123])).
% 0.21/0.46 tff(300,assumption,(~(inverse(sk_c2) = sk_c6)), introduced(assumption)).
% 0.21/0.46 tff(301,plain,
% 0.21/0.46 (((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5)) <=> ((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(302,axiom,((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_14')).
% 0.21/0.46 tff(303,plain,
% 0.21/0.46 ((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.21/0.46 tff(304,plain,
% 0.21/0.46 (multiply(sk_c6, sk_c4) = sk_c5),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[303, 300])).
% 0.21/0.46 tff(305,plain,
% 0.21/0.46 (multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5),
% 0.21/0.46 inference(transitivity,[status(thm)],[288, 304])).
% 0.21/0.46 tff(306,plain,
% 0.21/0.46 (((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c6)) <=> ((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c6))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(307,axiom,((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_16')).
% 0.21/0.46 tff(308,plain,
% 0.21/0.46 ((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c6)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.21/0.46 tff(309,plain,
% 0.21/0.46 (inverse(sk_c3) = sk_c6),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[308, 300])).
% 0.21/0.46 tff(310,plain,
% 0.21/0.46 (sk_c6 = inverse(sk_c3)),
% 0.21/0.46 inference(symmetry,[status(thm)],[309])).
% 0.21/0.46 tff(311,plain,
% 0.21/0.46 (multiply(sk_c6, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[310])).
% 0.21/0.46 tff(312,plain,
% 0.21/0.46 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c6, sk_c3)),
% 0.21/0.46 inference(symmetry,[status(thm)],[311])).
% 0.21/0.46 tff(313,plain,
% 0.21/0.46 (identity = multiply(sk_c6, sk_c3)),
% 0.21/0.46 inference(transitivity,[status(thm)],[199, 312])).
% 0.21/0.46 tff(314,plain,
% 0.21/0.46 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[313])).
% 0.21/0.46 tff(315,plain,
% 0.21/0.46 (multiply(multiply(sk_c6, sk_c3), sk_c6) = multiply(identity, sk_c6)),
% 0.21/0.46 inference(symmetry,[status(thm)],[314])).
% 0.21/0.46 tff(316,plain,
% 0.21/0.46 (sk_c5 = multiply(sk_c6, sk_c4)),
% 0.21/0.46 inference(symmetry,[status(thm)],[304])).
% 0.21/0.47 tff(317,plain,
% 0.21/0.47 (inverse(sk_c7) = sk_c6),
% 0.21/0.47 inference(transitivity,[status(thm)],[176, 316, 289, 205, 315, 65])).
% 0.21/0.47 tff(318,plain,
% 0.21/0.47 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[317])).
% 0.21/0.47 tff(319,plain,
% 0.21/0.47 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c6), sk_c6) = identity)),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(320,plain,
% 0.21/0.47 (multiply(inverse(sk_c6), sk_c6) = identity),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[319, 55])).
% 0.21/0.47 tff(321,plain,
% 0.21/0.47 (((inverse(sk_c2) = sk_c6) | (inverse(sk_c6) = sk_c5)) <=> ((inverse(sk_c2) = sk_c6) | (inverse(sk_c6) = sk_c5))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(322,axiom,((inverse(sk_c2) = sk_c6) | (inverse(sk_c6) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_12')).
% 0.21/0.47 tff(323,plain,
% 0.21/0.47 ((inverse(sk_c2) = sk_c6) | (inverse(sk_c6) = sk_c5)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.21/0.47 tff(324,plain,
% 0.21/0.47 (inverse(sk_c6) = sk_c5),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[323, 300])).
% 0.21/0.47 tff(325,plain,
% 0.21/0.47 (sk_c5 = inverse(sk_c6)),
% 0.21/0.47 inference(symmetry,[status(thm)],[324])).
% 0.21/0.47 tff(326,plain,
% 0.21/0.47 (multiply(sk_c6, sk_c7) = inverse(sk_c6)),
% 0.21/0.47 inference(transitivity,[status(thm)],[35, 325])).
% 0.21/0.47 tff(327,plain,
% 0.21/0.47 (multiply(multiply(sk_c6, sk_c7), sk_c6) = multiply(inverse(sk_c6), sk_c6)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[326])).
% 0.21/0.47 tff(328,plain,
% 0.21/0.47 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c7), sk_c6) = multiply(sk_c6, multiply(sk_c7, sk_c6)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(329,plain,
% 0.21/0.47 (multiply(multiply(sk_c6, sk_c7), sk_c6) = multiply(sk_c6, multiply(sk_c7, sk_c6))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[328, 46])).
% 0.21/0.47 tff(330,plain,
% 0.21/0.47 (multiply(sk_c6, multiply(sk_c7, sk_c6)) = multiply(multiply(sk_c6, sk_c7), sk_c6)),
% 0.21/0.47 inference(symmetry,[status(thm)],[329])).
% 0.21/0.47 tff(331,plain,
% 0.21/0.47 (sk_c5 = sk_c6),
% 0.21/0.47 inference(transitivity,[status(thm)],[316, 289, 205, 315, 65])).
% 0.21/0.47 tff(332,plain,
% 0.21/0.47 (multiply(sk_c5, multiply(sk_c7, sk_c6)) = multiply(sk_c6, multiply(sk_c7, sk_c6))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[331])).
% 0.21/0.47 tff(333,plain,
% 0.21/0.47 (sk_c6 = sk_c5),
% 0.21/0.47 inference(transitivity,[status(thm)],[66, 314, 204, 288, 304])).
% 0.21/0.47 tff(334,plain,
% 0.21/0.47 (multiply(sk_c7, sk_c6) = multiply(sk_c7, sk_c5)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[333])).
% 0.21/0.47 tff(335,plain,
% 0.21/0.47 (multiply(sk_c7, sk_c5) = multiply(sk_c7, sk_c6)),
% 0.21/0.47 inference(symmetry,[status(thm)],[334])).
% 0.21/0.47 tff(336,plain,
% 0.21/0.47 (identity = sk_c5),
% 0.21/0.47 inference(transitivity,[status(thm)],[166, 318, 35])).
% 0.21/0.47 tff(337,plain,
% 0.21/0.47 (multiply(identity, multiply(sk_c7, sk_c5)) = multiply(sk_c5, multiply(sk_c7, sk_c6))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[336, 335])).
% 0.21/0.47 tff(338,plain,
% 0.21/0.47 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c7, sk_c5)) = multiply(sk_c7, sk_c5))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(339,plain,
% 0.21/0.47 (multiply(identity, multiply(sk_c7, sk_c5)) = multiply(sk_c7, sk_c5)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[338, 7])).
% 0.21/0.47 tff(340,plain,
% 0.21/0.47 (multiply(sk_c7, sk_c5) = multiply(identity, multiply(sk_c7, sk_c5))),
% 0.21/0.47 inference(symmetry,[status(thm)],[339])).
% 0.21/0.47 tff(341,plain,
% 0.21/0.47 (multiply(sk_c7, sk_c5) = sk_c6),
% 0.21/0.47 inference(transitivity,[status(thm)],[340, 337, 332, 330, 327, 320, 166, 318, 35, 316, 289, 205, 315, 65])).
% 0.21/0.47 tff(342,plain,
% 0.21/0.47 (identity = inverse(sk_c7)),
% 0.21/0.47 inference(transitivity,[status(thm)],[166, 318, 35, 177])).
% 0.21/0.47 tff(343,plain,
% 0.21/0.47 (multiply(identity, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[342])).
% 0.21/0.47 tff(344,plain,
% 0.21/0.47 (sk_c7 = sk_c6),
% 0.21/0.47 inference(transitivity,[status(thm)],[169, 343, 318, 35, 316, 289, 205, 315, 65])).
% 0.21/0.47 tff(345,plain,
% 0.21/0.47 (multiply(sk_c3, sk_c6) = multiply(sk_c3, sk_c5)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[333])).
% 0.21/0.47 tff(346,plain,
% 0.21/0.47 ((multiply(sk_c3, sk_c6) = sk_c7) <=> (multiply(sk_c3, sk_c5) = sk_c6)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[345, 344])).
% 0.21/0.47 tff(347,plain,
% 0.21/0.47 ((multiply(sk_c3, sk_c5) = sk_c6) <=> (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.21/0.47 inference(symmetry,[status(thm)],[346])).
% 0.21/0.47 tff(348,plain,
% 0.21/0.47 (multiply(sk_c6, sk_c4) = inverse(sk_c7)),
% 0.21/0.47 inference(transitivity,[status(thm)],[304, 177])).
% 0.21/0.47 tff(349,plain,
% 0.21/0.47 (multiply(multiply(sk_c6, sk_c4), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[348])).
% 0.21/0.47 tff(350,plain,
% 0.21/0.47 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c4), sk_c7) = multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(351,plain,
% 0.21/0.47 (multiply(multiply(sk_c6, sk_c4), sk_c7) = multiply(sk_c6, multiply(sk_c4, sk_c7))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[350, 46])).
% 0.21/0.47 tff(352,plain,
% 0.21/0.47 (multiply(sk_c6, multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c6, sk_c4), sk_c7)),
% 0.21/0.47 inference(symmetry,[status(thm)],[351])).
% 0.21/0.47 tff(353,plain,
% 0.21/0.47 (sk_c4 = multiply(sk_c3, sk_c6)),
% 0.21/0.47 inference(symmetry,[status(thm)],[287])).
% 0.21/0.47 tff(354,plain,
% 0.21/0.47 (multiply(sk_c4, sk_c7) = multiply(multiply(sk_c3, sk_c6), sk_c7)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[353])).
% 0.21/0.47 tff(355,plain,
% 0.21/0.47 (multiply(multiply(sk_c3, sk_c6), sk_c7) = multiply(sk_c4, sk_c7)),
% 0.21/0.47 inference(symmetry,[status(thm)],[354])).
% 0.21/0.47 tff(356,plain,
% 0.21/0.47 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c6), sk_c7) = multiply(sk_c3, multiply(sk_c6, sk_c7)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(357,plain,
% 0.21/0.47 (multiply(multiply(sk_c3, sk_c6), sk_c7) = multiply(sk_c3, multiply(sk_c6, sk_c7))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[356, 46])).
% 0.21/0.47 tff(358,plain,
% 0.21/0.47 (multiply(sk_c3, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c3, sk_c6), sk_c7)),
% 0.21/0.47 inference(symmetry,[status(thm)],[357])).
% 0.21/0.47 tff(359,plain,
% 0.21/0.47 (multiply(sk_c3, multiply(sk_c6, sk_c7)) = multiply(sk_c4, sk_c7)),
% 0.21/0.47 inference(transitivity,[status(thm)],[358, 355])).
% 0.21/0.47 tff(360,plain,
% 0.21/0.47 (identity = sk_c6),
% 0.21/0.47 inference(transitivity,[status(thm)],[166, 318, 35, 316, 289, 205, 315, 65])).
% 0.21/0.47 tff(361,plain,
% 0.21/0.47 (multiply(identity, multiply(sk_c3, multiply(sk_c6, sk_c7))) = multiply(sk_c6, multiply(sk_c4, sk_c7))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[360, 359])).
% 0.21/0.47 tff(362,plain,
% 0.21/0.47 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c3, multiply(sk_c6, sk_c7))) = multiply(sk_c3, multiply(sk_c6, sk_c7)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(363,plain,
% 0.21/0.47 (multiply(identity, multiply(sk_c3, multiply(sk_c6, sk_c7))) = multiply(sk_c3, multiply(sk_c6, sk_c7))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[362, 7])).
% 0.21/0.47 tff(364,plain,
% 0.21/0.47 (multiply(sk_c3, multiply(sk_c6, sk_c7)) = multiply(identity, multiply(sk_c3, multiply(sk_c6, sk_c7)))),
% 0.21/0.47 inference(symmetry,[status(thm)],[363])).
% 0.21/0.47 tff(365,plain,
% 0.21/0.47 (multiply(sk_c3, sk_c5) = multiply(sk_c3, multiply(sk_c6, sk_c7))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[123])).
% 0.21/0.47 tff(366,plain,
% 0.21/0.47 (multiply(sk_c3, sk_c5) = sk_c6),
% 0.21/0.47 inference(transitivity,[status(thm)],[365, 364, 361, 352, 349, 318, 35, 316, 289, 205, 315, 65])).
% 0.21/0.47 tff(367,plain,
% 0.21/0.47 (multiply(sk_c3, sk_c6) = sk_c7),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[366, 347])).
% 0.21/0.47 tff(368,plain,
% 0.21/0.47 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c6)) | (~(inverse(sk_c3) = sk_c6)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c6)) | (~(inverse(sk_c3) = sk_c6)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(369,plain,
% 0.21/0.47 (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c3) = sk_c6)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5)) | (~(multiply(sk_c7, sk_c5) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c6)) | (~(inverse(sk_c3) = sk_c6)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(370,plain,
% 0.21/0.47 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c3) = sk_c6)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5)) | (~(multiply(sk_c7, sk_c5) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c6)) | (~(inverse(sk_c3) = sk_c6)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[369])).
% 0.21/0.47 tff(371,plain,
% 0.21/0.47 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c3) = sk_c6)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5)) | (~(multiply(sk_c7, sk_c5) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c6)) | (~(inverse(sk_c3) = sk_c6)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[370, 368])).
% 0.21/0.47 tff(372,plain,
% 0.21/0.47 ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c3) = sk_c6)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5)) | (~(multiply(sk_c7, sk_c5) = sk_c6)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(373,plain,
% 0.21/0.48 ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c6)) | (~(inverse(sk_c3) = sk_c6)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.21/0.48 tff(374,plain,
% 0.21/0.48 ((~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c6)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c3, sk_c6)) = sk_c5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[373, 35, 324, 176, 309, 277])).
% 0.21/0.48 tff(375,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[374, 367, 341, 317, 305])).
% 0.21/0.48 tff(376,plain,(inverse(sk_c2) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(377,plain,
% 0.21/0.48 (sk_c6 = inverse(sk_c2)),
% 0.21/0.48 inference(symmetry,[status(thm)],[376])).
% 0.21/0.48 tff(378,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[377])).
% 0.21/0.48 tff(379,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c2) = identity),
% 0.21/0.48 inference(transitivity,[status(thm)],[378, 89])).
% 0.21/0.48 tff(380,plain,
% 0.21/0.48 (multiply(multiply(sk_c6, sk_c2), sk_c6) = multiply(identity, multiply(sk_c6, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[379, 299])).
% 0.21/0.48 tff(381,plain,
% 0.21/0.48 (sk_c6 = sk_c5),
% 0.21/0.48 inference(transitivity,[status(thm)],[66, 201, 204, 288, 293])).
% 0.21/0.48 tff(382,plain,
% 0.21/0.48 (multiply(sk_c2, sk_c6) = multiply(sk_c2, sk_c5)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[381])).
% 0.21/0.48 tff(383,plain,
% 0.21/0.48 (multiply(sk_c2, sk_c5) = multiply(sk_c2, sk_c6)),
% 0.21/0.48 inference(symmetry,[status(thm)],[382])).
% 0.21/0.48 tff(384,plain,
% 0.21/0.48 (multiply(sk_c2, sk_c5) = multiply(sk_c2, multiply(sk_c6, sk_c4))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[294])).
% 0.21/0.48 tff(385,plain,
% 0.21/0.48 (multiply(sk_c2, multiply(sk_c6, sk_c4)) = multiply(sk_c2, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[384])).
% 0.21/0.48 tff(386,plain,
% 0.21/0.48 (multiply(sk_c2, multiply(sk_c6, sk_c4)) = multiply(sk_c2, sk_c6)),
% 0.21/0.48 inference(transitivity,[status(thm)],[385, 383])).
% 0.21/0.48 tff(387,plain,
% 0.21/0.48 (sk_c6 = inverse(sk_c7)),
% 0.21/0.48 inference(transitivity,[status(thm)],[66, 201, 204, 288, 293, 177])).
% 0.21/0.48 tff(388,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[387])).
% 0.21/0.48 tff(389,plain,
% 0.21/0.48 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[388])).
% 0.21/0.48 tff(390,plain,
% 0.21/0.48 (identity = sk_c6),
% 0.21/0.48 inference(transitivity,[status(thm)],[166, 389, 35, 294, 289, 205, 202, 65])).
% 0.21/0.48 tff(391,plain,
% 0.21/0.48 (multiply(identity, multiply(sk_c2, multiply(sk_c6, sk_c4))) = multiply(sk_c6, multiply(sk_c2, sk_c6))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[390, 386])).
% 0.21/0.48 tff(392,plain,
% 0.21/0.48 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c2, multiply(sk_c6, sk_c4))) = multiply(sk_c2, multiply(sk_c6, sk_c4)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(393,plain,
% 0.21/0.48 (multiply(identity, multiply(sk_c2, multiply(sk_c6, sk_c4))) = multiply(sk_c2, multiply(sk_c6, sk_c4))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[392, 7])).
% 0.21/0.48 tff(394,plain,
% 0.21/0.48 (multiply(sk_c2, multiply(sk_c6, sk_c4)) = multiply(identity, multiply(sk_c2, multiply(sk_c6, sk_c4)))),
% 0.21/0.48 inference(symmetry,[status(thm)],[393])).
% 0.21/0.48 tff(395,plain,
% 0.21/0.48 (multiply(sk_c2, sk_c5) = sk_c6),
% 0.21/0.48 inference(transitivity,[status(thm)],[384, 394, 391, 146, 380, 298, 295, 35, 294, 289, 205, 202, 65])).
% 0.21/0.48 tff(396,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[189, 395])).
% 0.21/0.48 tff(397,plain,(multiply(sk_c2, sk_c5) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(398,plain,
% 0.21/0.48 (multiply(sk_c2, sk_c5) = multiply(sk_c2, multiply(sk_c6, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[123])).
% 0.21/0.48 tff(399,plain,
% 0.21/0.48 (multiply(sk_c2, multiply(sk_c6, sk_c7)) = multiply(sk_c2, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[398])).
% 0.21/0.48 tff(400,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c6), sk_c7) = multiply(sk_c2, multiply(sk_c6, sk_c7)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(401,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, sk_c6), sk_c7) = multiply(sk_c2, multiply(sk_c6, sk_c7))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[400, 46])).
% 0.21/0.48 tff(402,plain,
% 0.21/0.48 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(403,plain,
% 0.21/0.48 (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(sk_c7, sk_c7)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[402, 7])).
% 0.21/0.48 tff(404,plain,
% 0.21/0.48 (multiply(sk_c7, sk_c7) = multiply(identity, multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(symmetry,[status(thm)],[403])).
% 0.21/0.48 tff(405,plain,
% 0.21/0.48 (multiply(sk_c2, multiply(sk_c7, sk_c7)) = multiply(sk_c2, multiply(identity, multiply(sk_c7, sk_c7)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[404])).
% 0.21/0.48 tff(406,plain,
% 0.21/0.48 (multiply(sk_c2, multiply(identity, multiply(sk_c7, sk_c7))) = multiply(sk_c2, multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(symmetry,[status(thm)],[405])).
% 0.21/0.48 tff(407,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, identity), multiply(sk_c7, sk_c7)) = multiply(sk_c2, multiply(identity, multiply(sk_c7, sk_c7))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(408,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, identity), multiply(sk_c7, sk_c7)) = multiply(sk_c2, multiply(identity, multiply(sk_c7, sk_c7)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[407, 46])).
% 0.21/0.48 tff(409,plain,
% 0.21/0.48 (sk_c6 = multiply(sk_c2, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[397])).
% 0.21/0.48 tff(410,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c7) = multiply(multiply(sk_c2, sk_c5), sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[409])).
% 0.21/0.48 tff(411,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, sk_c5), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[410])).
% 0.21/0.48 tff(412,plain,
% 0.21/0.48 (multiply(sk_c2, identity) = multiply(sk_c2, multiply(sk_c5, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[180])).
% 0.21/0.48 tff(413,plain,
% 0.21/0.48 (multiply(sk_c2, identity) = sk_c5),
% 0.21/0.48 inference(transitivity,[status(thm)],[412, 136, 411, 35])).
% 0.21/0.48 tff(414,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, identity), multiply(sk_c7, sk_c7)) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[413])).
% 0.21/0.48 tff(415,plain,
% 0.21/0.48 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c2, identity), multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(symmetry,[status(thm)],[414])).
% 0.21/0.48 tff(416,plain,
% 0.21/0.48 (sk_c7 = multiply(sk_c2, multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(transitivity,[status(thm)],[169, 181, 184, 415, 408, 406])).
% 0.21/0.48 tff(417,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, sk_c6), sk_c7) = sk_c6),
% 0.21/0.48 inference(transitivity,[status(thm)],[401, 399, 397])).
% 0.21/0.48 tff(418,plain,
% 0.21/0.48 (multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)) = multiply(sk_c2, sk_c6)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[417])).
% 0.21/0.48 tff(419,plain,
% 0.21/0.48 (multiply(sk_c2, sk_c6) = multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7))),
% 0.21/0.48 inference(symmetry,[status(thm)],[418])).
% 0.21/0.48 tff(420,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, sk_c6), sk_c7) = multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), multiply(sk_c2, multiply(sk_c7, sk_c7)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[419, 416])).
% 0.21/0.48 tff(421,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), multiply(sk_c2, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c2, sk_c6), sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[420])).
% 0.21/0.48 tff(422,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), sk_c2), multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), multiply(sk_c2, multiply(sk_c7, sk_c7))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(423,plain,
% 0.21/0.48 (multiply(multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), sk_c2), multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), multiply(sk_c2, multiply(sk_c7, sk_c7)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[422, 46])).
% 0.21/0.48 tff(424,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c2) = multiply(sk_c5, sk_c7)),
% 0.21/0.48 inference(transitivity,[status(thm)],[378, 89, 166, 179])).
% 0.21/0.48 tff(425,plain,
% 0.21/0.48 (multiply(sk_c2, multiply(sk_c6, sk_c2)) = multiply(sk_c2, multiply(sk_c5, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[424])).
% 0.21/0.48 tff(426,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c6), sk_c2) = multiply(sk_c2, multiply(sk_c6, sk_c2)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(427,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, sk_c6), sk_c2) = multiply(sk_c2, multiply(sk_c6, sk_c2))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[426, 46])).
% 0.21/0.48 tff(428,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), sk_c2) = multiply(multiply(sk_c2, sk_c6), sk_c2)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[418])).
% 0.21/0.48 tff(429,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), sk_c2) = sk_c5),
% 0.21/0.48 inference(transitivity,[status(thm)],[428, 427, 425, 136, 411, 35])).
% 0.21/0.48 tff(430,plain,
% 0.21/0.48 (multiply(multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), sk_c2), multiply(sk_c7, sk_c7)) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[429])).
% 0.21/0.48 tff(431,plain,
% 0.21/0.48 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = multiply(multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), sk_c2), multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(symmetry,[status(thm)],[430])).
% 0.21/0.48 tff(432,plain,
% 0.21/0.48 (sk_c7 = sk_c6),
% 0.21/0.48 inference(transitivity,[status(thm)],[169, 181, 184, 431, 423, 421, 401, 399, 397])).
% 0.21/0.48 tff(433,plain,
% 0.21/0.48 (multiply(sk_c1, sk_c7) = multiply(sk_c1, sk_c6)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[432])).
% 0.21/0.48 tff(434,plain,
% 0.21/0.48 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c1) = sk_c1)),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(435,plain,
% 0.21/0.48 (multiply(identity, sk_c1) = sk_c1),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[434, 7])).
% 0.21/0.48 tff(436,plain,
% 0.21/0.48 (sk_c1 = multiply(identity, sk_c1)),
% 0.21/0.48 inference(symmetry,[status(thm)],[435])).
% 0.21/0.48 tff(437,plain,
% 0.21/0.48 (sk_c2 = multiply(identity, sk_c2)),
% 0.21/0.48 inference(symmetry,[status(thm)],[69])).
% 0.21/0.48 tff(438,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, sk_c2), sk_c2) = multiply(multiply(sk_c2, sk_c2), multiply(identity, sk_c2))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[437])).
% 0.21/0.48 tff(439,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, sk_c2), multiply(identity, sk_c2)) = multiply(multiply(sk_c2, sk_c2), sk_c2)),
% 0.21/0.48 inference(symmetry,[status(thm)],[438])).
% 0.21/0.48 tff(440,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c2), multiply(identity, sk_c2)) = multiply(sk_c2, multiply(sk_c2, multiply(identity, sk_c2))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(441,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, sk_c2), multiply(identity, sk_c2)) = multiply(sk_c2, multiply(sk_c2, multiply(identity, sk_c2)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[440, 46])).
% 0.21/0.48 tff(442,plain,
% 0.21/0.48 (multiply(sk_c2, multiply(sk_c2, multiply(identity, sk_c2))) = multiply(multiply(sk_c2, sk_c2), multiply(identity, sk_c2))),
% 0.21/0.49 inference(symmetry,[status(thm)],[441])).
% 0.21/0.49 tff(443,plain,
% 0.21/0.49 (multiply(multiply(sk_c2, identity), sk_c2) = multiply(sk_c5, sk_c2)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[413])).
% 0.21/0.49 tff(444,plain,
% 0.21/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, identity), sk_c2) = multiply(sk_c2, multiply(identity, sk_c2)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(445,plain,
% 0.21/0.49 (multiply(multiply(sk_c2, identity), sk_c2) = multiply(sk_c2, multiply(identity, sk_c2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[444, 46])).
% 0.21/0.49 tff(446,plain,
% 0.21/0.49 (multiply(sk_c2, multiply(identity, sk_c2)) = multiply(multiply(sk_c2, identity), sk_c2)),
% 0.21/0.49 inference(symmetry,[status(thm)],[445])).
% 0.21/0.49 tff(447,plain,
% 0.21/0.49 (multiply(sk_c2, multiply(identity, sk_c2)) = multiply(sk_c5, sk_c2)),
% 0.21/0.49 inference(transitivity,[status(thm)],[446, 443])).
% 0.21/0.49 tff(448,plain,
% 0.21/0.49 (multiply(sk_c2, multiply(sk_c2, multiply(identity, sk_c2))) = multiply(sk_c2, multiply(sk_c5, sk_c2))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[447])).
% 0.21/0.49 tff(449,plain,
% 0.21/0.49 (multiply(sk_c2, multiply(sk_c5, sk_c2)) = multiply(sk_c2, multiply(sk_c2, multiply(identity, sk_c2)))),
% 0.21/0.49 inference(symmetry,[status(thm)],[448])).
% 0.21/0.49 tff(450,plain,
% 0.21/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c5), sk_c2) = multiply(sk_c2, multiply(sk_c5, sk_c2)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(451,plain,
% 0.21/0.49 (multiply(multiply(sk_c2, sk_c5), sk_c2) = multiply(sk_c2, multiply(sk_c5, sk_c2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[450, 46])).
% 0.21/0.49 tff(452,plain,
% 0.21/0.49 (multiply(sk_c2, sk_c5) = inverse(sk_c2)),
% 0.21/0.49 inference(transitivity,[status(thm)],[397, 377])).
% 0.21/0.49 tff(453,plain,
% 0.21/0.49 (multiply(multiply(sk_c2, sk_c5), sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[452])).
% 0.21/0.49 tff(454,plain,
% 0.21/0.49 (multiply(inverse(sk_c2), sk_c2) = multiply(multiply(sk_c2, sk_c5), sk_c2)),
% 0.21/0.49 inference(symmetry,[status(thm)],[453])).
% 0.21/0.49 tff(455,plain,
% 0.21/0.49 (identity = multiply(multiply(sk_c2, sk_c2), sk_c2)),
% 0.21/0.49 inference(transitivity,[status(thm)],[104, 454, 451, 449, 442, 439])).
% 0.21/0.49 tff(456,plain,
% 0.21/0.49 (multiply(identity, sk_c1) = multiply(multiply(multiply(sk_c2, sk_c2), sk_c2), multiply(identity, sk_c1))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[455, 436])).
% 0.21/0.49 tff(457,plain,
% 0.21/0.49 (multiply(multiply(multiply(sk_c2, sk_c2), sk_c2), multiply(identity, sk_c1)) = multiply(identity, sk_c1)),
% 0.21/0.49 inference(symmetry,[status(thm)],[456])).
% 0.21/0.49 tff(458,plain,
% 0.21/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c2, sk_c2), sk_c2), multiply(identity, sk_c1)) = multiply(multiply(sk_c2, sk_c2), multiply(sk_c2, multiply(identity, sk_c1))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(459,plain,
% 0.21/0.49 (multiply(multiply(multiply(sk_c2, sk_c2), sk_c2), multiply(identity, sk_c1)) = multiply(multiply(sk_c2, sk_c2), multiply(sk_c2, multiply(identity, sk_c1)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[458, 46])).
% 0.21/0.49 tff(460,plain,
% 0.21/0.49 (multiply(multiply(sk_c2, sk_c2), multiply(sk_c2, multiply(identity, sk_c1))) = multiply(multiply(multiply(sk_c2, sk_c2), sk_c2), multiply(identity, sk_c1))),
% 0.21/0.49 inference(symmetry,[status(thm)],[459])).
% 0.21/0.49 tff(461,plain,
% 0.21/0.49 (multiply(multiply(sk_c2, identity), sk_c1) = multiply(sk_c5, sk_c1)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[413])).
% 0.21/0.49 tff(462,plain,
% 0.21/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, identity), sk_c1) = multiply(sk_c2, multiply(identity, sk_c1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(463,plain,
% 0.21/0.49 (multiply(multiply(sk_c2, identity), sk_c1) = multiply(sk_c2, multiply(identity, sk_c1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[462, 46])).
% 0.21/0.49 tff(464,plain,
% 0.21/0.49 (multiply(sk_c2, multiply(identity, sk_c1)) = multiply(multiply(sk_c2, identity), sk_c1)),
% 0.21/0.49 inference(symmetry,[status(thm)],[463])).
% 0.21/0.49 tff(465,plain,
% 0.21/0.49 (multiply(sk_c2, multiply(identity, sk_c1)) = multiply(sk_c5, sk_c1)),
% 0.21/0.49 inference(transitivity,[status(thm)],[464, 461])).
% 0.21/0.49 tff(466,plain,
% 0.21/0.49 (multiply(multiply(sk_c2, sk_c2), multiply(sk_c2, multiply(identity, sk_c1))) = multiply(multiply(sk_c2, sk_c2), multiply(sk_c5, sk_c1))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[465])).
% 0.21/0.49 tff(467,plain,
% 0.21/0.49 (multiply(multiply(sk_c2, sk_c2), multiply(sk_c5, sk_c1)) = multiply(multiply(sk_c2, sk_c2), multiply(sk_c2, multiply(identity, sk_c1)))),
% 0.21/0.49 inference(symmetry,[status(thm)],[466])).
% 0.21/0.49 tff(468,plain,
% 0.21/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c2), multiply(sk_c5, sk_c1)) = multiply(sk_c2, multiply(sk_c2, multiply(sk_c5, sk_c1))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(469,plain,
% 0.21/0.49 (multiply(multiply(sk_c2, sk_c2), multiply(sk_c5, sk_c1)) = multiply(sk_c2, multiply(sk_c2, multiply(sk_c5, sk_c1)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[468, 46])).
% 0.21/0.49 tff(470,plain,
% 0.21/0.49 (multiply(sk_c2, multiply(sk_c2, multiply(sk_c5, sk_c1))) = multiply(multiply(sk_c2, sk_c2), multiply(sk_c5, sk_c1))),
% 0.21/0.49 inference(symmetry,[status(thm)],[469])).
% 0.21/0.49 tff(471,assumption,(~(inverse(sk_c1) = sk_c6)), introduced(assumption)).
% 0.21/0.49 tff(472,plain,
% 0.21/0.49 (((inverse(sk_c1) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5)) <=> ((inverse(sk_c1) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(473,axiom,((inverse(sk_c1) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_9')).
% 0.21/0.49 tff(474,plain,
% 0.21/0.49 ((inverse(sk_c1) = sk_c6) | (multiply(sk_c6, sk_c4) = sk_c5)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.21/0.49 tff(475,plain,
% 0.21/0.49 (multiply(sk_c6, sk_c4) = sk_c5),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[474, 471])).
% 0.21/0.49 tff(476,plain,
% 0.21/0.49 (((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c6)) <=> ((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c6))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(477,axiom,((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_11')).
% 0.21/0.49 tff(478,plain,
% 0.21/0.49 ((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.21/0.49 tff(479,plain,
% 0.21/0.49 (inverse(sk_c3) = sk_c6),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[478, 471])).
% 0.21/0.49 tff(480,plain,
% 0.21/0.49 (sk_c6 = inverse(sk_c3)),
% 0.21/0.49 inference(symmetry,[status(thm)],[479])).
% 0.21/0.49 tff(481,plain,
% 0.21/0.49 (multiply(sk_c6, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[480])).
% 0.21/0.49 tff(482,plain,
% 0.21/0.49 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c6, sk_c3)),
% 0.21/0.49 inference(symmetry,[status(thm)],[481])).
% 0.21/0.49 tff(483,plain,
% 0.21/0.49 (identity = multiply(sk_c6, sk_c3)),
% 0.21/0.49 inference(transitivity,[status(thm)],[199, 482])).
% 0.21/0.49 tff(484,plain,
% 0.21/0.49 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[483])).
% 0.21/0.49 tff(485,plain,
% 0.21/0.49 (sk_c6 = multiply(sk_c6, sk_c7)),
% 0.21/0.49 inference(transitivity,[status(thm)],[66, 484, 204, 288, 475, 123])).
% 0.21/0.49 tff(486,plain,
% 0.21/0.49 (multiply(multiply(sk_c6, sk_c2), sk_c6) = multiply(identity, multiply(sk_c6, sk_c7))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[379, 485])).
% 0.21/0.49 tff(487,plain,
% 0.21/0.49 (multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5),
% 0.21/0.49 inference(transitivity,[status(thm)],[146, 486, 298, 295, 35])).
% 0.21/0.49 tff(488,plain,
% 0.21/0.49 (multiply(multiply(sk_c6, sk_c3), sk_c6) = multiply(identity, sk_c6)),
% 0.21/0.49 inference(symmetry,[status(thm)],[484])).
% 0.21/0.49 tff(489,plain,
% 0.21/0.49 (sk_c5 = multiply(sk_c6, sk_c4)),
% 0.21/0.49 inference(symmetry,[status(thm)],[475])).
% 0.21/0.49 tff(490,plain,
% 0.21/0.49 (inverse(sk_c7) = sk_c6),
% 0.21/0.49 inference(transitivity,[status(thm)],[176, 489, 289, 205, 488, 65])).
% 0.21/0.49 tff(491,plain,
% 0.21/0.49 (((inverse(sk_c1) = sk_c6) | (inverse(sk_c6) = sk_c5)) <=> ((inverse(sk_c1) = sk_c6) | (inverse(sk_c6) = sk_c5))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(492,axiom,((inverse(sk_c1) = sk_c6) | (inverse(sk_c6) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_7')).
% 0.21/0.49 tff(493,plain,
% 0.21/0.49 ((inverse(sk_c1) = sk_c6) | (inverse(sk_c6) = sk_c5)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.21/0.49 tff(494,plain,
% 0.21/0.49 (inverse(sk_c6) = sk_c5),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[493, 471])).
% 0.21/0.49 tff(495,plain,
% 0.21/0.49 (sk_c6 = sk_c5),
% 0.21/0.49 inference(transitivity,[status(thm)],[66, 484, 204, 288, 475])).
% 0.21/0.49 tff(496,plain,
% 0.21/0.49 (multiply(sk_c2, sk_c6) = multiply(sk_c2, sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[495])).
% 0.21/0.49 tff(497,plain,
% 0.21/0.49 (multiply(sk_c2, sk_c5) = multiply(sk_c2, sk_c6)),
% 0.21/0.49 inference(symmetry,[status(thm)],[496])).
% 0.21/0.49 tff(498,plain,
% 0.21/0.49 (sk_c6 = inverse(sk_c7)),
% 0.21/0.49 inference(transitivity,[status(thm)],[66, 484, 204, 288, 475, 177])).
% 0.21/0.49 tff(499,plain,
% 0.21/0.49 (multiply(sk_c6, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[498])).
% 0.21/0.49 tff(500,plain,
% 0.21/0.49 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[499])).
% 0.21/0.49 tff(501,plain,
% 0.21/0.49 (identity = sk_c6),
% 0.21/0.49 inference(transitivity,[status(thm)],[166, 500, 35, 489, 289, 205, 488, 65])).
% 0.21/0.49 tff(502,plain,
% 0.21/0.49 (multiply(identity, multiply(sk_c2, sk_c5)) = multiply(sk_c6, multiply(sk_c2, sk_c6))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[501, 497])).
% 0.21/0.49 tff(503,plain,
% 0.21/0.49 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c2, sk_c5)) = multiply(sk_c2, sk_c5))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(504,plain,
% 0.21/0.49 (multiply(identity, multiply(sk_c2, sk_c5)) = multiply(sk_c2, sk_c5)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[503, 7])).
% 0.21/0.49 tff(505,plain,
% 0.21/0.49 (multiply(sk_c2, sk_c5) = multiply(identity, multiply(sk_c2, sk_c5))),
% 0.21/0.49 inference(symmetry,[status(thm)],[504])).
% 0.21/0.49 tff(506,plain,
% 0.21/0.49 (multiply(sk_c2, sk_c5) = sk_c6),
% 0.21/0.49 inference(transitivity,[status(thm)],[505, 502, 146, 486, 298, 295, 35, 489, 289, 205, 488, 65])).
% 0.21/0.49 tff(507,plain,
% 0.21/0.49 (identity = inverse(sk_c7)),
% 0.21/0.49 inference(transitivity,[status(thm)],[166, 500, 35, 177])).
% 0.21/0.49 tff(508,plain,
% 0.21/0.49 (multiply(identity, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[507])).
% 0.21/0.49 tff(509,plain,
% 0.21/0.49 (sk_c7 = sk_c6),
% 0.21/0.49 inference(transitivity,[status(thm)],[169, 508, 500, 35, 489, 289, 205, 488, 65])).
% 0.21/0.49 tff(510,plain,
% 0.21/0.49 (multiply(sk_c7, sk_c6) = multiply(sk_c7, sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[495])).
% 0.21/0.49 tff(511,plain,
% 0.21/0.49 ((multiply(sk_c7, sk_c6) = sk_c7) <=> (multiply(sk_c7, sk_c5) = sk_c6)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[510, 509])).
% 0.21/0.49 tff(512,plain,
% 0.21/0.49 ((multiply(sk_c7, sk_c5) = sk_c6) <=> (multiply(sk_c7, sk_c6) = sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[511])).
% 0.21/0.49 tff(513,plain,
% 0.21/0.49 (sk_c5 = inverse(sk_c6)),
% 0.21/0.49 inference(symmetry,[status(thm)],[494])).
% 0.21/0.49 tff(514,plain,
% 0.21/0.49 (multiply(sk_c6, sk_c7) = inverse(sk_c6)),
% 0.21/0.49 inference(transitivity,[status(thm)],[35, 513])).
% 0.21/0.49 tff(515,plain,
% 0.21/0.49 (multiply(multiply(sk_c6, sk_c7), sk_c6) = multiply(inverse(sk_c6), sk_c6)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[514])).
% 0.21/0.49 tff(516,plain,
% 0.21/0.49 (sk_c5 = sk_c6),
% 0.21/0.49 inference(transitivity,[status(thm)],[489, 289, 205, 488, 65])).
% 0.21/0.49 tff(517,plain,
% 0.21/0.49 (multiply(sk_c5, multiply(sk_c7, sk_c6)) = multiply(sk_c6, multiply(sk_c7, sk_c6))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[516])).
% 0.21/0.49 tff(518,plain,
% 0.21/0.49 (multiply(sk_c7, sk_c5) = multiply(sk_c7, sk_c6)),
% 0.21/0.49 inference(symmetry,[status(thm)],[510])).
% 0.21/0.49 tff(519,plain,
% 0.21/0.49 (identity = sk_c5),
% 0.21/0.49 inference(transitivity,[status(thm)],[166, 500, 35])).
% 0.21/0.49 tff(520,plain,
% 0.21/0.49 (multiply(identity, multiply(sk_c7, sk_c5)) = multiply(sk_c5, multiply(sk_c7, sk_c6))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[519, 518])).
% 0.21/0.49 tff(521,plain,
% 0.21/0.49 (multiply(sk_c7, sk_c5) = sk_c6),
% 0.21/0.49 inference(transitivity,[status(thm)],[340, 520, 517, 330, 515, 320, 166, 500, 35, 489, 289, 205, 488, 65])).
% 0.21/0.49 tff(522,plain,
% 0.21/0.49 (multiply(sk_c7, sk_c6) = sk_c7),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[521, 512])).
% 0.21/0.49 tff(523,plain,
% 0.21/0.49 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(524,plain,
% 0.21/0.50 (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5)) | (~(multiply(sk_c2, sk_c5) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(525,plain,
% 0.21/0.50 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5)) | (~(multiply(sk_c2, sk_c5) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[524])).
% 0.21/0.50 tff(526,plain,
% 0.21/0.50 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5)) | (~(multiply(sk_c2, sk_c5) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[525, 523])).
% 0.21/0.50 tff(527,plain,
% 0.21/0.50 ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5)) | (~(multiply(sk_c2, sk_c5) = sk_c6)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(528,plain,
% 0.21/0.50 ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c5) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[527, 526])).
% 0.21/0.50 tff(529,plain,
% 0.21/0.50 ((~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(multiply(sk_c2, sk_c5) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c2, sk_c6)) = sk_c5))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[528, 35, 176, 376, 277])).
% 0.21/0.50 tff(530,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[529, 522, 506, 494, 490, 487])).
% 0.21/0.50 tff(531,plain,(inverse(sk_c1) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(532,plain,
% 0.21/0.50 (sk_c6 = inverse(sk_c1)),
% 0.21/0.50 inference(symmetry,[status(thm)],[531])).
% 0.21/0.50 tff(533,plain,
% 0.21/0.50 (multiply(sk_c2, sk_c5) = inverse(sk_c1)),
% 0.21/0.50 inference(transitivity,[status(thm)],[397, 532])).
% 0.21/0.50 tff(534,plain,
% 0.21/0.50 (multiply(multiply(sk_c2, sk_c5), sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[533])).
% 0.21/0.50 tff(535,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c5), sk_c1) = multiply(sk_c2, multiply(sk_c5, sk_c1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(536,plain,
% 0.21/0.50 (multiply(multiply(sk_c2, sk_c5), sk_c1) = multiply(sk_c2, multiply(sk_c5, sk_c1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[535, 46])).
% 0.21/0.50 tff(537,plain,
% 0.21/0.50 (multiply(sk_c2, multiply(sk_c5, sk_c1)) = multiply(multiply(sk_c2, sk_c5), sk_c1)),
% 0.21/0.50 inference(symmetry,[status(thm)],[536])).
% 0.21/0.50 tff(538,plain,
% 0.21/0.50 (multiply(sk_c2, multiply(sk_c5, sk_c1)) = multiply(sk_c5, sk_c7)),
% 0.21/0.50 inference(transitivity,[status(thm)],[537, 534, 57, 166, 179])).
% 0.21/0.50 tff(539,plain,
% 0.21/0.50 (multiply(sk_c2, multiply(sk_c2, multiply(sk_c5, sk_c1))) = multiply(sk_c2, multiply(sk_c5, sk_c7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[538])).
% 0.21/0.50 tff(540,plain,
% 0.21/0.50 (multiply(sk_c2, multiply(sk_c5, sk_c7)) = multiply(sk_c2, multiply(sk_c2, multiply(sk_c5, sk_c1)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[539])).
% 0.21/0.50 tff(541,plain,
% 0.21/0.50 (inverse(sk_c7) = sk_c1),
% 0.21/0.50 inference(transitivity,[status(thm)],[176, 123, 410, 135, 540, 470, 467, 460, 457, 435])).
% 0.21/0.50 tff(542,plain,
% 0.21/0.50 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c1, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[541])).
% 0.21/0.50 tff(543,plain,
% 0.21/0.50 (multiply(sk_c5, sk_c7) = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[178, 542, 433, 36])).
% 0.21/0.50 tff(544,plain,
% 0.21/0.50 (multiply(sk_c2, multiply(sk_c5, sk_c2)) = multiply(multiply(sk_c2, sk_c5), sk_c2)),
% 0.21/0.50 inference(symmetry,[status(thm)],[451])).
% 0.21/0.50 tff(545,plain,
% 0.21/0.50 (multiply(sk_c2, multiply(sk_c5, sk_c2)) = multiply(sk_c5, sk_c7)),
% 0.21/0.50 inference(transitivity,[status(thm)],[544, 453, 89, 166, 179])).
% 0.21/0.50 tff(546,plain,
% 0.21/0.50 (multiply(sk_c2, multiply(sk_c2, multiply(sk_c5, sk_c2))) = multiply(sk_c2, multiply(sk_c5, sk_c7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[545])).
% 0.21/0.50 tff(547,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c2), multiply(sk_c5, sk_c2)) = multiply(sk_c2, multiply(sk_c2, multiply(sk_c5, sk_c2))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(548,plain,
% 0.21/0.50 (multiply(multiply(sk_c2, sk_c2), multiply(sk_c5, sk_c2)) = multiply(sk_c2, multiply(sk_c2, multiply(sk_c5, sk_c2)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[547, 46])).
% 0.21/0.50 tff(549,plain,
% 0.21/0.50 (multiply(multiply(sk_c2, sk_c2), multiply(sk_c2, multiply(identity, sk_c2))) = multiply(multiply(sk_c2, sk_c2), multiply(sk_c5, sk_c2))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[447])).
% 0.21/0.50 tff(550,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c2, sk_c2), sk_c2), multiply(identity, sk_c2)) = multiply(multiply(sk_c2, sk_c2), multiply(sk_c2, multiply(identity, sk_c2))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(551,plain,
% 0.21/0.50 (multiply(multiply(multiply(sk_c2, sk_c2), sk_c2), multiply(identity, sk_c2)) = multiply(multiply(sk_c2, sk_c2), multiply(sk_c2, multiply(identity, sk_c2)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[550, 46])).
% 0.21/0.50 tff(552,plain,
% 0.21/0.50 (multiply(identity, sk_c2) = multiply(multiply(multiply(sk_c2, sk_c2), sk_c2), multiply(identity, sk_c2))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[455, 437])).
% 0.21/0.50 tff(553,plain,
% 0.21/0.50 (sk_c2 = inverse(sk_c7)),
% 0.21/0.50 inference(transitivity,[status(thm)],[437, 552, 551, 549, 548, 546, 136, 411, 35, 177])).
% 0.21/0.50 tff(554,plain,
% 0.21/0.50 (multiply(sk_c2, multiply(sk_c5, sk_c7)) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[553, 543])).
% 0.21/0.50 tff(555,plain,
% 0.21/0.50 (inverse(sk_c7) = sk_c6),
% 0.21/0.50 inference(transitivity,[status(thm)],[176, 123, 410, 135, 554, 542, 433, 36, 169, 181, 184, 431, 423, 421, 401, 399, 397])).
% 0.21/0.50 tff(556,plain,
% 0.21/0.50 ((sk_c6 = inverse(sk_c7)) <=> (inverse(sk_c7) = sk_c6)),
% 0.21/0.50 inference(commutativity,[status(thm)],[])).
% 0.21/0.50 tff(557,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[532])).
% 0.21/0.50 tff(558,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c1) = multiply(sk_c5, sk_c7)),
% 0.21/0.50 inference(transitivity,[status(thm)],[557, 57, 166, 179])).
% 0.21/0.50 tff(559,plain,
% 0.21/0.50 (multiply(multiply(sk_c6, sk_c1), sk_c7) = multiply(multiply(sk_c5, sk_c7), sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[558])).
% 0.21/0.50 tff(560,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c1), sk_c7) = multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(561,plain,
% 0.21/0.50 (multiply(multiply(sk_c6, sk_c1), sk_c7) = multiply(sk_c6, multiply(sk_c1, sk_c7))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[560, 46])).
% 0.21/0.50 tff(562,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c6, sk_c1), sk_c7)),
% 0.21/0.50 inference(symmetry,[status(thm)],[561])).
% 0.21/0.50 tff(563,plain,
% 0.21/0.50 (multiply(sk_c1, sk_c6) = multiply(sk_c1, sk_c7)),
% 0.21/0.50 inference(symmetry,[status(thm)],[433])).
% 0.21/0.50 tff(564,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = multiply(sk_c6, multiply(sk_c1, sk_c7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[563])).
% 0.21/0.50 tff(565,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c6),
% 0.21/0.50 inference(transitivity,[status(thm)],[564, 562, 559, 184, 431, 423, 421, 401, 399, 397])).
% 0.21/0.50 tff(566,plain,
% 0.21/0.50 ((multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5) <=> (sk_c6 = inverse(sk_c7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[565, 177])).
% 0.21/0.50 tff(567,plain,
% 0.21/0.50 ((multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5) <=> (inverse(sk_c7) = sk_c6)),
% 0.21/0.50 inference(transitivity,[status(thm)],[566, 556])).
% 0.21/0.50 tff(568,plain,
% 0.21/0.50 ((~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) <=> (~(inverse(sk_c7) = sk_c6))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[567])).
% 0.21/0.50 tff(569,plain,
% 0.21/0.50 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c6, sk_c2)),
% 0.21/0.50 inference(symmetry,[status(thm)],[378])).
% 0.21/0.50 tff(570,plain,
% 0.21/0.50 (identity = multiply(sk_c6, sk_c2)),
% 0.21/0.50 inference(transitivity,[status(thm)],[104, 569])).
% 0.21/0.50 tff(571,plain,
% 0.21/0.50 (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c6, sk_c2), multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[570])).
% 0.21/0.50 tff(572,plain,
% 0.21/0.50 (multiply(multiply(sk_c6, sk_c2), multiply(sk_c7, sk_c7)) = multiply(identity, multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(symmetry,[status(thm)],[571])).
% 0.21/0.50 tff(573,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c2), multiply(sk_c7, sk_c7)) = multiply(sk_c6, multiply(sk_c2, multiply(sk_c7, sk_c7))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(574,plain,
% 0.21/0.50 (multiply(multiply(sk_c6, sk_c2), multiply(sk_c7, sk_c7)) = multiply(sk_c6, multiply(sk_c2, multiply(sk_c7, sk_c7)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[573, 46])).
% 0.21/0.50 tff(575,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c2, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c6, sk_c2), multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(symmetry,[status(thm)],[574])).
% 0.21/0.50 tff(576,plain,
% 0.21/0.50 (multiply(sk_c2, multiply(identity, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c2, identity), multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(symmetry,[status(thm)],[408])).
% 0.21/0.50 tff(577,plain,
% 0.21/0.50 (multiply(sk_c2, multiply(sk_c7, sk_c7)) = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[405, 576, 414, 185, 182, 9])).
% 0.21/0.50 tff(578,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c2, multiply(sk_c7, sk_c7))) = multiply(sk_c6, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[577])).
% 0.21/0.50 tff(579,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c2, multiply(sk_c7, sk_c7)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[578])).
% 0.21/0.50 tff(580,plain,
% 0.21/0.50 (sk_c5 = multiply(sk_c7, sk_c7)),
% 0.21/0.50 inference(transitivity,[status(thm)],[123, 579, 575, 572, 403])).
% 0.21/0.50 tff(581,plain,
% 0.21/0.50 (sk_c1 = sk_c5),
% 0.21/0.50 inference(transitivity,[status(thm)],[436, 456, 459, 466, 469, 539, 136, 411, 35])).
% 0.21/0.50 tff(582,plain,
% 0.21/0.50 (multiply(sk_c1, sk_c5) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[581, 580])).
% 0.21/0.50 tff(583,plain,
% 0.21/0.50 (multiply(sk_c1, sk_c5) = sk_c6),
% 0.21/0.50 inference(transitivity,[status(thm)],[582, 431, 423, 421, 401, 399, 397])).
% 0.21/0.50 tff(584,plain,
% 0.21/0.50 (multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), multiply(sk_c2, multiply(sk_c7, sk_c7))) = multiply(multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), sk_c2), multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(symmetry,[status(thm)],[423])).
% 0.21/0.50 tff(585,plain,
% 0.21/0.50 (multiply(sk_c2, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c2, sk_c6), sk_c7)),
% 0.21/0.50 inference(symmetry,[status(thm)],[401])).
% 0.21/0.50 tff(586,plain,
% 0.21/0.50 (sk_c6 = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[409, 398, 585, 420, 584, 430, 185, 182, 9])).
% 0.21/0.50 tff(587,plain,
% 0.21/0.50 (inverse(sk_c6) = inverse(sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[586])).
% 0.21/0.50 tff(588,plain,
% 0.21/0.50 (inverse(sk_c6) = sk_c5),
% 0.21/0.50 inference(transitivity,[status(thm)],[587, 176])).
% 0.21/0.50 tff(589,plain,
% 0.21/0.50 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c6)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(590,plain,
% 0.21/0.50 (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c6)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(591,plain,
% 0.21/0.50 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c6))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[590])).
% 0.21/0.50 tff(592,plain,
% 0.21/0.50 (((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c6)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[591, 589])).
% 0.21/0.50 tff(593,plain,
% 0.21/0.50 ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c6)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(594,plain,
% 0.21/0.50 ((~![X4: $i, X3: $i, X2: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X3) = sk_c6)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X3, sk_c6) = sk_c7)) | (~(inverse(X2) = sk_c6)) | (~(multiply(sk_c6, multiply(X2, sk_c6)) = sk_c5)) | (~(multiply(X4, sk_c5) = sk_c6)))) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c6) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c6))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.21/0.50 tff(595,plain,
% 0.21/0.50 ((~(inverse(sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c6))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[594, 35, 176, 531, 277])).
% 0.21/0.50 tff(596,plain,
% 0.21/0.50 ((~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[595, 588, 583])).
% 0.21/0.50 tff(597,plain,
% 0.21/0.50 (~(multiply(sk_c6, multiply(sk_c1, sk_c6)) = sk_c5)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[596, 36])).
% 0.21/0.50 tff(598,plain,
% 0.21/0.50 (~(inverse(sk_c7) = sk_c6)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[597, 568])).
% 0.21/0.50 tff(599,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[598, 555])).
% 0.21/0.50 tff(600,plain,(~(multiply(sk_c1, sk_c6) = sk_c7)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(601,plain,
% 0.21/0.50 (((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c6)) <=> ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c6))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(602,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_6')).
% 0.21/0.50 tff(603,plain,
% 0.21/0.50 ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c6)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.21/0.50 tff(604,plain,
% 0.21/0.50 ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c6)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[603, 601])).
% 0.21/0.50 tff(605,plain,
% 0.21/0.50 ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c6)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[604, 601])).
% 0.21/0.50 tff(606,plain,
% 0.21/0.50 ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c6)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[605, 601])).
% 0.21/0.50 tff(607,plain,
% 0.21/0.50 ((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c6)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[606, 601])).
% 0.21/0.50 tff(608,plain,
% 0.21/0.50 (inverse(sk_c3) = sk_c6),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[607, 600])).
% 0.21/0.50 tff(609,plain,
% 0.21/0.50 (sk_c6 = inverse(sk_c3)),
% 0.21/0.50 inference(symmetry,[status(thm)],[608])).
% 0.21/0.50 tff(610,plain,
% 0.21/0.50 (multiply(multiply(sk_c2, sk_c5), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[397])).
% 0.21/0.50 tff(611,plain,
% 0.21/0.50 (multiply(sk_c2, identity) = sk_c5),
% 0.21/0.50 inference(transitivity,[status(thm)],[412, 136, 610, 35])).
% 0.21/0.50 tff(612,plain,
% 0.21/0.50 (multiply(multiply(sk_c2, identity), multiply(sk_c7, sk_c7)) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[611])).
% 0.21/0.50 tff(613,plain,
% 0.21/0.50 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c2, identity), multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(symmetry,[status(thm)],[612])).
% 0.21/0.50 tff(614,plain,
% 0.21/0.50 (sk_c7 = multiply(sk_c2, multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(transitivity,[status(thm)],[169, 181, 184, 613, 408, 406])).
% 0.21/0.50 tff(615,plain,
% 0.21/0.50 (multiply(multiply(sk_c2, sk_c6), sk_c7) = multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), multiply(sk_c2, multiply(sk_c7, sk_c7)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[419, 614])).
% 0.21/0.50 tff(616,plain,
% 0.21/0.50 (multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), multiply(sk_c2, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c2, sk_c6), sk_c7)),
% 0.21/0.50 inference(symmetry,[status(thm)],[615])).
% 0.21/0.50 tff(617,plain,
% 0.21/0.50 (multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), sk_c2) = sk_c5),
% 0.21/0.50 inference(transitivity,[status(thm)],[428, 427, 425, 136, 610, 35])).
% 0.21/0.50 tff(618,plain,
% 0.21/0.50 (multiply(multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), sk_c2), multiply(sk_c7, sk_c7)) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[617])).
% 0.21/0.50 tff(619,plain,
% 0.21/0.50 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = multiply(multiply(multiply(sk_c2, multiply(multiply(sk_c2, sk_c6), sk_c7)), sk_c2), multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(symmetry,[status(thm)],[618])).
% 0.21/0.50 tff(620,plain,
% 0.21/0.50 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = inverse(sk_c3)),
% 0.21/0.50 inference(transitivity,[status(thm)],[619, 423, 616, 401, 399, 397, 609])).
% 0.21/0.50 tff(621,plain,
% 0.21/0.50 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[620])).
% 0.21/0.50 tff(622,plain,
% 0.21/0.50 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), sk_c3) = multiply(sk_c5, sk_c7)),
% 0.21/0.50 inference(transitivity,[status(thm)],[621, 188, 166, 179])).
% 0.21/0.50 tff(623,plain,
% 0.21/0.50 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), sk_c3), multiply(sk_c5, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c5, sk_c7), sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[622, 186])).
% 0.21/0.50 tff(624,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), sk_c3), multiply(sk_c5, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), multiply(sk_c3, multiply(sk_c5, multiply(sk_c7, sk_c7)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(625,plain,
% 0.21/0.50 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), sk_c3), multiply(sk_c5, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), multiply(sk_c3, multiply(sk_c5, multiply(sk_c7, sk_c7))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[624, 46])).
% 0.21/0.50 tff(626,plain,
% 0.21/0.50 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), multiply(sk_c3, multiply(sk_c5, multiply(sk_c7, sk_c7)))) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), sk_c3), multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[625])).
% 0.21/0.50 tff(627,plain,
% 0.21/0.50 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = sk_c6),
% 0.21/0.50 inference(transitivity,[status(thm)],[619, 423, 616, 401, 399, 397])).
% 0.21/0.50 tff(628,plain,
% 0.21/0.50 (multiply(sk_c3, multiply(sk_c5, multiply(sk_c7, sk_c7))) = multiply(sk_c3, sk_c6)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[627])).
% 0.21/0.50 tff(629,plain,
% 0.21/0.50 (multiply(sk_c3, sk_c6) = multiply(sk_c3, multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[628])).
% 0.21/0.50 tff(630,plain,
% 0.21/0.50 (sk_c4 = multiply(sk_c3, multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[353, 629])).
% 0.21/0.50 tff(631,plain,
% 0.21/0.50 (sk_c6 = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(transitivity,[status(thm)],[409, 398, 585, 615, 584, 618])).
% 0.21/0.50 tff(632,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c4) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), multiply(sk_c3, multiply(sk_c5, multiply(sk_c7, sk_c7))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[631, 630])).
% 0.21/0.50 tff(633,plain,
% 0.21/0.50 (((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c6, sk_c4) = sk_c5)) <=> ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c6, sk_c4) = sk_c5))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(634,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c6, sk_c4) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_4')).
% 0.21/0.50 tff(635,plain,
% 0.21/0.50 ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c6, sk_c4) = sk_c5)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[634, 633])).
% 0.21/0.50 tff(636,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c4) = sk_c5),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[635, 600])).
% 0.21/0.51 tff(637,plain,
% 0.21/0.51 (sk_c5 = multiply(sk_c6, sk_c4)),
% 0.21/0.51 inference(symmetry,[status(thm)],[636])).
% 0.21/0.51 tff(638,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(sk_c7, sk_c7)) = sk_c7),
% 0.21/0.51 inference(transitivity,[status(thm)],[405, 576, 612, 185, 182, 9])).
% 0.21/0.51 tff(639,plain,
% 0.21/0.51 (multiply(sk_c6, multiply(sk_c2, multiply(sk_c7, sk_c7))) = multiply(sk_c6, sk_c7)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[638])).
% 0.21/0.51 tff(640,plain,
% 0.21/0.51 (sk_c5 = sk_c7),
% 0.21/0.51 inference(transitivity,[status(thm)],[637, 632, 626, 623, 182, 9])).
% 0.21/0.51 tff(641,plain,
% 0.21/0.51 (multiply(sk_c7, sk_c5) = multiply(sk_c7, sk_c7)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[640])).
% 0.21/0.51 tff(642,plain,
% 0.21/0.51 (multiply(sk_c7, sk_c7) = sk_c5),
% 0.21/0.51 inference(transitivity,[status(thm)],[404, 571, 574, 639, 35])).
% 0.21/0.51 tff(643,plain,
% 0.21/0.51 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), multiply(sk_c7, sk_c7)) = multiply(sk_c7, sk_c5)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[186, 642])).
% 0.21/0.51 tff(644,plain,
% 0.21/0.51 (sk_c7 = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.51 inference(transitivity,[status(thm)],[169, 181, 184])).
% 0.21/0.51 tff(645,plain,
% 0.21/0.51 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c7)), multiply(sk_c7, sk_c7))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[644])).
% 0.21/0.51 tff(646,plain,
% 0.21/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(sk_c7, multiply(sk_c7, sk_c7)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(647,plain,
% 0.21/0.51 (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[646, 46])).
% 0.21/0.51 tff(648,plain,
% 0.21/0.51 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c2, multiply(sk_c7, sk_c7)))),
% 0.21/0.51 inference(symmetry,[status(thm)],[639])).
% 0.21/0.51 tff(649,plain,
% 0.21/0.51 (inverse(sk_c7) = multiply(sk_c7, sk_c7)),
% 0.21/0.51 inference(transitivity,[status(thm)],[176, 123, 648, 575, 572, 403])).
% 0.21/0.51 tff(650,plain,
% 0.21/0.51 (multiply(inverse(sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c7), sk_c7)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[649])).
% 0.21/0.51 tff(651,plain,
% 0.21/0.51 (multiply(sk_c6, sk_c7) = inverse(sk_c7)),
% 0.21/0.51 inference(transitivity,[status(thm)],[35, 177])).
% 0.21/0.51 tff(652,plain,
% 0.21/0.51 (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[651])).
% 0.21/0.51 tff(653,plain,
% 0.21/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(sk_c6, multiply(sk_c7, sk_c7)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(654,plain,
% 0.21/0.51 (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[653, 46])).
% 0.21/0.51 tff(655,plain,
% 0.21/0.51 (multiply(sk_c6, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c6, sk_c7), sk_c7)),
% 0.21/0.51 inference(symmetry,[status(thm)],[654])).
% 0.21/0.51 tff(656,plain,
% 0.21/0.51 (multiply(multiply(sk_c2, sk_c5), multiply(sk_c7, sk_c7)) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[397])).
% 0.21/0.51 tff(657,plain,
% 0.21/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c5), multiply(sk_c7, sk_c7)) = multiply(sk_c2, multiply(sk_c5, multiply(sk_c7, sk_c7))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(658,plain,
% 0.21/0.51 (multiply(multiply(sk_c2, sk_c5), multiply(sk_c7, sk_c7)) = multiply(sk_c2, multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[657, 46])).
% 0.21/0.51 tff(659,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(sk_c5, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c2, sk_c5), multiply(sk_c7, sk_c7))),
% 0.21/0.51 inference(symmetry,[status(thm)],[658])).
% 0.21/0.51 tff(660,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(identity, multiply(sk_c7, sk_c7))) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.51 inference(transitivity,[status(thm)],[576, 612])).
% 0.21/0.51 tff(661,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(sk_c2, multiply(identity, multiply(sk_c7, sk_c7)))) = multiply(sk_c2, multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[660])).
% 0.21/0.51 tff(662,plain,
% 0.21/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c2), multiply(identity, multiply(sk_c7, sk_c7))) = multiply(sk_c2, multiply(sk_c2, multiply(identity, multiply(sk_c7, sk_c7)))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(663,plain,
% 0.21/0.51 (multiply(multiply(sk_c2, sk_c2), multiply(identity, multiply(sk_c7, sk_c7))) = multiply(sk_c2, multiply(sk_c2, multiply(identity, multiply(sk_c7, sk_c7))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[662, 46])).
% 0.21/0.51 tff(664,plain,
% 0.21/0.51 (multiply(sk_c2, sk_c2) = multiply(sk_c2, multiply(identity, sk_c2))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[437])).
% 0.21/0.51 tff(665,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(identity, sk_c2)) = multiply(sk_c2, sk_c2)),
% 0.21/0.51 inference(symmetry,[status(thm)],[664])).
% 0.21/0.51 tff(666,plain,
% 0.21/0.51 (multiply(multiply(sk_c2, identity), sk_c2) = multiply(sk_c5, sk_c2)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[611])).
% 0.21/0.51 tff(667,plain,
% 0.21/0.51 (multiply(sk_c5, sk_c2) = multiply(multiply(sk_c2, identity), sk_c2)),
% 0.21/0.51 inference(symmetry,[status(thm)],[666])).
% 0.21/0.51 tff(668,plain,
% 0.21/0.51 (multiply(multiply(sk_c6, sk_c7), sk_c2) = multiply(sk_c5, sk_c2)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[35])).
% 0.21/0.51 tff(669,plain,
% 0.21/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c7), sk_c2) = multiply(sk_c6, multiply(sk_c7, sk_c2)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(670,plain,
% 0.21/0.51 (multiply(multiply(sk_c6, sk_c7), sk_c2) = multiply(sk_c6, multiply(sk_c7, sk_c2))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[669, 46])).
% 0.21/0.51 tff(671,plain,
% 0.21/0.51 (multiply(sk_c6, multiply(sk_c7, sk_c2)) = multiply(multiply(sk_c6, sk_c7), sk_c2)),
% 0.21/0.51 inference(symmetry,[status(thm)],[670])).
% 0.21/0.51 tff(672,plain,
% 0.21/0.51 (multiply(sk_c6, multiply(sk_c7, sk_c2)) = multiply(sk_c2, sk_c2)),
% 0.21/0.51 inference(transitivity,[status(thm)],[671, 668, 667, 445, 665])).
% 0.21/0.51 tff(673,plain,
% 0.21/0.51 (multiply(multiply(sk_c6, multiply(sk_c7, sk_c2)), multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c2, sk_c2), multiply(identity, multiply(sk_c7, sk_c7)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[672, 404])).
% 0.21/0.51 tff(674,plain,
% 0.21/0.51 (sk_c5 = multiply(sk_c7, sk_c7)),
% 0.21/0.51 inference(transitivity,[status(thm)],[123, 648, 575, 572, 403])).
% 0.21/0.51 tff(675,plain,
% 0.21/0.51 (multiply(sk_c5, sk_c2) = multiply(multiply(sk_c6, sk_c7), sk_c2)),
% 0.21/0.51 inference(symmetry,[status(thm)],[668])).
% 0.21/0.51 tff(676,plain,
% 0.21/0.51 (multiply(sk_c2, sk_c2) = multiply(sk_c6, multiply(sk_c7, sk_c2))),
% 0.21/0.51 inference(transitivity,[status(thm)],[664, 446, 666, 675, 670])).
% 0.21/0.51 tff(677,plain,
% 0.21/0.51 (multiply(multiply(sk_c2, sk_c2), sk_c5) = multiply(multiply(sk_c6, multiply(sk_c7, sk_c2)), multiply(sk_c7, sk_c7))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[676, 674])).
% 0.21/0.51 tff(678,plain,
% 0.21/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c2), sk_c5) = multiply(sk_c2, multiply(sk_c2, sk_c5)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(679,plain,
% 0.21/0.51 (multiply(multiply(sk_c2, sk_c2), sk_c5) = multiply(sk_c2, multiply(sk_c2, sk_c5))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[678, 46])).
% 0.21/0.51 tff(680,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(sk_c2, sk_c5)) = multiply(multiply(sk_c2, sk_c2), sk_c5)),
% 0.21/0.51 inference(symmetry,[status(thm)],[679])).
% 0.21/0.51 tff(681,plain,
% 0.21/0.51 (multiply(sk_c2, sk_c6) = multiply(sk_c2, multiply(sk_c2, sk_c5))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[409])).
% 0.21/0.51 tff(682,plain,
% 0.21/0.51 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.21/0.51 inference(transitivity,[status(thm)],[681, 680, 677, 673, 663, 661, 659, 656, 655, 652, 650, 647, 645, 643, 641, 404, 571, 574, 639, 35, 637, 632, 626, 623, 182, 9])).
% 0.21/0.51 tff(683,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(sk_c2, sk_c5)) = multiply(sk_c2, sk_c6)),
% 0.21/0.51 inference(symmetry,[status(thm)],[681])).
% 0.21/0.51 tff(684,plain,
% 0.21/0.51 (multiply(multiply(sk_c6, multiply(sk_c7, sk_c2)), multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c2, sk_c2), sk_c5)),
% 0.21/0.51 inference(symmetry,[status(thm)],[677])).
% 0.21/0.51 tff(685,plain,
% 0.21/0.51 (multiply(multiply(sk_c2, sk_c2), multiply(identity, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c6, multiply(sk_c7, sk_c2)), multiply(sk_c7, sk_c7))),
% 0.21/0.51 inference(symmetry,[status(thm)],[673])).
% 0.21/0.51 tff(686,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(sk_c2, multiply(identity, multiply(sk_c7, sk_c7)))) = multiply(multiply(sk_c2, sk_c2), multiply(identity, multiply(sk_c7, sk_c7)))),
% 0.21/0.51 inference(symmetry,[status(thm)],[663])).
% 0.21/0.51 tff(687,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(sk_c5, multiply(sk_c7, sk_c7))) = multiply(sk_c2, multiply(sk_c2, multiply(identity, multiply(sk_c7, sk_c7))))),
% 0.21/0.51 inference(symmetry,[status(thm)],[661])).
% 0.21/0.51 tff(688,plain,
% 0.21/0.51 (multiply(sk_c6, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c2, sk_c5), multiply(sk_c7, sk_c7))),
% 0.21/0.51 inference(symmetry,[status(thm)],[656])).
% 0.21/0.51 tff(689,plain,
% 0.21/0.51 (multiply(inverse(sk_c7), sk_c7) = multiply(multiply(sk_c6, sk_c7), sk_c7)),
% 0.21/0.51 inference(symmetry,[status(thm)],[652])).
% 0.21/0.51 tff(690,plain,
% 0.21/0.51 (multiply(multiply(sk_c2, identity), sk_c1) = multiply(sk_c5, sk_c1)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[611])).
% 0.21/0.51 tff(691,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(identity, sk_c1)) = multiply(sk_c5, sk_c1)),
% 0.21/0.51 inference(transitivity,[status(thm)],[464, 690])).
% 0.21/0.51 tff(692,plain,
% 0.21/0.51 (multiply(multiply(sk_c2, sk_c2), multiply(sk_c2, multiply(identity, sk_c1))) = multiply(multiply(sk_c2, sk_c2), multiply(sk_c5, sk_c1))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[691])).
% 0.21/0.51 tff(693,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(identity, sk_c2)) = multiply(sk_c5, sk_c2)),
% 0.21/0.51 inference(transitivity,[status(thm)],[446, 666])).
% 0.21/0.51 tff(694,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(sk_c2, multiply(identity, sk_c2))) = multiply(sk_c2, multiply(sk_c5, sk_c2))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[693])).
% 0.21/0.51 tff(695,plain,
% 0.21/0.51 (multiply(sk_c2, multiply(sk_c5, sk_c2)) = multiply(sk_c2, multiply(sk_c2, multiply(identity, sk_c2)))),
% 0.21/0.51 inference(symmetry,[status(thm)],[694])).
% 0.21/0.51 tff(696,plain,
% 0.21/0.51 (identity = multiply(multiply(sk_c2, sk_c2), sk_c2)),
% 0.21/0.51 inference(transitivity,[status(thm)],[104, 454, 451, 695, 442, 439])).
% 0.21/0.51 tff(697,plain,
% 0.21/0.51 (multiply(identity, sk_c1) = multiply(multiply(multiply(sk_c2, sk_c2), sk_c2), multiply(identity, sk_c1))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[696, 436])).
% 0.21/0.51 tff(698,plain,
% 0.21/0.51 (sk_c1 = inverse(sk_c7)),
% 0.21/0.51 inference(transitivity,[status(thm)],[436, 697, 459, 692, 469, 539, 136, 610, 35, 177])).
% 0.21/0.51 tff(699,plain,
% 0.21/0.51 (multiply(sk_c1, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[698])).
% 0.21/0.51 tff(700,plain,
% 0.21/0.51 (sk_c6 = sk_c7),
% 0.21/0.51 inference(transitivity,[status(thm)],[409, 398, 585, 615, 584, 618, 185, 182, 9])).
% 0.21/0.51 tff(701,plain,
% 0.21/0.51 (multiply(sk_c1, sk_c6) = multiply(sk_c1, sk_c7)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[700])).
% 0.21/0.51 tff(702,plain,
% 0.21/0.51 (multiply(sk_c1, sk_c6) = multiply(sk_c2, sk_c6)),
% 0.21/0.51 inference(transitivity,[status(thm)],[701, 699, 689, 654, 688, 658, 687, 686, 685, 684, 679, 683])).
% 0.21/0.51 tff(703,plain,
% 0.21/0.51 ((multiply(sk_c1, sk_c6) = sk_c7) <=> (multiply(sk_c2, sk_c6) = sk_c7)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[702])).
% 0.21/0.51 tff(704,plain,
% 0.21/0.51 ((~(multiply(sk_c1, sk_c6) = sk_c7)) <=> (~(multiply(sk_c2, sk_c6) = sk_c7))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[703])).
% 0.21/0.51 tff(705,plain,
% 0.21/0.51 (~(multiply(sk_c2, sk_c6) = sk_c7)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[600, 704])).
% 0.21/0.51 tff(706,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[705, 682])).
% 0.21/0.51 % SZS output end Proof
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------