%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP288-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:07:34 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP288-1 : TPTP v9.0.0. Released v2.5.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 15:54:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.49 % SZS status Unsatisfiable
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(sk_c7_type, type, (
% 0.21/0.49 sk_c7: $i)).
% 0.21/0.49 tff(multiply_type, type, (
% 0.21/0.49 multiply: ( $i * $i ) > $i)).
% 0.21/0.49 tff(sk_c6_type, type, (
% 0.21/0.49 sk_c6: $i)).
% 0.21/0.49 tff(sk_c2_type, type, (
% 0.21/0.49 sk_c2: $i)).
% 0.21/0.49 tff(identity_type, type, (
% 0.21/0.49 identity: $i)).
% 0.21/0.49 tff(sk_c1_type, type, (
% 0.21/0.49 sk_c1: $i)).
% 0.21/0.49 tff(inverse_type, type, (
% 0.21/0.49 inverse: $i > $i)).
% 0.21/0.49 tff(sk_c4_type, type, (
% 0.21/0.49 sk_c4: $i)).
% 0.21/0.49 tff(sk_c3_type, type, (
% 0.21/0.49 sk_c3: $i)).
% 0.21/0.49 tff(sk_c5_type, type, (
% 0.21/0.49 sk_c5: $i)).
% 0.21/0.49 tff(1,plain,
% 0.21/0.49 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(2,plain,
% 0.21/0.49 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(4,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.49 tff(6,plain,(
% 0.21/0.49 ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.49 inference(skolemize,[status(sab)],[5])).
% 0.21/0.49 tff(7,plain,
% 0.21/0.49 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 (multiply(identity, sk_c7) = sk_c7),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c6) = sk_c6)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (multiply(identity, sk_c6) = sk_c6),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.21/0.49 tff(12,assumption,(~(inverse(sk_c4) = sk_c6)), introduced(assumption)).
% 0.21/0.49 tff(13,plain,
% 0.21/0.49 (((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)) <=> ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(14,axiom,((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_5')).
% 0.21/0.49 tff(15,plain,
% 0.21/0.49 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.49 tff(16,plain,
% 0.21/0.49 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.21/0.49 tff(19,plain,
% 0.21/0.49 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 (multiply(sk_c7, sk_c6) = sk_c5),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[19, 12])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 (((inverse(sk_c4) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c6)) <=> ((inverse(sk_c4) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(22,plain,
% 0.21/0.49 (((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c4) = sk_c6)) <=> ((inverse(sk_c4) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(23,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_10')).
% 0.21/0.49 tff(24,plain,
% 0.21/0.49 ((inverse(sk_c4) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.49 tff(25,plain,
% 0.21/0.49 ((inverse(sk_c4) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.21/0.49 tff(26,plain,
% 0.21/0.49 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[25, 12])).
% 0.21/0.49 tff(27,plain,
% 0.21/0.49 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[26])).
% 0.21/0.49 tff(28,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(29,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.49 tff(30,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(31,axiom,(![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','associativity')).
% 0.21/0.49 tff(32,plain,
% 0.21/0.49 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.49 tff(33,plain,(
% 0.21/0.49 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[32])).
% 0.21/0.49 tff(34,plain,
% 0.21/0.49 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.49 tff(35,plain,
% 0.21/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(36,plain,
% 0.21/0.49 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c6)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c6))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(38,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_15')).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.49 tff(40,plain,
% 0.21/0.49 (inverse(sk_c1) = sk_c7),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[39, 12])).
% 0.21/0.49 tff(41,plain,
% 0.21/0.49 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[40])).
% 0.21/0.49 tff(42,plain,
% 0.21/0.49 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(43,plain,
% 0.21/0.49 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.49 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.49 tff(44,plain,
% 0.21/0.49 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(45,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.21/0.49 tff(46,plain,
% 0.21/0.49 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.49 tff(47,plain,(
% 0.21/0.49 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.49 inference(skolemize,[status(sab)],[46])).
% 0.21/0.49 tff(48,plain,
% 0.21/0.49 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.49 tff(49,plain,
% 0.21/0.49 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.49 inference(symmetry,[status(thm)],[50])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 (identity = multiply(sk_c7, sk_c1)),
% 0.21/0.49 inference(transitivity,[status(thm)],[51, 41])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[52])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 (sk_c7 = multiply(identity, sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[9])).
% 0.21/0.49 tff(55,plain,
% 0.21/0.49 (sk_c7 = sk_c5),
% 0.21/0.49 inference(transitivity,[status(thm)],[54, 53, 36, 27, 20])).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 ((multiply(sk_c1, sk_c6) = sk_c7) <=> (multiply(sk_c1, sk_c6) = sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.49 tff(57,plain,
% 0.21/0.49 ((~(multiply(sk_c1, sk_c6) = sk_c7)) <=> (~(multiply(sk_c1, sk_c6) = sk_c5))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.49 tff(58,plain,
% 0.21/0.49 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(59,plain,
% 0.21/0.49 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[58, 48])).
% 0.21/0.49 tff(60,plain,
% 0.21/0.49 (((inverse(sk_c2) = sk_c6) | (inverse(sk_c4) = sk_c6)) <=> ((inverse(sk_c2) = sk_c6) | (inverse(sk_c4) = sk_c6))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(61,axiom,((inverse(sk_c2) = sk_c6) | (inverse(sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_25')).
% 0.21/0.49 tff(62,plain,
% 0.21/0.49 ((inverse(sk_c2) = sk_c6) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 (inverse(sk_c2) = sk_c6),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[62, 12])).
% 0.21/0.49 tff(64,plain,
% 0.21/0.49 (sk_c6 = inverse(sk_c2)),
% 0.21/0.49 inference(symmetry,[status(thm)],[63])).
% 0.21/0.49 tff(65,plain,
% 0.21/0.49 (multiply(sk_c6, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[64])).
% 0.21/0.49 tff(66,plain,
% 0.21/0.49 (multiply(sk_c6, sk_c2) = multiply(sk_c7, sk_c1)),
% 0.21/0.49 inference(transitivity,[status(thm)],[65, 59, 51, 41])).
% 0.21/0.49 tff(67,plain,
% 0.21/0.49 (multiply(multiply(sk_c6, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[66])).
% 0.21/0.49 tff(68,plain,
% 0.21/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c2), sk_c7) = multiply(sk_c6, multiply(sk_c2, sk_c7)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(69,plain,
% 0.21/0.49 (multiply(multiply(sk_c6, sk_c2), sk_c7) = multiply(sk_c6, multiply(sk_c2, sk_c7))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[68, 34])).
% 0.21/0.49 tff(70,plain,
% 0.21/0.49 (multiply(sk_c6, multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c6, sk_c2), sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[69])).
% 0.21/0.49 tff(71,plain,
% 0.21/0.49 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[53])).
% 0.21/0.49 tff(72,plain,
% 0.21/0.49 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[36])).
% 0.21/0.49 tff(73,plain,
% 0.21/0.49 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.49 inference(symmetry,[status(thm)],[27])).
% 0.21/0.49 tff(74,plain,
% 0.21/0.49 (sk_c5 = multiply(sk_c7, sk_c6)),
% 0.21/0.49 inference(symmetry,[status(thm)],[20])).
% 0.21/0.49 tff(75,plain,
% 0.21/0.49 (((inverse(sk_c4) = sk_c6) | (multiply(sk_c2, sk_c6) = sk_c5)) <=> ((inverse(sk_c4) = sk_c6) | (multiply(sk_c2, sk_c6) = sk_c5))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(76,plain,
% 0.21/0.49 (((multiply(sk_c2, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)) <=> ((inverse(sk_c4) = sk_c6) | (multiply(sk_c2, sk_c6) = sk_c5))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(77,axiom,((multiply(sk_c2, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_20')).
% 0.21/0.49 tff(78,plain,
% 0.21/0.49 ((inverse(sk_c4) = sk_c6) | (multiply(sk_c2, sk_c6) = sk_c5)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.49 tff(79,plain,
% 0.21/0.49 ((inverse(sk_c4) = sk_c6) | (multiply(sk_c2, sk_c6) = sk_c5)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.21/0.49 tff(80,plain,
% 0.21/0.49 (multiply(sk_c2, sk_c6) = sk_c5),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[79, 12])).
% 0.21/0.49 tff(81,plain,
% 0.21/0.49 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.21/0.49 inference(transitivity,[status(thm)],[80, 74, 73, 72, 71, 9])).
% 0.21/0.49 tff(82,plain,
% 0.21/0.49 (multiply(sk_c2, multiply(sk_c2, sk_c6)) = multiply(sk_c2, sk_c7)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.49 tff(83,plain,
% 0.21/0.49 (sk_c5 = sk_c7),
% 0.21/0.49 inference(transitivity,[status(thm)],[74, 73, 72, 71, 9])).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 (multiply(sk_c5, sk_c6) = multiply(sk_c7, sk_c6)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.50 tff(85,plain,
% 0.21/0.50 (multiply(sk_c5, sk_c6) = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[84, 73, 72, 71, 9])).
% 0.21/0.50 tff(86,plain,
% 0.21/0.50 (multiply(sk_c1, multiply(sk_c5, sk_c6)) = multiply(sk_c1, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[85])).
% 0.21/0.50 tff(87,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c5), sk_c6) = multiply(sk_c1, multiply(sk_c5, sk_c6)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(88,plain,
% 0.21/0.50 (multiply(multiply(sk_c1, sk_c5), sk_c6) = multiply(sk_c1, multiply(sk_c5, sk_c6))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[87, 34])).
% 0.21/0.50 tff(89,plain,
% 0.21/0.50 (multiply(sk_c1, sk_c5) = multiply(sk_c1, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.50 tff(90,plain,
% 0.21/0.50 (multiply(sk_c1, sk_c7) = multiply(sk_c1, sk_c5)),
% 0.21/0.50 inference(symmetry,[status(thm)],[89])).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 (sk_c6 = multiply(sk_c1, sk_c7)),
% 0.21/0.50 inference(symmetry,[status(thm)],[26])).
% 0.21/0.50 tff(92,plain,
% 0.21/0.50 (sk_c6 = multiply(sk_c1, sk_c5)),
% 0.21/0.50 inference(transitivity,[status(thm)],[91, 90])).
% 0.21/0.50 tff(93,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c6) = multiply(multiply(sk_c1, sk_c5), sk_c6)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.50 tff(94,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c6) = sk_c6),
% 0.21/0.50 inference(transitivity,[status(thm)],[93, 88, 86, 26])).
% 0.21/0.50 tff(95,plain,
% 0.21/0.50 (multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c2, sk_c6))) = multiply(sk_c6, multiply(sk_c2, sk_c7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[94, 82])).
% 0.21/0.50 tff(96,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_c6), multiply(sk_c2, multiply(sk_c2, sk_c6))) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(97,plain,
% 0.21/0.50 (multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c2, sk_c6))) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[96, 34])).
% 0.21/0.50 tff(98,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6)))) = multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c2, sk_c6)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[97])).
% 0.21/0.50 tff(99,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6))) = multiply(sk_c6, multiply(sk_c2, sk_c7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[82])).
% 0.21/0.50 tff(100,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c2, sk_c7)) = multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[99])).
% 0.21/0.50 tff(101,plain,
% 0.21/0.50 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c6, sk_c2), sk_c7)),
% 0.21/0.50 inference(symmetry,[status(thm)],[67])).
% 0.21/0.50 tff(102,plain,
% 0.21/0.50 (sk_c7 = multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[54, 53, 101, 69, 100])).
% 0.21/0.50 tff(103,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[102])).
% 0.21/0.50 tff(104,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c2, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.50 tff(105,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), sk_c6) = multiply(sk_c6, multiply(sk_c2, sk_c6)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(106,plain,
% 0.21/0.50 (multiply(multiply(sk_c6, sk_c2), sk_c6) = multiply(sk_c6, multiply(sk_c2, sk_c6))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[105, 34])).
% 0.21/0.50 tff(107,plain,
% 0.21/0.50 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c6, sk_c2)),
% 0.21/0.50 inference(symmetry,[status(thm)],[65])).
% 0.21/0.50 tff(108,plain,
% 0.21/0.50 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.50 inference(symmetry,[status(thm)],[59])).
% 0.21/0.50 tff(109,plain,
% 0.21/0.50 (identity = multiply(sk_c6, sk_c2)),
% 0.21/0.50 inference(transitivity,[status(thm)],[108, 107])).
% 0.21/0.50 tff(110,plain,
% 0.21/0.50 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c2), sk_c6)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.50 tff(111,plain,
% 0.21/0.50 (sk_c6 = multiply(identity, sk_c6)),
% 0.21/0.50 inference(symmetry,[status(thm)],[11])).
% 0.21/0.50 tff(112,plain,
% 0.21/0.50 (sk_c6 = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[111, 110, 106, 104, 103, 98, 95, 70, 67, 71, 9])).
% 0.21/0.50 tff(113,plain,
% 0.21/0.50 (multiply(sk_c1, sk_c6) = multiply(sk_c1, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[112])).
% 0.21/0.50 tff(114,plain,
% 0.21/0.50 (multiply(sk_c1, sk_c6) = sk_c5),
% 0.21/0.50 inference(transitivity,[status(thm)],[113, 26, 111, 110, 106, 104, 103, 98, 95, 70, 67, 36, 27, 20])).
% 0.21/0.50 tff(115,plain,
% 0.21/0.50 (multiply(multiply(sk_c6, sk_c2), sk_c6) = multiply(identity, sk_c6)),
% 0.21/0.50 inference(symmetry,[status(thm)],[110])).
% 0.21/0.50 tff(116,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c2, sk_c6)) = multiply(multiply(sk_c6, sk_c2), sk_c6)),
% 0.21/0.50 inference(symmetry,[status(thm)],[106])).
% 0.21/0.50 tff(117,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c2, sk_c6))),
% 0.21/0.50 inference(symmetry,[status(thm)],[104])).
% 0.21/0.50 tff(118,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6)))) = multiply(sk_c6, sk_c7)),
% 0.21/0.50 inference(symmetry,[status(thm)],[103])).
% 0.21/0.50 tff(119,plain,
% 0.21/0.50 (multiply(sk_c6, multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c2, sk_c6)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[95])).
% 0.21/0.50 tff(120,plain,
% 0.21/0.50 (inverse(sk_c1) = sk_c6),
% 0.21/0.50 inference(transitivity,[status(thm)],[40, 54, 53, 101, 69, 119, 97, 118, 117, 116, 115, 11])).
% 0.21/0.50 tff(121,plain,
% 0.21/0.50 ((sk_c6 = inverse(sk_c1)) <=> (inverse(sk_c1) = sk_c6)),
% 0.21/0.50 inference(commutativity,[status(thm)],[])).
% 0.21/0.50 tff(122,plain,
% 0.21/0.50 (sk_c7 = inverse(sk_c1)),
% 0.21/0.50 inference(symmetry,[status(thm)],[40])).
% 0.21/0.50 tff(123,plain,
% 0.21/0.50 (sk_c5 = inverse(sk_c1)),
% 0.21/0.50 inference(transitivity,[status(thm)],[74, 73, 72, 71, 9, 122])).
% 0.21/0.50 tff(124,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c7) = sk_c6),
% 0.21/0.50 inference(transitivity,[status(thm)],[117, 116, 115, 11])).
% 0.21/0.50 tff(125,plain,
% 0.21/0.50 ((multiply(sk_c6, sk_c7) = sk_c5) <=> (sk_c6 = inverse(sk_c1))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[124, 123])).
% 0.21/0.50 tff(126,plain,
% 0.21/0.50 ((multiply(sk_c6, sk_c7) = sk_c5) <=> (inverse(sk_c1) = sk_c6)),
% 0.21/0.50 inference(transitivity,[status(thm)],[125, 121])).
% 0.21/0.50 tff(127,plain,
% 0.21/0.50 ((inverse(sk_c1) = sk_c6) <=> (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.50 inference(symmetry,[status(thm)],[126])).
% 0.21/0.50 tff(128,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[120, 127])).
% 0.21/0.50 tff(129,plain,
% 0.21/0.50 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(130,plain,
% 0.21/0.50 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.50 tff(131,plain,
% 0.21/0.50 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(132,plain,
% 0.21/0.50 (^[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_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X4, sk_c6) = sk_c5))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X4, sk_c6) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), ((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X4) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X4) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), ((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), (((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), ((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), ((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), (((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c6) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X2, sk_c6) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), (((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X2) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X2) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(133,plain,
% 0.21/0.51 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.51 tff(134,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_26')).
% 0.21/0.51 tff(135,plain,
% 0.21/0.51 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.51 tff(136,plain,
% 0.21/0.51 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.21/0.51 tff(137,plain,(
% 0.21/0.51 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[136])).
% 0.21/0.51 tff(138,plain,
% 0.21/0.51 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.21/0.51 tff(139,plain,
% 0.21/0.51 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(140,plain,
% 0.21/0.51 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(141,plain,
% 0.21/0.51 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.51 tff(142,plain,
% 0.21/0.51 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[141, 139])).
% 0.21/0.51 tff(143,plain,
% 0.21/0.51 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(144,plain,
% 0.21/0.51 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.21/0.51 tff(145,plain,
% 0.21/0.51 ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[144, 20, 26, 40, 138])).
% 0.21/0.51 tff(146,plain,
% 0.21/0.51 (~(multiply(sk_c1, sk_c6) = sk_c7)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[145, 128, 120, 114])).
% 0.21/0.51 tff(147,plain,
% 0.21/0.51 (~(multiply(sk_c1, sk_c6) = sk_c5)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[146, 57])).
% 0.21/0.51 tff(148,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[114, 147])).
% 0.21/0.51 tff(149,plain,(inverse(sk_c4) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(150,plain,
% 0.21/0.51 (sk_c6 = inverse(sk_c4)),
% 0.21/0.51 inference(symmetry,[status(thm)],[149])).
% 0.21/0.51 tff(151,plain,
% 0.21/0.51 (multiply(sk_c6, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[150])).
% 0.21/0.51 tff(152,plain,
% 0.21/0.51 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c6, sk_c4)),
% 0.21/0.51 inference(symmetry,[status(thm)],[151])).
% 0.21/0.51 tff(153,plain,
% 0.21/0.51 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(154,plain,
% 0.21/0.51 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[153, 48])).
% 0.21/0.51 tff(155,plain,
% 0.21/0.51 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.51 inference(symmetry,[status(thm)],[154])).
% 0.21/0.51 tff(156,plain,
% 0.21/0.51 (identity = multiply(sk_c6, sk_c4)),
% 0.21/0.51 inference(transitivity,[status(thm)],[155, 152])).
% 0.21/0.51 tff(157,plain,
% 0.21/0.51 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[156])).
% 0.21/0.51 tff(158,plain,
% 0.21/0.51 (multiply(multiply(sk_c6, sk_c4), sk_c6) = multiply(identity, sk_c6)),
% 0.21/0.51 inference(symmetry,[status(thm)],[157])).
% 0.21/0.51 tff(159,plain,
% 0.21/0.51 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c3), sk_c3) = identity)),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(160,plain,
% 0.21/0.51 (multiply(inverse(sk_c3), sk_c3) = identity),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[159, 48])).
% 0.21/0.51 tff(161,assumption,(~(inverse(sk_c3) = sk_c7)), introduced(assumption)).
% 0.21/0.51 tff(162,plain,
% 0.21/0.51 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(163,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_12')).
% 0.21/0.51 tff(164,plain,
% 0.21/0.51 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.21/0.51 tff(165,plain,
% 0.21/0.51 (inverse(sk_c1) = sk_c7),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[164, 161])).
% 0.21/0.51 tff(166,plain,
% 0.21/0.51 (sk_c7 = inverse(sk_c1)),
% 0.21/0.51 inference(symmetry,[status(thm)],[165])).
% 0.21/0.51 tff(167,plain,
% 0.21/0.51 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[166])).
% 0.21/0.51 tff(168,plain,
% 0.21/0.51 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.21/0.51 inference(symmetry,[status(thm)],[167])).
% 0.21/0.51 tff(169,plain,
% 0.21/0.51 (identity = multiply(sk_c7, sk_c1)),
% 0.21/0.51 inference(transitivity,[status(thm)],[51, 168])).
% 0.21/0.51 tff(170,plain,
% 0.21/0.51 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[169])).
% 0.21/0.51 tff(171,plain,
% 0.21/0.51 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.51 inference(symmetry,[status(thm)],[170])).
% 0.21/0.51 tff(172,plain,
% 0.21/0.51 (((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c6)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(173,plain,
% 0.21/0.51 (((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(174,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_7')).
% 0.21/0.51 tff(175,plain,
% 0.21/0.51 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.21/0.51 tff(176,plain,
% 0.21/0.51 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[175, 172])).
% 0.21/0.51 tff(177,plain,
% 0.21/0.51 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[176, 161])).
% 0.21/0.51 tff(178,plain,
% 0.21/0.51 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[177])).
% 0.21/0.51 tff(179,plain,
% 0.21/0.51 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.51 inference(symmetry,[status(thm)],[178])).
% 0.21/0.51 tff(180,assumption,(~(multiply(sk_c7, sk_c6) = sk_c5)), introduced(assumption)).
% 0.21/0.51 tff(181,plain,
% 0.21/0.51 (((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(182,axiom,((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_1')).
% 0.21/0.51 tff(183,plain,
% 0.21/0.51 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.21/0.51 tff(184,plain,
% 0.21/0.51 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[183, 181])).
% 0.21/0.51 tff(185,plain,
% 0.21/0.51 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[184, 181])).
% 0.21/0.51 tff(186,plain,
% 0.21/0.51 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.21/0.51 tff(187,plain,
% 0.21/0.51 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[186, 181])).
% 0.21/0.51 tff(188,plain,
% 0.21/0.51 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[187, 180])).
% 0.21/0.51 tff(189,plain,
% 0.21/0.51 (((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)) <=> ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(190,axiom,((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_2')).
% 0.21/0.51 tff(191,plain,
% 0.21/0.51 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.21/0.51 tff(192,plain,
% 0.21/0.51 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[191, 189])).
% 0.21/0.51 tff(193,plain,
% 0.21/0.51 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[192, 189])).
% 0.21/0.51 tff(194,plain,
% 0.21/0.51 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.21/0.51 tff(195,plain,
% 0.21/0.51 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[194, 189])).
% 0.21/0.51 tff(196,plain,
% 0.21/0.51 (inverse(sk_c3) = sk_c7),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[195, 180])).
% 0.21/0.51 tff(197,plain,
% 0.21/0.51 (sk_c7 = inverse(sk_c3)),
% 0.21/0.51 inference(symmetry,[status(thm)],[196])).
% 0.21/0.51 tff(198,plain,
% 0.21/0.51 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[197])).
% 0.21/0.51 tff(199,plain,
% 0.21/0.51 (multiply(sk_c7, sk_c3) = multiply(sk_c6, sk_c4)),
% 0.21/0.51 inference(transitivity,[status(thm)],[198, 160, 155, 152])).
% 0.21/0.51 tff(200,plain,
% 0.21/0.51 (multiply(multiply(sk_c7, sk_c3), sk_c6) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[199])).
% 0.21/0.51 tff(201,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_c3), sk_c6) = multiply(sk_c7, multiply(sk_c3, sk_c6)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(202,plain,
% 0.21/0.51 (multiply(multiply(sk_c7, sk_c3), sk_c6) = multiply(sk_c7, multiply(sk_c3, sk_c6))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[201, 34])).
% 0.21/0.51 tff(203,plain,
% 0.21/0.51 (multiply(sk_c7, multiply(sk_c3, sk_c6)) = multiply(multiply(sk_c7, sk_c3), sk_c6)),
% 0.21/0.51 inference(symmetry,[status(thm)],[202])).
% 0.21/0.51 tff(204,plain,
% 0.21/0.51 (((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(205,axiom,((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_3')).
% 0.21/0.52 tff(206,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.21/0.52 tff(207,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[206, 204])).
% 0.21/0.52 tff(208,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[207, 204])).
% 0.21/0.52 tff(209,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.21/0.52 tff(210,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[209, 204])).
% 0.21/0.52 tff(211,plain,
% 0.21/0.52 (multiply(sk_c3, sk_c6) = sk_c7),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[210, 180])).
% 0.21/0.52 tff(212,plain,
% 0.21/0.52 (sk_c7 = multiply(sk_c3, sk_c6)),
% 0.21/0.52 inference(symmetry,[status(thm)],[211])).
% 0.21/0.52 tff(213,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c7) = multiply(sk_c7, multiply(sk_c3, sk_c6))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[212])).
% 0.21/0.52 tff(214,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c7) = sk_c6),
% 0.21/0.52 inference(transitivity,[status(thm)],[213, 203, 200, 158, 11])).
% 0.21/0.52 tff(215,plain,
% 0.21/0.52 (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[214])).
% 0.21/0.52 tff(216,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(sk_c7, multiply(sk_c7, sk_c7)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(217,plain,
% 0.21/0.52 (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[216, 34])).
% 0.21/0.52 tff(218,plain,
% 0.21/0.52 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c7), sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[217])).
% 0.21/0.52 tff(219,plain,
% 0.21/0.52 (multiply(sk_c7, multiply(sk_c3, sk_c6)) = multiply(sk_c7, sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[213])).
% 0.21/0.52 tff(220,plain,
% 0.21/0.52 (multiply(multiply(sk_c6, sk_c4), sk_c6) = multiply(multiply(sk_c7, sk_c3), sk_c6)),
% 0.21/0.52 inference(symmetry,[status(thm)],[200])).
% 0.21/0.52 tff(221,plain,
% 0.21/0.52 (sk_c6 = multiply(sk_c7, sk_c7)),
% 0.21/0.52 inference(transitivity,[status(thm)],[111, 157, 220, 202, 219])).
% 0.21/0.52 tff(222,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[221])).
% 0.21/0.52 tff(223,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c6) = sk_c5),
% 0.21/0.52 inference(transitivity,[status(thm)],[222, 218, 215, 188])).
% 0.21/0.52 tff(224,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[180, 223])).
% 0.21/0.52 tff(225,plain,(multiply(sk_c7, sk_c6) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(226,plain,
% 0.21/0.52 (sk_c5 = multiply(sk_c7, sk_c6)),
% 0.21/0.52 inference(symmetry,[status(thm)],[225])).
% 0.21/0.52 tff(227,assumption,(~(multiply(sk_c6, sk_c7) = sk_c5)), introduced(assumption)).
% 0.21/0.52 tff(228,plain,
% 0.21/0.52 (((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(229,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_6')).
% 0.21/0.52 tff(230,plain,
% 0.21/0.52 ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.21/0.52 tff(231,plain,
% 0.21/0.52 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.21/0.52 tff(232,plain,
% 0.21/0.52 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[231])).
% 0.21/0.52 tff(233,plain,
% 0.21/0.52 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(234,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_11')).
% 0.21/0.52 tff(235,plain,
% 0.21/0.52 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.21/0.52 tff(236,plain,
% 0.21/0.52 (inverse(sk_c1) = sk_c7),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[235, 227])).
% 0.21/0.52 tff(237,plain,
% 0.21/0.52 (sk_c7 = inverse(sk_c1)),
% 0.21/0.52 inference(symmetry,[status(thm)],[236])).
% 0.21/0.52 tff(238,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[237])).
% 0.21/0.52 tff(239,plain,
% 0.21/0.52 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.21/0.52 inference(symmetry,[status(thm)],[238])).
% 0.21/0.52 tff(240,plain,
% 0.21/0.52 (((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(241,axiom,((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_21')).
% 0.21/0.52 tff(242,plain,
% 0.21/0.52 ((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.21/0.52 tff(243,plain,
% 0.21/0.52 (inverse(sk_c2) = sk_c6),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[242, 227])).
% 0.21/0.52 tff(244,plain,
% 0.21/0.52 (sk_c6 = inverse(sk_c2)),
% 0.21/0.52 inference(symmetry,[status(thm)],[243])).
% 0.21/0.52 tff(245,plain,
% 0.21/0.52 (multiply(sk_c6, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[244])).
% 0.21/0.52 tff(246,plain,
% 0.21/0.52 (multiply(sk_c6, sk_c2) = multiply(sk_c7, sk_c1)),
% 0.21/0.52 inference(transitivity,[status(thm)],[245, 59, 51, 239])).
% 0.21/0.52 tff(247,plain,
% 0.21/0.52 (multiply(multiply(sk_c6, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[246])).
% 0.21/0.52 tff(248,plain,
% 0.21/0.52 (identity = multiply(sk_c7, sk_c1)),
% 0.21/0.52 inference(transitivity,[status(thm)],[51, 239])).
% 0.21/0.52 tff(249,plain,
% 0.21/0.52 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[248])).
% 0.21/0.52 tff(250,plain,
% 0.21/0.52 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[249])).
% 0.21/0.52 tff(251,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.52 inference(symmetry,[status(thm)],[232])).
% 0.21/0.52 tff(252,plain,
% 0.21/0.52 (sk_c5 = sk_c7),
% 0.21/0.52 inference(transitivity,[status(thm)],[226, 251, 72, 250, 9])).
% 0.21/0.52 tff(253,plain,
% 0.21/0.52 (multiply(sk_c1, sk_c5) = multiply(sk_c1, sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[252])).
% 0.21/0.52 tff(254,plain,
% 0.21/0.52 (multiply(sk_c1, sk_c5) = sk_c6),
% 0.21/0.52 inference(transitivity,[status(thm)],[253, 231])).
% 0.21/0.52 tff(255,plain,
% 0.21/0.52 (multiply(multiply(sk_c1, sk_c5), multiply(sk_c2, sk_c7)) = multiply(sk_c6, multiply(sk_c2, sk_c7))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[254])).
% 0.21/0.52 tff(256,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c5), multiply(sk_c2, sk_c7)) = multiply(sk_c1, multiply(sk_c5, multiply(sk_c2, sk_c7))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(257,plain,
% 0.21/0.52 (multiply(multiply(sk_c1, sk_c5), multiply(sk_c2, sk_c7)) = multiply(sk_c1, multiply(sk_c5, multiply(sk_c2, sk_c7)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[256, 34])).
% 0.21/0.52 tff(258,plain,
% 0.21/0.52 (multiply(sk_c1, multiply(sk_c5, multiply(sk_c2, sk_c7))) = multiply(multiply(sk_c1, sk_c5), multiply(sk_c2, sk_c7))),
% 0.21/0.52 inference(symmetry,[status(thm)],[257])).
% 0.21/0.52 tff(259,plain,
% 0.21/0.52 (((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(260,axiom,((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_16')).
% 0.21/0.52 tff(261,plain,
% 0.21/0.52 ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.21/0.52 tff(262,plain,
% 0.21/0.52 (multiply(sk_c2, sk_c6) = sk_c5),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[261, 227])).
% 0.21/0.52 tff(263,plain,
% 0.21/0.52 (sk_c5 = multiply(sk_c2, sk_c6)),
% 0.21/0.52 inference(symmetry,[status(thm)],[262])).
% 0.21/0.52 tff(264,plain,
% 0.21/0.52 (multiply(sk_c5, multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c2, sk_c6), multiply(sk_c2, sk_c7))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[263])).
% 0.21/0.52 tff(265,plain,
% 0.21/0.52 (multiply(multiply(sk_c2, sk_c6), multiply(sk_c2, sk_c7)) = multiply(sk_c5, multiply(sk_c2, sk_c7))),
% 0.21/0.52 inference(symmetry,[status(thm)],[264])).
% 0.21/0.52 tff(266,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c6), multiply(sk_c2, sk_c7)) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c2, sk_c7))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(267,plain,
% 0.21/0.52 (multiply(multiply(sk_c2, sk_c6), multiply(sk_c2, sk_c7)) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c2, sk_c7)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[266, 34])).
% 0.21/0.52 tff(268,plain,
% 0.21/0.52 (multiply(sk_c2, multiply(sk_c6, multiply(sk_c2, sk_c7))) = multiply(multiply(sk_c2, sk_c6), multiply(sk_c2, sk_c7))),
% 0.21/0.52 inference(symmetry,[status(thm)],[267])).
% 0.21/0.52 tff(269,plain,
% 0.21/0.52 (multiply(sk_c6, multiply(sk_c2, sk_c7)) = sk_c7),
% 0.21/0.52 inference(transitivity,[status(thm)],[70, 247, 250, 9])).
% 0.21/0.52 tff(270,plain,
% 0.21/0.52 (multiply(sk_c2, multiply(sk_c6, multiply(sk_c2, sk_c7))) = multiply(sk_c2, sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[269])).
% 0.21/0.52 tff(271,plain,
% 0.21/0.52 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c2, sk_c7)))),
% 0.21/0.52 inference(symmetry,[status(thm)],[270])).
% 0.21/0.52 tff(272,plain,
% 0.21/0.52 ((~![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)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(273,plain,
% 0.21/0.52 (multiply(multiply(sk_c6, sk_c4), sk_c7) = multiply(sk_c6, multiply(sk_c4, sk_c7))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[272, 34])).
% 0.21/0.52 tff(274,plain,
% 0.21/0.52 (multiply(sk_c6, sk_c4) = multiply(sk_c7, sk_c1)),
% 0.21/0.52 inference(transitivity,[status(thm)],[151, 154, 51, 239])).
% 0.21/0.52 tff(275,plain,
% 0.21/0.52 (multiply(multiply(sk_c6, sk_c4), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[274])).
% 0.21/0.52 tff(276,plain,
% 0.21/0.52 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c6, sk_c4), sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[275])).
% 0.21/0.52 tff(277,plain,
% 0.21/0.52 (sk_c7 = multiply(sk_c6, multiply(sk_c4, sk_c7))),
% 0.21/0.52 inference(transitivity,[status(thm)],[54, 249, 276, 273])).
% 0.21/0.52 tff(278,plain,
% 0.21/0.52 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[277])).
% 0.21/0.52 tff(279,plain,
% 0.21/0.52 (multiply(sk_c2, multiply(sk_c6, multiply(sk_c4, sk_c7))) = multiply(sk_c2, sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[278])).
% 0.21/0.52 tff(280,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c6), multiply(sk_c4, sk_c7)) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c4, sk_c7))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(281,plain,
% 0.21/0.52 (multiply(multiply(sk_c2, sk_c6), multiply(sk_c4, sk_c7)) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[280, 34])).
% 0.21/0.52 tff(282,plain,
% 0.21/0.52 (multiply(sk_c5, sk_c6) = multiply(sk_c7, sk_c6)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[252])).
% 0.21/0.52 tff(283,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c6) = multiply(sk_c5, sk_c6)),
% 0.21/0.52 inference(symmetry,[status(thm)],[282])).
% 0.21/0.52 tff(284,plain,
% 0.21/0.52 (multiply(sk_c2, sk_c6) = multiply(sk_c5, sk_c6)),
% 0.21/0.52 inference(transitivity,[status(thm)],[262, 226, 283])).
% 0.21/0.52 tff(285,plain,
% 0.21/0.52 (multiply(multiply(sk_c2, sk_c6), multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c4, sk_c7))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[284])).
% 0.21/0.52 tff(286,plain,
% 0.21/0.52 (multiply(multiply(sk_c5, sk_c6), multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c2, sk_c6), multiply(sk_c4, sk_c7))),
% 0.21/0.52 inference(symmetry,[status(thm)],[285])).
% 0.21/0.52 tff(287,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c6), multiply(sk_c4, sk_c7)) = multiply(sk_c5, multiply(sk_c6, multiply(sk_c4, sk_c7))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(288,plain,
% 0.21/0.52 (multiply(multiply(sk_c5, sk_c6), multiply(sk_c4, sk_c7)) = multiply(sk_c5, multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[287, 34])).
% 0.21/0.52 tff(289,plain,
% 0.21/0.52 (multiply(sk_c5, multiply(sk_c6, multiply(sk_c4, sk_c7))) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c4, sk_c7))),
% 0.21/0.52 inference(symmetry,[status(thm)],[288])).
% 0.21/0.52 tff(290,plain,
% 0.21/0.52 (multiply(sk_c6, multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c6, sk_c4), sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[273])).
% 0.21/0.52 tff(291,plain,
% 0.21/0.52 (multiply(sk_c6, multiply(sk_c4, sk_c7)) = sk_c7),
% 0.21/0.52 inference(transitivity,[status(thm)],[290, 275, 250, 9])).
% 0.21/0.52 tff(292,plain,
% 0.21/0.52 (multiply(sk_c5, multiply(sk_c6, multiply(sk_c4, sk_c7))) = multiply(sk_c7, sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[252, 291])).
% 0.21/0.52 tff(293,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c7) = multiply(sk_c5, multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.21/0.52 inference(symmetry,[status(thm)],[292])).
% 0.21/0.52 tff(294,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c7) = multiply(sk_c5, multiply(sk_c2, sk_c7))),
% 0.21/0.52 inference(transitivity,[status(thm)],[293, 289, 286, 281, 279, 271, 268, 265])).
% 0.21/0.52 tff(295,plain,
% 0.21/0.52 (multiply(sk_c1, multiply(sk_c7, sk_c7)) = multiply(sk_c1, multiply(sk_c5, multiply(sk_c2, sk_c7)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[294])).
% 0.21/0.52 tff(296,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), sk_c7) = multiply(sk_c1, multiply(sk_c7, sk_c7)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(297,plain,
% 0.21/0.52 (multiply(multiply(sk_c1, sk_c7), sk_c7) = multiply(sk_c1, multiply(sk_c7, sk_c7))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[296, 34])).
% 0.21/0.52 tff(298,plain,
% 0.21/0.52 (sk_c6 = multiply(sk_c1, sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[231])).
% 0.21/0.52 tff(299,plain,
% 0.21/0.52 (multiply(sk_c6, sk_c7) = multiply(multiply(sk_c1, sk_c7), sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[298])).
% 0.21/0.52 tff(300,plain,
% 0.21/0.52 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.21/0.52 inference(transitivity,[status(thm)],[299, 297, 295, 258, 255, 70, 247, 36, 232, 225])).
% 0.21/0.52 tff(301,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[227, 300])).
% 0.21/0.52 tff(302,plain,(multiply(sk_c6, sk_c7) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(303,plain,
% 0.21/0.52 (sk_c5 = sk_c7),
% 0.21/0.52 inference(transitivity,[status(thm)],[226, 179, 72, 171, 9])).
% 0.21/0.52 tff(304,plain,
% 0.21/0.52 (sk_c7 = multiply(sk_c7, sk_c6)),
% 0.21/0.52 inference(transitivity,[status(thm)],[54, 170, 36, 178])).
% 0.21/0.52 tff(305,plain,
% 0.21/0.52 (multiply(sk_c1, sk_c7) = multiply(sk_c1, multiply(sk_c7, sk_c6))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[304])).
% 0.21/0.52 tff(306,plain,
% 0.21/0.52 (multiply(sk_c1, multiply(sk_c7, sk_c6)) = multiply(sk_c1, sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[305])).
% 0.21/0.52 tff(307,plain,
% 0.21/0.52 (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)),
% 0.21/0.52 inference(transitivity,[status(thm)],[302, 226])).
% 0.21/0.52 tff(308,plain,
% 0.21/0.52 (multiply(sk_c1, multiply(sk_c6, sk_c7)) = multiply(sk_c1, multiply(sk_c7, sk_c6))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[307])).
% 0.21/0.52 tff(309,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c6), sk_c7) = multiply(sk_c1, multiply(sk_c6, sk_c7)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(310,plain,
% 0.21/0.52 (multiply(multiply(sk_c1, sk_c6), sk_c7) = multiply(sk_c1, multiply(sk_c6, sk_c7))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[309, 34])).
% 0.21/0.52 tff(311,plain,
% 0.21/0.52 (multiply(multiply(sk_c1, sk_c6), sk_c5) = multiply(multiply(sk_c1, sk_c6), sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[303])).
% 0.21/0.52 tff(312,plain,
% 0.21/0.52 (multiply(multiply(sk_c1, sk_c6), sk_c5) = sk_c6),
% 0.21/0.52 inference(transitivity,[status(thm)],[311, 310, 308, 306, 177])).
% 0.21/0.52 tff(313,plain,
% 0.21/0.52 (multiply(multiply(multiply(sk_c1, sk_c6), sk_c5), sk_c5) = multiply(sk_c6, sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[312, 303])).
% 0.21/0.52 tff(314,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c1, sk_c6), sk_c5), sk_c5) = multiply(multiply(sk_c1, sk_c6), multiply(sk_c5, sk_c5)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(315,plain,
% 0.21/0.52 (multiply(multiply(multiply(sk_c1, sk_c6), sk_c5), sk_c5) = multiply(multiply(sk_c1, sk_c6), multiply(sk_c5, sk_c5))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[314, 34])).
% 0.21/0.52 tff(316,plain,
% 0.21/0.52 (multiply(multiply(sk_c1, sk_c6), multiply(sk_c5, sk_c5)) = multiply(multiply(multiply(sk_c1, sk_c6), sk_c5), sk_c5)),
% 0.21/0.52 inference(symmetry,[status(thm)],[315])).
% 0.21/0.52 tff(317,plain,
% 0.21/0.52 (multiply(sk_c5, sk_c5) = multiply(sk_c7, sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[303, 303])).
% 0.21/0.52 tff(318,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c7) = multiply(sk_c5, sk_c5)),
% 0.21/0.52 inference(symmetry,[status(thm)],[317])).
% 0.21/0.52 tff(319,assumption,(~(multiply(sk_c2, sk_c6) = sk_c5)), introduced(assumption)).
% 0.21/0.52 tff(320,plain,
% 0.21/0.52 (((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c4, sk_c6) = sk_c7)) <=> ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c4, sk_c6) = sk_c7))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(321,axiom,((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c4, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_19')).
% 0.21/0.52 tff(322,plain,
% 0.21/0.52 ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c4, sk_c6) = sk_c7)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.21/0.52 tff(323,plain,
% 0.21/0.52 (multiply(sk_c4, sk_c6) = sk_c7),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[322, 319])).
% 0.21/0.52 tff(324,plain,
% 0.21/0.52 (multiply(sk_c6, multiply(sk_c4, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[323])).
% 0.21/0.52 tff(325,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c4), sk_c6) = multiply(sk_c6, multiply(sk_c4, sk_c6)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(326,plain,
% 0.21/0.52 (multiply(multiply(sk_c6, sk_c4), sk_c6) = multiply(sk_c6, multiply(sk_c4, sk_c6))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[325, 34])).
% 0.21/0.52 tff(327,plain,
% 0.21/0.52 (((inverse(sk_c3) = sk_c7) | (multiply(sk_c2, sk_c6) = sk_c5)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c2, sk_c6) = sk_c5))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(328,plain,
% 0.21/0.52 (((multiply(sk_c2, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c2, sk_c6) = sk_c5))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(329,axiom,((multiply(sk_c2, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_17')).
% 0.21/0.52 tff(330,plain,
% 0.21/0.52 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c2, sk_c6) = sk_c5)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.21/0.52 tff(331,plain,
% 0.21/0.52 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c2, sk_c6) = sk_c5)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[330, 327])).
% 0.21/0.52 tff(332,plain,
% 0.21/0.52 (inverse(sk_c3) = sk_c7),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[331, 319])).
% 0.21/0.52 tff(333,plain,
% 0.21/0.52 (sk_c7 = inverse(sk_c3)),
% 0.21/0.52 inference(symmetry,[status(thm)],[332])).
% 0.21/0.52 tff(334,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[333])).
% 0.21/0.52 tff(335,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c3) = multiply(sk_c6, sk_c4)),
% 0.21/0.52 inference(transitivity,[status(thm)],[334, 160, 155, 152])).
% 0.21/0.52 tff(336,plain,
% 0.21/0.52 (multiply(multiply(sk_c7, sk_c3), sk_c6) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[335])).
% 0.21/0.52 tff(337,plain,
% 0.21/0.52 ((sk_c7 = inverse(sk_c4)) <=> (inverse(sk_c4) = sk_c7)),
% 0.21/0.52 inference(commutativity,[status(thm)],[])).
% 0.21/0.52 tff(338,assumption,(~(multiply(sk_c3, sk_c6) = sk_c7)), introduced(assumption)).
% 0.21/0.52 tff(339,plain,
% 0.21/0.52 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c7))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(340,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_13')).
% 0.21/0.52 tff(341,plain,
% 0.21/0.52 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.21/0.52 tff(342,plain,
% 0.21/0.52 (inverse(sk_c1) = sk_c7),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[341, 338])).
% 0.21/0.52 tff(343,plain,
% 0.21/0.52 (sk_c7 = inverse(sk_c1)),
% 0.21/0.52 inference(symmetry,[status(thm)],[342])).
% 0.21/0.52 tff(344,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[343])).
% 0.21/0.52 tff(345,plain,
% 0.21/0.52 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.21/0.52 inference(symmetry,[status(thm)],[344])).
% 0.21/0.52 tff(346,plain,
% 0.21/0.52 (identity = multiply(sk_c7, sk_c1)),
% 0.21/0.52 inference(transitivity,[status(thm)],[51, 345])).
% 0.21/0.52 tff(347,plain,
% 0.21/0.52 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[346])).
% 0.21/0.52 tff(348,plain,
% 0.21/0.52 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[347])).
% 0.21/0.52 tff(349,plain,
% 0.21/0.52 (((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(350,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_8')).
% 0.21/0.52 tff(351,plain,
% 0.21/0.52 ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.21/0.52 tff(352,plain,
% 0.21/0.52 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[351, 338])).
% 0.21/0.52 tff(353,plain,
% 0.21/0.52 (sk_c6 = multiply(sk_c1, sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[352])).
% 0.21/0.52 tff(354,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[353])).
% 0.21/0.52 tff(355,plain,
% 0.21/0.52 (sk_c5 = sk_c7),
% 0.21/0.52 inference(transitivity,[status(thm)],[226, 354, 72, 348, 9])).
% 0.21/0.52 tff(356,plain,
% 0.21/0.52 (multiply(sk_c6, sk_c5) = multiply(sk_c6, sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[355])).
% 0.21/0.52 tff(357,plain,
% 0.21/0.52 (multiply(sk_c6, sk_c7) = multiply(sk_c6, sk_c5)),
% 0.21/0.52 inference(symmetry,[status(thm)],[356])).
% 0.21/0.52 tff(358,plain,
% 0.21/0.52 (sk_c5 = multiply(sk_c6, sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[302])).
% 0.21/0.52 tff(359,plain,
% 0.21/0.52 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.21/0.52 inference(symmetry,[status(thm)],[354])).
% 0.21/0.52 tff(360,plain,
% 0.21/0.52 (sk_c7 = multiply(sk_c6, sk_c5)),
% 0.21/0.52 inference(transitivity,[status(thm)],[54, 347, 36, 359, 225, 358, 357])).
% 0.21/0.52 tff(361,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c1) = identity),
% 0.21/0.52 inference(transitivity,[status(thm)],[344, 50])).
% 0.21/0.52 tff(362,plain,
% 0.21/0.52 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, multiply(sk_c6, sk_c5))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[361, 360])).
% 0.21/0.52 tff(363,plain,
% 0.21/0.52 (multiply(identity, multiply(sk_c6, sk_c5)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[362])).
% 0.21/0.52 tff(364,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c6), sk_c5) = multiply(identity, multiply(sk_c6, sk_c5)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(365,plain,
% 0.21/0.52 (multiply(multiply(identity, sk_c6), sk_c5) = multiply(identity, multiply(sk_c6, sk_c5))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[364, 34])).
% 0.21/0.52 tff(366,plain,
% 0.21/0.52 (((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(367,axiom,((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_18')).
% 0.21/0.52 tff(368,plain,
% 0.21/0.52 ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.21/0.52 tff(369,plain,
% 0.21/0.52 (multiply(sk_c2, sk_c6) = sk_c5),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[368, 338])).
% 0.21/0.52 tff(370,plain,
% 0.21/0.53 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.21/0.53 inference(transitivity,[status(thm)],[369, 226, 354, 72, 348, 9])).
% 0.21/0.53 tff(371,plain,
% 0.21/0.53 (multiply(sk_c6, multiply(sk_c2, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[370])).
% 0.21/0.53 tff(372,assumption,(~(inverse(sk_c2) = sk_c6)), introduced(assumption)).
% 0.21/0.53 tff(373,plain,
% 0.21/0.53 (((inverse(sk_c2) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)) <=> ((inverse(sk_c2) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(374,axiom,((inverse(sk_c2) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_24')).
% 0.21/0.53 tff(375,plain,
% 0.21/0.53 ((inverse(sk_c2) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.21/0.53 tff(376,plain,
% 0.21/0.53 (multiply(sk_c4, sk_c6) = sk_c7),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[375, 372])).
% 0.21/0.53 tff(377,plain,
% 0.21/0.53 (multiply(sk_c6, multiply(sk_c4, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[376])).
% 0.21/0.53 tff(378,plain,
% 0.21/0.53 (((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c7))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(379,axiom,((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_22')).
% 0.21/0.53 tff(380,plain,
% 0.21/0.53 ((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.21/0.53 tff(381,plain,
% 0.21/0.53 (inverse(sk_c3) = sk_c7),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[380, 372])).
% 0.21/0.53 tff(382,plain,
% 0.21/0.53 (sk_c7 = inverse(sk_c3)),
% 0.21/0.53 inference(symmetry,[status(thm)],[381])).
% 0.21/0.53 tff(383,plain,
% 0.21/0.53 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[382])).
% 0.21/0.53 tff(384,plain,
% 0.21/0.53 (multiply(sk_c7, sk_c3) = multiply(sk_c6, sk_c4)),
% 0.21/0.53 inference(transitivity,[status(thm)],[383, 160, 155, 152])).
% 0.21/0.53 tff(385,plain,
% 0.21/0.53 (multiply(multiply(sk_c7, sk_c3), sk_c6) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[384])).
% 0.21/0.53 tff(386,plain,
% 0.21/0.53 (((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(387,axiom,((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_23')).
% 0.21/0.53 tff(388,plain,
% 0.21/0.53 ((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[387, 386])).
% 0.21/0.53 tff(389,plain,
% 0.21/0.53 (multiply(sk_c3, sk_c6) = sk_c7),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[388, 372])).
% 0.21/0.53 tff(390,plain,
% 0.21/0.53 (sk_c7 = multiply(sk_c3, sk_c6)),
% 0.21/0.53 inference(symmetry,[status(thm)],[389])).
% 0.21/0.53 tff(391,plain,
% 0.21/0.53 (multiply(sk_c6, multiply(sk_c4, sk_c6)) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.21/0.53 inference(symmetry,[status(thm)],[326])).
% 0.21/0.53 tff(392,plain,
% 0.21/0.53 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c4, sk_c6))),
% 0.21/0.53 inference(symmetry,[status(thm)],[377])).
% 0.21/0.53 tff(393,plain,
% 0.21/0.53 (sk_c5 = sk_c6),
% 0.21/0.53 inference(transitivity,[status(thm)],[358, 392, 391, 158, 11])).
% 0.21/0.53 tff(394,plain,
% 0.21/0.53 (multiply(sk_c4, sk_c5) = multiply(sk_c4, sk_c6)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[393])).
% 0.21/0.53 tff(395,plain,
% 0.21/0.53 (multiply(sk_c4, sk_c5) = sk_c7),
% 0.21/0.53 inference(transitivity,[status(thm)],[394, 376])).
% 0.21/0.53 tff(396,plain,
% 0.21/0.53 (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c7, multiply(sk_c3, sk_c6))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[395, 390])).
% 0.21/0.53 tff(397,plain,
% 0.21/0.53 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c4, multiply(sk_c5, sk_c7)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(398,plain,
% 0.21/0.53 (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c4, multiply(sk_c5, sk_c7))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[397, 34])).
% 0.21/0.53 tff(399,plain,
% 0.21/0.53 (multiply(sk_c4, multiply(sk_c5, sk_c7)) = multiply(multiply(sk_c4, sk_c5), sk_c7)),
% 0.21/0.53 inference(symmetry,[status(thm)],[398])).
% 0.21/0.53 tff(400,plain,
% 0.21/0.53 (multiply(sk_c5, sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[393])).
% 0.21/0.53 tff(401,plain,
% 0.21/0.53 (multiply(sk_c6, sk_c7) = multiply(sk_c5, sk_c7)),
% 0.21/0.53 inference(symmetry,[status(thm)],[400])).
% 0.21/0.53 tff(402,plain,
% 0.21/0.53 (sk_c6 = multiply(sk_c5, sk_c7)),
% 0.21/0.53 inference(transitivity,[status(thm)],[111, 157, 326, 377, 401])).
% 0.21/0.53 tff(403,plain,
% 0.21/0.53 (multiply(sk_c4, sk_c6) = multiply(sk_c4, multiply(sk_c5, sk_c7))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[402])).
% 0.21/0.53 tff(404,plain,
% 0.21/0.53 (multiply(sk_c4, sk_c6) = sk_c5),
% 0.21/0.53 inference(transitivity,[status(thm)],[403, 399, 396, 203, 385, 326, 377, 302])).
% 0.21/0.53 tff(405,plain,
% 0.21/0.53 (sk_c7 = multiply(sk_c4, sk_c6)),
% 0.21/0.53 inference(symmetry,[status(thm)],[376])).
% 0.21/0.53 tff(406,plain,
% 0.21/0.53 (sk_c7 = sk_c6),
% 0.21/0.53 inference(transitivity,[status(thm)],[405, 403, 399, 396, 203, 385, 158, 11])).
% 0.21/0.53 tff(407,plain,
% 0.21/0.53 (multiply(sk_c3, sk_c7) = multiply(sk_c3, sk_c6)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[406])).
% 0.21/0.53 tff(408,plain,
% 0.21/0.53 (multiply(sk_c3, sk_c7) = sk_c6),
% 0.21/0.53 inference(transitivity,[status(thm)],[407, 389, 405, 403, 399, 396, 203, 385, 158, 11])).
% 0.21/0.53 tff(409,plain,
% 0.21/0.53 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(410,plain,
% 0.21/0.53 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(411,plain,
% 0.21/0.53 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[410])).
% 0.21/0.53 tff(412,plain,
% 0.21/0.53 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[411, 409])).
% 0.21/0.53 tff(413,plain,
% 0.21/0.53 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(414,plain,
% 0.21/0.53 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.21/0.53 tff(415,plain,
% 0.21/0.53 ((~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c7) = sk_c6))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[414, 225, 302, 381, 389, 376, 149, 138])).
% 0.21/0.53 tff(416,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[415, 408, 404])).
% 0.21/0.53 tff(417,plain,(inverse(sk_c2) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(418,plain,
% 0.21/0.53 (sk_c6 = inverse(sk_c2)),
% 0.21/0.53 inference(symmetry,[status(thm)],[417])).
% 0.21/0.53 tff(419,plain,
% 0.21/0.53 (multiply(sk_c6, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[418])).
% 0.21/0.53 tff(420,plain,
% 0.21/0.53 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c6, sk_c2)),
% 0.21/0.53 inference(symmetry,[status(thm)],[419])).
% 0.21/0.53 tff(421,plain,
% 0.21/0.53 (identity = multiply(sk_c6, sk_c2)),
% 0.21/0.53 inference(transitivity,[status(thm)],[108, 420])).
% 0.21/0.53 tff(422,plain,
% 0.21/0.53 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c2), sk_c6)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[421])).
% 0.21/0.53 tff(423,plain,
% 0.21/0.53 (multiply(identity, sk_c6) = sk_c7),
% 0.21/0.53 inference(transitivity,[status(thm)],[422, 106, 371, 302, 226, 354, 72, 348, 9])).
% 0.21/0.53 tff(424,plain,
% 0.21/0.53 (multiply(multiply(identity, sk_c6), sk_c5) = multiply(sk_c7, sk_c7)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[423, 355])).
% 0.21/0.53 tff(425,plain,
% 0.21/0.53 (multiply(sk_c7, sk_c7) = multiply(multiply(identity, sk_c6), sk_c5)),
% 0.21/0.53 inference(symmetry,[status(thm)],[424])).
% 0.21/0.53 tff(426,plain,
% 0.21/0.53 (sk_c7 = sk_c5),
% 0.21/0.53 inference(transitivity,[status(thm)],[54, 347, 36, 359, 225])).
% 0.21/0.53 tff(427,plain,
% 0.21/0.53 (sk_c5 = multiply(sk_c2, sk_c6)),
% 0.21/0.53 inference(symmetry,[status(thm)],[369])).
% 0.21/0.53 tff(428,plain,
% 0.21/0.53 (sk_c7 = multiply(sk_c2, sk_c6)),
% 0.21/0.53 inference(transitivity,[status(thm)],[54, 347, 36, 359, 225, 427])).
% 0.21/0.53 tff(429,plain,
% 0.21/0.53 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c2, sk_c6), sk_c5)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[428, 426])).
% 0.21/0.53 tff(430,plain,
% 0.21/0.53 (multiply(multiply(sk_c2, sk_c6), sk_c5) = multiply(sk_c7, sk_c7)),
% 0.21/0.53 inference(symmetry,[status(thm)],[429])).
% 0.21/0.53 tff(431,plain,
% 0.21/0.53 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c6), sk_c5) = multiply(sk_c2, multiply(sk_c6, sk_c5)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(432,plain,
% 0.21/0.53 (multiply(multiply(sk_c2, sk_c6), sk_c5) = multiply(sk_c2, multiply(sk_c6, sk_c5))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[431, 34])).
% 0.21/0.53 tff(433,plain,
% 0.21/0.53 (multiply(sk_c2, multiply(sk_c6, sk_c5)) = multiply(multiply(sk_c2, sk_c6), sk_c5)),
% 0.21/0.53 inference(symmetry,[status(thm)],[432])).
% 0.21/0.53 tff(434,plain,
% 0.21/0.53 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(sk_c6, sk_c5))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[360])).
% 0.21/0.53 tff(435,plain,
% 0.21/0.53 (multiply(sk_c2, sk_c7) = sk_c7),
% 0.21/0.53 inference(transitivity,[status(thm)],[434, 433, 430, 425, 365, 363, 348, 9])).
% 0.21/0.53 tff(436,plain,
% 0.21/0.53 ((multiply(sk_c2, sk_c7) = sk_c6) <=> (sk_c7 = inverse(sk_c4))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[435, 150])).
% 0.21/0.53 tff(437,plain,
% 0.21/0.53 ((multiply(sk_c2, sk_c7) = sk_c6) <=> (inverse(sk_c4) = sk_c7)),
% 0.21/0.53 inference(transitivity,[status(thm)],[436, 337])).
% 0.21/0.53 tff(438,plain,
% 0.21/0.53 ((inverse(sk_c4) = sk_c7) <=> (multiply(sk_c2, sk_c7) = sk_c6)),
% 0.21/0.53 inference(symmetry,[status(thm)],[437])).
% 0.21/0.53 tff(439,plain,
% 0.21/0.53 ((~(inverse(sk_c4) = sk_c7)) <=> (~(multiply(sk_c2, sk_c7) = sk_c6))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[438])).
% 0.21/0.53 tff(440,plain,
% 0.21/0.53 (inverse(sk_c2) = inverse(sk_c4)),
% 0.21/0.53 inference(transitivity,[status(thm)],[417, 150])).
% 0.21/0.53 tff(441,plain,
% 0.21/0.53 ((inverse(sk_c2) = sk_c7) <=> (inverse(sk_c4) = sk_c7)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[440])).
% 0.21/0.53 tff(442,plain,
% 0.21/0.53 ((~(inverse(sk_c2) = sk_c7)) <=> (~(inverse(sk_c4) = sk_c7))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[441])).
% 0.21/0.53 tff(443,plain,
% 0.21/0.53 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(444,plain,
% 0.21/0.53 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(445,plain,
% 0.21/0.53 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[444])).
% 0.21/0.53 tff(446,plain,
% 0.21/0.53 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[445, 443])).
% 0.21/0.53 tff(447,plain,
% 0.21/0.53 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(448,plain,
% 0.21/0.54 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.21/0.54 tff(449,plain,
% 0.21/0.54 ((~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[448, 225, 302, 352, 342, 369, 417, 138])).
% 0.21/0.54 tff(450,plain,
% 0.21/0.54 (~(inverse(sk_c2) = sk_c7)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[449, 370])).
% 0.21/0.54 tff(451,plain,
% 0.21/0.54 (~(inverse(sk_c4) = sk_c7)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[450, 442])).
% 0.21/0.54 tff(452,plain,
% 0.21/0.54 (~(multiply(sk_c2, sk_c7) = sk_c6)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[451, 439])).
% 0.21/0.54 tff(453,plain,
% 0.21/0.54 (multiply(identity, multiply(sk_c6, sk_c5)) = multiply(multiply(identity, sk_c6), sk_c5)),
% 0.21/0.54 inference(symmetry,[status(thm)],[365])).
% 0.21/0.54 tff(454,plain,
% 0.21/0.54 (sk_c7 = multiply(sk_c7, sk_c7)),
% 0.21/0.54 inference(transitivity,[status(thm)],[54, 347, 362, 453, 424])).
% 0.21/0.54 tff(455,plain,
% 0.21/0.54 (multiply(sk_c1, sk_c7) = multiply(sk_c1, multiply(sk_c7, sk_c7))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[454])).
% 0.21/0.54 tff(456,plain,
% 0.21/0.54 (multiply(sk_c1, multiply(sk_c7, sk_c7)) = multiply(sk_c1, sk_c7)),
% 0.21/0.54 inference(symmetry,[status(thm)],[455])).
% 0.21/0.54 tff(457,plain,
% 0.21/0.54 (multiply(multiply(sk_c1, sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[352])).
% 0.21/0.54 tff(458,plain,
% 0.21/0.54 (multiply(sk_c6, sk_c7) = multiply(multiply(sk_c1, sk_c7), sk_c7)),
% 0.21/0.54 inference(symmetry,[status(thm)],[457])).
% 0.21/0.54 tff(459,plain,
% 0.21/0.54 (multiply(sk_c2, sk_c7) = sk_c6),
% 0.21/0.54 inference(transitivity,[status(thm)],[434, 433, 430, 425, 365, 363, 36, 359, 225, 358, 458, 297, 456, 352])).
% 0.21/0.54 tff(460,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[459, 452])).
% 0.21/0.54 tff(461,plain,(multiply(sk_c3, sk_c6) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(462,plain,
% 0.21/0.54 (sk_c7 = multiply(sk_c3, sk_c6)),
% 0.21/0.54 inference(symmetry,[status(thm)],[461])).
% 0.21/0.54 tff(463,plain,
% 0.21/0.54 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c4, sk_c6))),
% 0.21/0.54 inference(symmetry,[status(thm)],[324])).
% 0.21/0.54 tff(464,plain,
% 0.21/0.54 (sk_c5 = sk_c6),
% 0.21/0.54 inference(transitivity,[status(thm)],[358, 463, 391, 158, 11])).
% 0.21/0.54 tff(465,plain,
% 0.21/0.54 (multiply(sk_c4, sk_c5) = multiply(sk_c4, sk_c6)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[464])).
% 0.21/0.54 tff(466,plain,
% 0.21/0.54 (multiply(sk_c4, sk_c5) = sk_c7),
% 0.21/0.54 inference(transitivity,[status(thm)],[465, 323])).
% 0.21/0.54 tff(467,plain,
% 0.21/0.54 (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c7, multiply(sk_c3, sk_c6))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[466, 462])).
% 0.21/0.54 tff(468,plain,
% 0.21/0.54 (multiply(sk_c5, sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[464])).
% 0.21/0.54 tff(469,plain,
% 0.21/0.54 (multiply(sk_c6, sk_c7) = multiply(sk_c5, sk_c7)),
% 0.21/0.54 inference(symmetry,[status(thm)],[468])).
% 0.21/0.54 tff(470,plain,
% 0.21/0.54 (sk_c6 = multiply(sk_c5, sk_c7)),
% 0.21/0.54 inference(transitivity,[status(thm)],[111, 157, 326, 324, 469])).
% 0.21/0.54 tff(471,plain,
% 0.21/0.54 (multiply(sk_c4, sk_c6) = multiply(sk_c4, multiply(sk_c5, sk_c7))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[470])).
% 0.21/0.54 tff(472,plain,
% 0.21/0.54 (multiply(sk_c4, sk_c6) = sk_c5),
% 0.21/0.54 inference(transitivity,[status(thm)],[471, 399, 467, 203, 336, 326, 324, 302])).
% 0.21/0.54 tff(473,plain,
% 0.21/0.54 (sk_c7 = multiply(sk_c4, sk_c6)),
% 0.21/0.54 inference(symmetry,[status(thm)],[323])).
% 0.21/0.54 tff(474,plain,
% 0.21/0.54 (sk_c7 = sk_c6),
% 0.21/0.54 inference(transitivity,[status(thm)],[473, 471, 399, 467, 203, 336, 158, 11])).
% 0.21/0.54 tff(475,plain,
% 0.21/0.54 (multiply(sk_c3, sk_c7) = multiply(sk_c3, sk_c6)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[474])).
% 0.21/0.54 tff(476,plain,
% 0.21/0.54 (multiply(sk_c3, sk_c7) = sk_c6),
% 0.21/0.54 inference(transitivity,[status(thm)],[475, 461, 473, 471, 399, 467, 203, 336, 158, 11])).
% 0.21/0.54 tff(477,plain,
% 0.21/0.54 ((~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c7) = sk_c6))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[414, 225, 302, 332, 461, 323, 149, 138])).
% 0.21/0.54 tff(478,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[477, 476, 472])).
% 0.21/0.54 tff(479,plain,(multiply(sk_c2, sk_c6) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(480,plain,
% 0.21/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), sk_c6) = multiply(sk_c1, multiply(sk_c7, sk_c6)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(481,plain,
% 0.21/0.54 (multiply(multiply(sk_c1, sk_c7), sk_c6) = multiply(sk_c1, multiply(sk_c7, sk_c6))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[480, 34])).
% 0.21/0.54 tff(482,plain,
% 0.21/0.54 (sk_c6 = multiply(sk_c1, sk_c7)),
% 0.21/0.54 inference(symmetry,[status(thm)],[177])).
% 0.21/0.54 tff(483,plain,
% 0.21/0.54 (multiply(sk_c6, sk_c6) = multiply(multiply(sk_c1, sk_c7), sk_c6)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[482])).
% 0.21/0.54 tff(484,plain,
% 0.21/0.54 (multiply(sk_c6, multiply(sk_c1, sk_c7)) = multiply(sk_c6, sk_c6)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[177])).
% 0.21/0.54 tff(485,plain,
% 0.21/0.54 (multiply(sk_c6, multiply(sk_c1, sk_c7)) = sk_c6),
% 0.21/0.54 inference(transitivity,[status(thm)],[484, 483, 481, 306, 177])).
% 0.21/0.54 tff(486,plain,
% 0.21/0.54 (multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c2, sk_c6)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[485])).
% 0.21/0.54 tff(487,plain,
% 0.21/0.54 (multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))) = sk_c7),
% 0.21/0.54 inference(transitivity,[status(thm)],[486, 479, 226, 179, 72, 171, 9])).
% 0.21/0.54 tff(488,plain,
% 0.21/0.54 (multiply(multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c5) = multiply(sk_c7, sk_c7)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[487, 303])).
% 0.21/0.54 tff(489,plain,
% 0.21/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c5) = multiply(sk_c2, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(490,plain,
% 0.21/0.54 (multiply(multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c5) = multiply(sk_c2, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[489, 34])).
% 0.21/0.54 tff(491,plain,
% 0.21/0.54 (multiply(sk_c2, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5)) = multiply(multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c5)),
% 0.21/0.54 inference(symmetry,[status(thm)],[490])).
% 0.21/0.54 tff(492,plain,
% 0.21/0.54 (multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5) = multiply(sk_c6, sk_c7)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[485, 303])).
% 0.21/0.54 tff(493,plain,
% 0.21/0.54 (multiply(sk_c6, sk_c7) = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5)),
% 0.21/0.54 inference(symmetry,[status(thm)],[492])).
% 0.21/0.54 tff(494,plain,
% 0.21/0.54 (sk_c7 = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5)),
% 0.21/0.54 inference(transitivity,[status(thm)],[54, 170, 36, 178, 225, 358, 493])).
% 0.21/0.54 tff(495,plain,
% 0.21/0.54 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[494])).
% 0.21/0.54 tff(496,plain,
% 0.21/0.54 (multiply(sk_c2, sk_c7) = multiply(sk_c5, sk_c5)),
% 0.21/0.54 inference(transitivity,[status(thm)],[495, 491, 488, 318])).
% 0.21/0.54 tff(497,plain,
% 0.21/0.54 (multiply(sk_c1, multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c1, sk_c6)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[485])).
% 0.21/0.54 tff(498,plain,
% 0.21/0.54 (multiply(multiply(sk_c1, multiply(sk_c6, multiply(sk_c1, sk_c7))), multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c1, sk_c6), multiply(sk_c5, sk_c5))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[497, 496])).
% 0.21/0.54 tff(499,plain,
% 0.21/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, multiply(sk_c6, multiply(sk_c1, sk_c7))), multiply(sk_c2, sk_c7)) = multiply(sk_c1, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(500,plain,
% 0.21/0.54 (multiply(multiply(sk_c1, multiply(sk_c6, multiply(sk_c1, sk_c7))), multiply(sk_c2, sk_c7)) = multiply(sk_c1, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7)))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[499, 34])).
% 0.21/0.54 tff(501,plain,
% 0.21/0.54 (multiply(sk_c1, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7))) = multiply(multiply(sk_c1, multiply(sk_c6, multiply(sk_c1, sk_c7))), multiply(sk_c2, sk_c7))),
% 0.21/0.54 inference(symmetry,[status(thm)],[500])).
% 0.21/0.54 tff(502,plain,
% 0.21/0.54 (multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7)) = multiply(sk_c6, multiply(sk_c2, sk_c7))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[485])).
% 0.21/0.54 tff(503,plain,
% 0.21/0.54 (multiply(sk_c6, multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7))),
% 0.21/0.54 inference(symmetry,[status(thm)],[502])).
% 0.21/0.54 tff(504,plain,
% 0.21/0.54 (multiply(sk_c6, sk_c2) = multiply(sk_c7, sk_c1)),
% 0.21/0.54 inference(transitivity,[status(thm)],[419, 59, 51, 168])).
% 0.21/0.54 tff(505,plain,
% 0.21/0.54 (multiply(multiply(sk_c6, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[504])).
% 0.21/0.54 tff(506,plain,
% 0.21/0.54 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c6, sk_c2), sk_c7)),
% 0.21/0.54 inference(symmetry,[status(thm)],[505])).
% 0.21/0.54 tff(507,plain,
% 0.21/0.54 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7))),
% 0.21/0.54 inference(transitivity,[status(thm)],[179, 72, 506, 69, 503])).
% 0.21/0.54 tff(508,plain,
% 0.21/0.54 (multiply(sk_c1, multiply(sk_c7, sk_c6)) = multiply(sk_c1, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7)))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[507])).
% 0.21/0.54 tff(509,plain,
% 0.21/0.54 (inverse(sk_c4) = sk_c7),
% 0.21/0.54 inference(transitivity,[status(thm)],[149, 482, 305, 508, 501, 498, 316, 313, 302, 226, 179, 72, 171, 9])).
% 0.21/0.54 tff(510,plain,
% 0.21/0.54 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.21/0.54 inference(transitivity,[status(thm)],[479, 226, 179, 72, 171, 9])).
% 0.21/0.54 tff(511,plain,
% 0.21/0.54 ((~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[448, 225, 302, 177, 165, 479, 417, 138])).
% 0.21/0.54 tff(512,plain,
% 0.21/0.54 (~(inverse(sk_c2) = sk_c7)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[511, 510])).
% 0.21/0.54 tff(513,plain,
% 0.21/0.54 (~(inverse(sk_c4) = sk_c7)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[512, 442])).
% 0.21/0.54 tff(514,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[513, 509])).
% 0.21/0.54 tff(515,plain,(inverse(sk_c3) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(516,plain,
% 0.21/0.54 (sk_c7 = inverse(sk_c3)),
% 0.21/0.54 inference(symmetry,[status(thm)],[515])).
% 0.21/0.54 tff(517,plain,
% 0.21/0.54 (multiply(sk_c3, sk_c6) = inverse(sk_c3)),
% 0.21/0.54 inference(transitivity,[status(thm)],[461, 516])).
% 0.21/0.54 tff(518,plain,
% 0.21/0.54 (multiply(multiply(sk_c3, sk_c6), sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[517])).
% 0.21/0.54 tff(519,plain,
% 0.21/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c6), sk_c3) = multiply(sk_c3, multiply(sk_c6, sk_c3)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(520,plain,
% 0.21/0.54 (multiply(multiply(sk_c3, sk_c6), sk_c3) = multiply(sk_c3, multiply(sk_c6, sk_c3))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[519, 34])).
% 0.21/0.54 tff(521,plain,
% 0.21/0.54 (multiply(sk_c3, multiply(sk_c6, sk_c3)) = multiply(multiply(sk_c3, sk_c6), sk_c3)),
% 0.21/0.54 inference(symmetry,[status(thm)],[520])).
% 0.21/0.54 tff(522,plain,
% 0.21/0.54 (multiply(sk_c3, multiply(sk_c6, sk_c3)) = multiply(sk_c6, sk_c4)),
% 0.21/0.54 inference(transitivity,[status(thm)],[521, 518, 160, 155, 152])).
% 0.21/0.54 tff(523,plain,
% 0.21/0.54 (multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[522])).
% 0.21/0.54 tff(524,plain,
% 0.21/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(525,plain,
% 0.21/0.54 (multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[524, 34])).
% 0.21/0.54 tff(526,plain,
% 0.21/0.54 (multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6)) = multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6)),
% 0.21/0.54 inference(symmetry,[status(thm)],[525])).
% 0.21/0.54 tff(527,plain,
% 0.21/0.54 ((~![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)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(528,plain,
% 0.21/0.54 (multiply(multiply(sk_c6, sk_c3), sk_c6) = multiply(sk_c6, multiply(sk_c3, sk_c6))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[527, 34])).
% 0.21/0.54 tff(529,plain,
% 0.21/0.54 (multiply(sk_c6, multiply(sk_c3, sk_c6)) = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.21/0.54 inference(symmetry,[status(thm)],[528])).
% 0.21/0.54 tff(530,plain,
% 0.21/0.54 (multiply(sk_c6, multiply(sk_c3, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[461])).
% 0.21/0.54 tff(531,plain,
% 0.21/0.54 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c3, sk_c6))),
% 0.21/0.54 inference(symmetry,[status(thm)],[530])).
% 0.21/0.54 tff(532,assumption,(multiply(sk_c4, sk_c6) = sk_c7), introduced(assumption)).
% 0.21/0.54 tff(533,plain,
% 0.21/0.54 (multiply(sk_c6, multiply(sk_c4, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[532])).
% 0.21/0.54 tff(534,plain,
% 0.21/0.54 (sk_c6 = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.21/0.54 inference(transitivity,[status(thm)],[111, 157, 326, 533, 531, 529])).
% 0.21/0.54 tff(535,plain,
% 0.21/0.54 (multiply(sk_c3, sk_c6) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[534])).
% 0.21/0.54 tff(536,plain,
% 0.21/0.54 (sk_c7 = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.21/0.54 inference(transitivity,[status(thm)],[462, 535, 526, 523, 326, 533, 531, 529])).
% 0.21/0.54 tff(537,plain,
% 0.21/0.54 (multiply(sk_c3, sk_c7) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[536])).
% 0.21/0.54 tff(538,plain,
% 0.21/0.54 (multiply(sk_c3, sk_c7) = sk_c6),
% 0.21/0.54 inference(transitivity,[status(thm)],[537, 526, 523, 158, 11])).
% 0.21/0.54 tff(539,plain,
% 0.21/0.54 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(540,plain,
% 0.21/0.54 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(541,plain,
% 0.21/0.54 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[540])).
% 0.21/0.54 tff(542,plain,
% 0.21/0.54 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[541, 539])).
% 0.21/0.54 tff(543,plain,
% 0.21/0.54 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(544,plain,
% 0.21/0.55 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.21/0.55 tff(545,plain,
% 0.21/0.55 ((~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[544, 225, 302, 515, 461, 149, 479, 417, 138])).
% 0.21/0.55 tff(546,plain,
% 0.21/0.55 (~(multiply(sk_c3, sk_c7) = sk_c6)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[545, 532])).
% 0.21/0.55 tff(547,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[546, 538])).
% 0.21/0.55 tff(548,plain,(~(multiply(sk_c4, sk_c6) = sk_c7)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(549,plain,
% 0.21/0.55 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c6) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c6) = sk_c7))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(550,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_14')).
% 0.21/0.55 tff(551,plain,
% 0.21/0.55 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c6) = sk_c7)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.21/0.55 tff(552,plain,
% 0.21/0.55 (inverse(sk_c1) = sk_c7),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[551, 548])).
% 0.21/0.55 tff(553,plain,
% 0.21/0.55 (sk_c7 = inverse(sk_c1)),
% 0.21/0.55 inference(symmetry,[status(thm)],[552])).
% 0.21/0.55 tff(554,plain,
% 0.21/0.55 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[553])).
% 0.21/0.55 tff(555,plain,
% 0.21/0.55 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.21/0.55 inference(symmetry,[status(thm)],[554])).
% 0.21/0.55 tff(556,plain,
% 0.21/0.55 (identity = multiply(sk_c7, sk_c1)),
% 0.21/0.55 inference(transitivity,[status(thm)],[51, 555])).
% 0.21/0.55 tff(557,plain,
% 0.21/0.55 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[556])).
% 0.21/0.55 tff(558,plain,
% 0.21/0.55 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.55 inference(symmetry,[status(thm)],[557])).
% 0.21/0.55 tff(559,plain,
% 0.21/0.55 (((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(560,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_9')).
% 0.21/0.55 tff(561,plain,
% 0.21/0.55 ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.21/0.55 tff(562,plain,
% 0.21/0.55 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[561, 548])).
% 0.21/0.55 tff(563,plain,
% 0.21/0.55 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[562])).
% 0.21/0.55 tff(564,plain,
% 0.21/0.55 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.55 inference(symmetry,[status(thm)],[563])).
% 0.21/0.55 tff(565,plain,
% 0.21/0.55 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.21/0.55 inference(transitivity,[status(thm)],[479, 226, 564, 72, 558, 9])).
% 0.21/0.55 tff(566,plain,
% 0.21/0.55 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(567,plain,
% 0.21/0.55 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(568,plain,
% 0.21/0.55 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[567])).
% 0.21/0.55 tff(569,plain,
% 0.21/0.55 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)))),
% 0.21/0.55 inference(transitivity,[status(thm)],[568, 566])).
% 0.21/0.55 tff(570,plain,
% 0.21/0.55 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(571,plain,
% 0.21/0.55 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.21/0.55 tff(572,plain,
% 0.21/0.55 (~(multiply(sk_c2, sk_c6) = sk_c7)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[571, 225, 302, 515, 461, 562, 552, 479, 417, 138])).
% 0.21/0.55 tff(573,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[572, 565])).
% 0.21/0.55 % SZS output end Proof
% 0.21/0.55 % E exiting
%------------------------------------------------------------------------------