%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP304-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:07:35 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP304-1 : TPTP v9.0.0. Released v2.5.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 15:55:03 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.43 % SZS status Unsatisfiable
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 tff(sk_c6_type, type, (
% 0.22/0.43 sk_c6: $i)).
% 0.22/0.43 tff(multiply_type, type, (
% 0.22/0.43 multiply: ( $i * $i ) > $i)).
% 0.22/0.43 tff(sk_c7_type, type, (
% 0.22/0.43 sk_c7: $i)).
% 0.22/0.43 tff(sk_c5_type, type, (
% 0.22/0.43 sk_c5: $i)).
% 0.22/0.43 tff(sk_c1_type, type, (
% 0.22/0.43 sk_c1: $i)).
% 0.22/0.43 tff(identity_type, type, (
% 0.22/0.43 identity: $i)).
% 0.22/0.43 tff(sk_c3_type, type, (
% 0.22/0.43 sk_c3: $i)).
% 0.22/0.43 tff(inverse_type, type, (
% 0.22/0.43 inverse: $i > $i)).
% 0.22/0.43 tff(sk_c2_type, type, (
% 0.22/0.43 sk_c2: $i)).
% 0.22/0.43 tff(sk_c4_type, type, (
% 0.22/0.43 sk_c4: $i)).
% 0.22/0.43 tff(1,plain,
% 0.22/0.43 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(2,plain,
% 0.22/0.43 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.22/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.43 tff(3,plain,
% 0.22/0.43 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(4,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.22/0.43 tff(5,plain,
% 0.22/0.43 (![X: $i] : (multiply(identity, X) = X)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.43 tff(6,plain,(
% 0.22/0.43 ![X: $i] : (multiply(identity, X) = X)),
% 0.22/0.43 inference(skolemize,[status(sab)],[5])).
% 0.22/0.43 tff(7,plain,
% 0.22/0.43 (![X: $i] : (multiply(identity, X) = X)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.43 tff(8,plain,
% 0.22/0.43 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c7, multiply(sk_c7, sk_c7))) = multiply(sk_c7, multiply(sk_c7, sk_c7)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(9,plain,
% 0.22/0.43 (multiply(identity, multiply(sk_c7, multiply(sk_c7, sk_c7))) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.22/0.43 tff(10,plain,
% 0.22/0.43 ((sk_c7 = inverse(sk_c7)) <=> (inverse(sk_c7) = sk_c7)),
% 0.22/0.43 inference(commutativity,[status(thm)],[])).
% 0.22/0.43 tff(11,plain,
% 0.22/0.43 ((multiply(sk_c7, sk_c6) = sk_c5) <=> (multiply(sk_c7, sk_c6) = sk_c5)),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(12,axiom,(multiply(sk_c7, sk_c6) = sk_c5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_1')).
% 0.22/0.43 tff(13,plain,
% 0.22/0.43 (multiply(sk_c7, sk_c6) = sk_c5),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.22/0.43 tff(14,assumption,(~(inverse(sk_c7) = sk_c5)), introduced(assumption)).
% 0.22/0.43 tff(15,plain,
% 0.22/0.43 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c7) = sk_c6)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c7) = sk_c6))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(16,axiom,((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c7) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_7')).
% 0.22/0.43 tff(17,plain,
% 0.22/0.43 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c7) = sk_c6)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.22/0.43 tff(18,plain,
% 0.22/0.43 (multiply(sk_c2, sk_c7) = sk_c6),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.22/0.43 tff(19,plain,
% 0.22/0.43 (multiply(sk_c7, multiply(sk_c2, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[18])).
% 0.22/0.43 tff(20,plain,
% 0.22/0.43 (^[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))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(21,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[20])).
% 0.22/0.43 tff(22,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(23,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')).
% 0.22/0.43 tff(24,plain,
% 0.22/0.43 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.22/0.43 tff(25,plain,(
% 0.22/0.43 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[24])).
% 0.22/0.43 tff(26,plain,
% 0.22/0.43 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.22/0.43 tff(27,plain,
% 0.22/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(sk_c7, multiply(sk_c2, sk_c7)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(28,plain,
% 0.22/0.43 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(sk_c7, multiply(sk_c2, sk_c7))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.22/0.43 tff(29,plain,
% 0.22/0.43 (((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = sk_c5)) <=> ((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = sk_c5))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(30,plain,
% 0.22/0.43 (((inverse(sk_c7) = sk_c5) | (inverse(sk_c2) = sk_c7)) <=> ((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = sk_c5))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(31,axiom,((inverse(sk_c7) = sk_c5) | (inverse(sk_c2) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_8')).
% 0.22/0.43 tff(32,plain,
% 0.22/0.43 ((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.22/0.43 tff(33,plain,
% 0.22/0.43 ((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.22/0.43 tff(34,plain,
% 0.22/0.43 (inverse(sk_c2) = sk_c7),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[33, 14])).
% 0.22/0.43 tff(35,plain,
% 0.22/0.43 (sk_c7 = inverse(sk_c2)),
% 0.22/0.43 inference(symmetry,[status(thm)],[34])).
% 0.22/0.43 tff(36,plain,
% 0.22/0.43 (multiply(sk_c7, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[35])).
% 0.22/0.43 tff(37,plain,
% 0.22/0.43 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c7, sk_c2)),
% 0.22/0.43 inference(symmetry,[status(thm)],[36])).
% 0.22/0.43 tff(38,plain,
% 0.22/0.43 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(39,plain,
% 0.22/0.43 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.22/0.43 inference(quant_intro,[status(thm)],[38])).
% 0.22/0.43 tff(40,plain,
% 0.22/0.43 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(41,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.22/0.43 tff(42,plain,
% 0.22/0.43 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.22/0.43 tff(43,plain,(
% 0.22/0.43 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.22/0.43 inference(skolemize,[status(sab)],[42])).
% 0.22/0.43 tff(44,plain,
% 0.22/0.43 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.22/0.43 tff(45,plain,
% 0.22/0.43 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(46,plain,
% 0.22/0.43 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.22/0.43 tff(47,plain,
% 0.22/0.43 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.22/0.43 inference(symmetry,[status(thm)],[46])).
% 0.22/0.43 tff(48,plain,
% 0.22/0.43 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c3), sk_c3) = identity)),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(49,plain,
% 0.22/0.43 (multiply(inverse(sk_c3), sk_c3) = identity),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[48, 44])).
% 0.22/0.43 tff(50,plain,
% 0.22/0.43 (((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5)) <=> ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(51,plain,
% 0.22/0.43 (((inverse(sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(52,axiom,((inverse(sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_11')).
% 0.22/0.43 tff(53,plain,
% 0.22/0.43 ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.22/0.43 tff(54,plain,
% 0.22/0.43 ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.22/0.43 tff(55,plain,
% 0.22/0.43 (inverse(sk_c3) = sk_c7),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[54, 14])).
% 0.22/0.43 tff(56,plain,
% 0.22/0.43 (sk_c7 = inverse(sk_c3)),
% 0.22/0.43 inference(symmetry,[status(thm)],[55])).
% 0.22/0.43 tff(57,plain,
% 0.22/0.43 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[56])).
% 0.22/0.43 tff(58,plain,
% 0.22/0.43 (multiply(sk_c7, sk_c3) = multiply(sk_c7, sk_c2)),
% 0.22/0.43 inference(transitivity,[status(thm)],[57, 49, 47, 37])).
% 0.22/0.43 tff(59,plain,
% 0.22/0.43 (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[58])).
% 0.22/0.43 tff(60,plain,
% 0.22/0.43 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c7, sk_c3)),
% 0.22/0.43 inference(symmetry,[status(thm)],[57])).
% 0.22/0.43 tff(61,plain,
% 0.22/0.43 (identity = multiply(inverse(sk_c3), sk_c3)),
% 0.22/0.43 inference(symmetry,[status(thm)],[49])).
% 0.22/0.43 tff(62,plain,
% 0.22/0.43 (identity = multiply(sk_c7, sk_c3)),
% 0.22/0.43 inference(transitivity,[status(thm)],[61, 60])).
% 0.22/0.43 tff(63,plain,
% 0.22/0.43 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[62])).
% 0.22/0.43 tff(64,plain,
% 0.22/0.43 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(65,plain,
% 0.22/0.43 (multiply(identity, sk_c7) = sk_c7),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[64, 7])).
% 0.22/0.43 tff(66,plain,
% 0.22/0.43 (sk_c7 = multiply(identity, sk_c7)),
% 0.22/0.43 inference(symmetry,[status(thm)],[65])).
% 0.22/0.43 tff(67,plain,
% 0.22/0.43 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c2) = sk_c2)),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(68,plain,
% 0.22/0.43 (multiply(identity, sk_c2) = sk_c2),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[67, 7])).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(sk_c7, sk_c7))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(sk_c7, sk_c7)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[69, 7])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[62])).
% 0.22/0.43 tff(72,plain,
% 0.22/0.43 (multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7)) = multiply(identity, multiply(sk_c7, sk_c7))),
% 0.22/0.43 inference(symmetry,[status(thm)],[71])).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(74,plain,
% 0.22/0.43 (multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[73, 26])).
% 0.22/0.43 tff(75,plain,
% 0.22/0.43 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c6) = sk_c6)),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(76,plain,
% 0.22/0.43 (multiply(identity, sk_c6) = sk_c6),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[75, 7])).
% 0.22/0.43 tff(77,assumption,(~(multiply(sk_c7, sk_c4) = sk_c6)), introduced(assumption)).
% 0.22/0.43 tff(78,plain,
% 0.22/0.43 (((inverse(sk_c1) = sk_c6) | (multiply(sk_c7, sk_c4) = sk_c6)) <=> ((inverse(sk_c1) = sk_c6) | (multiply(sk_c7, sk_c4) = sk_c6))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(79,axiom,((inverse(sk_c1) = sk_c6) | (multiply(sk_c7, sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_19')).
% 0.22/0.43 tff(80,plain,
% 0.22/0.43 ((inverse(sk_c1) = sk_c6) | (multiply(sk_c7, sk_c4) = sk_c6)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.22/0.43 tff(81,plain,
% 0.22/0.43 (inverse(sk_c1) = sk_c6),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[80, 77])).
% 0.22/0.43 tff(82,plain,
% 0.22/0.43 (sk_c6 = inverse(sk_c1)),
% 0.22/0.43 inference(symmetry,[status(thm)],[81])).
% 0.22/0.43 tff(83,plain,
% 0.22/0.43 (multiply(sk_c6, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[82])).
% 0.22/0.43 tff(84,plain,
% 0.22/0.43 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c6, sk_c1)),
% 0.22/0.43 inference(symmetry,[status(thm)],[83])).
% 0.22/0.43 tff(85,plain,
% 0.22/0.43 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(86,plain,
% 0.22/0.43 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[85, 44])).
% 0.22/0.43 tff(87,plain,
% 0.22/0.43 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.22/0.43 inference(symmetry,[status(thm)],[86])).
% 0.22/0.43 tff(88,plain,
% 0.22/0.43 (identity = multiply(sk_c6, sk_c1)),
% 0.22/0.43 inference(transitivity,[status(thm)],[87, 84])).
% 0.22/0.43 tff(89,plain,
% 0.22/0.43 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[88])).
% 0.22/0.43 tff(90,plain,
% 0.22/0.43 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(identity, sk_c6)),
% 0.22/0.43 inference(symmetry,[status(thm)],[89])).
% 0.22/0.43 tff(91,plain,
% 0.22/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(sk_c6, multiply(sk_c1, sk_c6)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(92,plain,
% 0.22/0.43 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(sk_c6, multiply(sk_c1, sk_c6))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[91, 26])).
% 0.22/0.43 tff(93,plain,
% 0.22/0.43 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.22/0.43 inference(symmetry,[status(thm)],[92])).
% 0.22/0.43 tff(94,plain,
% 0.22/0.43 (((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c4) = sk_c6)) <=> ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c4) = sk_c6))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(95,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_14')).
% 0.22/0.43 tff(96,plain,
% 0.22/0.43 ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c4) = sk_c6)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.22/0.43 tff(97,plain,
% 0.22/0.43 (multiply(sk_c1, sk_c6) = sk_c7),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[96, 77])).
% 0.22/0.43 tff(98,plain,
% 0.22/0.43 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[97])).
% 0.22/0.43 tff(99,plain,
% 0.22/0.43 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c1, sk_c6))),
% 0.22/0.43 inference(symmetry,[status(thm)],[98])).
% 0.22/0.43 tff(100,assumption,(~(multiply(sk_c6, sk_c7) = sk_c5)), introduced(assumption)).
% 0.22/0.43 tff(101,plain,
% 0.22/0.43 (((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)) <=> ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(102,axiom,((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_4')).
% 0.22/0.43 tff(103,plain,
% 0.22/0.43 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.22/0.43 tff(104,plain,
% 0.22/0.43 (multiply(sk_c7, sk_c4) = sk_c6),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[103, 100])).
% 0.22/0.43 tff(105,assumption,(~(multiply(sk_c3, sk_c7) = sk_c4)), introduced(assumption)).
% 0.22/0.43 tff(106,plain,
% 0.22/0.43 (((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c7) = sk_c4))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(107,axiom,((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c7) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_20')).
% 0.22/0.43 tff(108,plain,
% 0.22/0.43 ((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.22/0.43 tff(109,plain,
% 0.22/0.43 (inverse(sk_c1) = sk_c6),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[108, 105])).
% 0.22/0.43 tff(110,plain,
% 0.22/0.43 (sk_c6 = inverse(sk_c1)),
% 0.22/0.43 inference(symmetry,[status(thm)],[109])).
% 0.22/0.43 tff(111,plain,
% 0.22/0.43 (multiply(sk_c6, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[110])).
% 0.22/0.43 tff(112,plain,
% 0.22/0.43 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c6, sk_c1)),
% 0.22/0.43 inference(symmetry,[status(thm)],[111])).
% 0.22/0.43 tff(113,plain,
% 0.22/0.44 (identity = multiply(sk_c6, sk_c1)),
% 0.22/0.44 inference(transitivity,[status(thm)],[87, 112])).
% 0.22/0.44 tff(114,plain,
% 0.22/0.44 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[113])).
% 0.22/0.44 tff(115,plain,
% 0.22/0.44 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(identity, sk_c6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[114])).
% 0.22/0.44 tff(116,plain,
% 0.22/0.44 (((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c7) = sk_c4))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(117,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c7) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_15')).
% 0.22/0.44 tff(118,plain,
% 0.22/0.44 ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.22/0.44 tff(119,plain,
% 0.22/0.44 (multiply(sk_c1, sk_c6) = sk_c7),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[118, 105])).
% 0.22/0.44 tff(120,plain,
% 0.22/0.44 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[119])).
% 0.22/0.44 tff(121,plain,
% 0.22/0.44 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c1, sk_c6))),
% 0.22/0.44 inference(symmetry,[status(thm)],[120])).
% 0.22/0.44 tff(122,plain,
% 0.22/0.44 (((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(123,axiom,((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_5')).
% 0.22/0.44 tff(124,plain,
% 0.22/0.44 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.22/0.44 tff(125,plain,
% 0.22/0.44 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[124, 122])).
% 0.22/0.44 tff(126,plain,
% 0.22/0.44 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[125, 122])).
% 0.22/0.44 tff(127,plain,
% 0.22/0.44 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.22/0.44 tff(128,plain,
% 0.22/0.44 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[127, 122])).
% 0.22/0.44 tff(129,plain,
% 0.22/0.44 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[128, 105])).
% 0.22/0.44 tff(130,plain,
% 0.22/0.44 (sk_c5 = multiply(sk_c6, sk_c7)),
% 0.22/0.44 inference(symmetry,[status(thm)],[129])).
% 0.22/0.44 tff(131,plain,
% 0.22/0.44 (sk_c6 = multiply(identity, sk_c6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[76])).
% 0.22/0.44 tff(132,plain,
% 0.22/0.44 (sk_c6 = multiply(sk_c6, sk_c7)),
% 0.22/0.44 inference(transitivity,[status(thm)],[131, 114, 92, 120])).
% 0.22/0.44 tff(133,plain,
% 0.22/0.44 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c6, sk_c7))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[132])).
% 0.22/0.44 tff(134,plain,
% 0.22/0.44 (multiply(sk_c7, multiply(sk_c6, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[133])).
% 0.22/0.44 tff(135,plain,
% 0.22/0.44 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(sk_c7, multiply(sk_c6, sk_c7)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(136,plain,
% 0.22/0.44 (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(sk_c7, multiply(sk_c6, sk_c7))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[135, 26])).
% 0.22/0.44 tff(137,plain,
% 0.22/0.44 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(138,axiom,((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_10')).
% 0.22/0.44 tff(139,plain,
% 0.22/0.44 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.22/0.44 tff(140,plain,
% 0.22/0.44 (inverse(sk_c7) = sk_c5),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[139, 105])).
% 0.22/0.44 tff(141,plain,
% 0.22/0.44 (sk_c5 = inverse(sk_c7)),
% 0.22/0.44 inference(symmetry,[status(thm)],[140])).
% 0.22/0.44 tff(142,plain,
% 0.22/0.44 (multiply(sk_c7, sk_c6) = inverse(sk_c7)),
% 0.22/0.44 inference(transitivity,[status(thm)],[13, 141])).
% 0.22/0.44 tff(143,plain,
% 0.22/0.44 (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[142])).
% 0.22/0.44 tff(144,plain,
% 0.22/0.44 (multiply(inverse(sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c6), sk_c7)),
% 0.22/0.44 inference(symmetry,[status(thm)],[143])).
% 0.22/0.44 tff(145,plain,
% 0.22/0.44 (multiply(sk_c6, sk_c7) = inverse(sk_c7)),
% 0.22/0.44 inference(transitivity,[status(thm)],[129, 141])).
% 0.22/0.44 tff(146,plain,
% 0.22/0.44 (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[145])).
% 0.22/0.44 tff(147,plain,
% 0.22/0.44 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(sk_c6, multiply(sk_c7, sk_c7)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(148,plain,
% 0.22/0.44 (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[147, 26])).
% 0.22/0.44 tff(149,plain,
% 0.22/0.44 (multiply(sk_c6, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c6, sk_c7), sk_c7)),
% 0.22/0.44 inference(symmetry,[status(thm)],[148])).
% 0.22/0.44 tff(150,plain,
% 0.22/0.44 (multiply(multiply(sk_c1, sk_c6), sk_c6) = multiply(sk_c7, sk_c6)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[119])).
% 0.22/0.44 tff(151,plain,
% 0.22/0.44 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c6), sk_c6) = multiply(sk_c1, multiply(sk_c6, sk_c6)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(152,plain,
% 0.22/0.44 (multiply(multiply(sk_c1, sk_c6), sk_c6) = multiply(sk_c1, multiply(sk_c6, sk_c6))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[151, 26])).
% 0.22/0.44 tff(153,plain,
% 0.22/0.44 (multiply(sk_c1, multiply(sk_c6, sk_c6)) = multiply(multiply(sk_c1, sk_c6), sk_c6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[152])).
% 0.22/0.44 tff(154,plain,
% 0.22/0.44 (sk_c5 = multiply(sk_c7, sk_c6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[13])).
% 0.22/0.44 tff(155,plain,
% 0.22/0.44 (sk_c6 = multiply(sk_c7, sk_c6)),
% 0.22/0.44 inference(transitivity,[status(thm)],[131, 114, 92, 120, 129, 154])).
% 0.22/0.44 tff(156,plain,
% 0.22/0.44 (sk_c6 = sk_c5),
% 0.22/0.44 inference(transitivity,[status(thm)],[131, 114, 92, 120, 129])).
% 0.22/0.44 tff(157,plain,
% 0.22/0.44 (multiply(sk_c6, sk_c6) = multiply(sk_c5, multiply(sk_c7, sk_c6))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[156, 155])).
% 0.22/0.44 tff(158,plain,
% 0.22/0.44 (multiply(sk_c5, multiply(sk_c7, sk_c6)) = multiply(sk_c6, sk_c6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[157])).
% 0.22/0.44 tff(159,plain,
% 0.22/0.44 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c7), sk_c6) = multiply(sk_c5, multiply(sk_c7, sk_c6)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(160,plain,
% 0.22/0.44 (multiply(multiply(sk_c5, sk_c7), sk_c6) = multiply(sk_c5, multiply(sk_c7, sk_c6))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[159, 26])).
% 0.22/0.44 tff(161,plain,
% 0.22/0.44 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c7), sk_c7) = identity)),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(162,plain,
% 0.22/0.44 (multiply(inverse(sk_c7), sk_c7) = identity),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[161, 44])).
% 0.22/0.44 tff(163,plain,
% 0.22/0.44 (multiply(sk_c5, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[141])).
% 0.22/0.44 tff(164,plain,
% 0.22/0.44 (multiply(sk_c5, sk_c7) = identity),
% 0.22/0.44 inference(transitivity,[status(thm)],[163, 162])).
% 0.22/0.44 tff(165,plain,
% 0.22/0.44 (multiply(multiply(sk_c5, sk_c7), sk_c6) = multiply(identity, multiply(sk_c6, sk_c7))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[164, 132])).
% 0.22/0.44 tff(166,plain,
% 0.22/0.44 (multiply(identity, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c5, sk_c7), sk_c6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[165])).
% 0.22/0.44 tff(167,plain,
% 0.22/0.44 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c6), sk_c7) = multiply(identity, multiply(sk_c6, sk_c7)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(168,plain,
% 0.22/0.44 (multiply(multiply(identity, sk_c6), sk_c7) = multiply(identity, multiply(sk_c6, sk_c7))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[167, 26])).
% 0.22/0.44 tff(169,plain,
% 0.22/0.44 (multiply(multiply(identity, sk_c6), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[76])).
% 0.22/0.44 tff(170,plain,
% 0.22/0.44 (multiply(sk_c6, sk_c7) = multiply(multiply(identity, sk_c6), sk_c7)),
% 0.22/0.44 inference(symmetry,[status(thm)],[169])).
% 0.22/0.44 tff(171,plain,
% 0.22/0.44 (sk_c6 = multiply(sk_c6, sk_c6)),
% 0.22/0.44 inference(transitivity,[status(thm)],[131, 114, 92, 120, 170, 168, 166, 160, 158])).
% 0.22/0.44 tff(172,plain,
% 0.22/0.44 (multiply(sk_c1, sk_c6) = multiply(sk_c1, multiply(sk_c6, sk_c6))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[171])).
% 0.22/0.44 tff(173,plain,
% 0.22/0.44 (sk_c7 = multiply(sk_c1, sk_c6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[119])).
% 0.22/0.44 tff(174,plain,
% 0.22/0.44 (sk_c7 = sk_c6),
% 0.22/0.44 inference(transitivity,[status(thm)],[173, 172, 153, 150, 13, 130, 121, 93, 115, 76])).
% 0.22/0.44 tff(175,plain,
% 0.22/0.44 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[174])).
% 0.22/0.44 tff(176,plain,
% 0.22/0.44 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6),
% 0.22/0.44 inference(transitivity,[status(thm)],[175, 149, 146, 144, 136, 134, 13, 130, 121, 93, 115, 76])).
% 0.22/0.44 tff(177,plain,
% 0.22/0.44 (multiply(sk_c1, multiply(sk_c6, sk_c6)) = multiply(sk_c1, sk_c6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[172])).
% 0.22/0.44 tff(178,plain,
% 0.22/0.44 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c1, sk_c6), sk_c6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[150])).
% 0.22/0.44 tff(179,plain,
% 0.22/0.44 (inverse(sk_c7) = sk_c7),
% 0.22/0.44 inference(transitivity,[status(thm)],[140, 154, 178, 152, 177, 119])).
% 0.22/0.44 tff(180,plain,
% 0.22/0.44 (multiply(identity, multiply(sk_c6, sk_c7)) = multiply(multiply(identity, sk_c6), sk_c7)),
% 0.22/0.44 inference(symmetry,[status(thm)],[168])).
% 0.22/0.44 tff(181,plain,
% 0.22/0.44 (multiply(sk_c5, multiply(sk_c7, sk_c6)) = multiply(multiply(sk_c5, sk_c7), sk_c6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[160])).
% 0.22/0.44 tff(182,plain,
% 0.22/0.44 (sk_c7 = multiply(sk_c7, sk_c6)),
% 0.22/0.44 inference(transitivity,[status(thm)],[173, 172, 153, 150])).
% 0.22/0.44 tff(183,plain,
% 0.22/0.44 (sk_c7 = sk_c5),
% 0.22/0.44 inference(transitivity,[status(thm)],[173, 172, 153, 150, 13])).
% 0.22/0.44 tff(184,plain,
% 0.22/0.44 (multiply(sk_c7, sk_c7) = multiply(sk_c5, multiply(sk_c7, sk_c6))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[183, 182])).
% 0.22/0.44 tff(185,plain,
% 0.22/0.44 (multiply(sk_c7, sk_c7) = sk_c6),
% 0.22/0.44 inference(transitivity,[status(thm)],[184, 181, 165, 180, 169, 121, 93, 115, 76])).
% 0.22/0.44 tff(186,plain,
% 0.22/0.44 (^[X4: $i, X2: $i, X1: $i] : refl(((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(187,plain,
% 0.22/0.44 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[186])).
% 0.22/0.44 tff(188,plain,
% 0.22/0.44 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(189,plain,
% 0.22/0.45 (^[X4: $i, X2: $i, X1: $i] : rewrite(((~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(190,plain,
% 0.22/0.45 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[189])).
% 0.22/0.45 tff(191,plain,
% 0.22/0.45 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)))),
% 0.22/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.45 tff(192,plain,
% 0.22/0.45 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)))),
% 0.22/0.45 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.22/0.45 tff(193,plain,
% 0.22/0.45 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[192, 191])).
% 0.22/0.45 tff(194,plain,
% 0.22/0.45 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[193, 190])).
% 0.22/0.45 tff(195,plain,
% 0.22/0.45 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(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)))), ((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)))), ((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5))))), (((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7)))), (((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7))))), ((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(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(sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(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(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), ((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(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(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), (((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(X1, sk_c7) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(X1, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), (((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), ((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X1) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), ((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), (((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), (((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(X4, sk_c7) = X3))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(X4, sk_c7) = X3))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), (((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X4) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X4) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), (((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(196,plain,
% 0.22/0.46 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = 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(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[195])).
% 0.22/0.46 tff(197,plain,
% 0.22/0.46 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))),
% 0.22/0.46 inference(transitivity,[status(thm)],[196, 194])).
% 0.22/0.46 tff(198,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_22')).
% 0.22/0.46 tff(199,plain,
% 0.22/0.46 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.22/0.46 tff(200,plain,
% 0.22/0.46 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[199, 188])).
% 0.22/0.46 tff(201,plain,(
% 0.22/0.46 ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))),
% 0.22/0.46 inference(skolemize,[status(sab)],[200])).
% 0.22/0.46 tff(202,plain,
% 0.22/0.46 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[201, 187])).
% 0.22/0.46 tff(203,plain,
% 0.22/0.46 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(204,plain,
% 0.22/0.47 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(205,plain,
% 0.22/0.47 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[204])).
% 0.22/0.47 tff(206,plain,
% 0.22/0.47 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))),
% 0.22/0.47 inference(transitivity,[status(thm)],[205, 203])).
% 0.22/0.47 tff(207,plain,
% 0.22/0.47 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(208,plain,
% 0.22/0.47 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.22/0.47 tff(209,plain,
% 0.22/0.47 ((~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[208, 13, 129, 140, 119, 109, 202])).
% 0.22/0.47 tff(210,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[209, 185, 179, 176])).
% 0.22/0.47 tff(211,plain,(multiply(sk_c3, sk_c7) = sk_c4), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(212,plain,
% 0.22/0.47 (sk_c4 = multiply(sk_c3, sk_c7)),
% 0.22/0.47 inference(symmetry,[status(thm)],[211])).
% 0.22/0.47 tff(213,plain,
% 0.22/0.47 (multiply(sk_c7, sk_c4) = multiply(sk_c7, multiply(sk_c3, sk_c7))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[212])).
% 0.22/0.47 tff(214,plain,
% 0.22/0.47 (multiply(sk_c7, multiply(sk_c3, sk_c7)) = multiply(sk_c7, sk_c4)),
% 0.22/0.47 inference(symmetry,[status(thm)],[213])).
% 0.22/0.47 tff(215,plain,
% 0.22/0.47 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(sk_c7, multiply(sk_c3, sk_c7)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(216,plain,
% 0.22/0.47 (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(sk_c7, multiply(sk_c3, sk_c7))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[215, 26])).
% 0.22/0.47 tff(217,plain,
% 0.22/0.47 (((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)) <=> ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(218,axiom,((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_6')).
% 0.22/0.47 tff(219,plain,
% 0.22/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.22/0.47 tff(220,plain,
% 0.22/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[219, 217])).
% 0.22/0.47 tff(221,plain,
% 0.22/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[220, 217])).
% 0.22/0.47 tff(222,plain,
% 0.22/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.22/0.47 tff(223,plain,
% 0.22/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[222, 217])).
% 0.22/0.47 tff(224,plain,
% 0.22/0.47 (inverse(sk_c3) = sk_c7),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[223, 100])).
% 0.22/0.47 tff(225,plain,
% 0.22/0.48 (sk_c7 = inverse(sk_c3)),
% 0.22/0.48 inference(symmetry,[status(thm)],[224])).
% 0.22/0.48 tff(226,plain,
% 0.22/0.48 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[225])).
% 0.22/0.48 tff(227,plain,
% 0.22/0.48 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c7, sk_c3)),
% 0.22/0.48 inference(symmetry,[status(thm)],[226])).
% 0.22/0.48 tff(228,plain,
% 0.22/0.48 (identity = multiply(sk_c7, sk_c3)),
% 0.22/0.48 inference(transitivity,[status(thm)],[61, 227])).
% 0.22/0.48 tff(229,plain,
% 0.22/0.48 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[228])).
% 0.22/0.48 tff(230,plain,
% 0.22/0.48 (sk_c7 = sk_c6),
% 0.22/0.48 inference(transitivity,[status(thm)],[66, 229, 216, 214, 104])).
% 0.22/0.48 tff(231,plain,
% 0.22/0.48 (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(identity, sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[229])).
% 0.22/0.48 tff(232,plain,
% 0.22/0.48 (multiply(sk_c7, multiply(sk_c3, sk_c7)) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[216])).
% 0.22/0.48 tff(233,plain,
% 0.22/0.48 (sk_c6 = multiply(sk_c7, sk_c4)),
% 0.22/0.48 inference(symmetry,[status(thm)],[104])).
% 0.22/0.48 tff(234,plain,
% 0.22/0.48 (sk_c6 = sk_c7),
% 0.22/0.48 inference(transitivity,[status(thm)],[233, 213, 232, 231, 65])).
% 0.22/0.48 tff(235,plain,
% 0.22/0.48 (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[234, 230])).
% 0.22/0.48 tff(236,plain,
% 0.22/0.48 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.22/0.48 inference(transitivity,[status(thm)],[235, 13])).
% 0.22/0.48 tff(237,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[100, 236])).
% 0.22/0.48 tff(238,plain,(multiply(sk_c6, sk_c7) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(239,plain,
% 0.22/0.48 (sk_c5 = multiply(sk_c6, sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[238])).
% 0.22/0.48 tff(240,plain,
% 0.22/0.48 (sk_c6 = multiply(sk_c6, sk_c7)),
% 0.22/0.48 inference(transitivity,[status(thm)],[131, 89, 92, 98])).
% 0.22/0.48 tff(241,plain,
% 0.22/0.48 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c6, sk_c7))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[240])).
% 0.22/0.48 tff(242,plain,
% 0.22/0.48 (multiply(sk_c7, multiply(sk_c6, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.22/0.48 inference(symmetry,[status(thm)],[241])).
% 0.22/0.48 tff(243,plain,
% 0.22/0.48 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(244,axiom,((inverse(sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_9')).
% 0.22/0.48 tff(245,plain,
% 0.22/0.48 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.22/0.48 tff(246,plain,
% 0.22/0.48 (inverse(sk_c7) = sk_c5),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[245, 77])).
% 0.22/0.48 tff(247,plain,
% 0.22/0.48 (sk_c5 = inverse(sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[246])).
% 0.22/0.48 tff(248,plain,
% 0.22/0.48 (multiply(sk_c7, sk_c6) = inverse(sk_c7)),
% 0.22/0.48 inference(transitivity,[status(thm)],[13, 247])).
% 0.22/0.48 tff(249,plain,
% 0.22/0.48 (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[248])).
% 0.22/0.48 tff(250,plain,
% 0.22/0.48 (multiply(inverse(sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c6), sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[249])).
% 0.22/0.48 tff(251,plain,
% 0.22/0.48 (multiply(sk_c6, sk_c7) = inverse(sk_c7)),
% 0.22/0.48 inference(transitivity,[status(thm)],[238, 247])).
% 0.22/0.48 tff(252,plain,
% 0.22/0.48 (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[251])).
% 0.22/0.48 tff(253,plain,
% 0.22/0.48 (multiply(multiply(sk_c1, sk_c6), sk_c6) = multiply(sk_c7, sk_c6)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[97])).
% 0.22/0.48 tff(254,plain,
% 0.22/0.48 (sk_c6 = multiply(sk_c7, sk_c6)),
% 0.22/0.48 inference(transitivity,[status(thm)],[131, 89, 92, 98, 238, 154])).
% 0.22/0.48 tff(255,plain,
% 0.22/0.48 (sk_c6 = sk_c5),
% 0.22/0.48 inference(transitivity,[status(thm)],[131, 89, 92, 98, 238])).
% 0.22/0.48 tff(256,plain,
% 0.22/0.48 (multiply(sk_c6, sk_c6) = multiply(sk_c5, multiply(sk_c7, sk_c6))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[255, 254])).
% 0.22/0.48 tff(257,plain,
% 0.22/0.48 (multiply(sk_c5, multiply(sk_c7, sk_c6)) = multiply(sk_c6, sk_c6)),
% 0.22/0.48 inference(symmetry,[status(thm)],[256])).
% 0.22/0.48 tff(258,plain,
% 0.22/0.48 (multiply(sk_c5, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[247])).
% 0.22/0.48 tff(259,plain,
% 0.22/0.48 (multiply(sk_c5, sk_c7) = identity),
% 0.22/0.48 inference(transitivity,[status(thm)],[258, 162])).
% 0.22/0.48 tff(260,plain,
% 0.22/0.48 (multiply(multiply(sk_c5, sk_c7), sk_c6) = multiply(identity, multiply(sk_c6, sk_c7))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[259, 240])).
% 0.22/0.48 tff(261,plain,
% 0.22/0.48 (multiply(identity, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c5, sk_c7), sk_c6)),
% 0.22/0.48 inference(symmetry,[status(thm)],[260])).
% 0.22/0.48 tff(262,plain,
% 0.22/0.48 (sk_c6 = multiply(sk_c6, sk_c6)),
% 0.22/0.48 inference(transitivity,[status(thm)],[131, 89, 92, 98, 170, 168, 261, 160, 257])).
% 0.22/0.48 tff(263,plain,
% 0.22/0.48 (multiply(sk_c1, sk_c6) = multiply(sk_c1, multiply(sk_c6, sk_c6))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[262])).
% 0.22/0.48 tff(264,plain,
% 0.22/0.48 (sk_c7 = multiply(sk_c1, sk_c6)),
% 0.22/0.48 inference(symmetry,[status(thm)],[97])).
% 0.22/0.48 tff(265,plain,
% 0.22/0.48 (sk_c7 = sk_c6),
% 0.22/0.48 inference(transitivity,[status(thm)],[264, 263, 153, 253, 13, 239, 99, 93, 90, 76])).
% 0.22/0.48 tff(266,plain,
% 0.22/0.48 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[265])).
% 0.22/0.48 tff(267,plain,
% 0.22/0.48 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6),
% 0.22/0.48 inference(transitivity,[status(thm)],[266, 149, 252, 250, 136, 242, 13, 239, 99, 93, 90, 76])).
% 0.22/0.48 tff(268,plain,
% 0.22/0.48 (multiply(sk_c1, multiply(sk_c6, sk_c6)) = multiply(sk_c1, sk_c6)),
% 0.22/0.48 inference(symmetry,[status(thm)],[263])).
% 0.22/0.48 tff(269,plain,
% 0.22/0.48 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c1, sk_c6), sk_c6)),
% 0.22/0.48 inference(symmetry,[status(thm)],[253])).
% 0.22/0.48 tff(270,plain,
% 0.22/0.48 (inverse(sk_c7) = sk_c7),
% 0.22/0.48 inference(transitivity,[status(thm)],[246, 154, 269, 152, 268, 97])).
% 0.22/0.48 tff(271,plain,
% 0.22/0.48 (sk_c7 = multiply(sk_c6, sk_c7)),
% 0.22/0.48 inference(transitivity,[status(thm)],[264, 263, 153, 253, 13, 239])).
% 0.22/0.48 tff(272,plain,
% 0.22/0.48 (multiply(sk_c7, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c7, sk_c6), sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[136])).
% 0.22/0.48 tff(273,plain,
% 0.22/0.48 (sk_c7 = identity),
% 0.22/0.48 inference(transitivity,[status(thm)],[264, 263, 153, 253, 241, 272, 249, 162])).
% 0.22/0.48 tff(274,plain,
% 0.22/0.48 (multiply(sk_c7, sk_c7) = multiply(identity, multiply(sk_c6, sk_c7))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[273, 271])).
% 0.22/0.48 tff(275,plain,
% 0.22/0.48 (multiply(sk_c7, sk_c7) = sk_c6),
% 0.22/0.48 inference(transitivity,[status(thm)],[274, 180, 169, 99, 93, 90, 76])).
% 0.22/0.48 tff(276,plain,
% 0.22/0.48 ((~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[208, 13, 238, 246, 97, 81, 202])).
% 0.22/0.48 tff(277,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[276, 275, 270, 267])).
% 0.22/0.48 tff(278,plain,(multiply(sk_c7, sk_c4) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(279,plain,
% 0.22/0.48 (multiply(multiply(sk_c7, sk_c3), sk_c7) = sk_c6),
% 0.22/0.48 inference(transitivity,[status(thm)],[216, 214, 278])).
% 0.22/0.48 tff(280,plain,
% 0.22/0.48 (multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[279])).
% 0.22/0.48 tff(281,plain,
% 0.22/0.48 (multiply(sk_c6, sk_c7) = multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[280])).
% 0.22/0.48 tff(282,plain,
% 0.22/0.48 (sk_c5 = multiply(sk_c7, sk_c7)),
% 0.22/0.48 inference(transitivity,[status(thm)],[239, 281, 74, 72, 70])).
% 0.22/0.48 tff(283,plain,
% 0.22/0.48 (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(identity, sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[63])).
% 0.22/0.48 tff(284,plain,
% 0.22/0.48 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[59])).
% 0.22/0.48 tff(285,plain,
% 0.22/0.48 (multiply(sk_c7, multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[28])).
% 0.22/0.48 tff(286,plain,
% 0.22/0.48 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c2, sk_c7))),
% 0.22/0.48 inference(symmetry,[status(thm)],[19])).
% 0.22/0.48 tff(287,plain,
% 0.22/0.48 (sk_c5 = sk_c7),
% 0.22/0.48 inference(transitivity,[status(thm)],[154, 286, 285, 284, 283, 65])).
% 0.22/0.48 tff(288,plain,
% 0.22/0.48 (multiply(inverse(sk_c7), sk_c5) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[287])).
% 0.22/0.48 tff(289,plain,
% 0.22/0.48 (multiply(inverse(sk_c7), sk_c5) = multiply(sk_c7, sk_c3)),
% 0.22/0.48 inference(transitivity,[status(thm)],[288, 162, 61, 60])).
% 0.22/0.48 tff(290,plain,
% 0.22/0.48 (multiply(multiply(inverse(sk_c7), sk_c5), sk_c5) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[289, 282])).
% 0.22/0.48 tff(291,plain,
% 0.22/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c7), sk_c5), sk_c5) = multiply(inverse(sk_c7), multiply(sk_c5, sk_c5)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(292,plain,
% 0.22/0.48 (multiply(multiply(inverse(sk_c7), sk_c5), sk_c5) = multiply(inverse(sk_c7), multiply(sk_c5, sk_c5))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[291, 26])).
% 0.22/0.48 tff(293,plain,
% 0.22/0.48 (multiply(inverse(sk_c7), multiply(sk_c5, sk_c5)) = multiply(multiply(inverse(sk_c7), sk_c5), sk_c5)),
% 0.22/0.48 inference(symmetry,[status(thm)],[292])).
% 0.22/0.48 tff(294,plain,
% 0.22/0.48 (multiply(sk_c5, sk_c5) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[282])).
% 0.22/0.48 tff(295,plain,
% 0.22/0.48 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = multiply(sk_c5, sk_c5)),
% 0.22/0.48 inference(symmetry,[status(thm)],[294])).
% 0.22/0.48 tff(296,plain,
% 0.22/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(297,plain,
% 0.22/0.48 (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[296, 26])).
% 0.22/0.48 tff(298,plain,
% 0.22/0.48 (sk_c5 = sk_c6),
% 0.22/0.48 inference(transitivity,[status(thm)],[154, 286, 285, 284, 216, 214, 278])).
% 0.22/0.48 tff(299,plain,
% 0.22/0.48 (multiply(sk_c5, sk_c7) = multiply(sk_c6, sk_c7)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[298])).
% 0.22/0.48 tff(300,plain,
% 0.22/0.48 (multiply(sk_c5, sk_c7) = sk_c6),
% 0.22/0.48 inference(transitivity,[status(thm)],[299, 238, 154, 286, 285, 284, 216, 214, 278])).
% 0.22/0.48 tff(301,plain,
% 0.22/0.48 (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[300])).
% 0.22/0.48 tff(302,plain,
% 0.22/0.48 (multiply(sk_c6, sk_c7) = multiply(multiply(sk_c5, sk_c7), sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[301])).
% 0.22/0.48 tff(303,plain,
% 0.22/0.48 (sk_c7 = multiply(sk_c5, sk_c5)),
% 0.22/0.48 inference(transitivity,[status(thm)],[66, 63, 59, 28, 19, 13, 239, 302, 297, 295])).
% 0.22/0.48 tff(304,plain,
% 0.22/0.48 (multiply(inverse(sk_c7), sk_c7) = multiply(inverse(sk_c7), multiply(sk_c5, sk_c5))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[303])).
% 0.22/0.48 tff(305,plain,
% 0.22/0.48 (identity = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[162])).
% 0.22/0.48 tff(306,plain,
% 0.22/0.48 (identity = multiply(sk_c7, sk_c7)),
% 0.22/0.48 inference(transitivity,[status(thm)],[305, 304, 293, 290, 72, 70])).
% 0.22/0.48 tff(307,plain,
% 0.22/0.48 (multiply(identity, sk_c2) = multiply(multiply(sk_c7, sk_c7), sk_c2)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[306])).
% 0.22/0.48 tff(308,plain,
% 0.22/0.48 (multiply(multiply(sk_c7, sk_c7), sk_c2) = multiply(identity, sk_c2)),
% 0.22/0.48 inference(symmetry,[status(thm)],[307])).
% 0.22/0.48 tff(309,plain,
% 0.22/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c7), sk_c2) = multiply(sk_c7, multiply(sk_c7, sk_c2)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(310,plain,
% 0.22/0.48 (multiply(multiply(sk_c7, sk_c7), sk_c2) = multiply(sk_c7, multiply(sk_c7, sk_c2))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[309, 26])).
% 0.22/0.48 tff(311,plain,
% 0.22/0.48 (multiply(sk_c7, multiply(sk_c7, sk_c2)) = multiply(multiply(sk_c7, sk_c7), sk_c2)),
% 0.22/0.48 inference(symmetry,[status(thm)],[310])).
% 0.22/0.48 tff(312,plain,
% 0.22/0.48 (multiply(sk_c7, sk_c2) = multiply(sk_c7, sk_c3)),
% 0.22/0.48 inference(transitivity,[status(thm)],[36, 46, 61, 60])).
% 0.22/0.48 tff(313,plain,
% 0.22/0.48 (multiply(sk_c7, multiply(sk_c7, sk_c2)) = multiply(sk_c7, multiply(sk_c7, sk_c3))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[312])).
% 0.22/0.48 tff(314,plain,
% 0.22/0.48 (multiply(sk_c7, multiply(sk_c7, sk_c3)) = multiply(sk_c7, multiply(sk_c7, sk_c2))),
% 0.22/0.48 inference(symmetry,[status(thm)],[313])).
% 0.22/0.48 tff(315,plain,
% 0.22/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c7), sk_c3) = multiply(sk_c7, multiply(sk_c7, sk_c3)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(316,plain,
% 0.22/0.48 (multiply(multiply(sk_c7, sk_c7), sk_c3) = multiply(sk_c7, multiply(sk_c7, sk_c3))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[315, 26])).
% 0.22/0.48 tff(317,plain,
% 0.22/0.48 (multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7)) = multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[74])).
% 0.22/0.48 tff(318,plain,
% 0.22/0.48 (multiply(sk_c7, sk_c7) = multiply(identity, multiply(sk_c7, sk_c7))),
% 0.22/0.48 inference(symmetry,[status(thm)],[70])).
% 0.22/0.48 tff(319,plain,
% 0.22/0.48 (multiply(sk_c7, sk_c7) = sk_c7),
% 0.22/0.48 inference(transitivity,[status(thm)],[318, 71, 317, 280, 238, 154, 286, 285, 284, 283, 65])).
% 0.22/0.48 tff(320,plain,
% 0.22/0.48 (multiply(multiply(sk_c7, sk_c7), sk_c3) = multiply(sk_c7, sk_c3)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[319])).
% 0.22/0.48 tff(321,plain,
% 0.22/0.48 (multiply(sk_c7, sk_c3) = multiply(multiply(sk_c7, sk_c7), sk_c3)),
% 0.22/0.48 inference(symmetry,[status(thm)],[320])).
% 0.22/0.48 tff(322,plain,
% 0.22/0.48 (multiply(inverse(sk_c7), multiply(sk_c5, sk_c5)) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[304])).
% 0.22/0.48 tff(323,plain,
% 0.22/0.48 (multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7)) = multiply(multiply(inverse(sk_c7), sk_c5), sk_c5)),
% 0.22/0.48 inference(symmetry,[status(thm)],[290])).
% 0.22/0.48 tff(324,plain,
% 0.22/0.48 (sk_c7 = sk_c2),
% 0.22/0.48 inference(transitivity,[status(thm)],[66, 63, 59, 28, 19, 13, 239, 281, 74, 323, 292, 322, 162, 61, 60, 321, 316, 314, 311, 308, 68])).
% 0.22/0.48 tff(325,plain,
% 0.22/0.48 (inverse(sk_c7) = inverse(sk_c2)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[324])).
% 0.22/0.48 tff(326,plain,
% 0.22/0.48 (inverse(sk_c7) = sk_c5),
% 0.22/0.48 inference(transitivity,[status(thm)],[325, 34, 66, 63, 59, 28, 19, 13])).
% 0.22/0.48 tff(327,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[14, 326])).
% 0.22/0.48 tff(328,plain,(inverse(sk_c7) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(329,plain,
% 0.22/0.48 (sk_c5 = inverse(sk_c7)),
% 0.22/0.48 inference(symmetry,[status(thm)],[328])).
% 0.22/0.48 tff(330,assumption,(~(inverse(sk_c3) = sk_c7)), introduced(assumption)).
% 0.22/0.48 tff(331,plain,
% 0.22/0.48 (((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(332,plain,
% 0.22/0.48 (((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(333,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_16')).
% 0.22/0.48 tff(334,plain,
% 0.22/0.48 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.22/0.48 tff(335,plain,
% 0.22/0.48 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[334, 331])).
% 0.22/0.48 tff(336,plain,
% 0.22/0.48 (multiply(sk_c1, sk_c6) = sk_c7),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[335, 330])).
% 0.22/0.48 tff(337,plain,
% 0.22/0.48 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[336])).
% 0.22/0.48 tff(338,plain,
% 0.22/0.48 (((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c7))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(339,axiom,((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_21')).
% 0.22/0.48 tff(340,plain,
% 0.22/0.48 ((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c7)),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.22/0.48 tff(341,plain,
% 0.22/0.48 (inverse(sk_c1) = sk_c6),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[340, 330])).
% 0.22/0.48 tff(342,plain,
% 0.22/0.48 (sk_c6 = inverse(sk_c1)),
% 0.22/0.48 inference(symmetry,[status(thm)],[341])).
% 0.22/0.48 tff(343,plain,
% 0.22/0.48 (multiply(sk_c6, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[342])).
% 0.22/0.48 tff(344,plain,
% 0.22/0.48 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c6, sk_c1)),
% 0.22/0.49 inference(symmetry,[status(thm)],[343])).
% 0.22/0.49 tff(345,plain,
% 0.22/0.49 (identity = multiply(sk_c6, sk_c1)),
% 0.22/0.49 inference(transitivity,[status(thm)],[87, 344])).
% 0.22/0.49 tff(346,plain,
% 0.22/0.49 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[345])).
% 0.22/0.49 tff(347,plain,
% 0.22/0.49 (sk_c6 = inverse(sk_c7)),
% 0.22/0.49 inference(transitivity,[status(thm)],[131, 346, 92, 337, 238, 329])).
% 0.22/0.49 tff(348,plain,
% 0.22/0.49 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(identity, sk_c6)),
% 0.22/0.49 inference(symmetry,[status(thm)],[346])).
% 0.22/0.49 tff(349,plain,
% 0.22/0.49 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c1, sk_c6))),
% 0.22/0.49 inference(symmetry,[status(thm)],[337])).
% 0.22/0.49 tff(350,plain,
% 0.22/0.49 (multiply(sk_c6, sk_c7) = sk_c6),
% 0.22/0.49 inference(transitivity,[status(thm)],[349, 93, 348, 76])).
% 0.22/0.49 tff(351,plain,
% 0.22/0.49 (multiply(sk_c1, multiply(sk_c6, sk_c7)) = multiply(sk_c1, sk_c6)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[350])).
% 0.22/0.49 tff(352,plain,
% 0.22/0.49 ((~![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)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(353,plain,
% 0.22/0.49 (multiply(multiply(sk_c1, sk_c6), sk_c7) = multiply(sk_c1, multiply(sk_c6, sk_c7))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[352, 26])).
% 0.22/0.49 tff(354,plain,
% 0.22/0.49 (sk_c7 = multiply(sk_c1, sk_c6)),
% 0.22/0.49 inference(symmetry,[status(thm)],[336])).
% 0.22/0.49 tff(355,plain,
% 0.22/0.49 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c1, sk_c6), sk_c7)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[354])).
% 0.22/0.49 tff(356,plain,
% 0.22/0.49 (multiply(sk_c7, sk_c7) = sk_c7),
% 0.22/0.49 inference(transitivity,[status(thm)],[355, 353, 351, 336])).
% 0.22/0.49 tff(357,plain,
% 0.22/0.49 ((multiply(sk_c7, sk_c7) = sk_c6) <=> (sk_c7 = inverse(sk_c7))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[356, 347])).
% 0.22/0.49 tff(358,plain,
% 0.22/0.49 ((multiply(sk_c7, sk_c7) = sk_c6) <=> (inverse(sk_c7) = sk_c7)),
% 0.22/0.49 inference(transitivity,[status(thm)],[357, 10])).
% 0.22/0.49 tff(359,plain,
% 0.22/0.49 ((inverse(sk_c7) = sk_c7) <=> (multiply(sk_c7, sk_c7) = sk_c6)),
% 0.22/0.49 inference(symmetry,[status(thm)],[358])).
% 0.22/0.49 tff(360,plain,
% 0.22/0.49 (inverse(sk_c1) = inverse(sk_c7)),
% 0.22/0.49 inference(transitivity,[status(thm)],[341, 131, 346, 92, 337, 238, 329])).
% 0.22/0.49 tff(361,plain,
% 0.22/0.49 ((inverse(sk_c1) = sk_c7) <=> (inverse(sk_c7) = sk_c7)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[360])).
% 0.22/0.49 tff(362,plain,
% 0.22/0.49 ((inverse(sk_c1) = sk_c7) <=> (multiply(sk_c7, sk_c7) = sk_c6)),
% 0.22/0.49 inference(transitivity,[status(thm)],[361, 359])).
% 0.22/0.49 tff(363,plain,
% 0.22/0.49 ((~(inverse(sk_c1) = sk_c7)) <=> (~(multiply(sk_c7, sk_c7) = sk_c6))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[362])).
% 0.22/0.49 tff(364,plain,
% 0.22/0.49 (sk_c6 = multiply(sk_c6, sk_c7)),
% 0.22/0.49 inference(transitivity,[status(thm)],[131, 346, 92, 337])).
% 0.22/0.49 tff(365,plain,
% 0.22/0.49 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c6, sk_c7))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[364])).
% 0.22/0.49 tff(366,plain,
% 0.22/0.49 (multiply(sk_c7, multiply(sk_c6, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.22/0.49 inference(symmetry,[status(thm)],[365])).
% 0.22/0.49 tff(367,plain,
% 0.22/0.49 (multiply(sk_c7, sk_c6) = multiply(sk_c6, sk_c7)),
% 0.22/0.49 inference(transitivity,[status(thm)],[13, 239])).
% 0.22/0.49 tff(368,plain,
% 0.22/0.49 (multiply(sk_c7, multiply(sk_c7, sk_c6)) = multiply(sk_c7, multiply(sk_c6, sk_c7))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[367])).
% 0.22/0.49 tff(369,plain,
% 0.22/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c7), sk_c6) = multiply(sk_c7, multiply(sk_c7, sk_c6)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(370,plain,
% 0.22/0.49 (multiply(multiply(sk_c7, sk_c7), sk_c6) = multiply(sk_c7, multiply(sk_c7, sk_c6))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[369, 26])).
% 0.22/0.49 tff(371,plain,
% 0.22/0.49 (multiply(sk_c7, sk_c6) = inverse(sk_c7)),
% 0.22/0.49 inference(transitivity,[status(thm)],[13, 329])).
% 0.22/0.49 tff(372,plain,
% 0.22/0.49 (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[371])).
% 0.22/0.49 tff(373,plain,
% 0.22/0.49 (multiply(inverse(sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c6), sk_c7)),
% 0.22/0.49 inference(symmetry,[status(thm)],[372])).
% 0.22/0.49 tff(374,plain,
% 0.22/0.49 (multiply(sk_c6, sk_c1) = sk_c6),
% 0.22/0.49 inference(transitivity,[status(thm)],[343, 86, 305, 373, 136, 366, 13, 239, 349, 93, 348, 76])).
% 0.22/0.49 tff(375,plain,
% 0.22/0.49 (multiply(sk_c7, multiply(sk_c1, sk_c6)) = multiply(sk_c7, sk_c7)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[336])).
% 0.22/0.49 tff(376,plain,
% 0.22/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c1), sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c6)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(377,plain,
% 0.22/0.49 (multiply(multiply(sk_c7, sk_c1), sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c6))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[376, 26])).
% 0.22/0.49 tff(378,plain,
% 0.22/0.49 (sk_c5 = sk_c6),
% 0.22/0.49 inference(transitivity,[status(thm)],[239, 349, 93, 348, 76])).
% 0.22/0.49 tff(379,plain,
% 0.22/0.49 (multiply(multiply(sk_c7, sk_c1), sk_c5) = multiply(multiply(sk_c7, sk_c1), sk_c6)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[378])).
% 0.22/0.49 tff(380,plain,
% 0.22/0.49 (multiply(multiply(sk_c7, sk_c1), multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c7, sk_c1), sk_c5)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[238])).
% 0.22/0.49 tff(381,plain,
% 0.22/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c1), sk_c6), sk_c7) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c6, sk_c7)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(382,plain,
% 0.22/0.49 (multiply(multiply(multiply(sk_c7, sk_c1), sk_c6), sk_c7) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c6, sk_c7))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[381, 26])).
% 0.22/0.49 tff(383,plain,
% 0.22/0.49 (multiply(sk_c7, multiply(sk_c1, sk_c6)) = multiply(multiply(sk_c7, sk_c1), sk_c6)),
% 0.22/0.49 inference(symmetry,[status(thm)],[377])).
% 0.22/0.49 tff(384,plain,
% 0.22/0.49 (multiply(sk_c7, sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c6))),
% 0.22/0.49 inference(symmetry,[status(thm)],[375])).
% 0.22/0.49 tff(385,plain,
% 0.22/0.49 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c6)),
% 0.22/0.49 inference(transitivity,[status(thm)],[384, 383])).
% 0.22/0.49 tff(386,plain,
% 0.22/0.49 (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(multiply(multiply(sk_c7, sk_c1), sk_c6), sk_c7)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[385])).
% 0.22/0.49 tff(387,plain,
% 0.22/0.49 ((~![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)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(388,plain,
% 0.22/0.49 (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[387, 26])).
% 0.22/0.49 tff(389,plain,
% 0.22/0.49 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c7), sk_c7)),
% 0.22/0.49 inference(symmetry,[status(thm)],[388])).
% 0.22/0.49 tff(390,plain,
% 0.22/0.49 (multiply(multiply(sk_c1, sk_c6), multiply(sk_c7, sk_c7)) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[336])).
% 0.22/0.49 tff(391,plain,
% 0.22/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c6), multiply(sk_c7, sk_c7)) = multiply(sk_c1, multiply(sk_c6, multiply(sk_c7, sk_c7))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(392,plain,
% 0.22/0.49 (multiply(multiply(sk_c1, sk_c6), multiply(sk_c7, sk_c7)) = multiply(sk_c1, multiply(sk_c6, multiply(sk_c7, sk_c7)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[391, 26])).
% 0.22/0.49 tff(393,plain,
% 0.22/0.49 (multiply(sk_c1, multiply(sk_c6, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c1, sk_c6), multiply(sk_c7, sk_c7))),
% 0.22/0.49 inference(symmetry,[status(thm)],[392])).
% 0.22/0.49 tff(394,plain,
% 0.22/0.49 (multiply(sk_c6, sk_c7) = inverse(sk_c7)),
% 0.22/0.49 inference(transitivity,[status(thm)],[238, 329])).
% 0.22/0.49 tff(395,plain,
% 0.22/0.49 (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[394])).
% 0.22/0.49 tff(396,plain,
% 0.22/0.49 (multiply(inverse(sk_c7), sk_c7) = multiply(multiply(sk_c6, sk_c7), sk_c7)),
% 0.22/0.49 inference(symmetry,[status(thm)],[395])).
% 0.22/0.49 tff(397,plain,
% 0.22/0.49 (multiply(sk_c6, sk_c1) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.22/0.49 inference(transitivity,[status(thm)],[343, 86, 305, 396, 148])).
% 0.22/0.49 tff(398,plain,
% 0.22/0.49 (multiply(sk_c1, multiply(sk_c6, sk_c1)) = multiply(sk_c1, multiply(sk_c6, multiply(sk_c7, sk_c7)))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[397])).
% 0.22/0.49 tff(399,plain,
% 0.22/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c6), sk_c1) = multiply(sk_c1, multiply(sk_c6, sk_c1)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(400,plain,
% 0.22/0.49 (multiply(multiply(sk_c1, sk_c6), sk_c1) = multiply(sk_c1, multiply(sk_c6, sk_c1))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[399, 26])).
% 0.22/0.49 tff(401,plain,
% 0.22/0.49 (multiply(sk_c7, sk_c1) = multiply(multiply(sk_c1, sk_c6), sk_c1)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[354])).
% 0.22/0.49 tff(402,plain,
% 0.22/0.49 (multiply(sk_c7, sk_c1) = multiply(sk_c7, sk_c7)),
% 0.22/0.49 inference(transitivity,[status(thm)],[401, 400, 398, 393, 390, 389, 386, 382, 380, 379, 377, 375])).
% 0.22/0.49 tff(403,plain,
% 0.22/0.49 (multiply(multiply(sk_c7, sk_c1), multiply(sk_c6, sk_c1)) = multiply(multiply(sk_c7, sk_c7), sk_c6)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[402, 374])).
% 0.22/0.49 tff(404,plain,
% 0.22/0.49 (sk_c6 = multiply(sk_c6, sk_c1)),
% 0.22/0.49 inference(transitivity,[status(thm)],[131, 346, 92, 337, 238, 154, 365, 272, 372, 162, 87, 344])).
% 0.22/0.49 tff(405,plain,
% 0.22/0.49 (multiply(multiply(sk_c1, sk_c6), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.22/0.49 inference(symmetry,[status(thm)],[401])).
% 0.22/0.49 tff(406,plain,
% 0.22/0.49 (multiply(sk_c1, multiply(sk_c6, sk_c1)) = multiply(multiply(sk_c1, sk_c6), sk_c1)),
% 0.22/0.49 inference(symmetry,[status(thm)],[400])).
% 0.22/0.49 tff(407,plain,
% 0.22/0.49 (multiply(sk_c1, multiply(sk_c6, multiply(sk_c7, sk_c7))) = multiply(sk_c1, multiply(sk_c6, sk_c1))),
% 0.22/0.49 inference(symmetry,[status(thm)],[398])).
% 0.22/0.49 tff(408,plain,
% 0.22/0.49 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c1, sk_c6), multiply(sk_c7, sk_c7))),
% 0.22/0.49 inference(symmetry,[status(thm)],[390])).
% 0.22/0.49 tff(409,plain,
% 0.22/0.49 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(sk_c7, sk_c1)),
% 0.22/0.49 inference(transitivity,[status(thm)],[408, 392, 407, 406, 405])).
% 0.22/0.49 tff(410,plain,
% 0.22/0.49 (multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c6) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c6, sk_c1))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[409, 404])).
% 0.22/0.49 tff(411,plain,
% 0.22/0.49 (identity = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.22/0.49 inference(transitivity,[status(thm)],[305, 396, 148])).
% 0.22/0.49 tff(412,plain,
% 0.22/0.49 (multiply(sk_c1, identity) = multiply(sk_c1, multiply(sk_c6, multiply(sk_c7, sk_c7)))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[411])).
% 0.22/0.49 tff(413,plain,
% 0.22/0.49 (multiply(sk_c1, identity) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.22/0.49 inference(transitivity,[status(thm)],[412, 393, 390])).
% 0.22/0.49 tff(414,plain,
% 0.22/0.49 (multiply(multiply(sk_c1, identity), sk_c6) = multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c6)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[413])).
% 0.22/0.49 tff(415,plain,
% 0.22/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, identity), sk_c6) = multiply(sk_c1, multiply(identity, sk_c6)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(416,plain,
% 0.22/0.49 (multiply(multiply(sk_c1, identity), sk_c6) = multiply(sk_c1, multiply(identity, sk_c6))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[415, 26])).
% 0.22/0.49 tff(417,plain,
% 0.22/0.49 (multiply(sk_c1, multiply(identity, sk_c6)) = multiply(multiply(sk_c1, identity), sk_c6)),
% 0.22/0.49 inference(symmetry,[status(thm)],[416])).
% 0.22/0.49 tff(418,plain,
% 0.22/0.49 (multiply(sk_c1, sk_c6) = multiply(sk_c1, multiply(identity, sk_c6))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[131])).
% 0.22/0.49 tff(419,plain,
% 0.22/0.49 (multiply(multiply(sk_c1, sk_c6), sk_c6) = multiply(sk_c7, sk_c6)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[336])).
% 0.22/0.49 tff(420,plain,
% 0.22/0.49 (multiply(sk_c1, multiply(sk_c6, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.22/0.49 inference(transitivity,[status(thm)],[153, 419, 13, 239])).
% 0.22/0.49 tff(421,plain,
% 0.22/0.49 (multiply(sk_c1, multiply(sk_c1, multiply(sk_c6, sk_c6))) = multiply(sk_c1, multiply(sk_c6, sk_c7))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[420])).
% 0.22/0.49 tff(422,plain,
% 0.22/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c1), multiply(sk_c6, sk_c6)) = multiply(sk_c1, multiply(sk_c1, multiply(sk_c6, sk_c6))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(423,plain,
% 0.22/0.49 (multiply(multiply(sk_c1, sk_c1), multiply(sk_c6, sk_c6)) = multiply(sk_c1, multiply(sk_c1, multiply(sk_c6, sk_c6)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[422, 26])).
% 0.22/0.49 tff(424,plain,
% 0.22/0.49 (sk_c6 = multiply(sk_c7, sk_c6)),
% 0.22/0.49 inference(transitivity,[status(thm)],[131, 346, 92, 337, 238, 154])).
% 0.22/0.49 tff(425,plain,
% 0.22/0.49 (sk_c6 = sk_c5),
% 0.22/0.49 inference(transitivity,[status(thm)],[131, 346, 92, 337, 238])).
% 0.22/0.49 tff(426,plain,
% 0.22/0.49 (multiply(sk_c6, sk_c6) = multiply(sk_c5, multiply(sk_c7, sk_c6))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[425, 424])).
% 0.22/0.49 tff(427,plain,
% 0.22/0.49 (multiply(sk_c5, multiply(sk_c7, sk_c6)) = multiply(sk_c6, sk_c6)),
% 0.22/0.49 inference(symmetry,[status(thm)],[426])).
% 0.22/0.49 tff(428,plain,
% 0.22/0.49 (multiply(sk_c5, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[329])).
% 0.22/0.49 tff(429,plain,
% 0.22/0.49 (multiply(sk_c5, sk_c7) = multiply(sk_c6, sk_c1)),
% 0.22/0.49 inference(transitivity,[status(thm)],[428, 162, 87, 344])).
% 0.22/0.49 tff(430,plain,
% 0.22/0.49 (multiply(multiply(sk_c5, sk_c7), sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c5)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[429, 425])).
% 0.22/0.49 tff(431,plain,
% 0.22/0.49 (multiply(multiply(sk_c6, sk_c1), sk_c5) = multiply(multiply(sk_c5, sk_c7), sk_c6)),
% 0.22/0.49 inference(symmetry,[status(thm)],[430])).
% 0.22/0.49 tff(432,plain,
% 0.22/0.49 (multiply(sk_c6, sk_c1) = identity),
% 0.22/0.49 inference(transitivity,[status(thm)],[343, 86])).
% 0.22/0.49 tff(433,plain,
% 0.22/0.49 (multiply(multiply(sk_c6, sk_c1), sk_c5) = multiply(identity, multiply(sk_c6, sk_c7))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[432, 239])).
% 0.22/0.49 tff(434,plain,
% 0.22/0.49 (multiply(identity, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c6, sk_c1), sk_c5)),
% 0.22/0.49 inference(symmetry,[status(thm)],[433])).
% 0.22/0.49 tff(435,plain,
% 0.22/0.49 (sk_c6 = multiply(sk_c6, sk_c6)),
% 0.22/0.49 inference(transitivity,[status(thm)],[131, 346, 92, 337, 170, 168, 434, 431, 160, 427])).
% 0.22/0.49 tff(436,plain,
% 0.22/0.49 (multiply(multiply(sk_c1, sk_c1), sk_c6) = multiply(multiply(sk_c1, sk_c1), multiply(sk_c6, sk_c6))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[435])).
% 0.22/0.49 tff(437,plain,
% 0.22/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c1), sk_c6) = multiply(sk_c1, multiply(sk_c1, sk_c6)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(438,plain,
% 0.22/0.49 (multiply(multiply(sk_c1, sk_c1), sk_c6) = multiply(sk_c1, multiply(sk_c1, sk_c6))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[437, 26])).
% 0.22/0.49 tff(439,plain,
% 0.22/0.49 (multiply(sk_c1, multiply(sk_c1, sk_c6)) = multiply(multiply(sk_c1, sk_c1), sk_c6)),
% 0.22/0.49 inference(symmetry,[status(thm)],[438])).
% 0.22/0.49 tff(440,plain,
% 0.22/0.49 (multiply(sk_c1, sk_c7) = multiply(sk_c1, multiply(sk_c1, sk_c6))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[354])).
% 0.22/0.49 tff(441,plain,
% 0.22/0.49 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.22/0.49 inference(transitivity,[status(thm)],[440, 439, 436, 423, 421, 351, 418, 417, 414, 410, 403, 370, 368, 366, 13, 239, 349, 93, 348, 76])).
% 0.22/0.49 tff(442,plain,
% 0.22/0.49 (multiply(identity, sk_c6) = inverse(sk_c1)),
% 0.22/0.49 inference(transitivity,[status(thm)],[76, 342])).
% 0.22/0.49 tff(443,plain,
% 0.22/0.49 (multiply(multiply(identity, sk_c6), sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[442])).
% 0.22/0.49 tff(444,plain,
% 0.22/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c6), sk_c1) = multiply(identity, multiply(sk_c6, sk_c1)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(445,plain,
% 0.22/0.49 (multiply(multiply(identity, sk_c6), sk_c1) = multiply(identity, multiply(sk_c6, sk_c1))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[444, 26])).
% 0.22/0.49 tff(446,plain,
% 0.22/0.49 (multiply(identity, multiply(sk_c6, sk_c1)) = multiply(multiply(identity, sk_c6), sk_c1)),
% 0.22/0.49 inference(symmetry,[status(thm)],[445])).
% 0.22/0.49 tff(447,plain,
% 0.22/0.49 (multiply(sk_c1, sk_c7) = multiply(sk_c6, sk_c1)),
% 0.22/0.49 inference(transitivity,[status(thm)],[440, 439, 436, 423, 421, 351, 418, 417, 414, 410, 403, 370, 368, 272, 372, 162, 87, 344])).
% 0.22/0.50 tff(448,plain,
% 0.22/0.50 (sk_c5 = identity),
% 0.22/0.50 inference(transitivity,[status(thm)],[154, 365, 272, 372, 162])).
% 0.22/0.50 tff(449,plain,
% 0.22/0.50 (multiply(sk_c5, multiply(sk_c1, sk_c7)) = multiply(identity, multiply(sk_c6, sk_c1))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[448, 447])).
% 0.22/0.50 tff(450,plain,
% 0.22/0.50 (multiply(sk_c1, multiply(sk_c6, sk_c7)) = sk_c5),
% 0.22/0.50 inference(transitivity,[status(thm)],[351, 418, 417, 414, 410, 403, 370, 368, 366, 13])).
% 0.22/0.50 tff(451,plain,
% 0.22/0.50 (multiply(multiply(sk_c1, multiply(sk_c6, sk_c7)), multiply(sk_c1, sk_c7)) = multiply(sk_c5, multiply(sk_c1, sk_c7))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[450])).
% 0.22/0.50 tff(452,plain,
% 0.22/0.50 (multiply(sk_c1, sk_c6) = multiply(sk_c1, multiply(sk_c6, sk_c7))),
% 0.22/0.50 inference(symmetry,[status(thm)],[351])).
% 0.22/0.50 tff(453,plain,
% 0.22/0.50 (sk_c7 = multiply(sk_c1, multiply(sk_c6, sk_c7))),
% 0.22/0.50 inference(transitivity,[status(thm)],[354, 452])).
% 0.22/0.50 tff(454,plain,
% 0.22/0.50 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c1, multiply(sk_c6, sk_c7)), multiply(sk_c1, sk_c7))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[453])).
% 0.22/0.50 tff(455,plain,
% 0.22/0.50 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6),
% 0.22/0.50 inference(transitivity,[status(thm)],[454, 451, 449, 446, 443, 86, 305, 373, 136, 366, 13, 239, 349, 93, 348, 76])).
% 0.22/0.50 tff(456,plain,
% 0.22/0.50 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(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_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(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_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(457,plain,
% 0.22/0.50 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(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_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(458,plain,
% 0.22/0.50 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(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_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[457])).
% 0.22/0.50 tff(459,plain,
% 0.22/0.50 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(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_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[458, 456])).
% 0.22/0.50 tff(460,plain,
% 0.22/0.50 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(461,plain,
% 0.22/0.50 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.22/0.50 tff(462,plain,
% 0.22/0.50 ((~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[461, 13, 238, 328, 336, 341, 202])).
% 0.22/0.50 tff(463,plain,
% 0.22/0.50 (~(inverse(sk_c1) = sk_c7)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[462, 455, 441])).
% 0.22/0.50 tff(464,plain,
% 0.22/0.50 (~(multiply(sk_c7, sk_c7) = sk_c6)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[463, 363])).
% 0.22/0.50 tff(465,plain,
% 0.22/0.50 (multiply(sk_c7, sk_c7) = sk_c6),
% 0.22/0.50 inference(transitivity,[status(thm)],[355, 353, 351, 418, 417, 414, 410, 403, 370, 368, 366, 13, 239, 349, 93, 348, 76])).
% 0.22/0.50 tff(466,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[465, 464])).
% 0.22/0.50 tff(467,plain,(inverse(sk_c3) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(468,plain,
% 0.22/0.50 (sk_c7 = inverse(sk_c3)),
% 0.22/0.50 inference(symmetry,[status(thm)],[467])).
% 0.22/0.50 tff(469,plain,
% 0.22/0.50 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[468])).
% 0.22/0.50 tff(470,plain,
% 0.22/0.50 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c7, sk_c3)),
% 0.22/0.50 inference(symmetry,[status(thm)],[469])).
% 0.22/0.50 tff(471,plain,
% 0.22/0.50 (identity = multiply(sk_c7, sk_c3)),
% 0.22/0.50 inference(transitivity,[status(thm)],[61, 470])).
% 0.22/0.50 tff(472,plain,
% 0.22/0.50 (multiply(identity, multiply(sk_c7, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, multiply(sk_c7, sk_c7)))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[471])).
% 0.22/0.50 tff(473,plain,
% 0.22/0.50 (multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, multiply(sk_c7, sk_c7))) = multiply(identity, multiply(sk_c7, multiply(sk_c7, sk_c7)))),
% 0.22/0.50 inference(symmetry,[status(thm)],[472])).
% 0.22/0.50 tff(474,plain,
% 0.22/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, multiply(sk_c7, sk_c7))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(475,plain,
% 0.22/0.50 (multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, multiply(sk_c7, sk_c7)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[474, 26])).
% 0.22/0.50 tff(476,plain,
% 0.22/0.50 (multiply(sk_c7, multiply(sk_c3, sk_c7)) = multiply(sk_c7, sk_c4)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[211])).
% 0.22/0.50 tff(477,plain,
% 0.22/0.50 (multiply(multiply(sk_c7, sk_c3), sk_c7) = sk_c6),
% 0.22/0.50 inference(transitivity,[status(thm)],[216, 476, 278])).
% 0.22/0.50 tff(478,plain,
% 0.22/0.50 (multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), multiply(sk_c7, sk_c7)) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[477])).
% 0.22/0.50 tff(479,plain,
% 0.22/0.50 (multiply(sk_c6, multiply(sk_c7, sk_c7)) = multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), multiply(sk_c7, sk_c7))),
% 0.22/0.50 inference(symmetry,[status(thm)],[478])).
% 0.22/0.50 tff(480,plain,
% 0.22/0.50 (multiply(sk_c5, sk_c7) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.22/0.50 inference(transitivity,[status(thm)],[428, 396, 148, 479, 475, 473, 9])).
% 0.22/0.50 tff(481,plain,
% 0.22/0.50 ((multiply(sk_c5, sk_c7) = sk_c6) <=> (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[480])).
% 0.22/0.50 tff(482,plain,
% 0.22/0.50 ((multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6) <=> (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.22/0.50 inference(symmetry,[status(thm)],[481])).
% 0.22/0.50 tff(483,plain,
% 0.22/0.50 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[471])).
% 0.22/0.50 tff(484,plain,
% 0.22/0.50 (sk_c7 = sk_c6),
% 0.22/0.50 inference(transitivity,[status(thm)],[66, 483, 216, 476, 278])).
% 0.22/0.50 tff(485,plain,
% 0.22/0.50 (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(identity, sk_c7)),
% 0.22/0.50 inference(symmetry,[status(thm)],[483])).
% 0.22/0.50 tff(486,plain,
% 0.22/0.50 (multiply(sk_c7, sk_c4) = multiply(sk_c7, multiply(sk_c3, sk_c7))),
% 0.22/0.50 inference(symmetry,[status(thm)],[476])).
% 0.22/0.50 tff(487,plain,
% 0.22/0.50 (sk_c6 = multiply(sk_c7, sk_c4)),
% 0.22/0.50 inference(symmetry,[status(thm)],[278])).
% 0.22/0.50 tff(488,plain,
% 0.22/0.50 (sk_c6 = sk_c7),
% 0.22/0.50 inference(transitivity,[status(thm)],[487, 486, 232, 485, 65])).
% 0.22/0.50 tff(489,plain,
% 0.22/0.50 (multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[477])).
% 0.22/0.50 tff(490,plain,
% 0.22/0.50 (multiply(sk_c5, sk_c7) = multiply(sk_c7, sk_c3)),
% 0.22/0.50 inference(transitivity,[status(thm)],[428, 162, 61, 470])).
% 0.22/0.50 tff(491,plain,
% 0.22/0.50 (multiply(multiply(sk_c5, sk_c7), multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[490])).
% 0.22/0.50 tff(492,plain,
% 0.22/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c7), multiply(sk_c7, sk_c7)) = multiply(sk_c5, multiply(sk_c7, multiply(sk_c7, sk_c7))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(493,plain,
% 0.22/0.51 (multiply(multiply(sk_c5, sk_c7), multiply(sk_c7, sk_c7)) = multiply(sk_c5, multiply(sk_c7, multiply(sk_c7, sk_c7)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[492, 26])).
% 0.22/0.51 tff(494,plain,
% 0.22/0.51 (multiply(sk_c5, multiply(sk_c7, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c5, sk_c7), multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(symmetry,[status(thm)],[493])).
% 0.22/0.51 tff(495,assumption,(~(inverse(sk_c1) = sk_c6)), introduced(assumption)).
% 0.22/0.51 tff(496,plain,
% 0.22/0.51 (((inverse(sk_c1) = sk_c6) | (multiply(sk_c2, sk_c7) = sk_c6)) <=> ((inverse(sk_c1) = sk_c6) | (multiply(sk_c2, sk_c7) = sk_c6))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(497,axiom,((inverse(sk_c1) = sk_c6) | (multiply(sk_c2, sk_c7) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_17')).
% 0.22/0.51 tff(498,plain,
% 0.22/0.51 ((inverse(sk_c1) = sk_c6) | (multiply(sk_c2, sk_c7) = sk_c6)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.22/0.51 tff(499,plain,
% 0.22/0.51 (multiply(sk_c2, sk_c7) = sk_c6),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[498, 495])).
% 0.22/0.51 tff(500,plain,
% 0.22/0.51 (sk_c6 = sk_c7),
% 0.22/0.51 inference(transitivity,[status(thm)],[487, 213, 232, 485, 65])).
% 0.22/0.51 tff(501,plain,
% 0.22/0.51 (multiply(sk_c2, sk_c6) = multiply(sk_c2, sk_c7)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[500])).
% 0.22/0.51 tff(502,plain,
% 0.22/0.51 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.22/0.51 inference(transitivity,[status(thm)],[501, 499, 487, 213, 232, 485, 65])).
% 0.22/0.51 tff(503,plain,
% 0.22/0.51 (sk_c7 = sk_c6),
% 0.22/0.51 inference(transitivity,[status(thm)],[66, 483, 216, 214, 278])).
% 0.22/0.51 tff(504,plain,
% 0.22/0.51 ((inverse(sk_c5) = sk_c7) <=> (inverse(sk_c5) = sk_c6)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[503])).
% 0.22/0.51 tff(505,plain,
% 0.22/0.51 ((inverse(sk_c5) = sk_c6) <=> (inverse(sk_c5) = sk_c7)),
% 0.22/0.51 inference(symmetry,[status(thm)],[504])).
% 0.22/0.51 tff(506,plain,
% 0.22/0.51 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c3) = sk_c3)),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(507,plain,
% 0.22/0.51 (multiply(identity, sk_c3) = sk_c3),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[506, 7])).
% 0.22/0.51 tff(508,plain,
% 0.22/0.51 (multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), multiply(sk_c7, sk_c7)) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[279])).
% 0.22/0.51 tff(509,plain,
% 0.22/0.51 (multiply(sk_c6, multiply(sk_c7, sk_c7)) = multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(symmetry,[status(thm)],[508])).
% 0.22/0.51 tff(510,plain,
% 0.22/0.51 (identity = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(transitivity,[status(thm)],[305, 396, 148, 509, 475, 473, 9])).
% 0.22/0.51 tff(511,plain,
% 0.22/0.51 (multiply(identity, sk_c3) = multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c3)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[510])).
% 0.22/0.51 tff(512,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c3) = multiply(identity, sk_c3)),
% 0.22/0.51 inference(symmetry,[status(thm)],[511])).
% 0.22/0.51 tff(513,plain,
% 0.22/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c3) = multiply(sk_c7, multiply(multiply(sk_c7, sk_c7), sk_c3)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(514,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c3) = multiply(sk_c7, multiply(multiply(sk_c7, sk_c7), sk_c3))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[513, 26])).
% 0.22/0.51 tff(515,plain,
% 0.22/0.51 (multiply(sk_c7, multiply(multiply(sk_c7, sk_c7), sk_c3)) = multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c3)),
% 0.22/0.51 inference(symmetry,[status(thm)],[514])).
% 0.22/0.51 tff(516,plain,
% 0.22/0.51 (multiply(sk_c7, multiply(multiply(sk_c7, sk_c7), sk_c3)) = multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3)))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[316])).
% 0.22/0.51 tff(517,plain,
% 0.22/0.51 (multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))) = multiply(sk_c7, multiply(multiply(sk_c7, sk_c7), sk_c3))),
% 0.22/0.51 inference(symmetry,[status(thm)],[516])).
% 0.22/0.51 tff(518,plain,
% 0.22/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c7), multiply(sk_c7, sk_c3)) = multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(519,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, sk_c7), multiply(sk_c7, sk_c3)) = multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[518, 26])).
% 0.22/0.51 tff(520,plain,
% 0.22/0.51 (multiply(sk_c7, sk_c3) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(transitivity,[status(thm)],[469, 49, 305, 396, 148])).
% 0.22/0.51 tff(521,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, sk_c7), multiply(sk_c7, sk_c3)) = multiply(multiply(sk_c7, sk_c7), multiply(sk_c6, multiply(sk_c7, sk_c7)))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[520])).
% 0.22/0.51 tff(522,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, sk_c7), multiply(sk_c6, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c7, sk_c7), multiply(sk_c7, sk_c3))),
% 0.22/0.51 inference(symmetry,[status(thm)],[521])).
% 0.22/0.51 tff(523,plain,
% 0.22/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c7), sk_c6), multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c7), multiply(sk_c6, multiply(sk_c7, sk_c7))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(524,plain,
% 0.22/0.51 (multiply(multiply(multiply(sk_c7, sk_c7), sk_c6), multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c7), multiply(sk_c6, multiply(sk_c7, sk_c7)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[523, 26])).
% 0.22/0.51 tff(525,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, sk_c7), sk_c6) = multiply(sk_c7, sk_c3)),
% 0.22/0.51 inference(transitivity,[status(thm)],[370, 368, 272, 372, 162, 61, 470])).
% 0.22/0.51 tff(526,plain,
% 0.22/0.51 (multiply(multiply(multiply(sk_c7, sk_c7), sk_c6), multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[525])).
% 0.22/0.51 tff(527,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7)) = multiply(multiply(multiply(sk_c7, sk_c7), sk_c6), multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(symmetry,[status(thm)],[526])).
% 0.22/0.51 tff(528,plain,
% 0.22/0.51 (sk_c5 = sk_c3),
% 0.22/0.51 inference(transitivity,[status(thm)],[239, 281, 74, 527, 524, 522, 519, 517, 515, 512, 507])).
% 0.22/0.51 tff(529,plain,
% 0.22/0.51 (inverse(sk_c5) = inverse(sk_c3)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[528])).
% 0.22/0.51 tff(530,plain,
% 0.22/0.51 (inverse(sk_c5) = sk_c6),
% 0.22/0.51 inference(transitivity,[status(thm)],[529, 467, 66, 483, 216, 214, 278])).
% 0.22/0.51 tff(531,plain,
% 0.22/0.51 (inverse(sk_c5) = sk_c7),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[530, 505])).
% 0.22/0.51 tff(532,plain,
% 0.22/0.51 (multiply(sk_c7, sk_c5) = multiply(sk_c7, multiply(sk_c6, sk_c7))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[239])).
% 0.22/0.51 tff(533,plain,
% 0.22/0.51 (multiply(sk_c7, sk_c5) = multiply(sk_c7, sk_c3)),
% 0.22/0.51 inference(transitivity,[status(thm)],[532, 272, 372, 162, 61, 470])).
% 0.22/0.51 tff(534,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, sk_c5), sk_c7) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[533])).
% 0.22/0.51 tff(535,plain,
% 0.22/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c5), sk_c7) = multiply(sk_c7, multiply(sk_c5, sk_c7)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(536,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, sk_c5), sk_c7) = multiply(sk_c7, multiply(sk_c5, sk_c7))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[535, 26])).
% 0.22/0.51 tff(537,plain,
% 0.22/0.51 (multiply(sk_c7, multiply(sk_c5, sk_c7)) = multiply(multiply(sk_c7, sk_c5), sk_c7)),
% 0.22/0.51 inference(symmetry,[status(thm)],[536])).
% 0.22/0.51 tff(538,plain,
% 0.22/0.51 (multiply(sk_c7, multiply(sk_c5, sk_c7)) = sk_c6),
% 0.22/0.51 inference(transitivity,[status(thm)],[537, 534, 216, 214, 278])).
% 0.22/0.51 tff(539,plain,
% 0.22/0.51 (((inverse(sk_c1) = sk_c6) | (inverse(sk_c2) = sk_c7)) <=> ((inverse(sk_c1) = sk_c6) | (inverse(sk_c2) = sk_c7))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(540,axiom,((inverse(sk_c1) = sk_c6) | (inverse(sk_c2) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_18')).
% 0.22/0.51 tff(541,plain,
% 0.22/0.51 ((inverse(sk_c1) = sk_c6) | (inverse(sk_c2) = sk_c7)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[540, 539])).
% 0.22/0.51 tff(542,plain,
% 0.22/0.51 (inverse(sk_c2) = sk_c7),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[541, 495])).
% 0.22/0.51 tff(543,plain,
% 0.22/0.51 (inverse(sk_c2) = sk_c6),
% 0.22/0.51 inference(transitivity,[status(thm)],[542, 66, 483, 216, 214, 278])).
% 0.22/0.51 tff(544,plain,
% 0.22/0.51 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c5, sk_c7)) = sk_c6)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c5, sk_c7)) = sk_c6)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(545,plain,
% 0.22/0.51 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c5, sk_c7)) = sk_c6)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(546,plain,
% 0.22/0.51 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c5, sk_c7)) = sk_c6))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.22/0.51 tff(547,plain,
% 0.22/0.51 ((~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[546, 13, 238, 499, 542, 328, 202, 543, 538])).
% 0.22/0.51 tff(548,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[547, 531, 502])).
% 0.22/0.51 tff(549,plain,(inverse(sk_c1) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(550,plain,
% 0.22/0.51 (sk_c6 = inverse(sk_c1)),
% 0.22/0.51 inference(symmetry,[status(thm)],[549])).
% 0.22/0.51 tff(551,plain,
% 0.22/0.51 (multiply(sk_c6, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[550])).
% 0.22/0.51 tff(552,plain,
% 0.22/0.51 (multiply(sk_c6, sk_c1) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(transitivity,[status(thm)],[551, 86, 305, 396, 148, 479, 475, 473, 9])).
% 0.22/0.51 tff(553,plain,
% 0.22/0.51 (multiply(sk_c5, multiply(sk_c6, sk_c1)) = multiply(sk_c5, multiply(sk_c7, multiply(sk_c7, sk_c7)))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[552])).
% 0.22/0.51 tff(554,plain,
% 0.22/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c6), sk_c1) = multiply(sk_c5, multiply(sk_c6, sk_c1)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(555,plain,
% 0.22/0.51 (multiply(multiply(sk_c5, sk_c6), sk_c1) = multiply(sk_c5, multiply(sk_c6, sk_c1))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[554, 26])).
% 0.22/0.51 tff(556,plain,
% 0.22/0.51 (multiply(sk_c5, sk_c6) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[329, 488])).
% 0.22/0.51 tff(557,plain,
% 0.22/0.51 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c5, sk_c6)),
% 0.22/0.51 inference(symmetry,[status(thm)],[556])).
% 0.22/0.51 tff(558,plain,
% 0.22/0.51 (identity = multiply(sk_c5, sk_c6)),
% 0.22/0.51 inference(transitivity,[status(thm)],[305, 557])).
% 0.22/0.51 tff(559,plain,
% 0.22/0.51 (multiply(identity, sk_c1) = multiply(multiply(sk_c5, sk_c6), sk_c1)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[558])).
% 0.22/0.51 tff(560,plain,
% 0.22/0.51 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c1) = sk_c1)),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(561,plain,
% 0.22/0.51 (multiply(identity, sk_c1) = sk_c1),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[560, 7])).
% 0.22/0.51 tff(562,plain,
% 0.22/0.51 (sk_c1 = multiply(identity, sk_c1)),
% 0.22/0.51 inference(symmetry,[status(thm)],[561])).
% 0.22/0.51 tff(563,plain,
% 0.22/0.51 (sk_c1 = inverse(sk_c7)),
% 0.22/0.51 inference(transitivity,[status(thm)],[562, 559, 555, 553, 494, 491, 317, 489, 238, 329])).
% 0.22/0.51 tff(564,plain,
% 0.22/0.51 (multiply(sk_c1, sk_c6) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[563, 488])).
% 0.22/0.51 tff(565,plain,
% 0.22/0.51 (multiply(sk_c1, sk_c6) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(transitivity,[status(thm)],[564, 396, 148, 479, 475, 473, 9])).
% 0.22/0.51 tff(566,plain,
% 0.22/0.51 ((multiply(sk_c1, sk_c6) = sk_c7) <=> (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[565, 484])).
% 0.22/0.51 tff(567,plain,
% 0.22/0.51 ((multiply(sk_c1, sk_c6) = sk_c7) <=> (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.22/0.51 inference(transitivity,[status(thm)],[566, 482])).
% 0.22/0.51 tff(568,assumption,(~(multiply(sk_c1, sk_c6) = sk_c7)), introduced(assumption)).
% 0.22/0.51 tff(569,plain,
% 0.22/0.51 (((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c2, sk_c7) = sk_c6)) <=> ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c2, sk_c7) = sk_c6))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(570,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c2, sk_c7) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_12')).
% 0.22/0.51 tff(571,plain,
% 0.22/0.51 ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c2, sk_c7) = sk_c6)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.22/0.51 tff(572,plain,
% 0.22/0.51 (multiply(sk_c2, sk_c7) = sk_c6),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[571, 568])).
% 0.22/0.51 tff(573,plain,
% 0.22/0.51 (multiply(sk_c2, sk_c6) = multiply(sk_c2, sk_c7)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[488])).
% 0.22/0.51 tff(574,plain,
% 0.22/0.51 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.22/0.51 inference(transitivity,[status(thm)],[573, 572, 487, 486, 232, 485, 65])).
% 0.22/0.51 tff(575,plain,
% 0.22/0.51 (((inverse(sk_c2) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)) <=> ((inverse(sk_c2) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(576,plain,
% 0.22/0.51 (((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c2) = sk_c7)) <=> ((inverse(sk_c2) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(577,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c2) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_13')).
% 0.22/0.51 tff(578,plain,
% 0.22/0.51 ((inverse(sk_c2) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.22/0.51 tff(579,plain,
% 0.22/0.51 ((inverse(sk_c2) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[578, 575])).
% 0.22/0.51 tff(580,plain,
% 0.22/0.51 (inverse(sk_c2) = sk_c7),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[579, 568])).
% 0.22/0.51 tff(581,plain,
% 0.22/0.51 (inverse(sk_c2) = sk_c6),
% 0.22/0.51 inference(transitivity,[status(thm)],[580, 66, 483, 216, 476, 278])).
% 0.22/0.51 tff(582,plain,
% 0.22/0.51 (multiply(sk_c7, multiply(sk_c5, sk_c7)) = sk_c6),
% 0.22/0.51 inference(transitivity,[status(thm)],[537, 534, 216, 476, 278])).
% 0.22/0.51 tff(583,plain,
% 0.22/0.51 ((inverse(sk_c5) = sk_c7) <=> (inverse(sk_c5) = sk_c6)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[484])).
% 0.22/0.51 tff(584,plain,
% 0.22/0.51 ((inverse(sk_c5) = sk_c6) <=> (inverse(sk_c5) = sk_c7)),
% 0.22/0.51 inference(symmetry,[status(thm)],[583])).
% 0.22/0.51 tff(585,plain,
% 0.22/0.51 (identity = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(transitivity,[status(thm)],[305, 396, 148, 479, 475, 473, 9])).
% 0.22/0.51 tff(586,plain,
% 0.22/0.51 (multiply(identity, sk_c3) = multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c3)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[585])).
% 0.22/0.51 tff(587,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c3) = multiply(identity, sk_c3)),
% 0.22/0.51 inference(symmetry,[status(thm)],[586])).
% 0.22/0.51 tff(588,plain,
% 0.22/0.51 (multiply(sk_c6, sk_c7) = multiply(multiply(multiply(sk_c7, sk_c3), sk_c7), sk_c7)),
% 0.22/0.51 inference(symmetry,[status(thm)],[489])).
% 0.22/0.51 tff(589,plain,
% 0.22/0.51 (sk_c5 = sk_c3),
% 0.22/0.51 inference(transitivity,[status(thm)],[239, 588, 74, 527, 524, 522, 519, 517, 515, 587, 507])).
% 0.22/0.51 tff(590,plain,
% 0.22/0.51 (inverse(sk_c5) = inverse(sk_c3)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[589])).
% 0.22/0.51 tff(591,plain,
% 0.22/0.51 (inverse(sk_c5) = sk_c6),
% 0.22/0.51 inference(transitivity,[status(thm)],[590, 467, 66, 483, 216, 476, 278])).
% 0.22/0.51 tff(592,plain,
% 0.22/0.51 (inverse(sk_c5) = sk_c7),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[591, 584])).
% 0.22/0.51 tff(593,plain,
% 0.22/0.51 (~(multiply(sk_c2, sk_c6) = sk_c7)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[546, 13, 238, 572, 580, 328, 202, 592, 582, 581])).
% 0.22/0.51 tff(594,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[593, 574])).
% 0.22/0.51 tff(595,plain,(multiply(sk_c1, sk_c6) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(596,plain,
% 0.22/0.51 (multiply(sk_c5, sk_c7) = sk_c6),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[595, 567])).
% 0.22/0.51 tff(597,plain,
% 0.22/0.51 (multiply(sk_c7, multiply(multiply(sk_c7, sk_c3), sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[477])).
% 0.22/0.51 tff(598,plain,
% 0.22/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), sk_c7) = multiply(sk_c7, multiply(multiply(sk_c7, sk_c3), sk_c7)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(599,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), sk_c7) = multiply(sk_c7, multiply(multiply(sk_c7, sk_c3), sk_c7))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[598, 26])).
% 0.22/0.51 tff(600,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.22/0.51 inference(transitivity,[status(thm)],[599, 597, 13, 239])).
% 0.22/0.51 tff(601,plain,
% 0.22/0.51 (multiply(sk_c7, multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), sk_c7)) = multiply(sk_c7, multiply(sk_c6, sk_c7))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[600])).
% 0.22/0.51 tff(602,plain,
% 0.22/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), sk_c7) = multiply(sk_c7, multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), sk_c7)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(603,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), sk_c7) = multiply(sk_c7, multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), sk_c7))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[602, 26])).
% 0.22/0.51 tff(604,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), sk_c7) = multiply(sk_c7, sk_c3)),
% 0.22/0.51 inference(transitivity,[status(thm)],[603, 601, 272, 372, 162, 61, 470])).
% 0.22/0.51 tff(605,plain,
% 0.22/0.51 (multiply(multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[604])).
% 0.22/0.51 tff(606,plain,
% 0.22/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), sk_c7), sk_c7) = multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), multiply(sk_c7, sk_c7)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(607,plain,
% 0.22/0.51 (multiply(multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), sk_c7), sk_c7) = multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[606, 26])).
% 0.22/0.51 tff(608,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), multiply(sk_c7, sk_c7)) = multiply(multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), sk_c7), sk_c7)),
% 0.22/0.51 inference(symmetry,[status(thm)],[607])).
% 0.22/0.51 tff(609,plain,
% 0.22/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), multiply(sk_c7, sk_c7)) = multiply(sk_c7, multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), multiply(sk_c7, sk_c7))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(610,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), multiply(sk_c7, sk_c7)) = multiply(sk_c7, multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), multiply(sk_c7, sk_c7)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[609, 26])).
% 0.22/0.51 tff(611,plain,
% 0.22/0.51 (multiply(sk_c7, multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c7, multiply(sk_c7, multiply(sk_c7, sk_c3))), multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(symmetry,[status(thm)],[610])).
% 0.22/0.51 tff(612,plain,
% 0.22/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), sk_c7), sk_c7) = multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), multiply(sk_c7, sk_c7)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(613,plain,
% 0.22/0.51 (multiply(multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), sk_c7), sk_c7) = multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[612, 26])).
% 0.22/0.51 tff(614,plain,
% 0.22/0.51 (multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), sk_c7) = inverse(sk_c7)),
% 0.22/0.51 inference(transitivity,[status(thm)],[599, 597, 13, 329])).
% 0.22/0.51 tff(615,plain,
% 0.22/0.51 (multiply(multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), sk_c7), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[614])).
% 0.22/0.51 tff(616,plain,
% 0.22/0.51 (multiply(inverse(sk_c7), sk_c7) = multiply(multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), sk_c7), sk_c7)),
% 0.22/0.51 inference(symmetry,[status(thm)],[615])).
% 0.22/0.51 tff(617,plain,
% 0.22/0.51 (multiply(sk_c7, sk_c3) = multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), multiply(sk_c7, sk_c7))),
% 0.22/0.51 inference(transitivity,[status(thm)],[469, 49, 305, 616, 613])).
% 0.22/0.51 tff(618,plain,
% 0.22/0.51 (multiply(sk_c7, multiply(sk_c7, sk_c3)) = multiply(sk_c7, multiply(multiply(sk_c7, multiply(sk_c7, sk_c3)), multiply(sk_c7, sk_c7)))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[617])).
% 0.22/0.51 tff(619,plain,
% 0.22/0.51 (multiply(sk_c7, multiply(multiply(sk_c7, sk_c7), sk_c6)) = multiply(sk_c7, multiply(sk_c7, sk_c3))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[525])).
% 0.22/0.51 tff(620,plain,
% 0.22/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c6) = multiply(sk_c7, multiply(multiply(sk_c7, sk_c7), sk_c6)))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(621,plain,
% 0.22/0.52 (multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c6) = multiply(sk_c7, multiply(multiply(sk_c7, sk_c7), sk_c6))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[620, 26])).
% 0.22/0.52 tff(622,plain,
% 0.22/0.52 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(multiply(sk_c7, multiply(sk_c7, sk_c7)), sk_c6)),
% 0.22/0.52 inference(monotonicity,[status(thm)],[552])).
% 0.22/0.52 tff(623,plain,
% 0.22/0.52 (multiply(sk_c1, sk_c7) = multiply(sk_c1, sk_c6)),
% 0.22/0.52 inference(monotonicity,[status(thm)],[484])).
% 0.22/0.52 tff(624,plain,
% 0.22/0.52 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c6, multiply(sk_c1, sk_c6))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[484, 623])).
% 0.22/0.52 tff(625,plain,
% 0.22/0.52 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6),
% 0.22/0.52 inference(transitivity,[status(thm)],[624, 93, 622, 621, 619, 618, 611, 608, 605, 216, 476, 278])).
% 0.22/0.52 tff(626,plain,
% 0.22/0.52 (inverse(sk_c1) = sk_c7),
% 0.22/0.52 inference(transitivity,[status(thm)],[549, 487, 486, 232, 485, 65])).
% 0.22/0.52 tff(627,plain,
% 0.22/0.52 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(628,plain,
% 0.22/0.52 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(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_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(629,plain,
% 0.22/0.52 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[628])).
% 0.22/0.52 tff(630,plain,
% 0.22/0.52 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6)))),
% 0.22/0.52 inference(transitivity,[status(thm)],[629, 627])).
% 0.22/0.52 tff(631,plain,
% 0.22/0.52 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(632,plain,
% 0.22/0.52 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[631, 630])).
% 0.22/0.52 tff(633,plain,
% 0.22/0.52 ((~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[632, 13, 238, 328, 549, 202, 626])).
% 0.22/0.52 tff(634,plain,
% 0.22/0.52 ((~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c6))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[633, 592, 625])).
% 0.22/0.52 tff(635,plain,
% 0.22/0.52 (~(multiply(sk_c5, sk_c7) = sk_c6)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[634, 595])).
% 0.22/0.52 tff(636,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[635, 596])).
% 0.22/0.52 % SZS output end Proof
% 0.22/0.52 % E exiting
%------------------------------------------------------------------------------