%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP361-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:39 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP361-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 15:59:05 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(sk_c6_type, type, (
% 0.21/0.43 sk_c6: $i)).
% 0.21/0.43 tff(multiply_type, type, (
% 0.21/0.43 multiply: ( $i * $i ) > $i)).
% 0.21/0.43 tff(sk_c7_type, type, (
% 0.21/0.43 sk_c7: $i)).
% 0.21/0.43 tff(sk_c5_type, type, (
% 0.21/0.43 sk_c5: $i)).
% 0.21/0.43 tff(sk_c2_type, type, (
% 0.21/0.43 sk_c2: $i)).
% 0.21/0.43 tff(sk_c1_type, type, (
% 0.21/0.43 sk_c1: $i)).
% 0.21/0.43 tff(inverse_type, type, (
% 0.21/0.43 inverse: $i > $i)).
% 0.21/0.43 tff(identity_type, type, (
% 0.21/0.43 identity: $i)).
% 0.21/0.43 tff(sk_c3_type, type, (
% 0.21/0.43 sk_c3: $i)).
% 0.21/0.43 tff(sk_c4_type, type, (
% 0.21/0.43 sk_c4: $i)).
% 0.21/0.43 tff(1,assumption,(~(multiply(sk_c5, sk_c7) = sk_c6)), introduced(assumption)).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (((multiply(sk_c5, sk_c7) = sk_c6) | (multiply(sk_c7, sk_c2) = sk_c6)) <=> ((multiply(sk_c5, sk_c7) = sk_c6) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (((multiply(sk_c7, sk_c2) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)) <=> ((multiply(sk_c5, sk_c7) = sk_c6) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(4,axiom,((multiply(sk_c7, sk_c2) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_14')).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 ((multiply(sk_c5, sk_c7) = sk_c6) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 ((multiply(sk_c5, sk_c7) = sk_c6) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (multiply(sk_c7, sk_c2) = sk_c6),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 (((multiply(sk_c1, sk_c7) = sk_c2) | (multiply(sk_c5, sk_c7) = sk_c6)) <=> ((multiply(sk_c1, sk_c7) = sk_c2) | (multiply(sk_c5, sk_c7) = sk_c6))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(9,axiom,((multiply(sk_c1, sk_c7) = sk_c2) | (multiply(sk_c5, sk_c7) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_20')).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 ((multiply(sk_c1, sk_c7) = sk_c2) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (multiply(sk_c1, sk_c7) = sk_c2),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[10, 1])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (sk_c2 = multiply(sk_c1, sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[11])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (multiply(sk_c7, sk_c2) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c2)),
% 0.21/0.43 inference(symmetry,[status(thm)],[13])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(18,axiom,(![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','associativity')).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.43 tff(20,plain,(
% 0.21/0.43 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[19])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(25,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_26')).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (inverse(sk_c1) = sk_c7),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[26, 1])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (sk_c7 = inverse(sk_c1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[27])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[28])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[29])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.43 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(34,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.43 tff(36,plain,(
% 0.21/0.43 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.43 inference(skolemize,[status(sab)],[35])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[39])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c7), sk_c7) = identity)),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (multiply(inverse(sk_c7), sk_c7) = identity),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[41, 37])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c5, sk_c7) = sk_c6)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c5, sk_c7) = sk_c6))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(44,axiom,((inverse(sk_c7) = sk_c5) | (multiply(sk_c5, sk_c7) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_8')).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (inverse(sk_c7) = sk_c5),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[45, 1])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (sk_c5 = inverse(sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[46])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (multiply(sk_c5, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[47])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)) <=> ((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(50,axiom,((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_2')).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 ((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 ((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[51, 49])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 ((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 ((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 ((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[54, 49])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c5) = sk_c7),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[55, 1])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (multiply(sk_c5, multiply(sk_c6, sk_c5)) = multiply(sk_c5, sk_c7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c6), sk_c5) = multiply(sk_c5, multiply(sk_c6, sk_c5)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (multiply(multiply(sk_c5, sk_c6), sk_c5) = multiply(sk_c5, multiply(sk_c6, sk_c5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[58, 21])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (multiply(multiply(sk_c5, sk_c6), sk_c5) = multiply(sk_c7, sk_c1)),
% 0.21/0.43 inference(transitivity,[status(thm)],[59, 57, 48, 42, 40, 30])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (multiply(multiply(multiply(sk_c5, sk_c6), sk_c5), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[60])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, sk_c6), sk_c5), sk_c7) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, sk_c7)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 (multiply(multiply(multiply(sk_c5, sk_c6), sk_c5), sk_c7) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, sk_c7))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[62, 21])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, sk_c7)) = multiply(multiply(multiply(sk_c5, sk_c6), sk_c5), sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[63])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c5, sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[48])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (identity = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[42])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c3), sk_c3) = identity)),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (multiply(inverse(sk_c3), sk_c3) = identity),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[67, 37])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (sk_c7 = multiply(sk_c6, sk_c5)),
% 0.21/0.43 inference(symmetry,[status(thm)],[56])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(73,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.43 tff(75,plain,(
% 0.21/0.43 ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.43 inference(skolemize,[status(sab)],[74])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (multiply(identity, sk_c7) = sk_c7),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.21/0.43 tff(79,assumption,(~(inverse(sk_c3) = sk_c7)), introduced(assumption)).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(81,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_27')).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 (inverse(sk_c1) = sk_c7),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.21/0.44 tff(84,plain,
% 0.21/0.44 (sk_c7 = inverse(sk_c1)),
% 0.21/0.44 inference(symmetry,[status(thm)],[83])).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.21/0.44 inference(symmetry,[status(thm)],[85])).
% 0.21/0.44 tff(87,plain,
% 0.21/0.44 (identity = multiply(sk_c7, sk_c1)),
% 0.21/0.44 inference(transitivity,[status(thm)],[40, 86])).
% 0.21/0.44 tff(88,plain,
% 0.21/0.44 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[87])).
% 0.21/0.44 tff(89,plain,
% 0.21/0.44 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[88])).
% 0.21/0.44 tff(90,plain,
% 0.21/0.44 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[23])).
% 0.21/0.44 tff(91,plain,
% 0.21/0.44 (((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c2)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(92,plain,
% 0.21/0.44 (((multiply(sk_c1, sk_c7) = sk_c2) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(93,axiom,((multiply(sk_c1, sk_c7) = sk_c2) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_21')).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.44 tff(95,plain,
% 0.21/0.44 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (multiply(sk_c1, sk_c7) = sk_c2),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[95, 79])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (sk_c2 = multiply(sk_c1, sk_c7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[96])).
% 0.21/0.44 tff(98,plain,
% 0.21/0.44 (multiply(sk_c7, sk_c2) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 (((inverse(sk_c3) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 (((multiply(sk_c7, sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(101,axiom,((multiply(sk_c7, sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_15')).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (multiply(sk_c7, sk_c2) = sk_c6),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[103, 79])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (sk_c6 = multiply(sk_c7, sk_c2)),
% 0.21/0.44 inference(symmetry,[status(thm)],[104])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (sk_c6 = sk_c7),
% 0.21/0.44 inference(transitivity,[status(thm)],[105, 98, 90, 89, 78])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 (multiply(sk_c7, sk_c6) = multiply(sk_c7, sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[106])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (multiply(sk_c7, sk_c7) = multiply(sk_c7, sk_c6)),
% 0.21/0.44 inference(symmetry,[status(thm)],[107])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 (((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5)) <=> ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (((inverse(sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(111,axiom,((inverse(sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_9')).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[112, 109])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (inverse(sk_c7) = sk_c5),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[113, 79])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c5, sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[114])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (multiply(sk_c5, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[115])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (multiply(sk_c5, sk_c7) = multiply(sk_c7, sk_c1)),
% 0.21/0.44 inference(transitivity,[status(thm)],[116, 42, 40, 86])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[119, 21])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c5, sk_c7), sk_c7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[120])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = sk_c7),
% 0.21/0.44 inference(transitivity,[status(thm)],[121, 118, 89, 78])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (multiply(sk_c7, multiply(sk_c5, multiply(sk_c7, sk_c7))) = multiply(sk_c7, sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[122])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c5), multiply(sk_c7, sk_c7)) = multiply(sk_c7, multiply(sk_c5, multiply(sk_c7, sk_c7))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (multiply(multiply(sk_c7, sk_c5), multiply(sk_c7, sk_c7)) = multiply(sk_c7, multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[124, 21])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c2)),
% 0.21/0.44 inference(symmetry,[status(thm)],[98])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (sk_c7 = multiply(identity, sk_c7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[78])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (sk_c7 = sk_c6),
% 0.21/0.44 inference(transitivity,[status(thm)],[127, 88, 23, 126, 104])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (multiply(sk_c7, sk_c5) = multiply(sk_c6, sk_c5)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[128])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (multiply(sk_c6, sk_c5) = multiply(sk_c7, sk_c5)),
% 0.21/0.44 inference(symmetry,[status(thm)],[129])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 (((multiply(sk_c6, sk_c5) = sk_c7) | (inverse(sk_c3) = sk_c7)) <=> ((multiply(sk_c6, sk_c5) = sk_c7) | (inverse(sk_c3) = sk_c7))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(132,axiom,((multiply(sk_c6, sk_c5) = sk_c7) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_3')).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 ((multiply(sk_c6, sk_c5) = sk_c7) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 ((multiply(sk_c6, sk_c5) = sk_c7) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[133, 131])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 ((multiply(sk_c6, sk_c5) = sk_c7) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[134, 131])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 ((multiply(sk_c6, sk_c5) = sk_c7) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 ((multiply(sk_c6, sk_c5) = sk_c7) | (inverse(sk_c3) = sk_c7)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[136, 131])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 (multiply(sk_c6, sk_c5) = sk_c7),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[137, 79])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (sk_c7 = multiply(sk_c6, sk_c5)),
% 0.21/0.44 inference(symmetry,[status(thm)],[138])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 (sk_c7 = multiply(sk_c7, sk_c5)),
% 0.21/0.44 inference(transitivity,[status(thm)],[139, 130])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c5), multiply(sk_c7, sk_c7))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.21/0.44 inference(transitivity,[status(thm)],[141, 125, 123, 108])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 ((multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6) <=> (multiply(sk_c7, sk_c6) = sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[142, 106])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 ((multiply(sk_c7, sk_c6) = sk_c7) <=> (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)),
% 0.21/0.44 inference(symmetry,[status(thm)],[143])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c5) = sk_c5)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 (multiply(identity, sk_c5) = sk_c5),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[145, 76])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 (multiply(sk_c5, sk_c6) = multiply(sk_c5, sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[106])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 (multiply(sk_c5, sk_c7) = multiply(sk_c5, sk_c6)),
% 0.21/0.44 inference(symmetry,[status(thm)],[147])).
% 0.21/0.44 tff(149,plain,
% 0.21/0.44 (identity = multiply(sk_c5, sk_c6)),
% 0.21/0.44 inference(transitivity,[status(thm)],[66, 115, 148])).
% 0.21/0.44 tff(150,plain,
% 0.21/0.44 (multiply(identity, sk_c5) = multiply(multiply(sk_c5, sk_c6), sk_c5)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[149])).
% 0.21/0.44 tff(151,plain,
% 0.21/0.44 (multiply(multiply(sk_c5, sk_c6), sk_c5) = multiply(identity, sk_c5)),
% 0.21/0.44 inference(symmetry,[status(thm)],[150])).
% 0.21/0.44 tff(152,plain,
% 0.21/0.44 (multiply(sk_c5, multiply(sk_c6, sk_c5)) = multiply(multiply(sk_c5, sk_c6), sk_c5)),
% 0.21/0.44 inference(symmetry,[status(thm)],[59])).
% 0.21/0.44 tff(153,plain,
% 0.21/0.44 (multiply(sk_c5, multiply(sk_c6, sk_c5)) = multiply(sk_c5, sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.44 tff(154,plain,
% 0.21/0.44 (multiply(sk_c5, sk_c7) = multiply(sk_c5, multiply(sk_c6, sk_c5))),
% 0.21/0.44 inference(symmetry,[status(thm)],[153])).
% 0.21/0.44 tff(155,plain,
% 0.21/0.44 (multiply(sk_c7, sk_c1) = sk_c5),
% 0.21/0.44 inference(transitivity,[status(thm)],[85, 39, 66, 115, 154, 152, 151, 146])).
% 0.21/0.44 tff(156,plain,
% 0.21/0.44 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c5, sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[155])).
% 0.21/0.44 tff(157,plain,
% 0.21/0.44 (multiply(sk_c5, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[156])).
% 0.21/0.44 tff(158,plain,
% 0.21/0.44 (sk_c5 = multiply(identity, sk_c5)),
% 0.21/0.44 inference(symmetry,[status(thm)],[146])).
% 0.21/0.44 tff(159,plain,
% 0.21/0.44 (sk_c5 = sk_c7),
% 0.21/0.44 inference(transitivity,[status(thm)],[158, 150, 59, 153, 157, 89, 78])).
% 0.21/0.44 tff(160,plain,
% 0.21/0.44 (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[106])).
% 0.21/0.44 tff(161,plain,
% 0.21/0.44 (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)),
% 0.21/0.44 inference(transitivity,[status(thm)],[160, 108])).
% 0.21/0.44 tff(162,plain,
% 0.21/0.44 ((multiply(sk_c6, sk_c7) = sk_c5) <=> (multiply(sk_c7, sk_c6) = sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[161, 159])).
% 0.21/0.44 tff(163,plain,
% 0.21/0.44 ((multiply(sk_c6, sk_c7) = sk_c5) <=> (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)),
% 0.21/0.44 inference(transitivity,[status(thm)],[162, 144])).
% 0.21/0.44 tff(164,plain,
% 0.21/0.44 (identity = sk_c5),
% 0.21/0.44 inference(transitivity,[status(thm)],[66, 115, 154, 152, 151, 146])).
% 0.21/0.44 tff(165,plain,
% 0.21/0.44 (multiply(sk_c7, identity) = multiply(sk_c7, sk_c5)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[164])).
% 0.21/0.44 tff(166,plain,
% 0.21/0.44 (multiply(sk_c5, sk_c7) = identity),
% 0.21/0.44 inference(transitivity,[status(thm)],[116, 42])).
% 0.21/0.44 tff(167,plain,
% 0.21/0.44 (multiply(sk_c7, multiply(sk_c5, sk_c7)) = multiply(sk_c7, identity)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[166])).
% 0.21/0.44 tff(168,plain,
% 0.21/0.44 ((~![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)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(169,plain,
% 0.21/0.44 (multiply(multiply(sk_c7, sk_c5), sk_c7) = multiply(sk_c7, multiply(sk_c5, sk_c7))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[168, 21])).
% 0.21/0.44 tff(170,plain,
% 0.21/0.44 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c7, sk_c5), sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.44 tff(171,plain,
% 0.21/0.44 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.21/0.44 inference(transitivity,[status(thm)],[160, 170, 169, 167, 165, 129, 138, 127, 88, 156, 154, 152, 151, 146])).
% 0.21/0.44 tff(172,plain,
% 0.21/0.44 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[171, 163])).
% 0.21/0.44 tff(173,plain,
% 0.21/0.44 (sk_c5 = inverse(sk_c7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[114])).
% 0.21/0.44 tff(174,plain,
% 0.21/0.44 (multiply(sk_c5, sk_c7) = inverse(sk_c7)),
% 0.21/0.44 inference(transitivity,[status(thm)],[154, 152, 151, 146, 173])).
% 0.21/0.44 tff(175,plain,
% 0.21/0.44 ((multiply(sk_c5, sk_c7) = sk_c6) <=> (inverse(sk_c7) = sk_c7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[174, 106])).
% 0.21/0.44 tff(176,plain,
% 0.21/0.44 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c2), sk_c5) = multiply(sk_c7, multiply(sk_c2, sk_c5)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(177,plain,
% 0.21/0.45 (multiply(multiply(sk_c7, sk_c2), sk_c5) = multiply(sk_c7, multiply(sk_c2, sk_c5))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[176, 21])).
% 0.21/0.45 tff(178,plain,
% 0.21/0.45 (multiply(multiply(sk_c7, sk_c2), sk_c5) = multiply(sk_c6, sk_c5)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[104])).
% 0.21/0.45 tff(179,plain,
% 0.21/0.45 (multiply(sk_c6, sk_c5) = multiply(multiply(sk_c7, sk_c2), sk_c5)),
% 0.21/0.45 inference(symmetry,[status(thm)],[178])).
% 0.21/0.45 tff(180,plain,
% 0.21/0.45 (sk_c7 = multiply(sk_c7, multiply(sk_c2, sk_c5))),
% 0.21/0.45 inference(transitivity,[status(thm)],[139, 179, 177])).
% 0.21/0.45 tff(181,plain,
% 0.21/0.45 (multiply(sk_c5, sk_c7) = multiply(sk_c5, multiply(sk_c7, multiply(sk_c2, sk_c5)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[180])).
% 0.21/0.45 tff(182,plain,
% 0.21/0.45 (multiply(sk_c5, multiply(sk_c7, multiply(sk_c2, sk_c5))) = multiply(sk_c5, sk_c7)),
% 0.21/0.45 inference(symmetry,[status(thm)],[181])).
% 0.21/0.45 tff(183,plain,
% 0.21/0.45 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c7), multiply(sk_c2, sk_c5)) = multiply(sk_c5, multiply(sk_c7, multiply(sk_c2, sk_c5))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(184,plain,
% 0.21/0.45 (multiply(multiply(sk_c5, sk_c7), multiply(sk_c2, sk_c5)) = multiply(sk_c5, multiply(sk_c7, multiply(sk_c2, sk_c5)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[183, 21])).
% 0.21/0.45 tff(185,plain,
% 0.21/0.45 (multiply(sk_c7, sk_c5) = sk_c7),
% 0.21/0.45 inference(transitivity,[status(thm)],[129, 138])).
% 0.21/0.45 tff(186,plain,
% 0.21/0.45 (multiply(sk_c1, multiply(sk_c7, sk_c5)) = multiply(sk_c1, sk_c7)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[185])).
% 0.21/0.45 tff(187,plain,
% 0.21/0.45 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), sk_c5) = multiply(sk_c1, multiply(sk_c7, sk_c5)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(188,plain,
% 0.21/0.45 (multiply(multiply(sk_c1, sk_c7), sk_c5) = multiply(sk_c1, multiply(sk_c7, sk_c5))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[187, 21])).
% 0.21/0.45 tff(189,plain,
% 0.21/0.45 (multiply(sk_c2, sk_c5) = multiply(multiply(sk_c1, sk_c7), sk_c5)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.45 tff(190,plain,
% 0.21/0.45 (multiply(sk_c2, sk_c5) = sk_c2),
% 0.21/0.45 inference(transitivity,[status(thm)],[189, 188, 186, 96])).
% 0.21/0.45 tff(191,plain,
% 0.21/0.45 (multiply(multiply(sk_c5, sk_c7), multiply(sk_c2, sk_c5)) = multiply(identity, sk_c2)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[166, 190])).
% 0.21/0.45 tff(192,plain,
% 0.21/0.45 (multiply(identity, sk_c2) = multiply(multiply(sk_c5, sk_c7), multiply(sk_c2, sk_c5))),
% 0.21/0.45 inference(symmetry,[status(thm)],[191])).
% 0.21/0.45 tff(193,plain,
% 0.21/0.45 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c2) = sk_c2)),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(194,plain,
% 0.21/0.45 (multiply(identity, sk_c2) = sk_c2),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[193, 76])).
% 0.21/0.45 tff(195,plain,
% 0.21/0.45 (sk_c2 = multiply(identity, sk_c2)),
% 0.21/0.45 inference(symmetry,[status(thm)],[194])).
% 0.21/0.45 tff(196,plain,
% 0.21/0.45 (multiply(sk_c1, sk_c6) = multiply(sk_c1, sk_c7)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[106])).
% 0.21/0.45 tff(197,plain,
% 0.21/0.45 (multiply(sk_c1, sk_c6) = multiply(sk_c5, sk_c7)),
% 0.21/0.45 inference(transitivity,[status(thm)],[196, 96, 195, 192, 184, 182])).
% 0.21/0.45 tff(198,plain,
% 0.21/0.45 ((multiply(sk_c1, sk_c6) = sk_c7) <=> (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[197, 128])).
% 0.21/0.45 tff(199,plain,
% 0.21/0.45 ((multiply(sk_c1, sk_c6) = sk_c7) <=> (inverse(sk_c7) = sk_c7)),
% 0.21/0.45 inference(transitivity,[status(thm)],[198, 175])).
% 0.21/0.45 tff(200,plain,
% 0.21/0.45 (multiply(sk_c1, sk_c6) = sk_c7),
% 0.21/0.45 inference(transitivity,[status(thm)],[196, 96, 195, 192, 184, 182, 157, 89, 78])).
% 0.21/0.45 tff(201,plain,
% 0.21/0.45 (inverse(sk_c7) = sk_c7),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.21/0.45 tff(202,plain,
% 0.21/0.45 (multiply(sk_c7, sk_c6) = sk_c7),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[171, 162])).
% 0.21/0.45 tff(203,plain,
% 0.21/0.45 (multiply(sk_c5, sk_c7) = sk_c6),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[200, 198])).
% 0.21/0.45 tff(204,plain,
% 0.21/0.45 (^[X4: $i, X2: $i, X1: $i] : refl(((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(205,plain,
% 0.21/0.45 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[204])).
% 0.21/0.45 tff(206,plain,
% 0.21/0.45 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(207,plain,
% 0.21/0.45 (^[X4: $i, X2: $i, X1: $i] : rewrite(((~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(208,plain,
% 0.21/0.45 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[207])).
% 0.21/0.45 tff(209,plain,
% 0.21/0.45 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.45 tff(210,plain,
% 0.21/0.45 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.45 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.45 tff(211,plain,
% 0.21/0.45 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[210, 209])).
% 0.21/0.45 tff(212,plain,
% 0.21/0.45 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[211, 208])).
% 0.21/0.46 tff(213,plain,
% 0.21/0.46 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)))), ((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) <=> (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))))), rewrite((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6)))), ((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6))))), (((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) <=> (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))))), rewrite((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)))), (((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))))), ((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) <=> (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(inverse(X4) = sk_c7))))), rewrite((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(inverse(X4) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)))), ((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))))), (((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) <=> (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))))), rewrite((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)))), (((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))))), ((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) <=> (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(sk_c5, sk_c7) = sk_c6))))), rewrite((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)))), ((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))))), (((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) <=> (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(inverse(X1) = sk_c7))))), rewrite((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(inverse(X1) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)))), (((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))))), ((((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) <=> (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X1, sk_c6) = sk_c7))))), rewrite((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X1, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)))), ((((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))))), (((((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c5) = sk_c7))) <=> (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X2, sk_c5) = sk_c7))))), rewrite((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X2, sk_c5) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)))), (((((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c5) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))))), ((((((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c5) = sk_c7))) | (~(inverse(X2) = sk_c5))) <=> (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(inverse(X2) = sk_c5))))), rewrite((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(inverse(X2) = sk_c5))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)))), ((((((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c5) = sk_c7))) | (~(inverse(X2) = sk_c5))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(214,plain,
% 0.21/0.47 (![X4: $i, X3: $i, X2: $i, X1: $i] : (((((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c5) = sk_c7))) | (~(inverse(X2) = sk_c5))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[213])).
% 0.21/0.47 tff(215,plain,
% 0.21/0.47 (![X4: $i, X3: $i, X2: $i, X1: $i] : (((((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c5) = sk_c7))) | (~(inverse(X2) = sk_c5))) <=> ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[214, 212])).
% 0.21/0.47 tff(216,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : (((((((((((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(multiply(sk_c5, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c5) = sk_c7))) | (~(inverse(X2) = sk_c5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_31')).
% 0.21/0.47 tff(217,plain,
% 0.21/0.47 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.21/0.47 tff(218,plain,
% 0.21/0.47 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[217, 206])).
% 0.21/0.47 tff(219,plain,(
% 0.21/0.47 ![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[218])).
% 0.21/0.47 tff(220,plain,
% 0.21/0.47 (![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[219, 205])).
% 0.21/0.47 tff(221,plain,
% 0.21/0.47 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c7)) | (~(multiply(sk_c7, 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_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(222,plain,
% 0.21/0.47 (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, sk_c5) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)) | (~(inverse(sk_c7) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(223,plain,
% 0.21/0.47 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, sk_c5) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[222])).
% 0.21/0.47 tff(224,plain,
% 0.21/0.47 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, sk_c5) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[223, 221])).
% 0.21/0.47 tff(225,plain,
% 0.21/0.47 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, sk_c5) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(226,plain,
% 0.21/0.47 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.21/0.47 tff(227,plain,
% 0.21/0.47 ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c5) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c7)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[226, 138, 114, 220])).
% 0.21/0.47 tff(228,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[227, 203, 171, 185, 202, 201, 172])).
% 0.21/0.47 tff(229,plain,(inverse(sk_c3) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(230,plain,
% 0.21/0.47 (inverse(sk_c3) = multiply(sk_c6, sk_c5)),
% 0.21/0.47 inference(transitivity,[status(thm)],[229, 69])).
% 0.21/0.47 tff(231,plain,
% 0.21/0.47 (multiply(inverse(sk_c3), sk_c3) = multiply(multiply(sk_c6, sk_c5), sk_c3)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[230])).
% 0.21/0.47 tff(232,plain,
% 0.21/0.47 (multiply(multiply(sk_c6, sk_c5), sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.47 inference(symmetry,[status(thm)],[231])).
% 0.21/0.47 tff(233,plain,
% 0.21/0.47 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c5), sk_c3) = multiply(sk_c6, multiply(sk_c5, sk_c3)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(234,plain,
% 0.21/0.47 (multiply(multiply(sk_c6, sk_c5), sk_c3) = multiply(sk_c6, multiply(sk_c5, sk_c3))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[233, 21])).
% 0.21/0.47 tff(235,plain,
% 0.21/0.47 (multiply(sk_c6, multiply(sk_c5, sk_c3)) = multiply(multiply(sk_c6, sk_c5), sk_c3)),
% 0.21/0.47 inference(symmetry,[status(thm)],[234])).
% 0.21/0.47 tff(236,plain,
% 0.21/0.47 (multiply(sk_c7, sk_c1) = identity),
% 0.21/0.47 inference(transitivity,[status(thm)],[29, 39])).
% 0.21/0.47 tff(237,plain,
% 0.21/0.47 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[236])).
% 0.21/0.47 tff(238,plain,
% 0.21/0.47 (sk_c6 = multiply(sk_c7, sk_c2)),
% 0.21/0.47 inference(symmetry,[status(thm)],[7])).
% 0.21/0.47 tff(239,plain,
% 0.21/0.47 (sk_c6 = sk_c7),
% 0.21/0.47 inference(transitivity,[status(thm)],[238, 13, 90, 237, 78])).
% 0.21/0.47 tff(240,plain,
% 0.21/0.47 (multiply(sk_c6, multiply(sk_c5, sk_c3)) = multiply(sk_c7, multiply(sk_c5, sk_c3))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[239])).
% 0.21/0.47 tff(241,plain,
% 0.21/0.47 (multiply(sk_c7, multiply(sk_c5, sk_c3)) = multiply(sk_c6, multiply(sk_c5, sk_c3))),
% 0.21/0.47 inference(symmetry,[status(thm)],[240])).
% 0.21/0.47 tff(242,plain,
% 0.21/0.47 (multiply(sk_c7, multiply(sk_c5, sk_c3)) = multiply(sk_c5, sk_c7)),
% 0.21/0.47 inference(transitivity,[status(thm)],[241, 235, 232, 68, 66, 65])).
% 0.21/0.47 tff(243,plain,
% 0.21/0.47 (multiply(sk_c5, sk_c6) = multiply(sk_c5, sk_c7)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[239])).
% 0.21/0.47 tff(244,plain,
% 0.21/0.47 (multiply(sk_c5, sk_c7) = multiply(sk_c5, sk_c6)),
% 0.21/0.47 inference(symmetry,[status(thm)],[243])).
% 0.21/0.47 tff(245,plain,
% 0.21/0.47 (identity = multiply(sk_c5, sk_c6)),
% 0.21/0.47 inference(transitivity,[status(thm)],[66, 65, 244])).
% 0.21/0.47 tff(246,plain,
% 0.21/0.47 (multiply(identity, multiply(sk_c7, multiply(sk_c5, sk_c3))) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, sk_c7))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[245, 242])).
% 0.21/0.47 tff(247,plain,
% 0.21/0.47 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c7), multiply(sk_c5, sk_c3)) = multiply(identity, multiply(sk_c7, multiply(sk_c5, sk_c3))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(248,plain,
% 0.21/0.47 (multiply(multiply(identity, sk_c7), multiply(sk_c5, sk_c3)) = multiply(identity, multiply(sk_c7, multiply(sk_c5, sk_c3)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[247, 21])).
% 0.21/0.47 tff(249,plain,
% 0.21/0.47 (multiply(sk_c7, multiply(sk_c5, sk_c3)) = multiply(multiply(identity, sk_c7), multiply(sk_c5, sk_c3))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.47 tff(250,plain,
% 0.21/0.47 (identity = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.47 inference(symmetry,[status(thm)],[68])).
% 0.21/0.47 tff(251,plain,
% 0.21/0.47 (multiply(sk_c5, sk_c7) = sk_c6),
% 0.21/0.47 inference(transitivity,[status(thm)],[48, 42, 250, 231, 234, 240, 249, 248, 246, 64, 61, 23, 14, 7])).
% 0.21/0.47 tff(252,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[1, 251])).
% 0.21/0.47 tff(253,plain,(multiply(sk_c5, sk_c7) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(254,assumption,(~(inverse(sk_c7) = sk_c5)), introduced(assumption)).
% 0.21/0.48 tff(255,plain,
% 0.21/0.48 (((inverse(sk_c4) = sk_c5) | (inverse(sk_c7) = sk_c5)) <=> ((inverse(sk_c4) = sk_c5) | (inverse(sk_c7) = sk_c5))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(256,plain,
% 0.21/0.48 (((inverse(sk_c7) = sk_c5) | (inverse(sk_c4) = sk_c5)) <=> ((inverse(sk_c4) = sk_c5) | (inverse(sk_c7) = sk_c5))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(257,axiom,((inverse(sk_c7) = sk_c5) | (inverse(sk_c4) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_12')).
% 0.21/0.48 tff(258,plain,
% 0.21/0.48 ((inverse(sk_c4) = sk_c5) | (inverse(sk_c7) = sk_c5)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.21/0.48 tff(259,plain,
% 0.21/0.48 ((inverse(sk_c4) = sk_c5) | (inverse(sk_c7) = sk_c5)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[258, 255])).
% 0.21/0.48 tff(260,plain,
% 0.21/0.48 (inverse(sk_c4) = sk_c5),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[259, 254])).
% 0.21/0.48 tff(261,plain,
% 0.21/0.48 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c4) = sk_c4)),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(262,plain,
% 0.21/0.48 (multiply(identity, sk_c4) = sk_c4),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[261, 76])).
% 0.21/0.48 tff(263,plain,
% 0.21/0.48 (sk_c5 = inverse(sk_c4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[260])).
% 0.21/0.48 tff(264,plain,
% 0.21/0.48 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(265,plain,
% 0.21/0.48 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[264, 37])).
% 0.21/0.48 tff(266,plain,
% 0.21/0.48 (multiply(sk_c5, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[263])).
% 0.21/0.48 tff(267,plain,
% 0.21/0.48 (multiply(sk_c5, sk_c4) = identity),
% 0.21/0.48 inference(transitivity,[status(thm)],[266, 265])).
% 0.21/0.48 tff(268,plain,
% 0.21/0.48 (multiply(multiply(sk_c5, sk_c4), sk_c5) = multiply(identity, sk_c5)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[267])).
% 0.21/0.48 tff(269,plain,
% 0.21/0.48 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c5, sk_c4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[266])).
% 0.21/0.48 tff(270,plain,
% 0.21/0.48 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[265])).
% 0.21/0.48 tff(271,plain,
% 0.21/0.48 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c5, sk_c4)),
% 0.21/0.48 inference(transitivity,[status(thm)],[42, 270, 269])).
% 0.21/0.48 tff(272,plain,
% 0.21/0.48 (multiply(multiply(inverse(sk_c7), sk_c7), sk_c5) = multiply(multiply(sk_c5, sk_c4), sk_c5)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[271])).
% 0.21/0.48 tff(273,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c7), sk_c7), sk_c5) = multiply(inverse(sk_c7), multiply(sk_c7, sk_c5)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(274,plain,
% 0.21/0.48 (multiply(multiply(inverse(sk_c7), sk_c7), sk_c5) = multiply(inverse(sk_c7), multiply(sk_c7, sk_c5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[273, 21])).
% 0.21/0.48 tff(275,plain,
% 0.21/0.48 (multiply(inverse(sk_c7), multiply(sk_c7, sk_c5)) = multiply(multiply(inverse(sk_c7), sk_c7), sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[274])).
% 0.21/0.48 tff(276,plain,
% 0.21/0.48 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(277,axiom,((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_10')).
% 0.21/0.48 tff(278,plain,
% 0.21/0.48 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.21/0.48 tff(279,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c6) = sk_c7),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[278, 254])).
% 0.21/0.48 tff(280,plain,
% 0.21/0.48 (sk_c7 = multiply(sk_c3, sk_c6)),
% 0.21/0.48 inference(symmetry,[status(thm)],[279])).
% 0.21/0.48 tff(281,plain,
% 0.21/0.48 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c3, sk_c6), sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[280])).
% 0.21/0.48 tff(282,plain,
% 0.21/0.48 (multiply(multiply(sk_c3, sk_c6), sk_c7) = multiply(sk_c7, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[281])).
% 0.21/0.48 tff(283,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c6), sk_c7) = multiply(sk_c3, multiply(sk_c6, sk_c7)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(284,plain,
% 0.21/0.48 (multiply(multiply(sk_c3, sk_c6), sk_c7) = multiply(sk_c3, multiply(sk_c6, sk_c7))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[283, 21])).
% 0.21/0.48 tff(285,plain,
% 0.21/0.48 (multiply(sk_c3, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c3, sk_c6), sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[284])).
% 0.21/0.48 tff(286,plain,
% 0.21/0.48 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(287,axiom,((inverse(sk_c7) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_7')).
% 0.21/0.48 tff(288,plain,
% 0.21/0.48 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.21/0.48 tff(289,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[288, 254])).
% 0.21/0.48 tff(290,plain,
% 0.21/0.48 (multiply(sk_c3, multiply(sk_c6, sk_c7)) = multiply(sk_c3, sk_c5)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[289])).
% 0.21/0.48 tff(291,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c5) = multiply(sk_c3, multiply(sk_c6, sk_c7))),
% 0.21/0.48 inference(symmetry,[status(thm)],[290])).
% 0.21/0.48 tff(292,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c3), sk_c6) = multiply(sk_c6, multiply(sk_c3, sk_c6)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(293,plain,
% 0.21/0.48 (multiply(multiply(sk_c6, sk_c3), sk_c6) = multiply(sk_c6, multiply(sk_c3, sk_c6))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[292, 21])).
% 0.21/0.48 tff(294,plain,
% 0.21/0.48 (multiply(sk_c6, multiply(sk_c3, sk_c6)) = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.21/0.48 inference(symmetry,[status(thm)],[293])).
% 0.21/0.48 tff(295,plain,
% 0.21/0.48 (multiply(sk_c6, multiply(sk_c3, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[279])).
% 0.21/0.48 tff(296,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c3, sk_c6))),
% 0.21/0.48 inference(symmetry,[status(thm)],[295])).
% 0.21/0.48 tff(297,plain,
% 0.21/0.48 (sk_c5 = multiply(sk_c6, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[289])).
% 0.21/0.48 tff(298,plain,
% 0.21/0.48 (sk_c5 = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.21/0.48 inference(transitivity,[status(thm)],[297, 296, 294])).
% 0.21/0.48 tff(299,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c5) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[298])).
% 0.21/0.48 tff(300,plain,
% 0.21/0.48 (multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6)) = multiply(sk_c3, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[299])).
% 0.21/0.48 tff(301,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(302,plain,
% 0.21/0.48 (multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[301, 21])).
% 0.21/0.48 tff(303,plain,
% 0.21/0.48 (sk_c6 = multiply(sk_c5, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[253])).
% 0.21/0.48 tff(304,plain,
% 0.21/0.48 (sk_c7 = inverse(sk_c3)),
% 0.21/0.48 inference(symmetry,[status(thm)],[229])).
% 0.21/0.48 tff(305,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c6) = inverse(sk_c3)),
% 0.21/0.48 inference(transitivity,[status(thm)],[279, 304])).
% 0.21/0.48 tff(306,plain,
% 0.21/0.48 (multiply(multiply(sk_c3, sk_c6), sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[305])).
% 0.21/0.48 tff(307,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c6), sk_c3) = multiply(sk_c3, multiply(sk_c6, sk_c3)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(308,plain,
% 0.21/0.48 (multiply(multiply(sk_c3, sk_c6), sk_c3) = multiply(sk_c3, multiply(sk_c6, sk_c3))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[307, 21])).
% 0.21/0.48 tff(309,plain,
% 0.21/0.48 (multiply(sk_c3, multiply(sk_c6, sk_c3)) = multiply(multiply(sk_c3, sk_c6), sk_c3)),
% 0.21/0.48 inference(symmetry,[status(thm)],[308])).
% 0.21/0.48 tff(310,plain,
% 0.21/0.48 (multiply(sk_c3, multiply(sk_c6, sk_c3)) = identity),
% 0.21/0.48 inference(transitivity,[status(thm)],[309, 306, 68])).
% 0.21/0.48 tff(311,plain,
% 0.21/0.48 (multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6) = multiply(identity, multiply(sk_c5, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[310, 303])).
% 0.21/0.48 tff(312,plain,
% 0.21/0.48 (multiply(identity, multiply(sk_c5, sk_c7)) = multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6)),
% 0.21/0.48 inference(symmetry,[status(thm)],[311])).
% 0.21/0.48 tff(313,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c5), sk_c7) = multiply(identity, multiply(sk_c5, sk_c7)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(314,plain,
% 0.21/0.48 (multiply(multiply(identity, sk_c5), sk_c7) = multiply(identity, multiply(sk_c5, sk_c7))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[313, 21])).
% 0.21/0.48 tff(315,plain,
% 0.21/0.48 (multiply(multiply(identity, sk_c5), sk_c7) = multiply(sk_c5, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[146])).
% 0.21/0.48 tff(316,plain,
% 0.21/0.48 (multiply(sk_c5, sk_c7) = multiply(multiply(identity, sk_c5), sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[315])).
% 0.21/0.48 tff(317,plain,
% 0.21/0.48 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c4, sk_c5) = sk_c7)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c4, sk_c5) = sk_c7))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(318,axiom,((inverse(sk_c7) = sk_c5) | (multiply(sk_c4, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_11')).
% 0.21/0.48 tff(319,plain,
% 0.21/0.48 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c4, sk_c5) = sk_c7)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.21/0.48 tff(320,plain,
% 0.21/0.48 (multiply(sk_c4, sk_c5) = sk_c7),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[319, 254])).
% 0.21/0.48 tff(321,plain,
% 0.21/0.48 (sk_c7 = multiply(sk_c4, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[320])).
% 0.21/0.48 tff(322,plain,
% 0.21/0.48 (multiply(sk_c5, sk_c7) = multiply(sk_c5, multiply(sk_c4, sk_c5))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[321])).
% 0.21/0.48 tff(323,plain,
% 0.21/0.48 (multiply(sk_c5, multiply(sk_c4, sk_c5)) = multiply(sk_c5, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[322])).
% 0.21/0.48 tff(324,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c4), sk_c5) = multiply(sk_c5, multiply(sk_c4, sk_c5)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(325,plain,
% 0.21/0.48 (multiply(multiply(sk_c5, sk_c4), sk_c5) = multiply(sk_c5, multiply(sk_c4, sk_c5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[324, 21])).
% 0.21/0.48 tff(326,plain,
% 0.21/0.48 (multiply(identity, sk_c5) = multiply(multiply(sk_c5, sk_c4), sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[268])).
% 0.21/0.48 tff(327,plain,
% 0.21/0.48 (sk_c5 = multiply(sk_c7, sk_c7)),
% 0.21/0.48 inference(transitivity,[status(thm)],[158, 326, 325, 323, 316, 314, 312, 302, 300, 291, 285, 282])).
% 0.21/0.48 tff(328,plain,
% 0.21/0.48 (multiply(sk_c7, sk_c5) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[327])).
% 0.21/0.48 tff(329,plain,
% 0.21/0.48 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(sk_c7, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[328])).
% 0.21/0.48 tff(330,plain,
% 0.21/0.48 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c4, sk_c5), multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[321])).
% 0.21/0.48 tff(331,plain,
% 0.21/0.48 (multiply(multiply(sk_c4, sk_c5), multiply(sk_c7, sk_c7)) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(symmetry,[status(thm)],[330])).
% 0.21/0.48 tff(332,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c5), multiply(sk_c7, sk_c7)) = multiply(sk_c4, multiply(sk_c5, multiply(sk_c7, sk_c7))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(333,plain,
% 0.21/0.48 (multiply(multiply(sk_c4, sk_c5), multiply(sk_c7, sk_c7)) = multiply(sk_c4, multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[332, 21])).
% 0.21/0.48 tff(334,plain,
% 0.21/0.48 (multiply(sk_c4, multiply(sk_c5, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c4, sk_c5), multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(symmetry,[status(thm)],[333])).
% 0.21/0.48 tff(335,plain,
% 0.21/0.48 (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[253])).
% 0.21/0.48 tff(336,plain,
% 0.21/0.48 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = sk_c5),
% 0.21/0.48 inference(transitivity,[status(thm)],[121, 335, 289])).
% 0.21/0.48 tff(337,plain,
% 0.21/0.48 (multiply(sk_c4, multiply(sk_c5, multiply(sk_c7, sk_c7))) = multiply(sk_c4, sk_c5)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[336])).
% 0.21/0.48 tff(338,plain,
% 0.21/0.48 (multiply(sk_c4, sk_c5) = multiply(sk_c4, multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.21/0.48 inference(symmetry,[status(thm)],[337])).
% 0.21/0.48 tff(339,plain,
% 0.21/0.48 (multiply(sk_c5, multiply(sk_c4, sk_c5)) = multiply(multiply(sk_c5, sk_c4), sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[325])).
% 0.21/0.48 tff(340,plain,
% 0.21/0.48 (sk_c6 = sk_c5),
% 0.21/0.48 inference(transitivity,[status(thm)],[303, 322, 339, 268, 146])).
% 0.21/0.48 tff(341,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c6) = multiply(sk_c3, sk_c5)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[340])).
% 0.21/0.48 tff(342,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c5) = multiply(sk_c3, sk_c6)),
% 0.21/0.48 inference(symmetry,[status(thm)],[341])).
% 0.21/0.48 tff(343,plain,
% 0.21/0.48 (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c7, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[320])).
% 0.21/0.48 tff(344,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c4, multiply(sk_c5, sk_c7)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(345,plain,
% 0.21/0.48 (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c4, multiply(sk_c5, sk_c7))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[344, 21])).
% 0.21/0.48 tff(346,plain,
% 0.21/0.48 (multiply(sk_c4, multiply(sk_c5, sk_c7)) = multiply(multiply(sk_c4, sk_c5), sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[345])).
% 0.21/0.48 tff(347,plain,
% 0.21/0.48 (multiply(sk_c4, sk_c6) = multiply(sk_c4, multiply(sk_c5, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[303])).
% 0.21/0.48 tff(348,plain,
% 0.21/0.48 (multiply(sk_c4, sk_c6) = multiply(sk_c7, sk_c5)),
% 0.21/0.48 inference(transitivity,[status(thm)],[347, 346, 343, 281, 284, 290, 342, 279, 321, 338, 334, 331, 329])).
% 0.21/0.48 tff(349,plain,
% 0.21/0.48 (multiply(inverse(sk_c7), multiply(sk_c4, sk_c6)) = multiply(inverse(sk_c7), multiply(sk_c7, sk_c5))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[348])).
% 0.21/0.48 tff(350,plain,
% 0.21/0.48 (multiply(sk_c4, multiply(sk_c5, sk_c7)) = multiply(sk_c4, sk_c6)),
% 0.21/0.48 inference(symmetry,[status(thm)],[347])).
% 0.21/0.48 tff(351,plain,
% 0.21/0.48 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c4, sk_c5), sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[343])).
% 0.21/0.48 tff(352,plain,
% 0.21/0.48 (sk_c7 = multiply(sk_c4, sk_c6)),
% 0.21/0.48 inference(transitivity,[status(thm)],[280, 341, 291, 285, 282, 351, 345, 350])).
% 0.21/0.48 tff(353,plain,
% 0.21/0.48 (multiply(inverse(sk_c7), sk_c7) = multiply(inverse(sk_c7), multiply(sk_c4, sk_c6))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[352])).
% 0.21/0.48 tff(354,plain,
% 0.21/0.48 (identity = inverse(sk_c4)),
% 0.21/0.48 inference(transitivity,[status(thm)],[66, 353, 349, 275, 272, 268, 146, 263])).
% 0.21/0.48 tff(355,plain,
% 0.21/0.48 (multiply(identity, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[354])).
% 0.21/0.48 tff(356,plain,
% 0.21/0.48 (multiply(inverse(sk_c4), sk_c4) = multiply(identity, sk_c4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[355])).
% 0.21/0.48 tff(357,plain,
% 0.21/0.48 (multiply(inverse(sk_c7), multiply(sk_c4, sk_c6)) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[353])).
% 0.21/0.48 tff(358,plain,
% 0.21/0.48 (multiply(inverse(sk_c7), multiply(sk_c7, sk_c5)) = multiply(inverse(sk_c7), multiply(sk_c4, sk_c6))),
% 0.21/0.48 inference(symmetry,[status(thm)],[349])).
% 0.21/0.48 tff(359,plain,
% 0.21/0.48 (multiply(multiply(sk_c5, sk_c4), sk_c5) = multiply(multiply(inverse(sk_c7), sk_c7), sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[272])).
% 0.21/0.48 tff(360,plain,
% 0.21/0.48 (multiply(identity, multiply(sk_c5, sk_c7)) = multiply(multiply(identity, sk_c5), sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[314])).
% 0.21/0.48 tff(361,plain,
% 0.21/0.48 (multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6)) = multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6)),
% 0.21/0.48 inference(symmetry,[status(thm)],[302])).
% 0.21/0.48 tff(362,plain,
% 0.21/0.48 (sk_c7 = sk_c4),
% 0.21/0.48 inference(transitivity,[status(thm)],[280, 341, 299, 361, 311, 360, 315, 322, 339, 359, 274, 358, 357, 42, 270, 356, 262])).
% 0.21/0.48 tff(363,plain,
% 0.21/0.48 (inverse(sk_c7) = inverse(sk_c4)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[362])).
% 0.21/0.48 tff(364,plain,
% 0.21/0.48 (inverse(sk_c7) = sk_c5),
% 0.21/0.48 inference(transitivity,[status(thm)],[363, 260])).
% 0.21/0.48 tff(365,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[254, 364])).
% 0.21/0.48 tff(366,plain,(inverse(sk_c7) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(367,plain,
% 0.21/0.48 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c5, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[366])).
% 0.21/0.48 tff(368,plain,
% 0.21/0.48 (identity = sk_c6),
% 0.21/0.48 inference(transitivity,[status(thm)],[66, 367, 253])).
% 0.21/0.48 tff(369,plain,
% 0.21/0.48 (multiply(identity, sk_c7) = multiply(sk_c6, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[368])).
% 0.21/0.48 tff(370,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[369])).
% 0.21/0.48 tff(371,plain,
% 0.21/0.48 (multiply(identity, sk_c5) = multiply(sk_c6, sk_c5)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[368])).
% 0.21/0.48 tff(372,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c5) = multiply(identity, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[371])).
% 0.21/0.48 tff(373,assumption,(~(multiply(sk_c6, sk_c7) = sk_c5)), introduced(assumption)).
% 0.21/0.48 tff(374,plain,
% 0.21/0.48 (((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(375,axiom,((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_1')).
% 0.21/0.48 tff(376,plain,
% 0.21/0.48 ((multiply(sk_c6, sk_c5) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.21/0.48 tff(377,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c5) = sk_c7),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[376, 373])).
% 0.21/0.48 tff(378,plain,
% 0.21/0.48 (sk_c7 = multiply(sk_c6, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[377])).
% 0.21/0.48 tff(379,plain,
% 0.21/0.48 (multiply(sk_c5, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[367])).
% 0.21/0.48 tff(380,plain,
% 0.21/0.48 (sk_c6 = identity),
% 0.21/0.48 inference(transitivity,[status(thm)],[303, 379, 42])).
% 0.21/0.48 tff(381,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[380])).
% 0.21/0.48 tff(382,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.21/0.48 inference(transitivity,[status(thm)],[381, 78, 378, 372, 146])).
% 0.21/0.48 tff(383,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[373, 382])).
% 0.21/0.48 tff(384,plain,(multiply(sk_c6, sk_c7) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(385,plain,
% 0.21/0.48 (sk_c7 = sk_c5),
% 0.21/0.48 inference(transitivity,[status(thm)],[127, 369, 384])).
% 0.21/0.48 tff(386,plain,
% 0.21/0.48 (multiply(sk_c7, sk_c7) = multiply(sk_c5, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[385])).
% 0.21/0.48 tff(387,plain,
% 0.21/0.48 (multiply(sk_c5, sk_c7) = multiply(sk_c7, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[386])).
% 0.21/0.48 tff(388,plain,
% 0.21/0.48 (sk_c6 = multiply(sk_c7, sk_c7)),
% 0.21/0.48 inference(transitivity,[status(thm)],[303, 387])).
% 0.21/0.48 tff(389,plain,
% 0.21/0.48 (multiply(sk_c7, sk_c6) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[385, 388])).
% 0.21/0.48 tff(390,assumption,(~(multiply(sk_c7, sk_c2) = sk_c6)), introduced(assumption)).
% 0.21/0.48 tff(391,plain,
% 0.21/0.48 (((inverse(sk_c4) = sk_c5) | (multiply(sk_c7, sk_c2) = sk_c6)) <=> ((inverse(sk_c4) = sk_c5) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(392,plain,
% 0.21/0.48 (((multiply(sk_c7, sk_c2) = sk_c6) | (inverse(sk_c4) = sk_c5)) <=> ((inverse(sk_c4) = sk_c5) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(393,axiom,((multiply(sk_c7, sk_c2) = sk_c6) | (inverse(sk_c4) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_18')).
% 0.21/0.48 tff(394,plain,
% 0.21/0.48 ((inverse(sk_c4) = sk_c5) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.21/0.48 tff(395,plain,
% 0.21/0.48 ((inverse(sk_c4) = sk_c5) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[394, 391])).
% 0.21/0.48 tff(396,plain,
% 0.21/0.48 (inverse(sk_c4) = sk_c5),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[395, 390])).
% 0.21/0.48 tff(397,plain,
% 0.21/0.48 (sk_c5 = inverse(sk_c4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[396])).
% 0.21/0.48 tff(398,plain,
% 0.21/0.48 (multiply(sk_c5, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[397])).
% 0.21/0.48 tff(399,plain,
% 0.21/0.48 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c5, sk_c4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[398])).
% 0.21/0.48 tff(400,plain,
% 0.21/0.48 (identity = multiply(sk_c5, sk_c4)),
% 0.21/0.48 inference(transitivity,[status(thm)],[270, 399])).
% 0.21/0.48 tff(401,plain,
% 0.21/0.48 (multiply(identity, sk_c5) = multiply(multiply(sk_c5, sk_c4), sk_c5)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[400])).
% 0.21/0.48 tff(402,plain,
% 0.21/0.48 (multiply(multiply(sk_c5, sk_c4), sk_c5) = multiply(identity, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[401])).
% 0.21/0.48 tff(403,plain,
% 0.21/0.48 (((multiply(sk_c4, sk_c5) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6)) <=> ((multiply(sk_c4, sk_c5) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(404,plain,
% 0.21/0.48 (((multiply(sk_c7, sk_c2) = sk_c6) | (multiply(sk_c4, sk_c5) = sk_c7)) <=> ((multiply(sk_c4, sk_c5) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(405,axiom,((multiply(sk_c7, sk_c2) = sk_c6) | (multiply(sk_c4, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_17')).
% 0.21/0.48 tff(406,plain,
% 0.21/0.48 ((multiply(sk_c4, sk_c5) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.21/0.48 tff(407,plain,
% 0.21/0.48 ((multiply(sk_c4, sk_c5) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[406, 403])).
% 0.21/0.48 tff(408,plain,
% 0.21/0.48 (multiply(sk_c4, sk_c5) = sk_c7),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[407, 390])).
% 0.21/0.48 tff(409,plain,
% 0.21/0.48 (sk_c7 = multiply(sk_c4, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[408])).
% 0.21/0.48 tff(410,plain,
% 0.21/0.48 (multiply(sk_c5, sk_c7) = multiply(sk_c5, multiply(sk_c4, sk_c5))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[409])).
% 0.21/0.48 tff(411,plain,
% 0.21/0.48 (((multiply(sk_c3, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6)) <=> ((multiply(sk_c3, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(412,plain,
% 0.21/0.48 (((multiply(sk_c7, sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((multiply(sk_c3, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(413,axiom,((multiply(sk_c7, sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_16')).
% 0.21/0.48 tff(414,plain,
% 0.21/0.48 ((multiply(sk_c3, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.21/0.48 tff(415,plain,
% 0.21/0.48 ((multiply(sk_c3, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[414, 411])).
% 0.21/0.48 tff(416,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c6) = sk_c7),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[415, 390])).
% 0.21/0.48 tff(417,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c6) = inverse(sk_c3)),
% 0.21/0.48 inference(transitivity,[status(thm)],[416, 304])).
% 0.21/0.48 tff(418,plain,
% 0.21/0.48 (multiply(multiply(sk_c3, sk_c6), sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[417])).
% 0.21/0.48 tff(419,plain,
% 0.21/0.48 (multiply(sk_c3, multiply(sk_c6, sk_c3)) = identity),
% 0.21/0.48 inference(transitivity,[status(thm)],[309, 418, 68])).
% 0.21/0.48 tff(420,plain,
% 0.21/0.48 (multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6) = multiply(identity, multiply(sk_c5, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[419, 303])).
% 0.21/0.48 tff(421,plain,
% 0.21/0.48 (multiply(sk_c6, multiply(sk_c3, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[416])).
% 0.21/0.48 tff(422,plain,
% 0.21/0.48 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c3, sk_c6))),
% 0.21/0.48 inference(symmetry,[status(thm)],[421])).
% 0.21/0.48 tff(423,plain,
% 0.21/0.48 (((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c2) = sk_c6)) <=> ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(424,plain,
% 0.21/0.49 (((multiply(sk_c7, sk_c2) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c2) = sk_c6))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(425,axiom,((multiply(sk_c7, sk_c2) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_13')).
% 0.21/0.49 tff(426,plain,
% 0.21/0.49 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.21/0.49 tff(427,plain,
% 0.21/0.49 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c2) = sk_c6)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[426, 423])).
% 0.21/0.49 tff(428,plain,
% 0.21/0.49 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[427, 390])).
% 0.21/0.49 tff(429,plain,
% 0.21/0.49 (sk_c5 = multiply(sk_c6, sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[428])).
% 0.21/0.49 tff(430,plain,
% 0.21/0.49 (sk_c5 = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.21/0.49 inference(transitivity,[status(thm)],[429, 422, 294])).
% 0.21/0.49 tff(431,plain,
% 0.21/0.49 (multiply(sk_c3, sk_c5) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[430])).
% 0.21/0.49 tff(432,plain,
% 0.21/0.49 (sk_c6 = sk_c5),
% 0.21/0.49 inference(transitivity,[status(thm)],[303, 410, 339, 402, 146])).
% 0.21/0.49 tff(433,plain,
% 0.21/0.49 (multiply(sk_c3, sk_c6) = multiply(sk_c3, sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[432])).
% 0.21/0.49 tff(434,plain,
% 0.21/0.49 (sk_c7 = multiply(sk_c3, sk_c6)),
% 0.21/0.49 inference(symmetry,[status(thm)],[416])).
% 0.21/0.49 tff(435,plain,
% 0.21/0.49 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c3) = sk_c3)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(436,plain,
% 0.21/0.49 (multiply(identity, sk_c3) = sk_c3),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[435, 76])).
% 0.21/0.49 tff(437,plain,
% 0.21/0.49 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[304])).
% 0.21/0.49 tff(438,plain,
% 0.21/0.49 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c7, sk_c3)),
% 0.21/0.49 inference(symmetry,[status(thm)],[437])).
% 0.21/0.49 tff(439,plain,
% 0.21/0.49 (identity = multiply(sk_c7, sk_c3)),
% 0.21/0.49 inference(transitivity,[status(thm)],[250, 438])).
% 0.21/0.49 tff(440,plain,
% 0.21/0.49 (multiply(sk_c5, identity) = multiply(sk_c5, multiply(sk_c7, sk_c3))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[439])).
% 0.21/0.49 tff(441,plain,
% 0.21/0.49 (multiply(sk_c5, multiply(sk_c7, sk_c3)) = multiply(sk_c5, identity)),
% 0.21/0.49 inference(symmetry,[status(thm)],[440])).
% 0.21/0.49 tff(442,plain,
% 0.21/0.49 (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c7, sk_c7)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[408])).
% 0.21/0.49 tff(443,plain,
% 0.21/0.49 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c4, sk_c5), sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[442])).
% 0.21/0.49 tff(444,plain,
% 0.21/0.49 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c3, sk_c6), sk_c7)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[434])).
% 0.21/0.49 tff(445,plain,
% 0.21/0.49 (multiply(multiply(sk_c3, sk_c6), sk_c7) = multiply(sk_c7, sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[444])).
% 0.21/0.49 tff(446,plain,
% 0.21/0.49 (multiply(sk_c3, multiply(sk_c6, sk_c7)) = multiply(sk_c3, sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[428])).
% 0.21/0.49 tff(447,plain,
% 0.21/0.49 (multiply(sk_c3, sk_c5) = multiply(sk_c3, multiply(sk_c6, sk_c7))),
% 0.21/0.49 inference(symmetry,[status(thm)],[446])).
% 0.21/0.49 tff(448,plain,
% 0.21/0.49 (multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6)) = multiply(sk_c3, sk_c5)),
% 0.21/0.49 inference(symmetry,[status(thm)],[431])).
% 0.21/0.49 tff(449,plain,
% 0.21/0.49 (multiply(identity, multiply(sk_c5, sk_c7)) = multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6)),
% 0.21/0.49 inference(symmetry,[status(thm)],[420])).
% 0.21/0.49 tff(450,plain,
% 0.21/0.49 (multiply(sk_c5, multiply(sk_c4, sk_c5)) = multiply(sk_c5, sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[410])).
% 0.21/0.49 tff(451,plain,
% 0.21/0.49 (sk_c5 = multiply(sk_c4, sk_c6)),
% 0.21/0.49 inference(transitivity,[status(thm)],[158, 401, 325, 450, 316, 314, 449, 302, 448, 447, 285, 445, 443, 345, 350])).
% 0.21/0.49 tff(452,plain,
% 0.21/0.49 (multiply(sk_c5, multiply(sk_c7, sk_c3)) = multiply(multiply(sk_c4, sk_c6), multiply(sk_c7, sk_c3))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[451])).
% 0.21/0.49 tff(453,plain,
% 0.21/0.49 (multiply(multiply(sk_c4, sk_c6), multiply(sk_c7, sk_c3)) = multiply(sk_c5, multiply(sk_c7, sk_c3))),
% 0.21/0.49 inference(symmetry,[status(thm)],[452])).
% 0.21/0.49 tff(454,plain,
% 0.21/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c4, sk_c6), sk_c7), sk_c3) = multiply(multiply(sk_c4, sk_c6), multiply(sk_c7, sk_c3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(455,plain,
% 0.21/0.49 (multiply(multiply(multiply(sk_c4, sk_c6), sk_c7), sk_c3) = multiply(multiply(sk_c4, sk_c6), multiply(sk_c7, sk_c3))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[454, 21])).
% 0.21/0.49 tff(456,plain,
% 0.21/0.49 (multiply(sk_c4, multiply(sk_c6, sk_c7)) = multiply(sk_c4, sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[428])).
% 0.21/0.49 tff(457,plain,
% 0.21/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c6), sk_c7) = multiply(sk_c4, multiply(sk_c6, sk_c7)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(458,plain,
% 0.21/0.49 (multiply(multiply(sk_c4, sk_c6), sk_c7) = multiply(sk_c4, multiply(sk_c6, sk_c7))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[457, 21])).
% 0.21/0.49 tff(459,plain,
% 0.21/0.49 (multiply(multiply(sk_c4, sk_c6), sk_c7) = inverse(sk_c3)),
% 0.21/0.49 inference(transitivity,[status(thm)],[458, 456, 408, 304])).
% 0.21/0.49 tff(460,plain,
% 0.21/0.49 (multiply(multiply(multiply(sk_c4, sk_c6), sk_c7), sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[459])).
% 0.21/0.49 tff(461,plain,
% 0.21/0.49 (multiply(inverse(sk_c3), sk_c3) = multiply(multiply(multiply(sk_c4, sk_c6), sk_c7), sk_c3)),
% 0.21/0.49 inference(symmetry,[status(thm)],[460])).
% 0.21/0.49 tff(462,plain,
% 0.21/0.49 (identity = multiply(sk_c5, identity)),
% 0.21/0.49 inference(transitivity,[status(thm)],[250, 461, 455, 453, 441])).
% 0.21/0.49 tff(463,plain,
% 0.21/0.49 (multiply(identity, sk_c3) = multiply(multiply(sk_c5, identity), sk_c3)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[462])).
% 0.21/0.49 tff(464,plain,
% 0.21/0.49 (multiply(multiply(sk_c5, identity), sk_c3) = multiply(identity, sk_c3)),
% 0.21/0.49 inference(symmetry,[status(thm)],[463])).
% 0.21/0.49 tff(465,plain,
% 0.21/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, identity), sk_c3) = multiply(sk_c5, multiply(identity, sk_c3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(466,plain,
% 0.21/0.49 (multiply(multiply(sk_c5, identity), sk_c3) = multiply(sk_c5, multiply(identity, sk_c3))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[465, 21])).
% 0.21/0.49 tff(467,plain,
% 0.21/0.49 (multiply(sk_c5, multiply(identity, sk_c3)) = multiply(multiply(sk_c5, identity), sk_c3)),
% 0.21/0.49 inference(symmetry,[status(thm)],[466])).
% 0.21/0.49 tff(468,plain,
% 0.21/0.49 (multiply(sk_c5, multiply(identity, sk_c3)) = multiply(sk_c5, sk_c3)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[436])).
% 0.21/0.49 tff(469,plain,
% 0.21/0.49 (multiply(sk_c5, sk_c3) = multiply(sk_c5, multiply(identity, sk_c3))),
% 0.21/0.49 inference(symmetry,[status(thm)],[468])).
% 0.21/0.49 tff(470,plain,
% 0.21/0.49 (sk_c5 = sk_c6),
% 0.21/0.49 inference(transitivity,[status(thm)],[158, 401, 325, 450, 253])).
% 0.21/0.49 tff(471,plain,
% 0.21/0.49 (multiply(sk_c5, sk_c3) = multiply(sk_c6, sk_c3)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[470])).
% 0.21/0.49 tff(472,plain,
% 0.21/0.49 (multiply(sk_c6, sk_c3) = multiply(sk_c5, sk_c3)),
% 0.21/0.49 inference(symmetry,[status(thm)],[471])).
% 0.21/0.49 tff(473,plain,
% 0.21/0.49 (multiply(sk_c6, sk_c3) = multiply(multiply(sk_c5, sk_c7), sk_c3)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[303])).
% 0.21/0.49 tff(474,plain,
% 0.21/0.49 (multiply(multiply(sk_c5, sk_c7), sk_c3) = multiply(sk_c6, sk_c3)),
% 0.21/0.49 inference(symmetry,[status(thm)],[473])).
% 0.21/0.49 tff(475,plain,
% 0.21/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c7), sk_c3) = multiply(sk_c5, multiply(sk_c7, sk_c3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(476,plain,
% 0.21/0.49 (multiply(multiply(sk_c5, sk_c7), sk_c3) = multiply(sk_c5, multiply(sk_c7, sk_c3))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[475, 21])).
% 0.21/0.49 tff(477,plain,
% 0.21/0.49 (multiply(sk_c5, multiply(sk_c7, sk_c3)) = multiply(multiply(sk_c5, sk_c7), sk_c3)),
% 0.21/0.49 inference(symmetry,[status(thm)],[476])).
% 0.21/0.49 tff(478,plain,
% 0.21/0.49 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c5), sk_c5) = identity)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(479,plain,
% 0.21/0.49 (multiply(inverse(sk_c5), sk_c5) = identity),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[478, 37])).
% 0.21/0.49 tff(480,plain,
% 0.21/0.49 (sk_c5 = multiply(sk_c7, sk_c7)),
% 0.21/0.49 inference(transitivity,[status(thm)],[158, 401, 325, 450, 316, 314, 449, 302, 448, 447, 285, 445])).
% 0.21/0.49 tff(481,plain,
% 0.21/0.49 (multiply(sk_c6, sk_c5) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[432, 480])).
% 0.21/0.49 tff(482,plain,
% 0.21/0.49 (multiply(sk_c5, sk_c5) = multiply(sk_c6, sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[470])).
% 0.21/0.49 tff(483,plain,
% 0.21/0.49 (multiply(sk_c5, sk_c5) = sk_c5),
% 0.21/0.49 inference(transitivity,[status(thm)],[482, 481, 121, 335, 428])).
% 0.21/0.49 tff(484,plain,
% 0.21/0.49 (multiply(sk_c3, sk_c5) = multiply(sk_c3, sk_c6)),
% 0.21/0.49 inference(symmetry,[status(thm)],[433])).
% 0.21/0.49 tff(485,plain,
% 0.21/0.49 (sk_c5 = sk_c7),
% 0.21/0.49 inference(transitivity,[status(thm)],[158, 401, 325, 450, 316, 314, 449, 302, 448, 484, 416])).
% 0.21/0.49 tff(486,plain,
% 0.21/0.49 (inverse(sk_c5) = inverse(sk_c7)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[485])).
% 0.21/0.49 tff(487,plain,
% 0.21/0.49 (inverse(sk_c7) = inverse(sk_c5)),
% 0.21/0.49 inference(symmetry,[status(thm)],[486])).
% 0.21/0.49 tff(488,plain,
% 0.21/0.49 (multiply(inverse(sk_c7), multiply(sk_c5, sk_c5)) = multiply(inverse(sk_c5), sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[487, 483])).
% 0.21/0.49 tff(489,plain,
% 0.21/0.49 ((~![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)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(490,plain,
% 0.21/0.49 (multiply(multiply(inverse(sk_c7), sk_c5), sk_c5) = multiply(inverse(sk_c7), multiply(sk_c5, sk_c5))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[489, 21])).
% 0.21/0.49 tff(491,plain,
% 0.21/0.49 (multiply(inverse(sk_c7), sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[487])).
% 0.21/0.49 tff(492,plain,
% 0.21/0.49 (multiply(inverse(sk_c5), sk_c5) = multiply(inverse(sk_c7), sk_c5)),
% 0.21/0.49 inference(symmetry,[status(thm)],[491])).
% 0.21/0.49 tff(493,plain,
% 0.21/0.49 (identity = multiply(inverse(sk_c5), sk_c5)),
% 0.21/0.49 inference(symmetry,[status(thm)],[479])).
% 0.21/0.49 tff(494,plain,
% 0.21/0.49 (multiply(sk_c5, sk_c4) = multiply(inverse(sk_c7), sk_c5)),
% 0.21/0.49 inference(transitivity,[status(thm)],[398, 265, 493, 492])).
% 0.21/0.49 tff(495,plain,
% 0.21/0.49 (multiply(multiply(sk_c5, sk_c4), sk_c5) = multiply(multiply(inverse(sk_c7), sk_c5), sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[494])).
% 0.21/0.49 tff(496,plain,
% 0.21/0.49 (sk_c7 = sk_c3),
% 0.21/0.49 inference(transitivity,[status(thm)],[434, 433, 431, 361, 420, 360, 315, 410, 339, 495, 490, 488, 479, 250, 461, 455, 453, 477, 474, 472, 469, 467, 464, 436])).
% 0.21/0.49 tff(497,plain,
% 0.21/0.49 (inverse(sk_c7) = inverse(sk_c3)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[496])).
% 0.21/0.49 tff(498,plain,
% 0.21/0.49 (inverse(sk_c7) = sk_c5),
% 0.21/0.49 inference(transitivity,[status(thm)],[497, 229, 434, 433, 431, 361, 420, 360, 315, 410, 339, 402, 146])).
% 0.21/0.49 tff(499,plain,
% 0.21/0.49 (sk_c7 = sk_c5),
% 0.21/0.49 inference(transitivity,[status(thm)],[434, 433, 431, 361, 420, 360, 315, 410, 339, 402, 146])).
% 0.21/0.49 tff(500,plain,
% 0.21/0.49 (multiply(sk_c3, sk_c7) = multiply(sk_c3, sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[499])).
% 0.21/0.49 tff(501,plain,
% 0.21/0.49 (multiply(sk_c3, sk_c7) = sk_c5),
% 0.21/0.49 inference(transitivity,[status(thm)],[500, 431, 361, 420, 360, 315, 410, 339, 402, 146])).
% 0.21/0.49 tff(502,plain,
% 0.21/0.49 (sk_c7 = sk_c6),
% 0.21/0.49 inference(transitivity,[status(thm)],[434, 433, 431, 361, 420, 360, 315, 253])).
% 0.21/0.49 tff(503,plain,
% 0.21/0.49 (multiply(sk_c7, multiply(sk_c3, sk_c7)) = multiply(sk_c6, sk_c5)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[502, 501])).
% 0.21/0.49 tff(504,plain,
% 0.21/0.49 (multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6),
% 0.21/0.49 inference(transitivity,[status(thm)],[503, 481, 121, 335, 428, 158, 401, 325, 450, 253])).
% 0.21/0.49 tff(505,plain,
% 0.21/0.49 (multiply(sk_c3, sk_c5) = multiply(sk_c4, sk_c6)),
% 0.21/0.49 inference(transitivity,[status(thm)],[447, 285, 445, 443, 345, 350])).
% 0.21/0.49 tff(506,plain,
% 0.21/0.49 ((multiply(sk_c3, sk_c5) = sk_c7) <=> (multiply(sk_c4, sk_c6) = sk_c7)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[505])).
% 0.21/0.49 tff(507,plain,
% 0.21/0.49 ((multiply(sk_c4, sk_c6) = sk_c7) <=> (multiply(sk_c3, sk_c5) = sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[506])).
% 0.21/0.49 tff(508,plain,
% 0.21/0.49 ((sk_c5 = inverse(sk_c3)) <=> (inverse(sk_c3) = sk_c5)),
% 0.21/0.49 inference(commutativity,[status(thm)],[])).
% 0.21/0.49 tff(509,plain,
% 0.21/0.49 (multiply(sk_c4, sk_c6) = sk_c5),
% 0.21/0.49 inference(transitivity,[status(thm)],[347, 346, 442, 444, 284, 446, 431, 361, 420, 360, 315, 410, 339, 402, 146])).
% 0.21/0.49 tff(510,plain,
% 0.21/0.49 ((multiply(sk_c4, sk_c6) = sk_c7) <=> (sk_c5 = inverse(sk_c3))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[509, 304])).
% 0.21/0.49 tff(511,plain,
% 0.21/0.49 ((multiply(sk_c4, sk_c6) = sk_c7) <=> (inverse(sk_c3) = sk_c5)),
% 0.21/0.49 inference(transitivity,[status(thm)],[510, 508])).
% 0.21/0.49 tff(512,plain,
% 0.21/0.49 ((inverse(sk_c3) = sk_c5) <=> (multiply(sk_c4, sk_c6) = sk_c7)),
% 0.21/0.49 inference(symmetry,[status(thm)],[511])).
% 0.21/0.49 tff(513,plain,
% 0.21/0.49 ((inverse(sk_c3) = sk_c5) <=> (multiply(sk_c3, sk_c5) = sk_c7)),
% 0.21/0.49 inference(transitivity,[status(thm)],[512, 507])).
% 0.21/0.49 tff(514,plain,
% 0.21/0.49 (inverse(sk_c3) = sk_c5),
% 0.21/0.49 inference(transitivity,[status(thm)],[229, 434, 433, 431, 361, 420, 360, 315, 410, 339, 402, 146])).
% 0.21/0.49 tff(515,plain,
% 0.21/0.49 (multiply(sk_c3, sk_c5) = sk_c7),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.21/0.49 tff(516,plain,
% 0.21/0.49 (multiply(sk_c6, sk_c5) = sk_c7),
% 0.21/0.49 inference(transitivity,[status(thm)],[481, 121, 335, 428, 158, 401, 325, 450, 316, 314, 449, 302, 448, 484, 416])).
% 0.21/0.49 tff(517,plain,
% 0.21/0.49 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c5)) | (~(multiply(sk_c3, sk_c5) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c5)) | (~(multiply(sk_c3, sk_c5) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(518,plain,
% 0.21/0.49 (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c5)) | (~(multiply(sk_c3, sk_c5) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6)) | (~(inverse(sk_c3) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c5)) | (~(multiply(sk_c3, sk_c5) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(519,plain,
% 0.21/0.49 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c5)) | (~(multiply(sk_c3, sk_c5) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c5)) | (~(multiply(sk_c3, sk_c5) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6)) | (~(inverse(sk_c3) = sk_c7))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[518])).
% 0.21/0.49 tff(520,plain,
% 0.21/0.49 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c5)) | (~(multiply(sk_c3, sk_c5) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c5)) | (~(multiply(sk_c3, sk_c5) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[519, 517])).
% 0.21/0.49 tff(521,plain,
% 0.21/0.49 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c5)) | (~(multiply(sk_c3, sk_c5) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(522,plain,
% 0.21/0.49 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c5)) | (~(multiply(sk_c3, sk_c5) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6)) | (~(inverse(sk_c3) = sk_c7))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[521, 520])).
% 0.21/0.50 tff(523,plain,
% 0.21/0.50 ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c5)) | (~(multiply(sk_c3, sk_c5) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c3, sk_c7)) = sk_c6))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[522, 229, 220])).
% 0.21/0.50 tff(524,plain,
% 0.21/0.50 (~(inverse(sk_c7) = sk_c5)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[523, 516, 253, 416, 428, 514, 515, 504])).
% 0.21/0.50 tff(525,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[524, 498])).
% 0.21/0.50 tff(526,plain,(multiply(sk_c7, sk_c2) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(527,plain,
% 0.21/0.50 (sk_c5 = multiply(sk_c6, sk_c7)),
% 0.21/0.50 inference(symmetry,[status(thm)],[384])).
% 0.21/0.50 tff(528,plain,
% 0.21/0.50 (sk_c5 = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[527, 370, 78])).
% 0.21/0.50 tff(529,plain,
% 0.21/0.50 (multiply(sk_c5, sk_c2) = multiply(sk_c7, sk_c2)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[528])).
% 0.21/0.50 tff(530,plain,
% 0.21/0.50 (multiply(sk_c5, sk_c2) = sk_c6),
% 0.21/0.50 inference(transitivity,[status(thm)],[529, 526])).
% 0.21/0.50 tff(531,plain,
% 0.21/0.50 (multiply(sk_c5, multiply(sk_c5, sk_c2)) = multiply(sk_c7, sk_c6)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[528, 530])).
% 0.21/0.50 tff(532,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c5), sk_c2) = multiply(sk_c5, multiply(sk_c5, sk_c2)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(533,plain,
% 0.21/0.50 (multiply(multiply(sk_c5, sk_c5), sk_c2) = multiply(sk_c5, multiply(sk_c5, sk_c2))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[532, 21])).
% 0.21/0.50 tff(534,plain,
% 0.21/0.50 (multiply(sk_c5, sk_c5) = multiply(sk_c5, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[528])).
% 0.21/0.50 tff(535,plain,
% 0.21/0.50 (multiply(sk_c5, sk_c7) = multiply(sk_c5, sk_c5)),
% 0.21/0.50 inference(symmetry,[status(thm)],[534])).
% 0.21/0.50 tff(536,plain,
% 0.21/0.50 (sk_c6 = multiply(sk_c5, sk_c5)),
% 0.21/0.50 inference(transitivity,[status(thm)],[303, 535])).
% 0.21/0.50 tff(537,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c2) = multiply(multiply(sk_c5, sk_c5), sk_c2)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[536])).
% 0.21/0.50 tff(538,plain,
% 0.21/0.50 (multiply(identity, sk_c2) = multiply(sk_c6, sk_c2)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[368])).
% 0.21/0.50 tff(539,plain,
% 0.21/0.50 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[385])).
% 0.21/0.50 tff(540,plain,
% 0.21/0.50 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(symmetry,[status(thm)],[539])).
% 0.21/0.50 tff(541,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c7) = multiply(multiply(sk_c5, sk_c7), sk_c7)),
% 0.21/0.50 inference(symmetry,[status(thm)],[335])).
% 0.21/0.50 tff(542,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c5) = multiply(sk_c6, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[528])).
% 0.21/0.50 tff(543,assumption,(~(inverse(sk_c4) = sk_c5)), introduced(assumption)).
% 0.21/0.50 tff(544,plain,
% 0.21/0.50 (((inverse(sk_c4) = sk_c5) | (multiply(sk_c1, sk_c7) = sk_c2)) <=> ((inverse(sk_c4) = sk_c5) | (multiply(sk_c1, sk_c7) = sk_c2))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(545,plain,
% 0.21/0.50 (((multiply(sk_c1, sk_c7) = sk_c2) | (inverse(sk_c4) = sk_c5)) <=> ((inverse(sk_c4) = sk_c5) | (multiply(sk_c1, sk_c7) = sk_c2))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(546,axiom,((multiply(sk_c1, sk_c7) = sk_c2) | (inverse(sk_c4) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_24')).
% 0.21/0.50 tff(547,plain,
% 0.21/0.50 ((inverse(sk_c4) = sk_c5) | (multiply(sk_c1, sk_c7) = sk_c2)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.21/0.50 tff(548,plain,
% 0.21/0.50 ((inverse(sk_c4) = sk_c5) | (multiply(sk_c1, sk_c7) = sk_c2)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[547, 544])).
% 0.21/0.50 tff(549,plain,
% 0.21/0.50 (multiply(sk_c1, sk_c7) = sk_c2),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[548, 543])).
% 0.21/0.50 tff(550,plain,
% 0.21/0.50 (multiply(sk_c1, sk_c5) = multiply(sk_c1, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[528])).
% 0.21/0.50 tff(551,plain,
% 0.21/0.50 (multiply(sk_c1, sk_c5) = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[550, 549, 195, 538, 537, 533, 531, 389, 121, 335, 370, 78])).
% 0.21/0.50 tff(552,plain,
% 0.21/0.50 (multiply(sk_c1, sk_c7) = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[549, 195, 538, 537, 533, 531, 389, 121, 335, 370, 78])).
% 0.21/0.50 tff(553,plain,
% 0.21/0.50 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c5, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[385, 552])).
% 0.21/0.50 tff(554,plain,
% 0.21/0.50 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6),
% 0.21/0.50 inference(transitivity,[status(thm)],[553, 253])).
% 0.21/0.50 tff(555,plain,
% 0.21/0.50 ((inverse(sk_c5) = sk_c7) <=> (inverse(sk_c5) = sk_c5)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[385])).
% 0.21/0.50 tff(556,plain,
% 0.21/0.50 ((inverse(sk_c5) = sk_c5) <=> (inverse(sk_c5) = sk_c7)),
% 0.21/0.50 inference(symmetry,[status(thm)],[555])).
% 0.21/0.50 tff(557,plain,
% 0.21/0.50 (inverse(sk_c5) = inverse(sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[528])).
% 0.21/0.50 tff(558,plain,
% 0.21/0.50 (inverse(sk_c5) = sk_c5),
% 0.21/0.50 inference(transitivity,[status(thm)],[557, 366])).
% 0.21/0.50 tff(559,plain,
% 0.21/0.50 (inverse(sk_c5) = sk_c7),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[558, 556])).
% 0.21/0.50 tff(560,plain,
% 0.21/0.50 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c5)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c5))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(561,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_30')).
% 0.21/0.50 tff(562,plain,
% 0.21/0.50 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c5)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.21/0.50 tff(563,plain,
% 0.21/0.50 (inverse(sk_c1) = sk_c7),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[562, 543])).
% 0.21/0.50 tff(564,plain,
% 0.21/0.50 (inverse(sk_c1) = sk_c5),
% 0.21/0.50 inference(transitivity,[status(thm)],[563, 127, 369, 384])).
% 0.21/0.50 tff(565,plain,
% 0.21/0.50 (multiply(sk_c5, sk_c6) = multiply(sk_c7, sk_c6)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[528])).
% 0.21/0.50 tff(566,plain,
% 0.21/0.50 (multiply(sk_c5, sk_c6) = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[565, 389, 121, 335, 370, 78])).
% 0.21/0.50 tff(567,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c7) = multiply(sk_c6, sk_c5)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[385])).
% 0.21/0.50 tff(568,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c5) = multiply(sk_c6, sk_c7)),
% 0.21/0.50 inference(symmetry,[status(thm)],[567])).
% 0.21/0.50 tff(569,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c5) = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[568, 370, 78])).
% 0.21/0.50 tff(570,plain,
% 0.21/0.50 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(571,plain,
% 0.21/0.50 (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c1) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(572,plain,
% 0.21/0.50 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[571])).
% 0.21/0.50 tff(573,plain,
% 0.21/0.50 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[572, 570])).
% 0.21/0.50 tff(574,plain,
% 0.21/0.50 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(575,plain,
% 0.21/0.50 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c5)) | (~(multiply(sk_c1, sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.21/0.50 tff(576,plain,
% 0.21/0.50 ((~(multiply(sk_c1, sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c1, sk_c7)) = sk_c6)) | (~(inverse(sk_c5) = sk_c7))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[575, 569, 384, 253, 366, 563, 220, 566, 564])).
% 0.21/0.50 tff(577,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[576, 559, 554, 551])).
% 0.21/0.50 tff(578,plain,(inverse(sk_c4) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(579,plain,
% 0.21/0.50 (sk_c5 = inverse(sk_c4)),
% 0.21/0.50 inference(symmetry,[status(thm)],[578])).
% 0.21/0.50 tff(580,plain,
% 0.21/0.50 (multiply(sk_c5, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[579])).
% 0.21/0.50 tff(581,plain,
% 0.21/0.50 (multiply(sk_c5, sk_c4) = sk_c6),
% 0.21/0.50 inference(transitivity,[status(thm)],[580, 265, 66, 367, 253])).
% 0.21/0.50 tff(582,plain,
% 0.21/0.50 (multiply(multiply(sk_c5, sk_c4), sk_c5) = multiply(sk_c6, sk_c5)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[581])).
% 0.21/0.50 tff(583,plain,
% 0.21/0.50 (multiply(sk_c4, sk_c7) = multiply(sk_c4, sk_c5)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[385])).
% 0.21/0.50 tff(584,plain,
% 0.21/0.50 (multiply(sk_c7, multiply(sk_c4, sk_c7)) = multiply(sk_c5, multiply(sk_c4, sk_c5))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[385, 583])).
% 0.21/0.50 tff(585,plain,
% 0.21/0.50 (multiply(sk_c7, multiply(sk_c4, sk_c7)) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(transitivity,[status(thm)],[584, 339, 582, 542, 541, 120, 540])).
% 0.21/0.50 tff(586,plain,
% 0.21/0.50 ((multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6) <=> (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[585])).
% 0.21/0.50 tff(587,plain,
% 0.21/0.50 ((multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6) <=> (multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)),
% 0.21/0.50 inference(symmetry,[status(thm)],[586])).
% 0.21/0.50 tff(588,plain,
% 0.21/0.50 ((sk_c6 = multiply(sk_c7, multiply(sk_c7, sk_c7))) <=> (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)),
% 0.21/0.50 inference(commutativity,[status(thm)],[])).
% 0.21/0.50 tff(589,plain,
% 0.21/0.50 (sk_c7 = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.21/0.50 inference(transitivity,[status(thm)],[127, 369, 541, 120, 540])).
% 0.21/0.50 tff(590,plain,
% 0.21/0.50 (multiply(sk_c5, multiply(sk_c5, sk_c4)) = multiply(sk_c7, sk_c6)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[528, 581])).
% 0.21/0.50 tff(591,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c5), sk_c4) = multiply(sk_c5, multiply(sk_c5, sk_c4)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(592,plain,
% 0.21/0.50 (multiply(multiply(sk_c5, sk_c5), sk_c4) = multiply(sk_c5, multiply(sk_c5, sk_c4))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[591, 21])).
% 0.21/0.50 tff(593,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c4) = multiply(multiply(sk_c5, sk_c5), sk_c4)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[536])).
% 0.21/0.50 tff(594,plain,
% 0.21/0.50 (multiply(identity, sk_c4) = multiply(sk_c6, sk_c4)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[368])).
% 0.21/0.50 tff(595,plain,
% 0.21/0.50 (sk_c4 = multiply(identity, sk_c4)),
% 0.21/0.50 inference(symmetry,[status(thm)],[262])).
% 0.21/0.50 tff(596,plain,
% 0.21/0.50 (sk_c4 = sk_c5),
% 0.21/0.50 inference(transitivity,[status(thm)],[595, 594, 593, 592, 590, 389, 121, 335, 384])).
% 0.21/0.50 tff(597,plain,
% 0.21/0.50 (multiply(sk_c4, sk_c5) = multiply(sk_c5, sk_c7)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[596, 528])).
% 0.21/0.50 tff(598,plain,
% 0.21/0.50 (multiply(sk_c4, sk_c5) = sk_c6),
% 0.21/0.50 inference(transitivity,[status(thm)],[597, 253])).
% 0.21/0.50 tff(599,plain,
% 0.21/0.50 ((multiply(sk_c4, sk_c5) = sk_c7) <=> (sk_c6 = multiply(sk_c7, multiply(sk_c7, sk_c7)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[598, 589])).
% 0.21/0.50 tff(600,plain,
% 0.21/0.50 ((multiply(sk_c4, sk_c5) = sk_c7) <=> (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)),
% 0.21/0.50 inference(transitivity,[status(thm)],[599, 588])).
% 0.21/0.50 tff(601,plain,
% 0.21/0.50 ((multiply(sk_c4, sk_c5) = sk_c7) <=> (multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)),
% 0.21/0.50 inference(transitivity,[status(thm)],[600, 587])).
% 0.21/0.50 tff(602,assumption,(multiply(sk_c4, sk_c5) = sk_c7), introduced(assumption)).
% 0.21/0.50 tff(603,plain,
% 0.21/0.50 (multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.21/0.50 tff(604,plain,
% 0.21/0.50 (inverse(sk_c4) = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[578, 527, 370, 78])).
% 0.21/0.50 tff(605,plain,
% 0.21/0.50 (multiply(sk_c6, sk_c5) = sk_c7),
% 0.21/0.50 inference(transitivity,[status(thm)],[542, 370, 78])).
% 0.21/0.50 tff(606,plain,
% 0.21/0.50 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(inverse(sk_c4) = sk_c5)) | (~(multiply(sk_c4, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(inverse(sk_c4) = sk_c5)) | (~(multiply(sk_c4, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(607,plain,
% 0.21/0.50 (((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c5)) | (~(multiply(sk_c4, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(inverse(sk_c4) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(inverse(sk_c4) = sk_c5)) | (~(multiply(sk_c4, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(608,plain,
% 0.21/0.50 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c5)) | (~(multiply(sk_c4, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(inverse(sk_c4) = sk_c5)) | (~(multiply(sk_c4, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[607])).
% 0.21/0.51 tff(609,plain,
% 0.21/0.51 (((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c5)) | (~(multiply(sk_c4, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)))) <=> ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(inverse(sk_c4) = sk_c5)) | (~(multiply(sk_c4, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[608, 606])).
% 0.21/0.51 tff(610,plain,
% 0.21/0.51 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c5)) | (~(multiply(sk_c4, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(611,plain,
% 0.21/0.51 ((~![X4: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c5)) | (~(multiply(X2, sk_c5) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(multiply(sk_c7, multiply(X4, sk_c7)) = sk_c6)) | (~(inverse(X4) = sk_c7)))) | (~(multiply(sk_c6, sk_c5) = sk_c7)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c5, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(inverse(sk_c4) = sk_c5)) | (~(multiply(sk_c4, sk_c5) = sk_c7)) | (~(multiply(sk_c5, sk_c6) = sk_c7)) | (~(inverse(sk_c5) = sk_c7))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.21/0.51 tff(612,plain,
% 0.21/0.51 ((~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(multiply(sk_c4, sk_c5) = sk_c7)) | (~(inverse(sk_c5) = sk_c7))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[611, 605, 384, 253, 578, 366, 220, 604, 566])).
% 0.21/0.51 tff(613,plain,
% 0.21/0.51 ((~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)) | (~(multiply(sk_c4, sk_c5) = sk_c7))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[612, 559])).
% 0.21/0.51 tff(614,plain,
% 0.21/0.51 (~(multiply(sk_c7, multiply(sk_c4, sk_c7)) = sk_c6)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[613, 602])).
% 0.21/0.51 tff(615,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[614, 603])).
% 0.21/0.51 tff(616,plain,(~(multiply(sk_c4, sk_c5) = sk_c7)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(617,plain,
% 0.21/0.51 (((multiply(sk_c1, sk_c7) = sk_c2) | (multiply(sk_c4, sk_c5) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c2) | (multiply(sk_c4, sk_c5) = sk_c7))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(618,axiom,((multiply(sk_c1, sk_c7) = sk_c2) | (multiply(sk_c4, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_23')).
% 0.21/0.51 tff(619,plain,
% 0.21/0.51 ((multiply(sk_c1, sk_c7) = sk_c2) | (multiply(sk_c4, sk_c5) = sk_c7)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.21/0.51 tff(620,plain,
% 0.21/0.51 (multiply(sk_c1, sk_c7) = sk_c2),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[619, 616])).
% 0.21/0.51 tff(621,plain,
% 0.21/0.51 (multiply(sk_c1, sk_c5) = sk_c7),
% 0.21/0.51 inference(transitivity,[status(thm)],[550, 620, 195, 538, 537, 533, 531, 389, 121, 335, 370, 78])).
% 0.21/0.51 tff(622,plain,
% 0.21/0.51 (multiply(sk_c5, multiply(sk_c1, sk_c5)) = multiply(sk_c5, sk_c7)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[621])).
% 0.21/0.51 tff(623,plain,
% 0.21/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c1), sk_c5) = multiply(sk_c5, multiply(sk_c1, sk_c5)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(624,plain,
% 0.21/0.51 (multiply(multiply(sk_c5, sk_c1), sk_c5) = multiply(sk_c5, multiply(sk_c1, sk_c5))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[623, 21])).
% 0.21/0.51 tff(625,plain,
% 0.21/0.51 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c5) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c5) = sk_c7))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(626,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_29')).
% 0.21/0.51 tff(627,plain,
% 0.21/0.51 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c5) = sk_c7)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.21/0.51 tff(628,plain,
% 0.21/0.51 (inverse(sk_c1) = sk_c7),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[627, 616])).
% 0.21/0.51 tff(629,plain,
% 0.21/0.51 (sk_c7 = inverse(sk_c1)),
% 0.21/0.51 inference(symmetry,[status(thm)],[628])).
% 0.21/0.51 tff(630,plain,
% 0.21/0.51 (sk_c5 = inverse(sk_c1)),
% 0.21/0.51 inference(transitivity,[status(thm)],[527, 370, 78, 629])).
% 0.21/0.51 tff(631,plain,
% 0.21/0.51 (multiply(sk_c5, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[630])).
% 0.21/0.51 tff(632,plain,
% 0.21/0.51 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c5, sk_c1)),
% 0.21/0.51 inference(symmetry,[status(thm)],[631])).
% 0.21/0.51 tff(633,plain,
% 0.21/0.51 (sk_c6 = multiply(sk_c5, sk_c1)),
% 0.21/0.51 inference(transitivity,[status(thm)],[303, 379, 42, 40, 632])).
% 0.21/0.51 tff(634,plain,
% 0.21/0.51 (multiply(sk_c6, sk_c5) = multiply(multiply(sk_c5, sk_c1), sk_c5)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[633])).
% 0.21/0.51 tff(635,plain,
% 0.21/0.51 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6),
% 0.21/0.51 inference(transitivity,[status(thm)],[539, 121, 335, 567, 634, 624, 622, 253])).
% 0.21/0.51 tff(636,plain,
% 0.21/0.51 ((~(multiply(sk_c4, sk_c5) = sk_c7)) <=> (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[600])).
% 0.21/0.51 tff(637,plain,
% 0.21/0.51 (~(multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[616, 636])).
% 0.21/0.51 tff(638,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[637, 635])).
% 0.21/0.51 % SZS output end Proof
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------