%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP233-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:30 AM UTC 2025
% Result : Unsatisfiable 0.47s 0.70s
% Output : Proof 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP233-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:52:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.47/0.70 % SZS status Unsatisfiable
% 0.47/0.70 % SZS output start Proof
% 0.47/0.70 tff(sk_c8_type, type, (
% 0.47/0.70 sk_c8: $i)).
% 0.47/0.70 tff(inverse_type, type, (
% 0.47/0.70 inverse: $i > $i)).
% 0.47/0.70 tff(multiply_type, type, (
% 0.47/0.70 multiply: ( $i * $i ) > $i)).
% 0.47/0.70 tff(sk_c7_type, type, (
% 0.47/0.70 sk_c7: $i)).
% 0.47/0.70 tff(sk_c4_type, type, (
% 0.47/0.70 sk_c4: $i)).
% 0.47/0.70 tff(sk_c1_type, type, (
% 0.47/0.70 sk_c1: $i)).
% 0.47/0.70 tff(identity_type, type, (
% 0.47/0.70 identity: $i)).
% 0.47/0.70 tff(sk_c2_type, type, (
% 0.47/0.70 sk_c2: $i)).
% 0.47/0.70 tff(sk_c3_type, type, (
% 0.47/0.70 sk_c3: $i)).
% 0.47/0.70 tff(sk_c6_type, type, (
% 0.47/0.70 sk_c6: $i)).
% 0.47/0.70 tff(sk_c5_type, type, (
% 0.47/0.70 sk_c5: $i)).
% 0.47/0.70 tff(1,plain,
% 0.47/0.70 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.47/0.70 inference(bind,[status(th)],[])).
% 0.47/0.70 tff(2,plain,
% 0.47/0.70 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.47/0.70 inference(quant_intro,[status(thm)],[1])).
% 0.47/0.70 tff(3,plain,
% 0.47/0.70 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(4,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.47/0.70 tff(5,plain,
% 0.47/0.70 (![X: $i] : (multiply(identity, X) = X)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.47/0.70 tff(6,plain,(
% 0.47/0.70 ![X: $i] : (multiply(identity, X) = X)),
% 0.47/0.70 inference(skolemize,[status(sab)],[5])).
% 0.47/0.70 tff(7,plain,
% 0.47/0.70 (![X: $i] : (multiply(identity, X) = X)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.47/0.70 tff(8,plain,
% 0.47/0.70 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c8) = sk_c8)),
% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(9,plain,
% 0.47/0.70 (multiply(identity, sk_c8) = sk_c8),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.47/0.70 tff(10,assumption,(~(inverse(sk_c4) = sk_c8)), introduced(assumption)).
% 0.47/0.70 tff(11,plain,
% 0.47/0.70 (((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(12,axiom,((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_26')).
% 0.47/0.70 tff(13,plain,
% 0.47/0.70 ((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.47/0.70 tff(14,plain,
% 0.47/0.70 (inverse(sk_c2) = sk_c8),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[13, 10])).
% 0.47/0.70 tff(15,plain,
% 0.47/0.70 (sk_c8 = inverse(sk_c2)),
% 0.47/0.70 inference(symmetry,[status(thm)],[14])).
% 0.47/0.70 tff(16,plain,
% 0.47/0.70 (multiply(sk_c8, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.47/0.70 inference(monotonicity,[status(thm)],[15])).
% 0.47/0.70 tff(17,plain,
% 0.47/0.70 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c8, sk_c2)),
% 0.47/0.70 inference(symmetry,[status(thm)],[16])).
% 0.47/0.70 tff(18,plain,
% 0.47/0.70 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.47/0.70 inference(bind,[status(th)],[])).
% 0.47/0.70 tff(19,plain,
% 0.47/0.70 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.47/0.70 inference(quant_intro,[status(thm)],[18])).
% 0.47/0.70 tff(20,plain,
% 0.47/0.70 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(21,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.47/0.70 tff(22,plain,
% 0.47/0.70 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.47/0.70 tff(23,plain,(
% 0.47/0.70 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.47/0.70 inference(skolemize,[status(sab)],[22])).
% 0.47/0.70 tff(24,plain,
% 0.47/0.70 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.47/0.70 tff(25,plain,
% 0.47/0.70 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(26,plain,
% 0.47/0.70 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.47/0.70 tff(27,plain,
% 0.47/0.70 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.47/0.70 inference(symmetry,[status(thm)],[26])).
% 0.47/0.70 tff(28,plain,
% 0.47/0.70 (identity = multiply(sk_c8, sk_c2)),
% 0.47/0.70 inference(transitivity,[status(thm)],[27, 17])).
% 0.47/0.70 tff(29,plain,
% 0.47/0.70 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.47/0.70 inference(monotonicity,[status(thm)],[28])).
% 0.47/0.70 tff(30,plain,
% 0.47/0.70 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(identity, sk_c8)),
% 0.47/0.70 inference(symmetry,[status(thm)],[29])).
% 0.47/0.70 tff(31,plain,
% 0.47/0.70 (^[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))))),
% 0.47/0.70 inference(bind,[status(th)],[])).
% 0.47/0.70 tff(32,plain,
% 0.47/0.70 (![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)))),
% 0.47/0.70 inference(quant_intro,[status(thm)],[31])).
% 0.47/0.70 tff(33,plain,
% 0.47/0.70 (![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)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(34,axiom,(![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','associativity')).
% 0.47/0.70 tff(35,plain,
% 0.47/0.70 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.47/0.70 tff(36,plain,(
% 0.47/0.70 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.47/0.70 inference(skolemize,[status(sab)],[35])).
% 0.47/0.70 tff(37,plain,
% 0.47/0.70 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.47/0.70 tff(38,plain,
% 0.47/0.70 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(39,plain,
% 0.47/0.70 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.47/0.70 tff(40,plain,
% 0.47/0.70 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.47/0.70 inference(symmetry,[status(thm)],[39])).
% 0.47/0.70 tff(41,plain,
% 0.47/0.70 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(42,plain,
% 0.47/0.70 (((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(43,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_21')).
% 0.47/0.70 tff(44,plain,
% 0.47/0.70 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.47/0.70 tff(45,plain,
% 0.47/0.70 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.47/0.70 tff(46,plain,
% 0.47/0.70 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[45, 10])).
% 0.47/0.70 tff(47,plain,
% 0.47/0.70 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.47/0.70 inference(monotonicity,[status(thm)],[46])).
% 0.47/0.70 tff(48,plain,
% 0.47/0.70 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.47/0.70 inference(symmetry,[status(thm)],[47])).
% 0.47/0.70 tff(49,assumption,(~(multiply(sk_c8, sk_c6) = sk_c7)), introduced(assumption)).
% 0.47/0.70 tff(50,plain,
% 0.47/0.70 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(51,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_28')).
% 0.47/0.70 tff(52,plain,
% 0.47/0.70 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.47/0.70 tff(53,plain,
% 0.47/0.70 (inverse(sk_c2) = sk_c8),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.47/0.70 tff(54,plain,
% 0.47/0.70 (sk_c8 = inverse(sk_c2)),
% 0.47/0.70 inference(symmetry,[status(thm)],[53])).
% 0.47/0.70 tff(55,plain,
% 0.47/0.70 (multiply(sk_c8, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.47/0.70 inference(monotonicity,[status(thm)],[54])).
% 0.47/0.70 tff(56,plain,
% 0.47/0.70 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c8, sk_c2)),
% 0.47/0.70 inference(symmetry,[status(thm)],[55])).
% 0.47/0.70 tff(57,plain,
% 0.47/0.70 (identity = multiply(sk_c8, sk_c2)),
% 0.47/0.70 inference(transitivity,[status(thm)],[27, 56])).
% 0.47/0.70 tff(58,plain,
% 0.47/0.70 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.47/0.70 inference(monotonicity,[status(thm)],[57])).
% 0.47/0.70 tff(59,plain,
% 0.47/0.70 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(identity, sk_c8)),
% 0.47/0.70 inference(symmetry,[status(thm)],[58])).
% 0.47/0.70 tff(60,plain,
% 0.47/0.70 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(61,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_23')).
% 0.47/0.70 tff(62,plain,
% 0.47/0.70 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.47/0.70 tff(63,plain,
% 0.47/0.70 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[62, 49])).
% 0.47/0.70 tff(64,plain,
% 0.47/0.70 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.47/0.70 inference(monotonicity,[status(thm)],[63])).
% 0.47/0.70 tff(65,plain,
% 0.47/0.70 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.47/0.70 inference(symmetry,[status(thm)],[64])).
% 0.47/0.70 tff(66,plain,
% 0.47/0.70 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(67,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_18')).
% 0.47/0.70 tff(68,plain,
% 0.47/0.70 ((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.47/0.70 tff(69,plain,
% 0.47/0.70 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[68, 49])).
% 0.47/0.70 tff(70,plain,
% 0.47/0.70 (sk_c7 = multiply(sk_c8, sk_c3)),
% 0.47/0.70 inference(symmetry,[status(thm)],[69])).
% 0.47/0.70 tff(71,plain,
% 0.47/0.70 (((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(72,axiom,((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_8')).
% 0.47/0.70 tff(73,plain,
% 0.47/0.70 ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.47/0.70 tff(74,plain,
% 0.47/0.70 (multiply(sk_c1, sk_c8) = sk_c7),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[73, 49])).
% 0.47/0.70 tff(75,plain,
% 0.47/0.70 (sk_c7 = sk_c8),
% 0.47/0.70 inference(transitivity,[status(thm)],[70, 65, 40, 59, 9])).
% 0.47/0.70 tff(76,plain,
% 0.47/0.70 (multiply(sk_c1, sk_c7) = multiply(sk_c1, sk_c8)),
% 0.47/0.70 inference(monotonicity,[status(thm)],[75])).
% 0.47/0.70 tff(77,plain,
% 0.47/0.70 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.47/0.70 inference(transitivity,[status(thm)],[76, 74, 70, 65, 40, 59, 9])).
% 0.47/0.70 tff(78,plain,
% 0.47/0.70 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.47/0.70 inference(transitivity,[status(thm)],[64, 69])).
% 0.47/0.70 tff(79,plain,
% 0.47/0.70 (^[X6: $i, X4: $i, X3: $i, X1: $i] : refl(((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))))),
% 0.47/0.70 inference(bind,[status(th)],[])).
% 0.47/0.70 tff(80,plain,
% 0.47/0.70 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.70 inference(quant_intro,[status(thm)],[79])).
% 0.47/0.70 tff(81,plain,
% 0.47/0.70 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(82,plain,
% 0.47/0.70 (^[X6: $i, X4: $i, X3: $i, X1: $i] : rewrite(((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))))),
% 0.47/0.70 inference(bind,[status(th)],[])).
% 0.47/0.70 tff(83,plain,
% 0.47/0.70 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.70 inference(quant_intro,[status(thm)],[82])).
% 0.47/0.70 tff(84,plain,
% 0.47/0.70 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.70 inference(elim_unused_vars,[status(thm)],[])).
% 0.47/0.70 tff(85,plain,
% 0.47/0.70 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.71 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.47/0.71 tff(86,plain,
% 0.47/0.71 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.71 inference(transitivity,[status(thm)],[85, 84])).
% 0.47/0.71 tff(87,plain,
% 0.47/0.71 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.71 inference(transitivity,[status(thm)],[86, 83])).
% 0.47/0.71 tff(88,plain,
% 0.47/0.71 (^[X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), (((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), (((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), ((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), ((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), (((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X6) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X6) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), (((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), ((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), ((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), (((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X1, sk_c7) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), (((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), ((((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(sk_c8, X2) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), ((((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), ((((((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X3) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X3) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), ((((((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))))),
% 0.47/0.71 inference(bind,[status(th)],[])).
% 0.47/0.71 tff(89,plain,
% 0.47/0.71 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))),
% 0.47/0.71 inference(quant_intro,[status(thm)],[88])).
% 0.47/0.71 tff(90,plain,
% 0.47/0.71 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.71 inference(transitivity,[status(thm)],[89, 87])).
% 0.47/0.71 tff(91,axiom,(![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_31')).
% 0.47/0.72 tff(92,plain,
% 0.47/0.72 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.47/0.72 tff(93,plain,
% 0.47/0.72 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[92, 81])).
% 0.47/0.72 tff(94,plain,(
% 0.47/0.72 ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.72 inference(skolemize,[status(sab)],[93])).
% 0.47/0.72 tff(95,plain,
% 0.47/0.72 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[94, 80])).
% 0.47/0.72 tff(96,plain,
% 0.47/0.72 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(97,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_13')).
% 0.47/0.72 tff(98,plain,
% 0.47/0.72 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.47/0.72 tff(99,plain,
% 0.47/0.72 (inverse(sk_c1) = sk_c8),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[98, 49])).
% 0.47/0.72 tff(100,plain,
% 0.47/0.72 (((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(101,axiom,((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_3')).
% 0.47/0.72 tff(102,plain,
% 0.47/0.72 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.47/0.72 tff(103,plain,
% 0.47/0.72 (inverse(sk_c8) = sk_c7),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[102, 49])).
% 0.47/0.72 tff(104,plain,
% 0.47/0.72 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(105,plain,
% 0.47/0.72 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(106,plain,
% 0.47/0.72 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7))))),
% 0.47/0.72 inference(monotonicity,[status(thm)],[105])).
% 0.47/0.72 tff(107,plain,
% 0.47/0.72 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)))),
% 0.47/0.72 inference(transitivity,[status(thm)],[106, 104])).
% 0.47/0.72 tff(108,plain,
% 0.47/0.72 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)))),
% 0.47/0.72 inference(quant_inst,[status(thm)],[])).
% 0.47/0.72 tff(109,plain,
% 0.47/0.72 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.47/0.72 tff(110,plain,
% 0.47/0.72 ((~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[109, 103, 74, 99, 53, 95])).
% 0.47/0.72 tff(111,plain,
% 0.47/0.72 (~(multiply(sk_c1, sk_c7) = sk_c8)),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[110, 78])).
% 0.47/0.72 tff(112,plain,
% 0.47/0.72 ($false),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[111, 77])).
% 0.47/0.72 tff(113,plain,(multiply(sk_c8, sk_c6) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.47/0.72 tff(114,assumption,(~(multiply(sk_c8, sk_c3) = sk_c7)), introduced(assumption)).
% 0.47/0.72 tff(115,plain,
% 0.47/0.72 (((multiply(sk_c5, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((multiply(sk_c5, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(116,plain,
% 0.47/0.72 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((multiply(sk_c5, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(117,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_19')).
% 0.47/0.72 tff(118,plain,
% 0.47/0.72 ((multiply(sk_c5, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.47/0.72 tff(119,plain,
% 0.47/0.72 ((multiply(sk_c5, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[118, 115])).
% 0.47/0.72 tff(120,plain,
% 0.47/0.72 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[119, 114])).
% 0.47/0.72 tff(121,plain,
% 0.47/0.72 (sk_c6 = multiply(sk_c5, sk_c8)),
% 0.47/0.72 inference(symmetry,[status(thm)],[120])).
% 0.47/0.72 tff(122,plain,
% 0.47/0.72 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.47/0.72 inference(monotonicity,[status(thm)],[121])).
% 0.47/0.72 tff(123,plain,
% 0.47/0.72 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.47/0.72 inference(symmetry,[status(thm)],[122])).
% 0.47/0.72 tff(124,plain,
% 0.47/0.72 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(sk_c8, multiply(sk_c5, sk_c8)))),
% 0.47/0.72 inference(quant_inst,[status(thm)],[])).
% 0.47/0.72 tff(125,plain,
% 0.47/0.72 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[124, 37])).
% 0.47/0.72 tff(126,plain,
% 0.47/0.72 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c5), sk_c5) = identity)),
% 0.47/0.72 inference(quant_inst,[status(thm)],[])).
% 0.47/0.72 tff(127,plain,
% 0.47/0.72 (multiply(inverse(sk_c5), sk_c5) = identity),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[126, 24])).
% 0.47/0.72 tff(128,plain,
% 0.47/0.72 (((inverse(sk_c5) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(129,plain,
% 0.47/0.72 (((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(130,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_20')).
% 0.47/0.72 tff(131,plain,
% 0.47/0.72 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.47/0.72 tff(132,plain,
% 0.47/0.72 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[131, 128])).
% 0.56/0.72 tff(133,plain,
% 0.56/0.72 (inverse(sk_c5) = sk_c8),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[132, 114])).
% 0.56/0.72 tff(134,plain,
% 0.56/0.72 (sk_c8 = inverse(sk_c5)),
% 0.56/0.72 inference(symmetry,[status(thm)],[133])).
% 0.56/0.72 tff(135,plain,
% 0.56/0.72 (multiply(sk_c8, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[134])).
% 0.56/0.72 tff(136,plain,
% 0.56/0.72 (multiply(sk_c8, sk_c5) = identity),
% 0.56/0.72 inference(transitivity,[status(thm)],[135, 127])).
% 0.56/0.72 tff(137,plain,
% 0.56/0.72 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[136])).
% 0.56/0.72 tff(138,plain,
% 0.56/0.72 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.56/0.72 inference(symmetry,[status(thm)],[137])).
% 0.56/0.72 tff(139,plain,
% 0.56/0.72 (sk_c8 = multiply(identity, sk_c8)),
% 0.56/0.72 inference(symmetry,[status(thm)],[9])).
% 0.56/0.72 tff(140,plain,
% 0.56/0.72 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(141,plain,
% 0.56/0.72 (((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(142,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_16')).
% 0.56/0.72 tff(143,plain,
% 0.56/0.72 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.56/0.72 tff(144,plain,
% 0.56/0.72 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[143, 140])).
% 0.56/0.72 tff(145,plain,
% 0.56/0.72 (inverse(sk_c4) = sk_c8),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[144, 114])).
% 0.56/0.72 tff(146,plain,
% 0.56/0.72 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c4) = sk_c4)),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(147,plain,
% 0.56/0.72 (multiply(identity, sk_c4) = sk_c4),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[146, 7])).
% 0.56/0.72 tff(148,plain,
% 0.56/0.72 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.56/0.72 inference(symmetry,[status(thm)],[135])).
% 0.56/0.72 tff(149,plain,
% 0.56/0.72 (identity = multiply(inverse(sk_c5), sk_c5)),
% 0.56/0.72 inference(symmetry,[status(thm)],[127])).
% 0.56/0.72 tff(150,plain,
% 0.56/0.72 (identity = multiply(sk_c8, sk_c5)),
% 0.56/0.72 inference(transitivity,[status(thm)],[149, 148])).
% 0.56/0.72 tff(151,plain,
% 0.56/0.72 (multiply(identity, sk_c4) = multiply(multiply(sk_c8, sk_c5), sk_c4)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[150])).
% 0.56/0.72 tff(152,plain,
% 0.56/0.72 (multiply(multiply(sk_c8, sk_c5), sk_c4) = multiply(identity, sk_c4)),
% 0.56/0.72 inference(symmetry,[status(thm)],[151])).
% 0.56/0.72 tff(153,plain,
% 0.56/0.72 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c5), sk_c4) = multiply(sk_c8, multiply(sk_c5, sk_c4)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(154,plain,
% 0.56/0.72 (multiply(multiply(sk_c8, sk_c5), sk_c4) = multiply(sk_c8, multiply(sk_c5, sk_c4))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[153, 37])).
% 0.56/0.72 tff(155,plain,
% 0.56/0.72 (multiply(sk_c8, multiply(sk_c5, sk_c4)) = multiply(multiply(sk_c8, sk_c5), sk_c4)),
% 0.56/0.72 inference(symmetry,[status(thm)],[154])).
% 0.56/0.72 tff(156,plain,
% 0.56/0.72 (sk_c8 = sk_c7),
% 0.56/0.72 inference(transitivity,[status(thm)],[139, 138, 125, 123, 113])).
% 0.56/0.72 tff(157,plain,
% 0.56/0.72 (multiply(sk_c4, sk_c8) = multiply(sk_c4, sk_c7)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[156])).
% 0.56/0.72 tff(158,plain,
% 0.56/0.72 (multiply(sk_c4, sk_c7) = multiply(sk_c4, sk_c8)),
% 0.56/0.72 inference(symmetry,[status(thm)],[157])).
% 0.56/0.72 tff(159,plain,
% 0.56/0.72 (((multiply(sk_c4, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((multiply(sk_c4, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(160,plain,
% 0.56/0.72 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((multiply(sk_c4, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(161,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_17')).
% 0.56/0.72 tff(162,plain,
% 0.56/0.72 ((multiply(sk_c4, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.56/0.72 tff(163,plain,
% 0.56/0.72 ((multiply(sk_c4, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[162, 159])).
% 0.56/0.72 tff(164,plain,
% 0.56/0.72 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[163, 114])).
% 0.56/0.72 tff(165,plain,
% 0.56/0.72 (sk_c8 = multiply(sk_c4, sk_c7)),
% 0.56/0.72 inference(symmetry,[status(thm)],[164])).
% 0.56/0.72 tff(166,plain,
% 0.56/0.72 (sk_c8 = multiply(sk_c4, sk_c8)),
% 0.56/0.72 inference(transitivity,[status(thm)],[165, 158])).
% 0.56/0.72 tff(167,plain,
% 0.56/0.72 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[166])).
% 0.56/0.72 tff(168,plain,
% 0.56/0.72 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c8)),
% 0.56/0.72 inference(symmetry,[status(thm)],[167])).
% 0.56/0.72 tff(169,plain,
% 0.56/0.72 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(170,plain,
% 0.56/0.72 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[169, 37])).
% 0.56/0.72 tff(171,plain,
% 0.56/0.72 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(172,plain,
% 0.56/0.72 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[171, 24])).
% 0.56/0.72 tff(173,plain,
% 0.56/0.72 (sk_c8 = inverse(sk_c4)),
% 0.56/0.72 inference(symmetry,[status(thm)],[145])).
% 0.56/0.72 tff(174,plain,
% 0.56/0.72 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[173])).
% 0.56/0.72 tff(175,plain,
% 0.56/0.72 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c5)),
% 0.56/0.72 inference(transitivity,[status(thm)],[174, 172, 149, 148])).
% 0.56/0.72 tff(176,plain,
% 0.56/0.72 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[175])).
% 0.56/0.72 tff(177,plain,
% 0.56/0.72 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.56/0.72 inference(symmetry,[status(thm)],[176])).
% 0.56/0.72 tff(178,plain,
% 0.56/0.72 (sk_c8 = multiply(sk_c8, sk_c8)),
% 0.56/0.72 inference(transitivity,[status(thm)],[139, 138, 177, 170, 168])).
% 0.56/0.72 tff(179,plain,
% 0.56/0.72 (multiply(sk_c8, multiply(sk_c5, sk_c4)) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[178])).
% 0.56/0.72 tff(180,plain,
% 0.56/0.72 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4)) = multiply(sk_c8, multiply(sk_c5, sk_c4))),
% 0.56/0.72 inference(symmetry,[status(thm)],[179])).
% 0.56/0.72 tff(181,plain,
% 0.56/0.72 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4)) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4))))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(182,plain,
% 0.56/0.72 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4)) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4)))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[181, 37])).
% 0.56/0.72 tff(183,plain,
% 0.56/0.72 (multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4))) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4))),
% 0.56/0.72 inference(symmetry,[status(thm)],[182])).
% 0.56/0.72 tff(184,plain,
% 0.56/0.72 (multiply(sk_c8, multiply(sk_c5, sk_c4)) = sk_c4),
% 0.56/0.72 inference(transitivity,[status(thm)],[155, 152, 147])).
% 0.56/0.72 tff(185,plain,
% 0.56/0.72 (multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4))) = multiply(inverse(sk_c4), sk_c4)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[173, 184])).
% 0.56/0.72 tff(186,plain,
% 0.56/0.72 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4)))),
% 0.56/0.72 inference(symmetry,[status(thm)],[185])).
% 0.56/0.72 tff(187,plain,
% 0.56/0.72 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.56/0.72 inference(symmetry,[status(thm)],[172])).
% 0.56/0.72 tff(188,plain,
% 0.56/0.72 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c8), sk_c8) = identity)),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(189,plain,
% 0.56/0.73 (multiply(inverse(sk_c8), sk_c8) = identity),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[188, 24])).
% 0.56/0.73 tff(190,plain,
% 0.56/0.73 (multiply(inverse(sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[178])).
% 0.56/0.73 tff(191,plain,
% 0.56/0.73 (multiply(inverse(sk_c8), multiply(sk_c8, sk_c8)) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[190])).
% 0.56/0.73 tff(192,plain,
% 0.56/0.73 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(193,plain,
% 0.56/0.73 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[192, 37])).
% 0.56/0.73 tff(194,plain,
% 0.56/0.73 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c8, sk_c5)),
% 0.56/0.73 inference(transitivity,[status(thm)],[189, 149, 148])).
% 0.56/0.73 tff(195,plain,
% 0.56/0.73 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[194])).
% 0.56/0.73 tff(196,plain,
% 0.56/0.73 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(multiply(inverse(sk_c8), sk_c8), sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[195])).
% 0.56/0.73 tff(197,plain,
% 0.56/0.73 (sk_c8 = sk_c4),
% 0.56/0.73 inference(transitivity,[status(thm)],[139, 138, 196, 193, 191, 189, 187, 186, 183, 180, 155, 152, 147])).
% 0.56/0.73 tff(198,plain,
% 0.56/0.73 (inverse(sk_c8) = inverse(sk_c4)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[197])).
% 0.56/0.73 tff(199,plain,
% 0.56/0.73 (inverse(sk_c8) = sk_c7),
% 0.56/0.73 inference(transitivity,[status(thm)],[198, 145, 139, 138, 125, 123, 113])).
% 0.56/0.73 tff(200,plain,
% 0.56/0.73 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7),
% 0.56/0.73 inference(transitivity,[status(thm)],[123, 113])).
% 0.56/0.73 tff(201,plain,
% 0.56/0.73 (multiply(sk_c4, sk_c8) = sk_c7),
% 0.56/0.73 inference(transitivity,[status(thm)],[157, 164, 139, 138, 125, 123, 113])).
% 0.56/0.73 tff(202,plain,
% 0.56/0.73 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(203,plain,
% 0.56/0.73 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(204,plain,
% 0.56/0.73 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[203])).
% 0.56/0.73 tff(205,plain,
% 0.56/0.73 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)))),
% 0.56/0.73 inference(transitivity,[status(thm)],[204, 202])).
% 0.56/0.73 tff(206,plain,
% 0.56/0.73 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(207,plain,
% 0.56/0.73 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.56/0.73 tff(208,plain,
% 0.56/0.73 ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[207, 145, 164, 133, 95])).
% 0.56/0.73 tff(209,plain,
% 0.56/0.73 (~(inverse(sk_c8) = sk_c7)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[208, 201, 200])).
% 0.56/0.73 tff(210,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[209, 199])).
% 0.56/0.73 tff(211,plain,(multiply(sk_c8, sk_c3) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(212,plain,
% 0.56/0.73 (sk_c7 = multiply(sk_c8, sk_c3)),
% 0.56/0.73 inference(symmetry,[status(thm)],[211])).
% 0.56/0.73 tff(213,plain,
% 0.56/0.73 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c7)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c7))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(214,plain,
% 0.56/0.73 (((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c7))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(215,axiom,((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_6')).
% 0.56/0.73 tff(216,plain,
% 0.56/0.73 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c7)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.56/0.73 tff(217,plain,
% 0.56/0.73 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c7)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[216, 213])).
% 0.56/0.73 tff(218,plain,
% 0.56/0.73 (multiply(sk_c1, sk_c8) = sk_c7),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[217, 10])).
% 0.56/0.73 tff(219,plain,
% 0.56/0.73 (sk_c7 = sk_c8),
% 0.56/0.73 inference(transitivity,[status(thm)],[212, 48, 40, 30, 9])).
% 0.56/0.73 tff(220,plain,
% 0.56/0.73 (multiply(sk_c1, sk_c7) = multiply(sk_c1, sk_c8)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[219])).
% 0.56/0.73 tff(221,plain,
% 0.56/0.73 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.56/0.73 inference(transitivity,[status(thm)],[220, 218, 212, 48, 40, 30, 9])).
% 0.56/0.73 tff(222,plain,
% 0.56/0.73 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.56/0.73 inference(transitivity,[status(thm)],[47, 211])).
% 0.56/0.73 tff(223,plain,
% 0.56/0.73 (((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(224,axiom,((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_11')).
% 0.56/0.73 tff(225,plain,
% 0.56/0.73 ((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.56/0.73 tff(226,plain,
% 0.56/0.73 (inverse(sk_c1) = sk_c8),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[225, 10])).
% 0.56/0.73 tff(227,assumption,(~(inverse(sk_c8) = sk_c7)), introduced(assumption)).
% 0.56/0.73 tff(228,plain,
% 0.56/0.73 (((inverse(sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(229,axiom,((inverse(sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_4')).
% 0.56/0.73 tff(230,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.56/0.73 tff(231,plain,
% 0.56/0.73 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.56/0.73 tff(232,plain,
% 0.56/0.73 (sk_c6 = multiply(sk_c5, sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[231])).
% 0.56/0.73 tff(233,plain,
% 0.56/0.73 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[232])).
% 0.56/0.73 tff(234,plain,
% 0.56/0.73 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.56/0.73 inference(symmetry,[status(thm)],[233])).
% 0.56/0.73 tff(235,plain,
% 0.56/0.73 (((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(236,axiom,((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_5')).
% 0.56/0.73 tff(237,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.56/0.73 tff(238,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[237, 235])).
% 0.56/0.73 tff(239,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[238, 235])).
% 0.56/0.73 tff(240,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[239, 235])).
% 0.56/0.73 tff(241,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[240, 235])).
% 0.56/0.73 tff(242,plain,
% 0.56/0.73 (inverse(sk_c5) = sk_c8),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[241, 227])).
% 0.56/0.73 tff(243,plain,
% 0.56/0.73 (sk_c8 = inverse(sk_c5)),
% 0.56/0.73 inference(symmetry,[status(thm)],[242])).
% 0.56/0.73 tff(244,plain,
% 0.56/0.73 (multiply(sk_c8, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[243])).
% 0.56/0.73 tff(245,plain,
% 0.56/0.73 (multiply(sk_c8, sk_c5) = identity),
% 0.56/0.73 inference(transitivity,[status(thm)],[244, 127])).
% 0.56/0.73 tff(246,plain,
% 0.56/0.73 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[245])).
% 0.56/0.73 tff(247,plain,
% 0.56/0.73 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[246])).
% 0.56/0.73 tff(248,plain,
% 0.56/0.73 (((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(249,axiom,((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_1')).
% 0.56/0.73 tff(250,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.56/0.73 tff(251,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[250, 248])).
% 0.56/0.73 tff(252,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[251, 248])).
% 0.56/0.73 tff(253,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[252, 248])).
% 0.56/0.73 tff(254,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[253, 248])).
% 0.56/0.73 tff(255,plain,
% 0.56/0.73 (inverse(sk_c4) = sk_c8),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[254, 227])).
% 0.56/0.73 tff(256,plain,
% 0.56/0.73 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.56/0.73 inference(symmetry,[status(thm)],[244])).
% 0.56/0.73 tff(257,plain,
% 0.56/0.73 (identity = multiply(sk_c8, sk_c5)),
% 0.56/0.73 inference(transitivity,[status(thm)],[149, 256])).
% 0.56/0.73 tff(258,plain,
% 0.56/0.73 (multiply(identity, sk_c4) = multiply(multiply(sk_c8, sk_c5), sk_c4)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[257])).
% 0.56/0.73 tff(259,plain,
% 0.56/0.73 (multiply(multiply(sk_c8, sk_c5), sk_c4) = multiply(identity, sk_c4)),
% 0.56/0.73 inference(symmetry,[status(thm)],[258])).
% 0.56/0.73 tff(260,plain,
% 0.56/0.73 (sk_c8 = sk_c7),
% 0.56/0.73 inference(transitivity,[status(thm)],[139, 247, 125, 234, 113])).
% 0.56/0.73 tff(261,plain,
% 0.56/0.73 (multiply(sk_c4, sk_c8) = multiply(sk_c4, sk_c7)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[260])).
% 0.56/0.73 tff(262,plain,
% 0.56/0.73 (multiply(sk_c4, sk_c7) = multiply(sk_c4, sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[261])).
% 0.56/0.73 tff(263,plain,
% 0.56/0.73 (((inverse(sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(264,axiom,((inverse(sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_2')).
% 0.56/0.73 tff(265,plain,
% 0.56/0.73 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.56/0.73 tff(266,plain,
% 0.56/0.73 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[265, 227])).
% 0.56/0.73 tff(267,plain,
% 0.56/0.73 (sk_c8 = multiply(sk_c4, sk_c7)),
% 0.56/0.73 inference(symmetry,[status(thm)],[266])).
% 0.56/0.73 tff(268,plain,
% 0.56/0.73 (sk_c8 = multiply(sk_c4, sk_c8)),
% 0.56/0.73 inference(transitivity,[status(thm)],[267, 262])).
% 0.56/0.73 tff(269,plain,
% 0.56/0.73 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[268])).
% 0.56/0.73 tff(270,plain,
% 0.56/0.73 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[269])).
% 0.56/0.73 tff(271,plain,
% 0.56/0.73 (sk_c8 = inverse(sk_c4)),
% 0.56/0.73 inference(symmetry,[status(thm)],[255])).
% 0.56/0.73 tff(272,plain,
% 0.56/0.73 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[271])).
% 0.56/0.73 tff(273,plain,
% 0.56/0.73 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c5)),
% 0.56/0.73 inference(transitivity,[status(thm)],[272, 172, 149, 256])).
% 0.56/0.73 tff(274,plain,
% 0.56/0.73 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[273])).
% 0.56/0.73 tff(275,plain,
% 0.56/0.73 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[274])).
% 0.56/0.73 tff(276,plain,
% 0.56/0.73 (sk_c8 = multiply(sk_c8, sk_c8)),
% 0.56/0.73 inference(transitivity,[status(thm)],[139, 247, 275, 170, 270])).
% 0.56/0.73 tff(277,plain,
% 0.56/0.73 (multiply(sk_c8, multiply(sk_c5, sk_c4)) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[276])).
% 0.56/0.73 tff(278,plain,
% 0.56/0.73 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4)) = multiply(sk_c8, multiply(sk_c5, sk_c4))),
% 0.56/0.73 inference(symmetry,[status(thm)],[277])).
% 0.56/0.73 tff(279,plain,
% 0.56/0.73 (multiply(sk_c8, multiply(sk_c5, sk_c4)) = sk_c4),
% 0.56/0.73 inference(transitivity,[status(thm)],[155, 259, 147])).
% 0.56/0.73 tff(280,plain,
% 0.56/0.73 (multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4))) = multiply(inverse(sk_c4), sk_c4)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[271, 279])).
% 0.56/0.73 tff(281,plain,
% 0.56/0.73 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4)))),
% 0.56/0.73 inference(symmetry,[status(thm)],[280])).
% 0.56/0.73 tff(282,plain,
% 0.56/0.73 (multiply(inverse(sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[276])).
% 0.56/0.73 tff(283,plain,
% 0.56/0.73 (multiply(inverse(sk_c8), multiply(sk_c8, sk_c8)) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[282])).
% 0.56/0.73 tff(284,plain,
% 0.56/0.73 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c8, sk_c5)),
% 0.56/0.73 inference(transitivity,[status(thm)],[189, 149, 256])).
% 0.56/0.73 tff(285,plain,
% 0.56/0.73 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[284])).
% 0.56/0.73 tff(286,plain,
% 0.56/0.73 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(multiply(inverse(sk_c8), sk_c8), sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[285])).
% 0.56/0.73 tff(287,plain,
% 0.56/0.73 (sk_c8 = sk_c4),
% 0.56/0.73 inference(transitivity,[status(thm)],[139, 247, 286, 193, 283, 189, 187, 281, 183, 278, 155, 259, 147])).
% 0.56/0.73 tff(288,plain,
% 0.56/0.73 (inverse(sk_c8) = inverse(sk_c4)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[287])).
% 0.56/0.73 tff(289,plain,
% 0.56/0.73 (inverse(sk_c8) = sk_c7),
% 0.56/0.73 inference(transitivity,[status(thm)],[288, 255, 139, 247, 125, 234, 113])).
% 0.56/0.73 tff(290,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[227, 289])).
% 0.56/0.73 tff(291,plain,(inverse(sk_c8) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(292,plain,
% 0.56/0.73 ((~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[109, 291, 218, 226, 14, 95])).
% 0.56/0.73 tff(293,plain,
% 0.56/0.73 (~(multiply(sk_c1, sk_c7) = sk_c8)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[292, 222])).
% 0.56/0.73 tff(294,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[293, 221])).
% 0.56/0.73 tff(295,plain,(inverse(sk_c4) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(296,plain,
% 0.56/0.73 (sk_c7 = inverse(sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[291])).
% 0.56/0.73 tff(297,assumption,(~(multiply(sk_c1, sk_c8) = sk_c7)), introduced(assumption)).
% 0.56/0.73 tff(298,plain,
% 0.56/0.73 (((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(299,axiom,((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_9')).
% 0.56/0.73 tff(300,plain,
% 0.56/0.73 ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.56/0.73 tff(301,plain,
% 0.56/0.73 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[300, 297])).
% 0.56/0.73 tff(302,plain,
% 0.56/0.73 (sk_c6 = multiply(sk_c5, sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[301])).
% 0.56/0.73 tff(303,plain,
% 0.56/0.73 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[302])).
% 0.56/0.73 tff(304,plain,
% 0.56/0.73 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.56/0.73 inference(symmetry,[status(thm)],[303])).
% 0.56/0.73 tff(305,plain,
% 0.56/0.73 (((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c7)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c7))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(306,plain,
% 0.56/0.73 (((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c7))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(307,axiom,((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_10')).
% 0.56/0.73 tff(308,plain,
% 0.56/0.73 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c7)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.56/0.73 tff(309,plain,
% 0.56/0.73 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c7)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[308, 305])).
% 0.56/0.73 tff(310,plain,
% 0.56/0.73 (inverse(sk_c5) = sk_c8),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[309, 297])).
% 0.56/0.73 tff(311,plain,
% 0.56/0.73 (sk_c8 = inverse(sk_c5)),
% 0.56/0.73 inference(symmetry,[status(thm)],[310])).
% 0.56/0.73 tff(312,plain,
% 0.56/0.73 (multiply(sk_c8, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[311])).
% 0.56/0.73 tff(313,plain,
% 0.56/0.73 (multiply(sk_c8, sk_c5) = identity),
% 0.56/0.73 inference(transitivity,[status(thm)],[312, 127])).
% 0.56/0.73 tff(314,plain,
% 0.56/0.73 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[313])).
% 0.56/0.73 tff(315,plain,
% 0.56/0.73 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[314])).
% 0.56/0.73 tff(316,plain,
% 0.56/0.73 (((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(317,axiom,((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_7')).
% 0.56/0.73 tff(318,plain,
% 0.56/0.73 ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.56/0.73 tff(319,plain,
% 0.56/0.73 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[318, 297])).
% 0.56/0.73 tff(320,plain,
% 0.56/0.73 (sk_c8 = sk_c7),
% 0.56/0.73 inference(transitivity,[status(thm)],[139, 315, 125, 304, 113])).
% 0.56/0.73 tff(321,plain,
% 0.56/0.73 (multiply(sk_c4, sk_c8) = multiply(sk_c4, sk_c7)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[320])).
% 0.56/0.73 tff(322,plain,
% 0.56/0.73 (multiply(sk_c4, sk_c8) = sk_c7),
% 0.56/0.73 inference(transitivity,[status(thm)],[321, 319, 139, 315, 125, 304, 113])).
% 0.56/0.73 tff(323,plain,
% 0.56/0.73 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7),
% 0.56/0.73 inference(transitivity,[status(thm)],[304, 113])).
% 0.56/0.73 tff(324,plain,
% 0.56/0.73 ((~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[207, 291, 295, 319, 310, 95])).
% 0.56/0.73 tff(325,plain,
% 0.56/0.73 (~(multiply(sk_c4, sk_c8) = sk_c7)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[324, 323])).
% 0.56/0.73 tff(326,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[325, 322])).
% 0.56/0.73 tff(327,plain,(multiply(sk_c1, sk_c8) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(328,plain,
% 0.56/0.73 (multiply(sk_c1, sk_c8) = inverse(sk_c8)),
% 0.56/0.73 inference(transitivity,[status(thm)],[327, 296])).
% 0.56/0.73 tff(329,plain,
% 0.56/0.73 (multiply(multiply(sk_c1, sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[328])).
% 0.56/0.73 tff(330,plain,
% 0.56/0.73 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c8), sk_c8) = multiply(sk_c1, multiply(sk_c8, sk_c8)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(331,plain,
% 0.56/0.73 (multiply(multiply(sk_c1, sk_c8), sk_c8) = multiply(sk_c1, multiply(sk_c8, sk_c8))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[330, 37])).
% 0.56/0.73 tff(332,plain,
% 0.56/0.73 (multiply(sk_c1, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c1, sk_c8), sk_c8)),
% 0.56/0.73 inference(symmetry,[status(thm)],[331])).
% 0.56/0.73 tff(333,assumption,(~(multiply(sk_c4, sk_c7) = sk_c8)), introduced(assumption)).
% 0.56/0.74 tff(334,plain,
% 0.56/0.74 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(335,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_27')).
% 0.56/0.74 tff(336,plain,
% 0.56/0.74 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.56/0.74 tff(337,plain,
% 0.56/0.74 (inverse(sk_c2) = sk_c8),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[336, 333])).
% 0.56/0.74 tff(338,plain,
% 0.56/0.74 (sk_c8 = inverse(sk_c2)),
% 0.56/0.74 inference(symmetry,[status(thm)],[337])).
% 0.56/0.74 tff(339,plain,
% 0.56/0.74 (multiply(sk_c8, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[338])).
% 0.56/0.74 tff(340,plain,
% 0.56/0.74 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c8, sk_c2)),
% 0.56/0.74 inference(symmetry,[status(thm)],[339])).
% 0.56/0.74 tff(341,plain,
% 0.56/0.74 (identity = multiply(sk_c8, sk_c2)),
% 0.56/0.74 inference(transitivity,[status(thm)],[27, 340])).
% 0.56/0.74 tff(342,plain,
% 0.56/0.74 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[341])).
% 0.56/0.74 tff(343,plain,
% 0.56/0.74 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(identity, sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[342])).
% 0.56/0.74 tff(344,plain,
% 0.56/0.74 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(345,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_22')).
% 0.56/0.74 tff(346,plain,
% 0.56/0.74 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.56/0.74 tff(347,plain,
% 0.56/0.74 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[346, 333])).
% 0.56/0.74 tff(348,plain,
% 0.56/0.74 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[347])).
% 0.56/0.74 tff(349,plain,
% 0.56/0.74 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.56/0.74 inference(symmetry,[status(thm)],[348])).
% 0.56/0.74 tff(350,plain,
% 0.56/0.74 (sk_c7 = sk_c8),
% 0.56/0.74 inference(transitivity,[status(thm)],[212, 349, 40, 343, 9])).
% 0.56/0.74 tff(351,plain,
% 0.56/0.74 (multiply(sk_c1, sk_c7) = multiply(sk_c1, sk_c8)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[350])).
% 0.56/0.74 tff(352,plain,
% 0.56/0.74 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.56/0.74 inference(transitivity,[status(thm)],[351, 327, 212, 349, 40, 343, 9])).
% 0.56/0.74 tff(353,plain,
% 0.56/0.74 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.56/0.74 inference(transitivity,[status(thm)],[348, 211])).
% 0.56/0.74 tff(354,plain,
% 0.56/0.74 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(355,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_12')).
% 0.56/0.74 tff(356,plain,
% 0.56/0.74 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.56/0.74 tff(357,plain,
% 0.56/0.74 (inverse(sk_c1) = sk_c8),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[356, 333])).
% 0.56/0.74 tff(358,plain,
% 0.56/0.74 ((~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[109, 291, 327, 357, 337, 95])).
% 0.56/0.74 tff(359,plain,
% 0.56/0.74 (~(multiply(sk_c1, sk_c7) = sk_c8)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[358, 353])).
% 0.56/0.74 tff(360,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[359, 352])).
% 0.56/0.74 tff(361,plain,(multiply(sk_c4, sk_c7) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(362,plain,
% 0.56/0.74 (multiply(sk_c8, multiply(sk_c4, sk_c7)) = multiply(sk_c8, sk_c8)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[361])).
% 0.56/0.74 tff(363,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(sk_c8, multiply(sk_c4, sk_c7)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(364,plain,
% 0.56/0.74 (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(sk_c8, multiply(sk_c4, sk_c7))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[363, 37])).
% 0.56/0.74 tff(365,plain,
% 0.56/0.74 (sk_c8 = inverse(sk_c4)),
% 0.56/0.74 inference(symmetry,[status(thm)],[295])).
% 0.56/0.74 tff(366,plain,
% 0.56/0.74 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[365])).
% 0.56/0.74 tff(367,plain,
% 0.56/0.74 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.56/0.74 inference(symmetry,[status(thm)],[366])).
% 0.56/0.74 tff(368,plain,
% 0.56/0.74 (identity = multiply(sk_c8, sk_c4)),
% 0.56/0.74 inference(transitivity,[status(thm)],[187, 367])).
% 0.56/0.74 tff(369,plain,
% 0.56/0.74 (multiply(identity, sk_c7) = multiply(multiply(sk_c8, sk_c4), sk_c7)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[368])).
% 0.56/0.74 tff(370,plain,
% 0.56/0.74 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(371,plain,
% 0.56/0.74 (multiply(identity, sk_c7) = sk_c7),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[370, 7])).
% 0.56/0.74 tff(372,plain,
% 0.56/0.74 (sk_c7 = multiply(identity, sk_c7)),
% 0.56/0.74 inference(symmetry,[status(thm)],[371])).
% 0.56/0.74 tff(373,plain,
% 0.56/0.74 (multiply(sk_c8, sk_c6) = multiply(sk_c8, sk_c8)),
% 0.56/0.74 inference(transitivity,[status(thm)],[113, 372, 369, 364, 362])).
% 0.56/0.74 tff(374,plain,
% 0.56/0.74 (multiply(sk_c1, multiply(sk_c8, sk_c6)) = multiply(sk_c1, multiply(sk_c8, sk_c8))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[373])).
% 0.56/0.74 tff(375,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c8), sk_c6) = multiply(sk_c1, multiply(sk_c8, sk_c6)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(376,plain,
% 0.56/0.74 (multiply(multiply(sk_c1, sk_c8), sk_c6) = multiply(sk_c1, multiply(sk_c8, sk_c6))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[375, 37])).
% 0.56/0.74 tff(377,plain,
% 0.56/0.74 (sk_c7 = multiply(sk_c1, sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[327])).
% 0.56/0.74 tff(378,plain,
% 0.56/0.74 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c1, sk_c8), sk_c6)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[377])).
% 0.56/0.74 tff(379,plain,
% 0.56/0.74 (multiply(sk_c7, sk_c6) = identity),
% 0.56/0.74 inference(transitivity,[status(thm)],[378, 376, 374, 332, 329, 189])).
% 0.56/0.74 tff(380,plain,
% 0.56/0.74 (multiply(multiply(sk_c7, sk_c6), sk_c4) = multiply(identity, sk_c4)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[379])).
% 0.56/0.74 tff(381,plain,
% 0.56/0.74 (multiply(identity, sk_c4) = multiply(multiply(sk_c7, sk_c6), sk_c4)),
% 0.56/0.74 inference(symmetry,[status(thm)],[380])).
% 0.56/0.74 tff(382,plain,
% 0.56/0.74 (sk_c4 = multiply(identity, sk_c4)),
% 0.56/0.74 inference(symmetry,[status(thm)],[147])).
% 0.56/0.74 tff(383,plain,
% 0.56/0.74 (sk_c4 = multiply(multiply(sk_c7, sk_c6), sk_c4)),
% 0.56/0.74 inference(transitivity,[status(thm)],[382, 381])).
% 0.56/0.74 tff(384,plain,
% 0.56/0.74 (multiply(identity, sk_c4) = multiply(identity, multiply(multiply(sk_c7, sk_c6), sk_c4))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[383])).
% 0.56/0.74 tff(385,plain,
% 0.56/0.74 (multiply(identity, multiply(multiply(sk_c7, sk_c6), sk_c4)) = multiply(identity, sk_c4)),
% 0.56/0.74 inference(symmetry,[status(thm)],[384])).
% 0.56/0.74 tff(386,plain,
% 0.56/0.74 (multiply(multiply(sk_c7, sk_c6), sk_c4) = sk_c4),
% 0.56/0.74 inference(transitivity,[status(thm)],[380, 147])).
% 0.56/0.74 tff(387,plain,
% 0.56/0.74 (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(identity, sk_c7)),
% 0.56/0.74 inference(symmetry,[status(thm)],[369])).
% 0.56/0.74 tff(388,plain,
% 0.56/0.74 (multiply(sk_c8, multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c8, sk_c4), sk_c7)),
% 0.56/0.74 inference(symmetry,[status(thm)],[364])).
% 0.56/0.74 tff(389,plain,
% 0.56/0.74 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c7))),
% 0.56/0.74 inference(symmetry,[status(thm)],[362])).
% 0.56/0.74 tff(390,plain,
% 0.56/0.74 (sk_c8 = multiply(sk_c4, sk_c7)),
% 0.56/0.74 inference(symmetry,[status(thm)],[361])).
% 0.56/0.74 tff(391,plain,
% 0.56/0.74 (multiply(sk_c8, sk_c8) = multiply(multiply(sk_c4, sk_c7), sk_c8)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[390])).
% 0.56/0.74 tff(392,plain,
% 0.56/0.74 (multiply(multiply(sk_c4, sk_c7), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[391])).
% 0.56/0.74 tff(393,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c7), sk_c8) = multiply(sk_c4, multiply(sk_c7, sk_c8)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(394,plain,
% 0.56/0.74 (multiply(multiply(sk_c4, sk_c7), sk_c8) = multiply(sk_c4, multiply(sk_c7, sk_c8))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[393, 37])).
% 0.56/0.74 tff(395,plain,
% 0.56/0.74 (multiply(sk_c4, multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c4, sk_c7), sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[394])).
% 0.56/0.74 tff(396,plain,
% 0.56/0.74 (multiply(sk_c4, multiply(sk_c7, sk_c8)) = sk_c7),
% 0.56/0.74 inference(transitivity,[status(thm)],[395, 392, 389, 388, 387, 371])).
% 0.56/0.74 tff(397,plain,
% 0.56/0.74 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c6) = multiply(sk_c7, sk_c6)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[396])).
% 0.56/0.74 tff(398,plain,
% 0.56/0.74 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c6)),
% 0.56/0.74 inference(symmetry,[status(thm)],[397])).
% 0.56/0.74 tff(399,plain,
% 0.56/0.74 (multiply(multiply(sk_c1, sk_c8), sk_c6) = multiply(sk_c7, sk_c6)),
% 0.56/0.74 inference(symmetry,[status(thm)],[378])).
% 0.56/0.74 tff(400,plain,
% 0.56/0.74 (multiply(sk_c1, multiply(sk_c8, sk_c6)) = multiply(multiply(sk_c1, sk_c8), sk_c6)),
% 0.56/0.74 inference(symmetry,[status(thm)],[376])).
% 0.56/0.74 tff(401,plain,
% 0.56/0.74 (multiply(sk_c1, multiply(sk_c8, sk_c8)) = multiply(sk_c1, multiply(sk_c8, sk_c6))),
% 0.56/0.74 inference(symmetry,[status(thm)],[374])).
% 0.56/0.74 tff(402,plain,
% 0.56/0.74 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c1, sk_c8), sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[329])).
% 0.56/0.74 tff(403,plain,
% 0.56/0.74 (identity = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[189])).
% 0.56/0.74 tff(404,plain,
% 0.56/0.74 (identity = multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c6)),
% 0.56/0.74 inference(transitivity,[status(thm)],[403, 402, 331, 401, 400, 399, 398])).
% 0.56/0.74 tff(405,plain,
% 0.56/0.74 (multiply(identity, multiply(multiply(sk_c7, sk_c6), sk_c4)) = multiply(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c6), sk_c4)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[404, 386])).
% 0.56/0.74 tff(406,plain,
% 0.56/0.74 (multiply(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c6), sk_c4) = multiply(identity, multiply(multiply(sk_c7, sk_c6), sk_c4))),
% 0.56/0.74 inference(symmetry,[status(thm)],[405])).
% 0.56/0.74 tff(407,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c6), sk_c4) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), multiply(sk_c6, sk_c4)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(408,plain,
% 0.56/0.74 (multiply(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c6), sk_c4) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), multiply(sk_c6, sk_c4))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[407, 37])).
% 0.56/0.74 tff(409,plain,
% 0.56/0.74 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), multiply(sk_c6, sk_c4)) = multiply(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c6), sk_c4)),
% 0.56/0.74 inference(symmetry,[status(thm)],[408])).
% 0.56/0.74 tff(410,plain,
% 0.56/0.74 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), multiply(sk_c6, sk_c4)) = multiply(sk_c7, multiply(sk_c6, sk_c4))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[396])).
% 0.56/0.74 tff(411,plain,
% 0.56/0.74 (multiply(sk_c7, multiply(sk_c6, sk_c4)) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), multiply(sk_c6, sk_c4))),
% 0.56/0.74 inference(symmetry,[status(thm)],[410])).
% 0.56/0.74 tff(412,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c1), sk_c8) = multiply(identity, multiply(sk_c1, sk_c8)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(413,plain,
% 0.56/0.74 (multiply(multiply(identity, sk_c1), sk_c8) = multiply(identity, multiply(sk_c1, sk_c8))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[412, 37])).
% 0.56/0.74 tff(414,plain,
% 0.56/0.74 (multiply(identity, multiply(sk_c1, sk_c8)) = multiply(multiply(identity, sk_c1), sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[413])).
% 0.56/0.74 tff(415,plain,
% 0.56/0.74 (multiply(identity, multiply(sk_c1, sk_c8)) = multiply(multiply(sk_c8, sk_c4), sk_c7)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[368, 327])).
% 0.56/0.74 tff(416,plain,
% 0.56/0.74 (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(identity, multiply(sk_c1, sk_c8))),
% 0.56/0.74 inference(symmetry,[status(thm)],[415])).
% 0.56/0.74 tff(417,plain,
% 0.56/0.74 (sk_c7 = multiply(multiply(identity, sk_c1), sk_c8)),
% 0.56/0.74 inference(transitivity,[status(thm)],[372, 369, 416, 414])).
% 0.56/0.74 tff(418,plain,
% 0.56/0.74 (multiply(sk_c7, multiply(sk_c6, sk_c4)) = multiply(multiply(multiply(identity, sk_c1), sk_c8), multiply(sk_c6, sk_c4))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[417])).
% 0.56/0.74 tff(419,plain,
% 0.56/0.74 (multiply(multiply(multiply(identity, sk_c1), sk_c8), multiply(sk_c6, sk_c4)) = multiply(sk_c7, multiply(sk_c6, sk_c4))),
% 0.56/0.74 inference(symmetry,[status(thm)],[418])).
% 0.56/0.74 tff(420,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(identity, sk_c1), sk_c8), multiply(sk_c6, sk_c4)) = multiply(multiply(identity, sk_c1), multiply(sk_c8, multiply(sk_c6, sk_c4))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(421,plain,
% 0.56/0.74 (multiply(multiply(multiply(identity, sk_c1), sk_c8), multiply(sk_c6, sk_c4)) = multiply(multiply(identity, sk_c1), multiply(sk_c8, multiply(sk_c6, sk_c4)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[420, 37])).
% 0.56/0.74 tff(422,plain,
% 0.56/0.74 (multiply(multiply(identity, sk_c1), multiply(sk_c8, multiply(sk_c6, sk_c4))) = multiply(multiply(multiply(identity, sk_c1), sk_c8), multiply(sk_c6, sk_c4))),
% 0.56/0.74 inference(symmetry,[status(thm)],[421])).
% 0.56/0.74 tff(423,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c3), sk_c4) = multiply(sk_c8, multiply(sk_c3, sk_c4)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(424,plain,
% 0.56/0.74 (multiply(multiply(sk_c8, sk_c3), sk_c4) = multiply(sk_c8, multiply(sk_c3, sk_c4))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[423, 37])).
% 0.56/0.74 tff(425,plain,
% 0.56/0.74 (multiply(multiply(sk_c8, sk_c3), sk_c4) = multiply(sk_c7, sk_c4)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[211])).
% 0.56/0.74 tff(426,plain,
% 0.56/0.74 (multiply(sk_c7, sk_c4) = multiply(multiply(sk_c8, sk_c3), sk_c4)),
% 0.56/0.74 inference(symmetry,[status(thm)],[425])).
% 0.56/0.74 tff(427,plain,
% 0.56/0.74 (multiply(multiply(sk_c8, sk_c6), sk_c4) = multiply(sk_c7, sk_c4)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[113])).
% 0.56/0.74 tff(428,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c6), sk_c4) = multiply(sk_c8, multiply(sk_c6, sk_c4)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(429,plain,
% 0.56/0.74 (multiply(multiply(sk_c8, sk_c6), sk_c4) = multiply(sk_c8, multiply(sk_c6, sk_c4))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[428, 37])).
% 0.56/0.74 tff(430,plain,
% 0.56/0.74 (multiply(sk_c8, multiply(sk_c6, sk_c4)) = multiply(multiply(sk_c8, sk_c6), sk_c4)),
% 0.56/0.74 inference(symmetry,[status(thm)],[429])).
% 0.56/0.74 tff(431,plain,
% 0.56/0.74 (multiply(sk_c8, multiply(sk_c6, sk_c4)) = multiply(sk_c8, multiply(sk_c3, sk_c4))),
% 0.56/0.74 inference(transitivity,[status(thm)],[430, 427, 426, 424])).
% 0.56/0.74 tff(432,plain,
% 0.56/0.74 (multiply(multiply(identity, sk_c1), multiply(sk_c8, multiply(sk_c6, sk_c4))) = multiply(multiply(identity, sk_c1), multiply(sk_c8, multiply(sk_c3, sk_c4)))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[431])).
% 0.56/0.74 tff(433,plain,
% 0.56/0.74 (multiply(multiply(identity, sk_c1), multiply(sk_c8, multiply(sk_c3, sk_c4))) = multiply(multiply(identity, sk_c1), multiply(sk_c8, multiply(sk_c6, sk_c4)))),
% 0.56/0.74 inference(symmetry,[status(thm)],[432])).
% 0.56/0.74 tff(434,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(identity, sk_c1), sk_c8), multiply(sk_c3, sk_c4)) = multiply(multiply(identity, sk_c1), multiply(sk_c8, multiply(sk_c3, sk_c4))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(435,plain,
% 0.56/0.74 (multiply(multiply(multiply(identity, sk_c1), sk_c8), multiply(sk_c3, sk_c4)) = multiply(multiply(identity, sk_c1), multiply(sk_c8, multiply(sk_c3, sk_c4)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[434, 37])).
% 0.56/0.74 tff(436,plain,
% 0.56/0.74 (multiply(multiply(identity, sk_c1), sk_c8) = sk_c7),
% 0.56/0.74 inference(transitivity,[status(thm)],[413, 415, 387, 371])).
% 0.56/0.74 tff(437,plain,
% 0.56/0.74 (multiply(multiply(multiply(identity, sk_c1), sk_c8), multiply(sk_c3, sk_c4)) = multiply(sk_c7, multiply(sk_c3, sk_c4))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[436])).
% 0.56/0.74 tff(438,plain,
% 0.56/0.74 (multiply(sk_c7, multiply(sk_c3, sk_c4)) = multiply(multiply(multiply(identity, sk_c1), sk_c8), multiply(sk_c3, sk_c4))),
% 0.56/0.74 inference(symmetry,[status(thm)],[437])).
% 0.56/0.74 tff(439,plain,
% 0.56/0.74 (multiply(sk_c7, multiply(sk_c3, sk_c4)) = multiply(multiply(sk_c1, sk_c8), multiply(sk_c3, sk_c4))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[377])).
% 0.56/0.74 tff(440,plain,
% 0.56/0.74 (multiply(multiply(sk_c1, sk_c8), multiply(sk_c3, sk_c4)) = multiply(sk_c7, multiply(sk_c3, sk_c4))),
% 0.56/0.74 inference(symmetry,[status(thm)],[439])).
% 0.56/0.74 tff(441,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c8), multiply(sk_c3, sk_c4)) = multiply(sk_c1, multiply(sk_c8, multiply(sk_c3, sk_c4))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(442,plain,
% 0.56/0.74 (multiply(multiply(sk_c1, sk_c8), multiply(sk_c3, sk_c4)) = multiply(sk_c1, multiply(sk_c8, multiply(sk_c3, sk_c4)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[441, 37])).
% 0.56/0.74 tff(443,plain,
% 0.56/0.74 (multiply(sk_c1, multiply(sk_c8, multiply(sk_c3, sk_c4))) = multiply(multiply(sk_c1, sk_c8), multiply(sk_c3, sk_c4))),
% 0.56/0.74 inference(symmetry,[status(thm)],[442])).
% 0.56/0.74 tff(444,plain,
% 0.56/0.74 (multiply(multiply(sk_c7, sk_c6), sk_c8) = multiply(identity, sk_c8)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[379])).
% 0.56/0.74 tff(445,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c6), sk_c8) = multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(446,plain,
% 0.56/0.74 (multiply(multiply(sk_c7, sk_c6), sk_c8) = multiply(sk_c7, multiply(sk_c6, sk_c8))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[445, 37])).
% 0.56/0.74 tff(447,plain,
% 0.56/0.74 (multiply(sk_c7, multiply(sk_c6, sk_c8)) = multiply(multiply(sk_c7, sk_c6), sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[446])).
% 0.56/0.74 tff(448,plain,
% 0.56/0.74 (multiply(sk_c6, sk_c8) = multiply(sk_c6, multiply(sk_c4, sk_c7))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[390])).
% 0.56/0.74 tff(449,plain,
% 0.56/0.74 (multiply(sk_c6, multiply(sk_c4, sk_c7)) = multiply(sk_c6, sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[448])).
% 0.56/0.74 tff(450,plain,
% 0.56/0.74 (multiply(multiply(sk_c1, sk_c8), multiply(sk_c6, multiply(sk_c4, sk_c7))) = multiply(sk_c7, multiply(sk_c6, sk_c8))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[327, 449])).
% 0.56/0.74 tff(451,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c8), multiply(sk_c6, multiply(sk_c4, sk_c7))) = multiply(sk_c1, multiply(sk_c8, multiply(sk_c6, multiply(sk_c4, sk_c7)))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(452,plain,
% 0.56/0.74 (multiply(multiply(sk_c1, sk_c8), multiply(sk_c6, multiply(sk_c4, sk_c7))) = multiply(sk_c1, multiply(sk_c8, multiply(sk_c6, multiply(sk_c4, sk_c7))))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[451, 37])).
% 0.56/0.74 tff(453,plain,
% 0.56/0.74 (multiply(sk_c1, multiply(sk_c8, multiply(sk_c6, multiply(sk_c4, sk_c7)))) = multiply(multiply(sk_c1, sk_c8), multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.56/0.74 inference(symmetry,[status(thm)],[452])).
% 0.56/0.74 tff(454,plain,
% 0.56/0.74 (multiply(sk_c8, multiply(sk_c6, multiply(sk_c4, sk_c7))) = multiply(sk_c8, multiply(sk_c6, sk_c8))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[449])).
% 0.56/0.74 tff(455,plain,
% 0.56/0.74 (multiply(sk_c8, multiply(sk_c6, sk_c8)) = multiply(sk_c8, multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.56/0.74 inference(symmetry,[status(thm)],[454])).
% 0.56/0.74 tff(456,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c6), sk_c8) = multiply(sk_c8, multiply(sk_c6, sk_c8)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(457,plain,
% 0.56/0.74 (multiply(multiply(sk_c8, sk_c6), sk_c8) = multiply(sk_c8, multiply(sk_c6, sk_c8))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[456, 37])).
% 0.56/0.74 tff(458,plain,
% 0.56/0.74 (multiply(sk_c8, sk_c6) = inverse(sk_c8)),
% 0.56/0.74 inference(transitivity,[status(thm)],[113, 296])).
% 0.56/0.74 tff(459,plain,
% 0.56/0.74 (multiply(multiply(sk_c8, sk_c6), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[458])).
% 0.56/0.74 tff(460,plain,
% 0.56/0.74 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c6), sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[459])).
% 0.56/0.74 tff(461,plain,
% 0.56/0.74 (multiply(sk_c8, sk_c4) = multiply(sk_c8, multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.56/0.74 inference(transitivity,[status(thm)],[366, 172, 403, 460, 457, 455])).
% 0.56/0.74 tff(462,plain,
% 0.56/0.74 (multiply(sk_c1, multiply(sk_c8, sk_c4)) = multiply(sk_c1, multiply(sk_c8, multiply(sk_c6, multiply(sk_c4, sk_c7))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[461])).
% 0.56/0.74 tff(463,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c8), sk_c4) = multiply(sk_c1, multiply(sk_c8, sk_c4)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(464,plain,
% 0.56/0.74 (multiply(multiply(sk_c1, sk_c8), sk_c4) = multiply(sk_c1, multiply(sk_c8, sk_c4))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[463, 37])).
% 0.56/0.74 tff(465,plain,
% 0.56/0.74 (multiply(sk_c7, sk_c4) = multiply(multiply(sk_c1, sk_c8), sk_c4)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[377])).
% 0.56/0.74 tff(466,plain,
% 0.56/0.74 (multiply(sk_c8, multiply(sk_c3, sk_c4)) = multiply(multiply(sk_c8, sk_c3), sk_c4)),
% 0.56/0.74 inference(symmetry,[status(thm)],[424])).
% 0.56/0.74 tff(467,plain,
% 0.56/0.74 (multiply(sk_c8, multiply(sk_c3, sk_c4)) = multiply(identity, sk_c8)),
% 0.56/0.74 inference(transitivity,[status(thm)],[466, 425, 465, 464, 462, 453, 450, 447, 444])).
% 0.56/0.74 tff(468,plain,
% 0.56/0.74 (multiply(sk_c1, multiply(sk_c8, multiply(sk_c3, sk_c4))) = multiply(sk_c1, multiply(identity, sk_c8))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[467])).
% 0.56/0.74 tff(469,plain,
% 0.56/0.74 (multiply(sk_c1, multiply(identity, sk_c8)) = multiply(sk_c1, multiply(sk_c8, multiply(sk_c3, sk_c4)))),
% 0.56/0.74 inference(symmetry,[status(thm)],[468])).
% 0.56/0.74 tff(470,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, identity), sk_c8) = multiply(sk_c1, multiply(identity, sk_c8)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(471,plain,
% 0.56/0.74 (multiply(multiply(sk_c1, identity), sk_c8) = multiply(sk_c1, multiply(identity, sk_c8))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[470, 37])).
% 0.56/0.74 tff(472,plain,
% 0.56/0.74 (multiply(multiply(sk_c1, sk_c8), sk_c4) = multiply(sk_c7, sk_c4)),
% 0.56/0.74 inference(symmetry,[status(thm)],[465])).
% 0.56/0.74 tff(473,plain,
% 0.56/0.74 (multiply(sk_c1, multiply(sk_c8, sk_c4)) = multiply(multiply(sk_c1, sk_c8), sk_c4)),
% 0.56/0.74 inference(symmetry,[status(thm)],[464])).
% 0.56/0.74 tff(474,plain,
% 0.56/0.74 (multiply(sk_c1, identity) = multiply(sk_c1, multiply(sk_c8, sk_c4))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[368])).
% 0.56/0.74 tff(475,plain,
% 0.56/0.74 (multiply(sk_c1, identity) = multiply(sk_c7, sk_c4)),
% 0.56/0.74 inference(transitivity,[status(thm)],[474, 473, 472])).
% 0.56/0.74 tff(476,plain,
% 0.56/0.74 (multiply(multiply(sk_c1, identity), sk_c8) = multiply(multiply(sk_c7, sk_c4), sk_c8)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[475])).
% 0.56/0.74 tff(477,plain,
% 0.56/0.74 (multiply(multiply(sk_c7, sk_c4), sk_c8) = multiply(multiply(sk_c1, identity), sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[476])).
% 0.56/0.74 tff(478,plain,
% 0.56/0.74 (multiply(sk_c7, sk_c4) = multiply(identity, sk_c8)),
% 0.56/0.74 inference(transitivity,[status(thm)],[465, 464, 462, 453, 450, 447, 444])).
% 0.56/0.74 tff(479,plain,
% 0.56/0.74 (multiply(multiply(sk_c7, sk_c4), sk_c8) = multiply(multiply(identity, sk_c8), sk_c8)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[478])).
% 0.56/0.74 tff(480,plain,
% 0.56/0.74 (multiply(multiply(identity, sk_c8), sk_c8) = multiply(multiply(sk_c7, sk_c4), sk_c8)),
% 0.56/0.74 inference(symmetry,[status(thm)],[479])).
% 0.56/0.74 tff(481,plain,
% 0.56/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c8), sk_c8) = multiply(identity, multiply(sk_c8, sk_c8)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(482,plain,
% 0.56/0.74 (multiply(multiply(identity, sk_c8), sk_c8) = multiply(identity, multiply(sk_c8, sk_c8))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[481, 37])).
% 0.56/0.74 tff(483,plain,
% 0.56/0.74 (multiply(identity, multiply(sk_c8, sk_c8)) = multiply(multiply(identity, sk_c8), sk_c8)),
% 0.56/0.75 inference(symmetry,[status(thm)],[482])).
% 0.56/0.75 tff(484,plain,
% 0.56/0.75 (multiply(sk_c8, sk_c8) = sk_c7),
% 0.56/0.75 inference(transitivity,[status(thm)],[389, 388, 387, 371])).
% 0.56/0.75 tff(485,plain,
% 0.56/0.75 (multiply(identity, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c8, sk_c4), sk_c7)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[368, 484])).
% 0.56/0.75 tff(486,plain,
% 0.56/0.75 (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(identity, multiply(sk_c8, sk_c8))),
% 0.56/0.75 inference(symmetry,[status(thm)],[485])).
% 0.56/0.75 tff(487,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(sk_c7, sk_c8)) = sk_c4),
% 0.56/0.75 inference(transitivity,[status(thm)],[395, 392, 389, 388, 486, 483, 480, 477, 471, 469, 443, 440, 438, 435, 433, 422, 419, 411, 409, 406, 385, 147])).
% 0.56/0.75 tff(488,plain,
% 0.56/0.75 (inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = inverse(sk_c4)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[487])).
% 0.56/0.75 tff(489,plain,
% 0.56/0.75 (inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8),
% 0.56/0.75 inference(transitivity,[status(thm)],[488, 295])).
% 0.56/0.75 tff(490,plain,
% 0.56/0.75 (multiply(sk_c7, multiply(sk_c6, sk_c8)) = sk_c8),
% 0.56/0.75 inference(transitivity,[status(thm)],[447, 444, 9])).
% 0.56/0.75 tff(491,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(sk_c8, sk_c8)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[490, 490])).
% 0.56/0.75 tff(492,plain,
% 0.56/0.75 (multiply(identity, sk_c8) = multiply(multiply(sk_c7, sk_c6), sk_c8)),
% 0.56/0.75 inference(symmetry,[status(thm)],[444])).
% 0.56/0.75 tff(493,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c1), sk_c8) = multiply(sk_c4, multiply(sk_c1, sk_c8)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(494,plain,
% 0.56/0.75 (multiply(multiply(sk_c4, sk_c1), sk_c8) = multiply(sk_c4, multiply(sk_c1, sk_c8))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[493, 37])).
% 0.56/0.75 tff(495,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(sk_c1, sk_c8)) = multiply(multiply(sk_c4, sk_c1), sk_c8)),
% 0.56/0.75 inference(symmetry,[status(thm)],[494])).
% 0.56/0.75 tff(496,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(sk_c1, sk_c8)) = multiply(sk_c4, sk_c7)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[327])).
% 0.56/0.75 tff(497,plain,
% 0.56/0.75 (multiply(sk_c4, sk_c7) = multiply(sk_c4, multiply(sk_c1, sk_c8))),
% 0.56/0.75 inference(symmetry,[status(thm)],[496])).
% 0.56/0.75 tff(498,plain,
% 0.56/0.75 (sk_c8 = multiply(multiply(sk_c4, sk_c1), sk_c8)),
% 0.56/0.75 inference(transitivity,[status(thm)],[390, 497, 495])).
% 0.56/0.75 tff(499,plain,
% 0.56/0.75 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c1), sk_c8))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[291, 498])).
% 0.56/0.75 tff(500,plain,
% 0.56/0.75 (multiply(sk_c7, multiply(multiply(sk_c4, sk_c1), sk_c8)) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.75 inference(symmetry,[status(thm)],[499])).
% 0.56/0.75 tff(501,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c1), sk_c8)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(502,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c1), sk_c8))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[501, 37])).
% 0.56/0.75 tff(503,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8) = identity),
% 0.56/0.75 inference(transitivity,[status(thm)],[502, 500, 189])).
% 0.56/0.75 tff(504,plain,
% 0.56/0.75 (multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8), sk_c8) = multiply(identity, sk_c8)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[503])).
% 0.56/0.75 tff(505,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8), sk_c8) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), multiply(sk_c8, sk_c8)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(506,plain,
% 0.56/0.75 (multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8), sk_c8) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), multiply(sk_c8, sk_c8))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[505, 37])).
% 0.56/0.75 tff(507,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), multiply(sk_c8, sk_c8)) = multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8), sk_c8)),
% 0.56/0.75 inference(symmetry,[status(thm)],[506])).
% 0.56/0.75 tff(508,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), multiply(sk_c8, sk_c6)) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), multiply(sk_c8, sk_c8))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[373])).
% 0.56/0.75 tff(509,plain,
% 0.56/0.75 (sk_c7 = multiply(sk_c8, sk_c6)),
% 0.56/0.75 inference(symmetry,[status(thm)],[113])).
% 0.56/0.75 tff(510,plain,
% 0.56/0.75 (multiply(sk_c8, sk_c3) = multiply(sk_c8, sk_c6)),
% 0.56/0.75 inference(transitivity,[status(thm)],[211, 509])).
% 0.56/0.75 tff(511,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), multiply(sk_c8, sk_c3)) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), multiply(sk_c8, sk_c6))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[510])).
% 0.56/0.75 tff(512,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8), sk_c3) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), multiply(sk_c8, sk_c3)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(513,plain,
% 0.56/0.75 (multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8), sk_c3) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), multiply(sk_c8, sk_c3))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[512, 37])).
% 0.56/0.75 tff(514,plain,
% 0.56/0.75 (multiply(sk_c7, multiply(multiply(sk_c4, sk_c1), sk_c8)) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8)),
% 0.56/0.75 inference(symmetry,[status(thm)],[502])).
% 0.56/0.75 tff(515,plain,
% 0.56/0.75 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8)),
% 0.56/0.75 inference(transitivity,[status(thm)],[378, 376, 374, 332, 329, 499, 514])).
% 0.56/0.75 tff(516,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, sk_c6), sk_c3) = multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8), sk_c3)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[515])).
% 0.56/0.75 tff(517,plain,
% 0.56/0.75 (identity = multiply(sk_c7, sk_c6)),
% 0.56/0.75 inference(transitivity,[status(thm)],[403, 402, 331, 401, 400, 399])).
% 0.56/0.75 tff(518,plain,
% 0.56/0.75 (multiply(identity, sk_c3) = multiply(multiply(sk_c7, sk_c6), sk_c3)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[517])).
% 0.56/0.75 tff(519,plain,
% 0.56/0.75 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c3) = sk_c3)),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(520,plain,
% 0.56/0.75 (multiply(identity, sk_c3) = sk_c3),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[519, 7])).
% 0.56/0.75 tff(521,plain,
% 0.56/0.75 (sk_c3 = multiply(identity, sk_c3)),
% 0.56/0.75 inference(symmetry,[status(thm)],[520])).
% 0.56/0.75 tff(522,plain,
% 0.56/0.75 (multiply(multiply(sk_c4, sk_c1), sk_c8) = sk_c8),
% 0.56/0.75 inference(transitivity,[status(thm)],[494, 496, 361])).
% 0.56/0.75 tff(523,plain,
% 0.56/0.75 (multiply(sk_c7, multiply(multiply(sk_c4, sk_c1), sk_c8)) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[296, 522])).
% 0.56/0.75 tff(524,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8) = identity),
% 0.56/0.75 inference(transitivity,[status(thm)],[502, 523, 189])).
% 0.56/0.75 tff(525,plain,
% 0.56/0.75 (multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8), sk_c8) = multiply(identity, sk_c8)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[524])).
% 0.56/0.75 tff(526,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8), sk_c6) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), multiply(sk_c8, sk_c6)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(527,plain,
% 0.56/0.75 (multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8), sk_c6) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), multiply(sk_c8, sk_c6))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[526, 37])).
% 0.56/0.75 tff(528,plain,
% 0.56/0.75 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c1), sk_c8))),
% 0.56/0.75 inference(symmetry,[status(thm)],[523])).
% 0.56/0.75 tff(529,plain,
% 0.56/0.75 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8)),
% 0.56/0.75 inference(transitivity,[status(thm)],[378, 376, 374, 332, 329, 528, 514])).
% 0.56/0.75 tff(530,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, sk_c6), sk_c6) = multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c1)), sk_c8), sk_c6)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[529])).
% 0.56/0.75 tff(531,plain,
% 0.56/0.75 (multiply(identity, sk_c6) = multiply(multiply(sk_c7, sk_c6), sk_c6)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[517])).
% 0.56/0.75 tff(532,plain,
% 0.56/0.75 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c6) = sk_c6)),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(533,plain,
% 0.56/0.75 (multiply(identity, sk_c6) = sk_c6),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[532, 7])).
% 0.56/0.75 tff(534,plain,
% 0.56/0.75 (sk_c6 = multiply(identity, sk_c6)),
% 0.56/0.75 inference(symmetry,[status(thm)],[533])).
% 0.56/0.75 tff(535,assumption,(~(multiply(sk_c2, sk_c8) = sk_c3)), introduced(assumption)).
% 0.56/0.75 tff(536,plain,
% 0.56/0.75 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(537,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_24')).
% 0.56/0.75 tff(538,plain,
% 0.56/0.75 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.56/0.75 tff(539,plain,
% 0.56/0.75 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[538, 535])).
% 0.56/0.75 tff(540,plain,
% 0.56/0.75 (multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(sk_c5, sk_c8)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[490])).
% 0.56/0.75 tff(541,plain,
% 0.56/0.75 (multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(sk_c7, multiply(sk_c6, sk_c8))),
% 0.56/0.75 inference(transitivity,[status(thm)],[540, 539, 534, 531, 530, 527, 508, 507, 525, 492, 446])).
% 0.56/0.75 tff(542,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c8)))) = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[541])).
% 0.56/0.75 tff(543,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c8)))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(544,plain,
% 0.56/0.75 (multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c8))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[543, 37])).
% 0.56/0.75 tff(545,plain,
% 0.56/0.75 (((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(546,plain,
% 0.56/0.75 (((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(547,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_25')).
% 0.56/0.75 tff(548,plain,
% 0.56/0.75 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.56/0.75 tff(549,plain,
% 0.56/0.75 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[548, 545])).
% 0.56/0.75 tff(550,plain,
% 0.56/0.75 (inverse(sk_c5) = sk_c8),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[549, 535])).
% 0.56/0.75 tff(551,plain,
% 0.56/0.75 (sk_c8 = inverse(sk_c5)),
% 0.56/0.75 inference(symmetry,[status(thm)],[550])).
% 0.56/0.75 tff(552,plain,
% 0.56/0.75 (multiply(sk_c7, multiply(sk_c6, sk_c8)) = inverse(sk_c5)),
% 0.56/0.75 inference(transitivity,[status(thm)],[447, 444, 9, 551])).
% 0.56/0.75 tff(553,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[552])).
% 0.56/0.75 tff(554,plain,
% 0.56/0.75 (multiply(inverse(sk_c5), sk_c5) = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5)),
% 0.56/0.75 inference(symmetry,[status(thm)],[553])).
% 0.56/0.75 tff(555,plain,
% 0.56/0.75 (identity = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5)),
% 0.56/0.75 inference(transitivity,[status(thm)],[149, 554])).
% 0.56/0.75 tff(556,plain,
% 0.56/0.75 (multiply(identity, multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[555])).
% 0.56/0.75 tff(557,plain,
% 0.56/0.75 (sk_c8 = multiply(sk_c7, multiply(sk_c6, sk_c8))),
% 0.56/0.75 inference(transitivity,[status(thm)],[139, 492, 446])).
% 0.56/0.75 tff(558,plain,
% 0.56/0.75 (multiply(identity, sk_c8) = multiply(identity, multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[557])).
% 0.56/0.75 tff(559,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(sk_c8, sk_c8)) = multiply(sk_c4, sk_c7)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[484])).
% 0.56/0.75 tff(560,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c8), sk_c8) = multiply(sk_c4, multiply(sk_c8, sk_c8)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(561,plain,
% 0.56/0.75 (multiply(multiply(sk_c4, sk_c8), sk_c8) = multiply(sk_c4, multiply(sk_c8, sk_c8))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[560, 37])).
% 0.56/0.75 tff(562,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(sk_c4, multiply(sk_c7, sk_c8))) = multiply(sk_c4, sk_c7)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[396])).
% 0.56/0.75 tff(563,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8),
% 0.56/0.75 inference(transitivity,[status(thm)],[562, 361])).
% 0.56/0.75 tff(564,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(sk_c8, sk_c6)) = multiply(sk_c4, sk_c7)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[113])).
% 0.56/0.75 tff(565,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c8), sk_c6) = multiply(sk_c4, multiply(sk_c8, sk_c6)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(566,plain,
% 0.56/0.75 (multiply(multiply(sk_c4, sk_c8), sk_c6) = multiply(sk_c4, multiply(sk_c8, sk_c6))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[565, 37])).
% 0.56/0.75 tff(567,plain,
% 0.56/0.75 (multiply(multiply(sk_c4, sk_c8), sk_c6) = sk_c8),
% 0.56/0.75 inference(transitivity,[status(thm)],[566, 564, 361])).
% 0.56/0.75 tff(568,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)) = multiply(sk_c4, sk_c8)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[567])).
% 0.56/0.75 tff(569,plain,
% 0.56/0.75 (multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), multiply(sk_c4, multiply(sk_c4, multiply(sk_c7, sk_c8)))) = multiply(multiply(sk_c4, sk_c8), sk_c8)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[568, 563])).
% 0.56/0.75 tff(570,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), sk_c4), multiply(sk_c4, multiply(sk_c7, sk_c8))) = multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), multiply(sk_c4, multiply(sk_c4, multiply(sk_c7, sk_c8)))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(571,plain,
% 0.56/0.75 (multiply(multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), sk_c4), multiply(sk_c4, multiply(sk_c7, sk_c8))) = multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), multiply(sk_c4, multiply(sk_c4, multiply(sk_c7, sk_c8))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[570, 37])).
% 0.56/0.75 tff(572,plain,
% 0.56/0.75 (sk_c7 = multiply(sk_c4, multiply(sk_c7, sk_c8))),
% 0.56/0.75 inference(transitivity,[status(thm)],[372, 369, 364, 362, 391, 394])).
% 0.56/0.75 tff(573,plain,
% 0.56/0.75 (multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), sk_c4) = multiply(multiply(sk_c4, sk_c8), sk_c4)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[568])).
% 0.56/0.75 tff(574,plain,
% 0.56/0.75 (multiply(multiply(sk_c4, sk_c8), sk_c4) = multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), sk_c4)),
% 0.56/0.75 inference(symmetry,[status(thm)],[573])).
% 0.56/0.75 tff(575,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c8), sk_c4) = multiply(sk_c4, multiply(sk_c8, sk_c4)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(576,plain,
% 0.56/0.75 (multiply(multiply(sk_c4, sk_c8), sk_c4) = multiply(sk_c4, multiply(sk_c8, sk_c4))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[575, 37])).
% 0.56/0.75 tff(577,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(sk_c8, sk_c4)) = multiply(multiply(sk_c4, sk_c8), sk_c4)),
% 0.56/0.75 inference(symmetry,[status(thm)],[576])).
% 0.56/0.75 tff(578,plain,
% 0.56/0.75 (multiply(sk_c7, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[296])).
% 0.56/0.75 tff(579,plain,
% 0.56/0.75 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, sk_c8)),
% 0.56/0.75 inference(symmetry,[status(thm)],[578])).
% 0.56/0.75 tff(580,plain,
% 0.56/0.75 (multiply(sk_c8, sk_c4) = multiply(sk_c7, sk_c8)),
% 0.56/0.75 inference(transitivity,[status(thm)],[366, 172, 403, 579])).
% 0.56/0.75 tff(581,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(sk_c8, sk_c4)) = multiply(sk_c4, multiply(sk_c7, sk_c8))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[580])).
% 0.56/0.75 tff(582,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(sk_c7, sk_c8)) = multiply(sk_c4, multiply(sk_c8, sk_c4))),
% 0.56/0.75 inference(symmetry,[status(thm)],[581])).
% 0.56/0.75 tff(583,plain,
% 0.56/0.75 (multiply(sk_c4, multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), sk_c4)),
% 0.56/0.75 inference(transitivity,[status(thm)],[582, 577, 574])).
% 0.56/0.75 tff(584,plain,
% 0.56/0.75 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = multiply(multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), sk_c4), multiply(sk_c4, multiply(sk_c7, sk_c8)))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[583, 572])).
% 0.56/0.75 tff(585,plain,
% 0.56/0.75 (multiply(sk_c7, multiply(sk_c6, sk_c8)) = multiply(sk_c4, multiply(sk_c7, sk_c8))),
% 0.56/0.75 inference(transitivity,[status(thm)],[447, 444, 558, 556, 544, 542, 491, 391, 394])).
% 0.56/0.75 tff(586,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c7) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[585])).
% 0.56/0.75 tff(587,plain,
% 0.56/0.75 (multiply(sk_c7, sk_c4) = multiply(sk_c7, multiply(sk_c6, sk_c8))),
% 0.56/0.75 inference(transitivity,[status(thm)],[465, 464, 462, 453, 450])).
% 0.56/0.75 tff(588,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, sk_c4), sk_c7) = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c7)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[587])).
% 0.56/0.75 tff(589,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c4), sk_c7) = multiply(sk_c7, multiply(sk_c4, sk_c7)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(590,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, sk_c4), sk_c7) = multiply(sk_c7, multiply(sk_c4, sk_c7))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[589, 37])).
% 0.56/0.75 tff(591,plain,
% 0.56/0.75 (multiply(sk_c7, multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c7, sk_c4), sk_c7)),
% 0.56/0.75 inference(symmetry,[status(thm)],[590])).
% 0.56/0.75 tff(592,plain,
% 0.56/0.75 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, multiply(sk_c4, sk_c7))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[291, 390])).
% 0.56/0.75 tff(593,plain,
% 0.56/0.75 (multiply(sk_c8, sk_c8) = inverse(sk_c8)),
% 0.56/0.75 inference(transitivity,[status(thm)],[389, 388, 387, 371, 296])).
% 0.56/0.75 tff(594,plain,
% 0.56/0.75 (multiply(multiply(sk_c8, sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[593])).
% 0.56/0.75 tff(595,plain,
% 0.56/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), sk_c8) = multiply(sk_c8, multiply(sk_c8, sk_c8)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(596,plain,
% 0.56/0.75 (multiply(multiply(sk_c8, sk_c8), sk_c8) = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[595, 37])).
% 0.56/0.75 tff(597,plain,
% 0.56/0.75 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c8, sk_c8), sk_c8)),
% 0.56/0.75 inference(symmetry,[status(thm)],[596])).
% 0.56/0.75 tff(598,plain,
% 0.56/0.75 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7),
% 0.56/0.75 inference(transitivity,[status(thm)],[597, 594, 592, 591, 588, 586, 584, 571, 569, 561, 559, 361, 139, 558, 556, 544, 542, 491, 389, 388, 387, 371])).
% 0.56/0.75 tff(599,plain,
% 0.56/0.75 (multiply(identity, multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(identity, sk_c8)),
% 0.56/0.75 inference(symmetry,[status(thm)],[558])).
% 0.56/0.75 tff(600,plain,
% 0.56/0.75 (multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(identity, multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.75 inference(symmetry,[status(thm)],[556])).
% 0.56/0.75 tff(601,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c8)))) = multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.75 inference(symmetry,[status(thm)],[544])).
% 0.56/0.75 tff(602,plain,
% 0.56/0.75 (multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c8))))),
% 0.56/0.75 inference(symmetry,[status(thm)],[542])).
% 0.56/0.75 tff(603,plain,
% 0.56/0.75 (multiply(sk_c8, sk_c8) = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.75 inference(symmetry,[status(thm)],[491])).
% 0.56/0.75 tff(604,plain,
% 0.56/0.75 (inverse(sk_c8) = sk_c8),
% 0.56/0.75 inference(transitivity,[status(thm)],[291, 372, 369, 364, 362, 603, 602, 601, 600, 599, 9])).
% 0.56/0.75 tff(605,plain,
% 0.56/0.75 (sk_c8 = sk_c7),
% 0.56/0.75 inference(transitivity,[status(thm)],[139, 558, 556, 544, 542, 491, 389, 388, 387, 371])).
% 0.56/0.75 tff(606,plain,
% 0.56/0.75 (sk_c7 = multiply(sk_c8, sk_c8)),
% 0.56/0.75 inference(transitivity,[status(thm)],[372, 369, 364, 362])).
% 0.56/0.75 tff(607,plain,
% 0.56/0.75 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[606])).
% 0.56/0.75 tff(608,plain,
% 0.56/0.75 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[607, 605])).
% 0.56/0.75 tff(609,plain,
% 0.56/0.75 ((multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.56/0.75 inference(symmetry,[status(thm)],[608])).
% 0.56/0.75 tff(610,plain,
% 0.56/0.75 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[598, 609])).
% 0.56/0.75 tff(611,plain,
% 0.56/0.75 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c8) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c8) = sk_c7)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(612,plain,
% 0.56/0.75 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(inverse(sk_c8) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c8) = sk_c7)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(613,plain,
% 0.56/0.75 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c8) = sk_c7))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[612])).
% 0.56/0.76 tff(614,plain,
% 0.56/0.76 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c8) = sk_c7)))),
% 0.56/0.76 inference(transitivity,[status(thm)],[613, 611])).
% 0.56/0.76 tff(615,plain,
% 0.56/0.76 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(616,plain,
% 0.56/0.76 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c8) = sk_c7))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.56/0.76 tff(617,plain,
% 0.56/0.76 ((~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c8) = sk_c7))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[616, 291, 95])).
% 0.56/0.76 tff(618,plain,
% 0.56/0.76 ((~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[617, 484])).
% 0.56/0.76 tff(619,plain,
% 0.56/0.76 ($false),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[618, 610, 604, 598])).
% 0.56/0.76 tff(620,plain,(multiply(sk_c2, sk_c8) = sk_c3), inference(lemma,lemma(discharge,[]))).
% 0.56/0.76 tff(621,plain,
% 0.56/0.76 (multiply(sk_c2, sk_c8) = multiply(sk_c7, multiply(sk_c6, sk_c8))),
% 0.56/0.76 inference(transitivity,[status(thm)],[620, 521, 518, 516, 513, 511, 508, 507, 504, 492, 446])).
% 0.56/0.76 tff(622,plain,
% 0.56/0.76 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[557, 621])).
% 0.56/0.76 tff(623,plain,
% 0.56/0.76 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.56/0.76 inference(transitivity,[status(thm)],[622, 491, 389, 388, 387, 371])).
% 0.56/0.76 tff(624,plain,
% 0.56/0.76 (multiply(sk_c4, sk_c7) = multiply(sk_c4, multiply(sk_c8, sk_c8))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[606])).
% 0.56/0.76 tff(625,plain,
% 0.56/0.76 (multiply(sk_c4, multiply(sk_c8, sk_c8)) = multiply(sk_c4, sk_c7)),
% 0.56/0.76 inference(symmetry,[status(thm)],[624])).
% 0.56/0.76 tff(626,plain,
% 0.56/0.76 (multiply(sk_c4, sk_c7) = multiply(sk_c4, multiply(sk_c4, multiply(sk_c7, sk_c8)))),
% 0.56/0.76 inference(symmetry,[status(thm)],[562])).
% 0.56/0.76 tff(627,plain,
% 0.56/0.76 (sk_c8 = multiply(sk_c4, multiply(sk_c4, multiply(sk_c7, sk_c8)))),
% 0.56/0.76 inference(transitivity,[status(thm)],[390, 626])).
% 0.56/0.76 tff(628,plain,
% 0.56/0.76 (multiply(sk_c4, sk_c8) = multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6))),
% 0.56/0.76 inference(symmetry,[status(thm)],[568])).
% 0.56/0.76 tff(629,plain,
% 0.56/0.76 (multiply(multiply(sk_c4, sk_c8), sk_c8) = multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), multiply(sk_c4, multiply(sk_c4, multiply(sk_c7, sk_c8))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[628, 627])).
% 0.56/0.76 tff(630,plain,
% 0.56/0.76 (multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), multiply(sk_c4, multiply(sk_c4, multiply(sk_c7, sk_c8)))) = multiply(multiply(sk_c4, sk_c8), sk_c8)),
% 0.56/0.76 inference(symmetry,[status(thm)],[629])).
% 0.56/0.76 tff(631,plain,
% 0.56/0.76 (multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), sk_c4) = multiply(sk_c4, multiply(sk_c7, sk_c8))),
% 0.56/0.76 inference(transitivity,[status(thm)],[573, 576, 581])).
% 0.56/0.76 tff(632,plain,
% 0.56/0.76 (multiply(multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), sk_c4), multiply(sk_c4, multiply(sk_c7, sk_c8))) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7)),
% 0.56/0.76 inference(monotonicity,[status(thm)],[631, 396])).
% 0.56/0.76 tff(633,plain,
% 0.56/0.76 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = multiply(multiply(multiply(sk_c4, multiply(multiply(sk_c4, sk_c8), sk_c6)), sk_c4), multiply(sk_c4, multiply(sk_c7, sk_c8)))),
% 0.56/0.76 inference(symmetry,[status(thm)],[632])).
% 0.56/0.76 tff(634,plain,
% 0.56/0.76 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = sk_c8),
% 0.56/0.76 inference(transitivity,[status(thm)],[633, 571, 630, 561, 625, 361])).
% 0.56/0.76 tff(635,assumption,(inverse(sk_c5) = sk_c8), introduced(assumption)).
% 0.56/0.76 tff(636,plain,
% 0.56/0.76 (sk_c8 = inverse(sk_c5)),
% 0.56/0.76 inference(symmetry,[status(thm)],[635])).
% 0.56/0.76 tff(637,plain,
% 0.56/0.76 (multiply(sk_c7, multiply(sk_c6, sk_c8)) = inverse(sk_c5)),
% 0.56/0.76 inference(transitivity,[status(thm)],[447, 444, 9, 636])).
% 0.56/0.76 tff(638,plain,
% 0.56/0.76 (multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.56/0.76 inference(monotonicity,[status(thm)],[637])).
% 0.56/0.76 tff(639,plain,
% 0.56/0.76 (multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5) = multiply(sk_c8, sk_c4)),
% 0.56/0.76 inference(transitivity,[status(thm)],[638, 127, 187, 367])).
% 0.56/0.76 tff(640,plain,
% 0.56/0.76 (multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c4, multiply(sk_c7, sk_c8))) = multiply(multiply(sk_c8, sk_c4), sk_c7)),
% 0.56/0.76 inference(monotonicity,[status(thm)],[639, 396])).
% 0.56/0.76 tff(641,plain,
% 0.56/0.76 (multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(sk_c4, multiply(sk_c7, sk_c8))),
% 0.56/0.76 inference(transitivity,[status(thm)],[491, 391, 394])).
% 0.56/0.76 tff(642,plain,
% 0.56/0.76 (multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8)))) = multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c4, multiply(sk_c7, sk_c8)))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[641])).
% 0.56/0.76 tff(643,plain,
% 0.56/0.76 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c7, multiply(sk_c6, sk_c8))), multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8)))))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(644,plain,
% 0.56/0.76 (multiply(multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c7, multiply(sk_c6, sk_c8))), multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8))))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[643, 37])).
% 0.56/0.76 tff(645,assumption,(~(multiply(sk_c5, sk_c8) = sk_c6)), introduced(assumption)).
% 0.56/0.76 tff(646,plain,
% 0.56/0.76 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(647,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_29')).
% 0.56/0.76 tff(648,plain,
% 0.56/0.76 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.56/0.76 tff(649,plain,
% 0.56/0.76 (inverse(sk_c2) = sk_c8),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[648, 645])).
% 0.56/0.76 tff(650,plain,
% 0.56/0.76 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(651,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_14')).
% 0.56/0.76 tff(652,plain,
% 0.56/0.76 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.56/0.76 tff(653,plain,
% 0.56/0.76 (inverse(sk_c1) = sk_c8),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[652, 645])).
% 0.56/0.76 tff(654,plain,
% 0.56/0.76 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8)) | (~(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8)) | (~(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = sk_c8)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(655,plain,
% 0.56/0.76 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8)) | (~(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = sk_c8)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(656,plain,
% 0.56/0.76 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8)) | (~(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = sk_c8))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[655])).
% 0.56/0.76 tff(657,plain,
% 0.56/0.76 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8)) | (~(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = sk_c8)))),
% 0.56/0.76 inference(transitivity,[status(thm)],[656, 654])).
% 0.56/0.76 tff(658,plain,
% 0.56/0.76 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)))),
% 0.56/0.77 inference(quant_inst,[status(thm)],[])).
% 0.56/0.77 tff(659,plain,
% 0.56/0.77 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8)) | (~(multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), sk_c7) = sk_c8))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.56/0.77 tff(660,plain,
% 0.56/0.77 ((~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[659, 291, 327, 653, 649, 95, 634])).
% 0.56/0.77 tff(661,plain,
% 0.56/0.77 ($false),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[660, 623, 489])).
% 0.56/0.77 tff(662,plain,(multiply(sk_c5, sk_c8) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.56/0.77 tff(663,plain,
% 0.56/0.77 (multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(sk_c7, multiply(sk_c6, sk_c8))),
% 0.56/0.77 inference(transitivity,[status(thm)],[540, 662, 534, 531, 530, 527, 508, 507, 525, 492, 446])).
% 0.56/0.77 tff(664,plain,
% 0.56/0.77 (multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c8)))) = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.77 inference(monotonicity,[status(thm)],[663])).
% 0.56/0.77 tff(665,plain,
% 0.56/0.77 (multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c8))))),
% 0.56/0.77 inference(symmetry,[status(thm)],[664])).
% 0.56/0.77 tff(666,plain,
% 0.56/0.77 (multiply(sk_c4, multiply(sk_c7, sk_c8)) = multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.77 inference(transitivity,[status(thm)],[395, 392, 603, 665, 601])).
% 0.56/0.77 tff(667,plain,
% 0.56/0.77 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c7, multiply(sk_c6, sk_c8))), multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.77 inference(monotonicity,[status(thm)],[666])).
% 0.56/0.77 tff(668,plain,
% 0.56/0.77 (inverse(sk_c8) = multiply(sk_c4, multiply(sk_c7, sk_c8))),
% 0.56/0.77 inference(transitivity,[status(thm)],[291, 372, 369, 364, 362, 391, 394])).
% 0.56/0.77 tff(669,plain,
% 0.56/0.77 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c8)), multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.77 inference(monotonicity,[status(thm)],[668, 557])).
% 0.56/0.77 tff(670,plain,
% 0.56/0.77 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7),
% 0.56/0.77 inference(transitivity,[status(thm)],[597, 594, 669, 667, 644, 642, 640, 387, 371])).
% 0.56/0.77 tff(671,plain,
% 0.56/0.77 (multiply(inverse(sk_c5), sk_c5) = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5)),
% 0.56/0.77 inference(symmetry,[status(thm)],[638])).
% 0.56/0.77 tff(672,plain,
% 0.56/0.77 (identity = multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5)),
% 0.56/0.77 inference(transitivity,[status(thm)],[149, 671])).
% 0.56/0.77 tff(673,plain,
% 0.56/0.77 (multiply(identity, multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.77 inference(monotonicity,[status(thm)],[672])).
% 0.56/0.77 tff(674,plain,
% 0.56/0.77 (multiply(multiply(multiply(sk_c7, multiply(sk_c6, sk_c8)), sk_c5), multiply(sk_c7, multiply(sk_c6, sk_c8))) = multiply(identity, multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.56/0.77 inference(symmetry,[status(thm)],[673])).
% 0.56/0.77 tff(675,plain,
% 0.56/0.77 (inverse(sk_c8) = sk_c8),
% 0.56/0.77 inference(transitivity,[status(thm)],[291, 372, 369, 364, 362, 603, 665, 601, 674, 599, 9])).
% 0.56/0.77 tff(676,plain,
% 0.56/0.77 (sk_c8 = sk_c7),
% 0.56/0.77 inference(transitivity,[status(thm)],[139, 558, 673, 544, 664, 491, 389, 388, 387, 371])).
% 0.56/0.77 tff(677,plain,
% 0.56/0.77 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)),
% 0.56/0.77 inference(monotonicity,[status(thm)],[607, 676])).
% 0.56/0.77 tff(678,plain,
% 0.56/0.77 ((multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.56/0.77 inference(symmetry,[status(thm)],[677])).
% 0.56/0.77 tff(679,plain,
% 0.56/0.77 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[670, 678])).
% 0.56/0.77 tff(680,plain,
% 0.56/0.77 ($false),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[618, 679, 675, 670])).
% 0.56/0.77 tff(681,plain,(~(inverse(sk_c5) = sk_c8)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.77 tff(682,plain,
% 0.56/0.77 (((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c8))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(683,axiom,((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_30')).
% 0.56/0.77 tff(684,plain,
% 0.56/0.77 ((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c8)),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.56/0.77 tff(685,plain,
% 0.56/0.77 (inverse(sk_c2) = sk_c8),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[684, 681])).
% 0.56/0.77 tff(686,plain,
% 0.56/0.77 (((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(687,axiom,((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_15')).
% 0.56/0.77 tff(688,plain,
% 0.56/0.77 ((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8)),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[687, 686])).
% 0.56/0.77 tff(689,plain,
% 0.56/0.77 (inverse(sk_c1) = sk_c8),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[688, 681])).
% 0.56/0.77 tff(690,plain,
% 0.56/0.77 ((~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(multiply(sk_c4, multiply(sk_c7, sk_c8))) = sk_c8))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[659, 291, 327, 689, 685, 95, 634])).
% 0.56/0.77 tff(691,plain,
% 0.56/0.77 ($false),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[690, 623, 489])).
% 0.56/0.77 % SZS output end Proof
% 0.56/0.77 % E exiting
%------------------------------------------------------------------------------