%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP227-1 : 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 05:07:29 AM UTC 2025
% Result : Unsatisfiable 0.51s 0.72s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP227-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 15:48:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.51/0.72 % SZS status Unsatisfiable
% 0.51/0.72 % SZS output start Proof
% 0.51/0.72 tff(sk_c8_type, type, (
% 0.51/0.72 sk_c8: $i)).
% 0.51/0.72 tff(multiply_type, type, (
% 0.51/0.72 multiply: ( $i * $i ) > $i)).
% 0.51/0.72 tff(sk_c7_type, type, (
% 0.51/0.72 sk_c7: $i)).
% 0.51/0.72 tff(inverse_type, type, (
% 0.51/0.72 inverse: $i > $i)).
% 0.51/0.72 tff(sk_c3_type, type, (
% 0.51/0.72 sk_c3: $i)).
% 0.51/0.72 tff(sk_c4_type, type, (
% 0.51/0.72 sk_c4: $i)).
% 0.51/0.72 tff(identity_type, type, (
% 0.51/0.72 identity: $i)).
% 0.51/0.72 tff(sk_c1_type, type, (
% 0.51/0.72 sk_c1: $i)).
% 0.51/0.72 tff(sk_c2_type, type, (
% 0.51/0.72 sk_c2: $i)).
% 0.51/0.72 tff(sk_c5_type, type, (
% 0.51/0.72 sk_c5: $i)).
% 0.51/0.72 tff(sk_c6_type, type, (
% 0.51/0.72 sk_c6: $i)).
% 0.51/0.72 tff(1,plain,
% 0.51/0.72 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.51/0.72 inference(bind,[status(th)],[])).
% 0.51/0.72 tff(2,plain,
% 0.51/0.72 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.51/0.72 inference(quant_intro,[status(thm)],[1])).
% 0.51/0.72 tff(3,plain,
% 0.51/0.72 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(4,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.51/0.72 tff(5,plain,
% 0.51/0.72 (![X: $i] : (multiply(identity, X) = X)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.51/0.72 tff(6,plain,(
% 0.51/0.72 ![X: $i] : (multiply(identity, X) = X)),
% 0.51/0.72 inference(skolemize,[status(sab)],[5])).
% 0.51/0.72 tff(7,plain,
% 0.51/0.72 (![X: $i] : (multiply(identity, X) = X)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.51/0.72 tff(8,plain,
% 0.51/0.72 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c8) = sk_c8)),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(9,plain,
% 0.51/0.72 (multiply(identity, sk_c8) = sk_c8),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.51/0.72 tff(10,assumption,(~(inverse(sk_c4) = sk_c8)), introduced(assumption)).
% 0.51/0.72 tff(11,plain,
% 0.51/0.72 (((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(12,axiom,((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_3')).
% 0.51/0.72 tff(13,plain,
% 0.51/0.72 ((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.51/0.72 tff(14,plain,
% 0.51/0.72 (inverse(sk_c1) = sk_c8),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[13, 10])).
% 0.51/0.72 tff(15,plain,
% 0.51/0.72 (multiply(sk_c1, inverse(sk_c1)) = multiply(sk_c1, sk_c8)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[14])).
% 0.51/0.72 tff(16,plain,
% 0.51/0.72 ((multiply(sk_c1, inverse(sk_c1)) = sk_c7) <=> (multiply(sk_c1, sk_c8) = sk_c7)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[15])).
% 0.51/0.72 tff(17,plain,
% 0.51/0.72 ((~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) <=> (~(multiply(sk_c1, sk_c8) = sk_c7))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[16])).
% 0.51/0.72 tff(18,plain,
% 0.51/0.72 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(19,plain,
% 0.51/0.72 (((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(20,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_15')).
% 0.51/0.72 tff(21,plain,
% 0.51/0.72 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.51/0.72 tff(22,plain,
% 0.51/0.72 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.51/0.72 tff(23,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[22, 10])).
% 0.51/0.72 tff(24,plain,
% 0.51/0.72 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(25,plain,
% 0.51/0.72 (((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(26,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_21')).
% 0.51/0.72 tff(27,plain,
% 0.51/0.72 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.51/0.72 tff(28,plain,
% 0.51/0.72 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.51/0.72 tff(29,plain,
% 0.51/0.72 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[28, 10])).
% 0.51/0.72 tff(30,plain,
% 0.51/0.72 (sk_c3 = multiply(sk_c2, sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[29])).
% 0.51/0.72 tff(31,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[30])).
% 0.51/0.72 tff(32,plain,
% 0.51/0.72 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.51/0.72 inference(symmetry,[status(thm)],[31])).
% 0.51/0.72 tff(33,plain,
% 0.51/0.72 (^[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))))),
% 0.51/0.72 inference(bind,[status(th)],[])).
% 0.51/0.72 tff(34,plain,
% 0.51/0.72 (![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)))),
% 0.51/0.72 inference(quant_intro,[status(thm)],[33])).
% 0.51/0.72 tff(35,plain,
% 0.51/0.72 (![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)))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(36,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')).
% 0.51/0.72 tff(37,plain,
% 0.51/0.72 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.51/0.72 tff(38,plain,(
% 0.51/0.72 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.51/0.72 inference(skolemize,[status(sab)],[37])).
% 0.51/0.72 tff(39,plain,
% 0.51/0.72 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.51/0.72 tff(40,plain,
% 0.51/0.72 ((~![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)))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(41,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.51/0.72 tff(42,plain,
% 0.51/0.72 (((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(43,axiom,((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_27')).
% 0.51/0.72 tff(44,plain,
% 0.51/0.72 ((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.51/0.72 tff(45,plain,
% 0.51/0.72 (inverse(sk_c2) = sk_c8),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[44, 10])).
% 0.51/0.72 tff(46,plain,
% 0.51/0.72 (sk_c8 = inverse(sk_c2)),
% 0.51/0.72 inference(symmetry,[status(thm)],[45])).
% 0.51/0.72 tff(47,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[46])).
% 0.51/0.72 tff(48,plain,
% 0.51/0.72 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c8, sk_c2)),
% 0.51/0.72 inference(symmetry,[status(thm)],[47])).
% 0.51/0.72 tff(49,plain,
% 0.51/0.72 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.51/0.72 inference(bind,[status(th)],[])).
% 0.51/0.72 tff(50,plain,
% 0.51/0.72 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.51/0.72 inference(quant_intro,[status(thm)],[49])).
% 0.51/0.72 tff(51,plain,
% 0.51/0.72 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(52,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.51/0.72 tff(53,plain,
% 0.51/0.72 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.51/0.72 tff(54,plain,(
% 0.51/0.72 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.51/0.72 inference(skolemize,[status(sab)],[53])).
% 0.51/0.72 tff(55,plain,
% 0.51/0.72 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.51/0.72 tff(56,plain,
% 0.51/0.72 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(57,plain,
% 0.51/0.72 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.51/0.72 tff(58,plain,
% 0.51/0.72 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.51/0.72 inference(symmetry,[status(thm)],[57])).
% 0.51/0.72 tff(59,plain,
% 0.51/0.72 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(60,plain,
% 0.51/0.72 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[59, 55])).
% 0.51/0.72 tff(61,plain,
% 0.51/0.72 (sk_c8 = inverse(sk_c1)),
% 0.51/0.72 inference(symmetry,[status(thm)],[14])).
% 0.51/0.72 tff(62,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[61])).
% 0.51/0.72 tff(63,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c1) = multiply(sk_c8, sk_c2)),
% 0.51/0.72 inference(transitivity,[status(thm)],[62, 60, 58, 48])).
% 0.51/0.72 tff(64,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[63])).
% 0.51/0.72 tff(65,plain,
% 0.51/0.72 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c8)))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(66,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[65, 39])).
% 0.51/0.72 tff(67,plain,
% 0.51/0.72 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(multiply(sk_c8, sk_c1), sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[66])).
% 0.51/0.72 tff(68,plain,
% 0.51/0.72 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7),
% 0.51/0.72 inference(transitivity,[status(thm)],[67, 64, 41, 32, 23])).
% 0.51/0.72 tff(69,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c2) = identity),
% 0.51/0.72 inference(transitivity,[status(thm)],[47, 57])).
% 0.51/0.72 tff(70,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(identity, sk_c8)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[69])).
% 0.51/0.72 tff(71,plain,
% 0.51/0.72 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[70])).
% 0.51/0.72 tff(72,plain,
% 0.51/0.72 (sk_c8 = multiply(identity, sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[9])).
% 0.51/0.72 tff(73,plain,
% 0.51/0.72 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(74,plain,
% 0.51/0.72 (((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(75,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_9')).
% 0.51/0.72 tff(76,plain,
% 0.51/0.72 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.51/0.72 tff(77,plain,
% 0.51/0.72 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[76, 73])).
% 0.51/0.72 tff(78,plain,
% 0.51/0.72 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[77, 10])).
% 0.51/0.72 tff(79,plain,
% 0.51/0.72 (sk_c8 = sk_c7),
% 0.51/0.72 inference(transitivity,[status(thm)],[72, 71, 41, 32, 23])).
% 0.51/0.72 tff(80,plain,
% 0.51/0.72 (multiply(sk_c1, sk_c8) = multiply(sk_c1, sk_c7)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[79])).
% 0.51/0.72 tff(81,plain,
% 0.51/0.72 (multiply(sk_c1, sk_c8) = sk_c7),
% 0.51/0.72 inference(transitivity,[status(thm)],[80, 78, 72, 71, 41, 32, 23])).
% 0.51/0.72 tff(82,plain,
% 0.51/0.72 (multiply(sk_c1, sk_c7) = multiply(sk_c1, sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[80])).
% 0.51/0.72 tff(83,plain,
% 0.51/0.72 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.51/0.72 inference(symmetry,[status(thm)],[78])).
% 0.51/0.72 tff(84,plain,
% 0.51/0.72 (sk_c8 = multiply(sk_c1, sk_c8)),
% 0.51/0.72 inference(transitivity,[status(thm)],[83, 82])).
% 0.51/0.72 tff(85,plain,
% 0.51/0.72 (multiply(inverse(sk_c1), sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[14, 84])).
% 0.51/0.72 tff(86,plain,
% 0.51/0.72 (multiply(inverse(sk_c1), sk_c8) = sk_c7),
% 0.51/0.72 inference(transitivity,[status(thm)],[85, 67, 64, 41, 32, 23])).
% 0.51/0.72 tff(87,assumption,(multiply(sk_c8, sk_c3) = sk_c7), introduced(assumption)).
% 0.51/0.72 tff(88,assumption,(multiply(sk_c2, sk_c8) = sk_c3), introduced(assumption)).
% 0.51/0.72 tff(89,plain,
% 0.51/0.72 (sk_c3 = multiply(sk_c2, sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[88])).
% 0.51/0.72 tff(90,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[89])).
% 0.51/0.72 tff(91,plain,
% 0.51/0.72 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.51/0.72 inference(symmetry,[status(thm)],[90])).
% 0.51/0.72 tff(92,assumption,(inverse(sk_c2) = sk_c8), introduced(assumption)).
% 0.51/0.72 tff(93,plain,
% 0.51/0.72 (sk_c8 = inverse(sk_c2)),
% 0.51/0.72 inference(symmetry,[status(thm)],[92])).
% 0.51/0.72 tff(94,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[93])).
% 0.51/0.72 tff(95,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c2) = identity),
% 0.51/0.72 inference(transitivity,[status(thm)],[94, 57])).
% 0.51/0.72 tff(96,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(identity, sk_c8)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[95])).
% 0.51/0.72 tff(97,plain,
% 0.51/0.72 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[96])).
% 0.51/0.72 tff(98,assumption,(inverse(sk_c1) = sk_c8), introduced(assumption)).
% 0.51/0.72 tff(99,plain,
% 0.51/0.72 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c1) = sk_c1)),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(100,plain,
% 0.51/0.72 (multiply(identity, sk_c1) = sk_c1),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[99, 7])).
% 0.51/0.72 tff(101,plain,
% 0.51/0.72 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c8, sk_c2)),
% 0.51/0.72 inference(symmetry,[status(thm)],[94])).
% 0.51/0.72 tff(102,plain,
% 0.51/0.72 (identity = multiply(sk_c8, sk_c2)),
% 0.51/0.72 inference(transitivity,[status(thm)],[58, 101])).
% 0.51/0.72 tff(103,plain,
% 0.51/0.72 (multiply(identity, sk_c1) = multiply(multiply(sk_c8, sk_c2), sk_c1)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[102])).
% 0.51/0.72 tff(104,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c2), sk_c1) = multiply(identity, sk_c1)),
% 0.51/0.72 inference(symmetry,[status(thm)],[103])).
% 0.51/0.72 tff(105,plain,
% 0.51/0.72 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c2), sk_c1) = multiply(sk_c8, multiply(sk_c2, sk_c1)))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(106,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c2), sk_c1) = multiply(sk_c8, multiply(sk_c2, sk_c1))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[105, 39])).
% 0.51/0.72 tff(107,plain,
% 0.51/0.72 (multiply(sk_c8, multiply(sk_c2, sk_c1)) = multiply(multiply(sk_c8, sk_c2), sk_c1)),
% 0.51/0.72 inference(symmetry,[status(thm)],[106])).
% 0.51/0.72 tff(108,plain,
% 0.51/0.72 (sk_c8 = inverse(sk_c1)),
% 0.51/0.72 inference(symmetry,[status(thm)],[98])).
% 0.51/0.72 tff(109,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c8) = multiply(inverse(sk_c1), sk_c8)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[108])).
% 0.51/0.72 tff(110,plain,
% 0.51/0.72 (multiply(inverse(sk_c1), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[109])).
% 0.51/0.72 tff(111,plain,
% 0.51/0.72 (sk_c8 = sk_c7),
% 0.51/0.72 inference(transitivity,[status(thm)],[72, 97, 41, 91, 87])).
% 0.51/0.72 tff(112,plain,
% 0.51/0.72 (multiply(sk_c1, sk_c8) = multiply(sk_c1, sk_c7)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[111])).
% 0.51/0.72 tff(113,plain,
% 0.51/0.72 (multiply(sk_c1, sk_c7) = multiply(sk_c1, sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[112])).
% 0.51/0.72 tff(114,assumption,(multiply(sk_c1, sk_c7) = sk_c8), introduced(assumption)).
% 0.51/0.72 tff(115,plain,
% 0.51/0.72 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.51/0.72 inference(symmetry,[status(thm)],[114])).
% 0.51/0.72 tff(116,plain,
% 0.51/0.72 (sk_c8 = multiply(sk_c1, sk_c8)),
% 0.51/0.72 inference(transitivity,[status(thm)],[115, 113])).
% 0.51/0.72 tff(117,plain,
% 0.51/0.72 (multiply(inverse(sk_c1), sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[98, 116])).
% 0.51/0.72 tff(118,plain,
% 0.51/0.72 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(inverse(sk_c1), sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[117])).
% 0.51/0.72 tff(119,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[108])).
% 0.51/0.72 tff(120,plain,
% 0.51/0.72 (multiply(sk_c8, sk_c1) = multiply(sk_c8, sk_c2)),
% 0.51/0.72 inference(transitivity,[status(thm)],[119, 60, 58, 101])).
% 0.51/0.72 tff(121,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[120])).
% 0.51/0.72 tff(122,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(multiply(sk_c8, sk_c1), sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[121])).
% 0.51/0.72 tff(123,plain,
% 0.51/0.72 (sk_c8 = multiply(sk_c8, sk_c8)),
% 0.51/0.72 inference(transitivity,[status(thm)],[72, 97, 122, 66, 118, 110])).
% 0.51/0.72 tff(124,plain,
% 0.51/0.72 (multiply(sk_c8, multiply(sk_c2, sk_c1)) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c1))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[123])).
% 0.51/0.72 tff(125,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c1)) = multiply(sk_c8, multiply(sk_c2, sk_c1))),
% 0.51/0.72 inference(symmetry,[status(thm)],[124])).
% 0.51/0.72 tff(126,plain,
% 0.51/0.72 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c1)) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c1))))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(127,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c1)) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c1)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[126, 39])).
% 0.51/0.72 tff(128,plain,
% 0.51/0.72 (multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c1))) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c1))),
% 0.51/0.72 inference(symmetry,[status(thm)],[127])).
% 0.51/0.72 tff(129,plain,
% 0.51/0.72 (multiply(sk_c8, multiply(sk_c2, sk_c1)) = sk_c1),
% 0.51/0.72 inference(transitivity,[status(thm)],[107, 104, 100])).
% 0.51/0.72 tff(130,plain,
% 0.51/0.72 (multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c1))) = multiply(inverse(sk_c1), sk_c1)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[108, 129])).
% 0.51/0.72 tff(131,plain,
% 0.51/0.72 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c1)))),
% 0.51/0.72 inference(symmetry,[status(thm)],[130])).
% 0.51/0.72 tff(132,plain,
% 0.51/0.72 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.51/0.72 inference(symmetry,[status(thm)],[60])).
% 0.51/0.72 tff(133,plain,
% 0.51/0.72 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c8), sk_c8) = identity)),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(134,plain,
% 0.51/0.72 (multiply(inverse(sk_c8), sk_c8) = identity),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[133, 55])).
% 0.51/0.72 tff(135,plain,
% 0.51/0.72 (multiply(inverse(sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[123])).
% 0.51/0.72 tff(136,plain,
% 0.51/0.72 (multiply(inverse(sk_c8), multiply(sk_c8, sk_c8)) = multiply(inverse(sk_c8), sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[135])).
% 0.51/0.72 tff(137,plain,
% 0.51/0.72 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8)))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(138,plain,
% 0.51/0.72 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[137, 39])).
% 0.51/0.72 tff(139,plain,
% 0.51/0.72 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c8, sk_c2)),
% 0.51/0.72 inference(transitivity,[status(thm)],[134, 58, 101])).
% 0.51/0.72 tff(140,plain,
% 0.51/0.72 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[139])).
% 0.51/0.72 tff(141,plain,
% 0.51/0.72 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(multiply(inverse(sk_c8), sk_c8), sk_c8)),
% 0.51/0.72 inference(symmetry,[status(thm)],[140])).
% 0.51/0.72 tff(142,plain,
% 0.51/0.72 (sk_c8 = sk_c1),
% 0.51/0.72 inference(transitivity,[status(thm)],[72, 97, 141, 138, 136, 134, 132, 131, 128, 125, 107, 104, 100])).
% 0.51/0.72 tff(143,plain,
% 0.51/0.72 (inverse(sk_c8) = inverse(sk_c1)),
% 0.51/0.72 inference(monotonicity,[status(thm)],[142])).
% 0.51/0.72 tff(144,plain,
% 0.51/0.72 (inverse(sk_c8) = sk_c7),
% 0.51/0.72 inference(transitivity,[status(thm)],[143, 98, 72, 97, 41, 91, 87])).
% 0.51/0.72 tff(145,assumption,(~(inverse(sk_c8) = sk_c7)), introduced(assumption)).
% 0.51/0.72 tff(146,plain,
% 0.51/0.72 ($false),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.51/0.72 tff(147,plain,((inverse(sk_c8) = sk_c7) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c3)) | (~(multiply(sk_c1, sk_c7) = sk_c8))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.72 tff(148,plain,
% 0.51/0.72 (inverse(sk_c8) = sk_c7),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[147, 14, 23, 45, 29, 78])).
% 0.51/0.72 tff(149,plain,
% 0.51/0.72 (^[X6: $i, X4: $i, X3: $i, X1: $i] : refl(((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))),
% 0.51/0.72 inference(bind,[status(th)],[])).
% 0.51/0.72 tff(150,plain,
% 0.51/0.72 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.51/0.72 inference(quant_intro,[status(thm)],[149])).
% 0.51/0.72 tff(151,plain,
% 0.51/0.72 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(152,plain,
% 0.51/0.72 (^[X6: $i, X4: $i, X3: $i, X1: $i] : rewrite(((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))),
% 0.51/0.72 inference(bind,[status(th)],[])).
% 0.51/0.72 tff(153,plain,
% 0.51/0.72 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.51/0.73 inference(quant_intro,[status(thm)],[152])).
% 0.51/0.73 tff(154,plain,
% 0.51/0.73 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.51/0.73 inference(elim_unused_vars,[status(thm)],[])).
% 0.51/0.73 tff(155,plain,
% 0.51/0.73 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X2, sk_c8) = sk_c7)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.51/0.73 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.51/0.73 tff(156,plain,
% 0.51/0.73 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X2, sk_c8) = sk_c7)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.51/0.73 inference(transitivity,[status(thm)],[155, 154])).
% 0.51/0.73 tff(157,plain,
% 0.51/0.73 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X2, sk_c8) = sk_c7)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.51/0.73 inference(transitivity,[status(thm)],[156, 153])).
% 0.51/0.73 tff(158,plain,
% 0.51/0.73 (^[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(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) <=> ((~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), (((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) <=> (((~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X6, sk_c8) = X5))))), rewrite((((~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X6, sk_c8) = X5))) <=> ((~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), (((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) <=> ((~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), ((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) <=> (((~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X6) = sk_c8))))), rewrite((((~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X6) = sk_c8))) <=> ((~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), ((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) <=> ((~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), (((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = 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)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))))), rewrite((((~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), (((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), ((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), ((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), (((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X1) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), (((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), ((((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X3, X2) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X3, X2) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X3, X2) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), ((((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X3, X2) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), (((((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X3, X2) = sk_c7))) | (~(inverse(X3) = X2))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X3) = X2))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X3) = X2))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), (((((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X3, X2) = sk_c7))) | (~(inverse(X3) = X2))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), ((((((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X3, X2) = sk_c7))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c8) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X2, sk_c8) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X2, sk_c8) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X2, sk_c8) = sk_c7)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), ((((((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X3, X2) = sk_c7))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c8) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X2, sk_c8) = sk_c7)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))))),
% 0.57/0.73 inference(bind,[status(th)],[])).
% 0.57/0.73 tff(159,plain,
% 0.57/0.73 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X3, X2) = sk_c7))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c8) = sk_c7))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X2, sk_c8) = sk_c7)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[158])).
% 0.57/0.73 tff(160,plain,
% 0.57/0.73 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X3, X2) = sk_c7))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c8) = sk_c7))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.57/0.73 inference(transitivity,[status(thm)],[159, 157])).
% 0.57/0.73 tff(161,axiom,(![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(sk_c8) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X3, X2) = sk_c7))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c8) = sk_c7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_31')).
% 0.57/0.73 tff(162,plain,
% 0.57/0.73 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.57/0.73 tff(163,plain,
% 0.57/0.73 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[162, 151])).
% 0.57/0.73 tff(164,plain,(
% 0.57/0.73 ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.57/0.73 inference(skolemize,[status(sab)],[163])).
% 0.57/0.73 tff(165,plain,
% 0.57/0.73 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[164, 150])).
% 0.57/0.73 tff(166,plain,
% 0.57/0.73 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c1), sk_c8) = sk_c7)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c1), sk_c8) = sk_c7)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(167,plain,
% 0.57/0.74 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c8) = sk_c7)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c1), sk_c8) = sk_c7)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(168,plain,
% 0.57/0.74 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c8) = sk_c7)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c1), sk_c8) = sk_c7)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[167])).
% 0.57/0.74 tff(169,plain,
% 0.57/0.74 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c8) = sk_c7)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c1), sk_c8) = sk_c7)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.57/0.74 inference(transitivity,[status(thm)],[168, 166])).
% 0.57/0.74 tff(170,plain,
% 0.57/0.74 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c8) = sk_c7)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(171,plain,
% 0.57/0.74 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c1), sk_c8) = sk_c7)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.57/0.74 tff(172,plain,
% 0.57/0.74 ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c1), sk_c8) = sk_c7)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[171, 14, 78, 165])).
% 0.57/0.74 tff(173,plain,
% 0.57/0.74 (~(multiply(sk_c1, inverse(sk_c1)) = sk_c7)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[172, 148, 86, 81, 68])).
% 0.57/0.74 tff(174,plain,
% 0.57/0.74 (~(multiply(sk_c1, sk_c8) = sk_c7)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[173, 17])).
% 0.57/0.74 tff(175,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[81, 174])).
% 0.57/0.74 tff(176,plain,(inverse(sk_c4) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(177,plain,
% 0.57/0.74 (sk_c8 = inverse(sk_c4)),
% 0.57/0.74 inference(symmetry,[status(thm)],[176])).
% 0.57/0.74 tff(178,plain,
% 0.57/0.74 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[177])).
% 0.57/0.74 tff(179,plain,
% 0.57/0.74 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.57/0.74 inference(symmetry,[status(thm)],[178])).
% 0.57/0.74 tff(180,plain,
% 0.57/0.74 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(181,plain,
% 0.57/0.74 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[180, 55])).
% 0.57/0.74 tff(182,plain,
% 0.57/0.74 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.57/0.74 inference(symmetry,[status(thm)],[181])).
% 0.57/0.74 tff(183,plain,
% 0.57/0.74 (identity = multiply(sk_c8, sk_c4)),
% 0.57/0.74 inference(transitivity,[status(thm)],[182, 179])).
% 0.57/0.74 tff(184,plain,
% 0.57/0.74 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[183])).
% 0.57/0.74 tff(185,plain,
% 0.57/0.74 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, sk_c8)),
% 0.57/0.74 inference(symmetry,[status(thm)],[184])).
% 0.57/0.74 tff(186,assumption,(~(multiply(sk_c1, sk_c7) = sk_c8)), introduced(assumption)).
% 0.57/0.74 tff(187,plain,
% 0.57/0.74 (((inverse(sk_c8) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c8)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(188,plain,
% 0.57/0.74 (((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c8) = sk_c7)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(189,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_7')).
% 0.57/0.74 tff(190,plain,
% 0.57/0.74 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.57/0.74 tff(191,plain,
% 0.57/0.74 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[190, 187])).
% 0.57/0.74 tff(192,plain,
% 0.57/0.74 (inverse(sk_c8) = sk_c7),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[191, 186])).
% 0.57/0.74 tff(193,plain,
% 0.57/0.74 (sk_c7 = inverse(sk_c8)),
% 0.57/0.74 inference(symmetry,[status(thm)],[192])).
% 0.57/0.74 tff(194,plain,
% 0.57/0.74 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(195,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_8')).
% 0.57/0.74 tff(196,plain,
% 0.57/0.74 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.57/0.74 tff(197,plain,
% 0.57/0.74 (multiply(sk_c4, sk_c8) = sk_c7),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[196, 186])).
% 0.57/0.74 tff(198,plain,
% 0.57/0.74 (multiply(sk_c4, sk_c8) = inverse(sk_c8)),
% 0.57/0.74 inference(transitivity,[status(thm)],[197, 193])).
% 0.57/0.74 tff(199,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[198])).
% 0.57/0.74 tff(200,plain,
% 0.57/0.74 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c4, sk_c8), sk_c8)),
% 0.57/0.74 inference(symmetry,[status(thm)],[199])).
% 0.57/0.74 tff(201,plain,
% 0.57/0.74 (identity = multiply(inverse(sk_c8), sk_c8)),
% 0.57/0.74 inference(symmetry,[status(thm)],[134])).
% 0.57/0.74 tff(202,plain,
% 0.57/0.74 (identity = multiply(multiply(sk_c4, sk_c8), sk_c8)),
% 0.57/0.74 inference(transitivity,[status(thm)],[201, 200])).
% 0.57/0.74 tff(203,plain,
% 0.57/0.74 (multiply(identity, multiply(sk_c4, sk_c8)) = multiply(multiply(multiply(sk_c4, sk_c8), sk_c8), multiply(sk_c4, sk_c8))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[202])).
% 0.57/0.74 tff(204,plain,
% 0.57/0.74 (multiply(multiply(multiply(sk_c4, sk_c8), sk_c8), multiply(sk_c4, sk_c8)) = multiply(identity, multiply(sk_c4, sk_c8))),
% 0.57/0.74 inference(symmetry,[status(thm)],[203])).
% 0.57/0.74 tff(205,plain,
% 0.57/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c4, sk_c8), sk_c8), multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, multiply(sk_c4, sk_c8))))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(206,plain,
% 0.57/0.74 (multiply(multiply(multiply(sk_c4, sk_c8), sk_c8), multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[205, 39])).
% 0.57/0.74 tff(207,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, multiply(sk_c4, sk_c8))) = multiply(multiply(multiply(sk_c4, sk_c8), sk_c8), multiply(sk_c4, sk_c8))),
% 0.57/0.74 inference(symmetry,[status(thm)],[206])).
% 0.57/0.74 tff(208,assumption,(~(multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8)))), introduced(assumption)).
% 0.57/0.74 tff(209,plain,
% 0.57/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(210,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[209, 39, 208])).
% 0.57/0.74 tff(211,plain,(multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(212,plain,
% 0.57/0.74 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.57/0.74 inference(symmetry,[status(thm)],[211])).
% 0.57/0.74 tff(213,plain,
% 0.57/0.74 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c8),
% 0.57/0.74 inference(transitivity,[status(thm)],[212, 185, 9])).
% 0.57/0.74 tff(214,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, multiply(sk_c4, sk_c8))) = multiply(inverse(sk_c8), sk_c8)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[198, 213])).
% 0.57/0.74 tff(215,plain,
% 0.57/0.74 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.57/0.74 inference(symmetry,[status(thm)],[214])).
% 0.57/0.74 tff(216,plain,
% 0.57/0.74 (multiply(sk_c8, sk_c4) = multiply(identity, multiply(sk_c4, sk_c8))),
% 0.57/0.74 inference(transitivity,[status(thm)],[178, 181, 201, 215, 207, 204])).
% 0.57/0.74 tff(217,plain,
% 0.57/0.74 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(identity, multiply(sk_c4, sk_c8)), sk_c8)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[216])).
% 0.57/0.74 tff(218,plain,
% 0.57/0.74 (multiply(multiply(identity, multiply(sk_c4, sk_c8)), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.57/0.74 inference(symmetry,[status(thm)],[217])).
% 0.57/0.74 tff(219,plain,
% 0.57/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, multiply(sk_c4, sk_c8)), sk_c8) = multiply(identity, multiply(multiply(sk_c4, sk_c8), sk_c8)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(220,plain,
% 0.57/0.74 (multiply(multiply(identity, multiply(sk_c4, sk_c8)), sk_c8) = multiply(identity, multiply(multiply(sk_c4, sk_c8), sk_c8))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[219, 39])).
% 0.57/0.74 tff(221,plain,
% 0.57/0.74 (multiply(identity, multiply(multiply(sk_c4, sk_c8), sk_c8)) = multiply(multiply(identity, multiply(sk_c4, sk_c8)), sk_c8)),
% 0.57/0.74 inference(symmetry,[status(thm)],[220])).
% 0.57/0.74 tff(222,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, sk_c8), sk_c8) = identity),
% 0.57/0.74 inference(transitivity,[status(thm)],[199, 134])).
% 0.57/0.74 tff(223,plain,
% 0.57/0.74 (multiply(identity, multiply(multiply(sk_c4, sk_c8), sk_c8)) = multiply(identity, identity)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[222])).
% 0.57/0.74 tff(224,plain,
% 0.57/0.74 (multiply(identity, identity) = multiply(identity, multiply(multiply(sk_c4, sk_c8), sk_c8))),
% 0.57/0.74 inference(symmetry,[status(thm)],[223])).
% 0.57/0.74 tff(225,plain,
% 0.57/0.74 (multiply(identity, identity) = multiply(identity, multiply(sk_c8, sk_c4))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[183])).
% 0.57/0.74 tff(226,plain,
% 0.57/0.74 (multiply(identity, multiply(sk_c8, sk_c4)) = multiply(identity, identity)),
% 0.57/0.74 inference(symmetry,[status(thm)],[225])).
% 0.57/0.74 tff(227,plain,
% 0.57/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c8), sk_c4) = multiply(identity, multiply(sk_c8, sk_c4)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(228,plain,
% 0.57/0.74 (multiply(multiply(identity, sk_c8), sk_c4) = multiply(identity, multiply(sk_c8, sk_c4))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[227, 39])).
% 0.57/0.74 tff(229,plain,
% 0.57/0.74 (multiply(identity, sk_c8) = inverse(sk_c4)),
% 0.57/0.74 inference(transitivity,[status(thm)],[9, 177])).
% 0.57/0.74 tff(230,plain,
% 0.57/0.74 (multiply(multiply(identity, sk_c8), sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[229])).
% 0.57/0.74 tff(231,plain,
% 0.57/0.74 (multiply(inverse(sk_c4), sk_c4) = multiply(multiply(identity, sk_c8), sk_c4)),
% 0.57/0.74 inference(symmetry,[status(thm)],[230])).
% 0.57/0.74 tff(232,plain,
% 0.57/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c8)) = multiply(sk_c4, multiply(sk_c8, multiply(sk_c4, sk_c8))))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(233,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c8)) = multiply(sk_c4, multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[232, 39])).
% 0.57/0.74 tff(234,plain,
% 0.57/0.74 (multiply(sk_c4, multiply(sk_c8, multiply(sk_c4, sk_c8))) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c8))),
% 0.57/0.74 inference(symmetry,[status(thm)],[233])).
% 0.57/0.74 tff(235,plain,
% 0.57/0.74 (multiply(sk_c4, multiply(sk_c8, multiply(sk_c4, sk_c8))) = multiply(sk_c4, sk_c8)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[213])).
% 0.57/0.74 tff(236,plain,
% 0.57/0.74 (multiply(sk_c4, sk_c8) = multiply(sk_c4, multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.57/0.74 inference(symmetry,[status(thm)],[235])).
% 0.57/0.74 tff(237,plain,
% 0.57/0.74 (sk_c7 = multiply(sk_c4, sk_c8)),
% 0.57/0.74 inference(symmetry,[status(thm)],[197])).
% 0.57/0.74 tff(238,plain,
% 0.57/0.74 (inverse(sk_c8) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c8))),
% 0.57/0.74 inference(transitivity,[status(thm)],[192, 237, 236, 234])).
% 0.57/0.74 tff(239,plain,
% 0.57/0.74 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c8)), sk_c8)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[238])).
% 0.57/0.74 tff(240,plain,
% 0.57/0.74 (multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c8)), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.57/0.74 inference(symmetry,[status(thm)],[239])).
% 0.57/0.74 tff(241,plain,
% 0.57/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c8)), sk_c8) = multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c8)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(242,plain,
% 0.57/0.74 (multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c8)), sk_c8) = multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c8))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[241, 39])).
% 0.57/0.74 tff(243,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c8)) = multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c8)), sk_c8)),
% 0.57/0.74 inference(symmetry,[status(thm)],[242])).
% 0.57/0.74 tff(244,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c8)) = multiply(multiply(sk_c4, sk_c8), identity)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[222])).
% 0.57/0.74 tff(245,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, sk_c8), identity) = multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c8))),
% 0.57/0.74 inference(symmetry,[status(thm)],[244])).
% 0.57/0.74 tff(246,plain,
% 0.57/0.74 (identity = sk_c8),
% 0.57/0.74 inference(transitivity,[status(thm)],[182, 231, 228, 226, 224, 221, 218, 185, 9])).
% 0.57/0.74 tff(247,plain,
% 0.57/0.74 (multiply(sk_c4, identity) = multiply(sk_c4, sk_c8)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[246])).
% 0.57/0.74 tff(248,plain,
% 0.57/0.74 (multiply(sk_c4, sk_c8) = multiply(sk_c4, identity)),
% 0.57/0.74 inference(symmetry,[status(thm)],[247])).
% 0.57/0.74 tff(249,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, sk_c8), identity) = multiply(multiply(sk_c4, identity), identity)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[248])).
% 0.57/0.74 tff(250,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, identity), identity) = multiply(multiply(sk_c4, sk_c8), identity)),
% 0.57/0.74 inference(symmetry,[status(thm)],[249])).
% 0.57/0.74 tff(251,plain,
% 0.57/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, identity), identity) = multiply(sk_c4, multiply(identity, identity)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(252,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, identity), identity) = multiply(sk_c4, multiply(identity, identity))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[251, 39])).
% 0.57/0.74 tff(253,plain,
% 0.57/0.74 (multiply(sk_c4, multiply(identity, identity)) = multiply(multiply(sk_c4, identity), identity)),
% 0.57/0.74 inference(symmetry,[status(thm)],[252])).
% 0.57/0.74 tff(254,plain,
% 0.57/0.74 (multiply(identity, multiply(sk_c8, sk_c4)) = multiply(multiply(identity, sk_c8), sk_c4)),
% 0.57/0.74 inference(symmetry,[status(thm)],[228])).
% 0.57/0.74 tff(255,plain,
% 0.57/0.74 (multiply(identity, identity) = identity),
% 0.57/0.74 inference(transitivity,[status(thm)],[225, 254, 230, 181])).
% 0.57/0.74 tff(256,plain,
% 0.57/0.74 (multiply(sk_c4, multiply(identity, identity)) = multiply(sk_c4, identity)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[255])).
% 0.57/0.74 tff(257,plain,
% 0.57/0.74 (multiply(sk_c4, identity) = multiply(sk_c4, multiply(identity, identity))),
% 0.57/0.74 inference(symmetry,[status(thm)],[256])).
% 0.57/0.74 tff(258,plain,
% 0.57/0.74 (multiply(sk_c8, sk_c4) = identity),
% 0.57/0.74 inference(transitivity,[status(thm)],[178, 181])).
% 0.57/0.74 tff(259,plain,
% 0.57/0.74 (multiply(sk_c4, multiply(sk_c8, sk_c4)) = multiply(sk_c4, identity)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[258])).
% 0.57/0.74 tff(260,plain,
% 0.57/0.74 ((~![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)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(261,plain,
% 0.57/0.74 (multiply(multiply(sk_c4, sk_c8), sk_c4) = multiply(sk_c4, multiply(sk_c8, sk_c4))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[260, 39])).
% 0.57/0.74 tff(262,plain,
% 0.57/0.74 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c6, sk_c8) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c6, sk_c8) = sk_c7))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(263,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c6, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_12')).
% 0.57/0.75 tff(264,plain,
% 0.57/0.75 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c6, sk_c8) = sk_c7)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.57/0.75 tff(265,plain,
% 0.57/0.75 (multiply(sk_c6, sk_c8) = sk_c7),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[264, 186])).
% 0.57/0.75 tff(266,plain,
% 0.57/0.75 (multiply(sk_c6, sk_c8) = multiply(sk_c4, sk_c8)),
% 0.57/0.75 inference(transitivity,[status(thm)],[265, 237])).
% 0.57/0.75 tff(267,plain,
% 0.57/0.75 (multiply(multiply(sk_c6, sk_c8), sk_c4) = multiply(multiply(sk_c4, sk_c8), sk_c4)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[266])).
% 0.57/0.75 tff(268,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), sk_c4) = multiply(sk_c6, multiply(sk_c8, sk_c4)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(269,plain,
% 0.57/0.75 (multiply(multiply(sk_c6, sk_c8), sk_c4) = multiply(sk_c6, multiply(sk_c8, sk_c4))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[268, 39])).
% 0.57/0.75 tff(270,plain,
% 0.57/0.75 (multiply(sk_c6, multiply(sk_c8, sk_c4)) = multiply(multiply(sk_c6, sk_c8), sk_c4)),
% 0.57/0.75 inference(symmetry,[status(thm)],[269])).
% 0.57/0.75 tff(271,plain,
% 0.57/0.75 (multiply(sk_c6, identity) = multiply(sk_c6, multiply(sk_c8, sk_c4))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[183])).
% 0.57/0.75 tff(272,plain,
% 0.57/0.75 (multiply(sk_c6, multiply(multiply(sk_c4, sk_c8), sk_c8)) = multiply(sk_c6, identity)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[222])).
% 0.57/0.75 tff(273,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, multiply(sk_c4, sk_c8)), sk_c8) = multiply(sk_c6, multiply(multiply(sk_c4, sk_c8), sk_c8)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(274,plain,
% 0.57/0.75 (multiply(multiply(sk_c6, multiply(sk_c4, sk_c8)), sk_c8) = multiply(sk_c6, multiply(multiply(sk_c4, sk_c8), sk_c8))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[273, 39])).
% 0.57/0.75 tff(275,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c4), sk_c8) = multiply(sk_c6, multiply(sk_c4, sk_c8)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(276,plain,
% 0.57/0.75 (multiply(multiply(sk_c6, sk_c4), sk_c8) = multiply(sk_c6, multiply(sk_c4, sk_c8))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[275, 39])).
% 0.57/0.75 tff(277,plain,
% 0.57/0.75 (sk_c8 = identity),
% 0.57/0.75 inference(transitivity,[status(thm)],[72, 184, 217, 220, 223, 225, 254, 230, 181])).
% 0.57/0.75 tff(278,plain,
% 0.57/0.75 (multiply(multiply(sk_c6, sk_c4), sk_c8) = multiply(multiply(sk_c6, sk_c4), identity)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[277])).
% 0.57/0.75 tff(279,plain,
% 0.57/0.75 (multiply(multiply(sk_c6, sk_c4), identity) = multiply(multiply(sk_c6, sk_c4), sk_c8)),
% 0.57/0.75 inference(symmetry,[status(thm)],[278])).
% 0.57/0.75 tff(280,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c4), identity) = multiply(sk_c6, multiply(sk_c4, identity)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(281,plain,
% 0.57/0.75 (multiply(multiply(sk_c6, sk_c4), identity) = multiply(sk_c6, multiply(sk_c4, identity))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[280, 39])).
% 0.57/0.75 tff(282,plain,
% 0.57/0.75 (multiply(sk_c6, multiply(sk_c4, identity)) = multiply(multiply(sk_c6, sk_c4), identity)),
% 0.57/0.75 inference(symmetry,[status(thm)],[281])).
% 0.57/0.75 tff(283,plain,
% 0.57/0.75 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = inverse(sk_c4)),
% 0.57/0.75 inference(transitivity,[status(thm)],[212, 185, 9, 177])).
% 0.57/0.75 tff(284,plain,
% 0.57/0.75 (multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[283])).
% 0.57/0.75 tff(285,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), sk_c4) = multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(286,plain,
% 0.57/0.75 (multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), sk_c4) = multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[285, 39])).
% 0.57/0.75 tff(287,plain,
% 0.57/0.75 (multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), sk_c4)),
% 0.57/0.75 inference(symmetry,[status(thm)],[286])).
% 0.57/0.75 tff(288,plain,
% 0.57/0.75 (multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)) = identity),
% 0.57/0.75 inference(transitivity,[status(thm)],[287, 284, 181])).
% 0.57/0.75 tff(289,plain,
% 0.57/0.75 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(sk_c4, identity)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[288])).
% 0.57/0.75 tff(290,plain,
% 0.57/0.75 (multiply(sk_c4, identity) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.57/0.75 inference(symmetry,[status(thm)],[289])).
% 0.57/0.75 tff(291,plain,
% 0.57/0.75 (multiply(sk_c6, multiply(sk_c4, identity)) = multiply(sk_c6, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[290])).
% 0.57/0.75 tff(292,plain,
% 0.57/0.75 (multiply(sk_c6, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c6, multiply(sk_c4, identity))),
% 0.57/0.75 inference(symmetry,[status(thm)],[291])).
% 0.57/0.75 tff(293,plain,
% 0.57/0.75 (multiply(sk_c6, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c6, multiply(sk_c4, sk_c8))),
% 0.57/0.75 inference(transitivity,[status(thm)],[292, 282, 279, 276])).
% 0.57/0.75 tff(294,plain,
% 0.57/0.75 (multiply(multiply(sk_c6, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), identity) = multiply(multiply(sk_c6, multiply(sk_c4, sk_c8)), sk_c8)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[293, 246])).
% 0.57/0.75 tff(295,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), identity) = multiply(sk_c6, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(296,plain,
% 0.57/0.75 (multiply(multiply(sk_c6, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), identity) = multiply(sk_c6, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[295, 39])).
% 0.57/0.75 tff(297,plain,
% 0.57/0.75 (multiply(sk_c6, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity)) = multiply(multiply(sk_c6, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), identity)),
% 0.57/0.75 inference(symmetry,[status(thm)],[296])).
% 0.57/0.75 tff(298,plain,
% 0.57/0.75 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity) = multiply(multiply(sk_c4, identity), identity)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[289])).
% 0.57/0.75 tff(299,plain,
% 0.57/0.75 (multiply(multiply(sk_c4, identity), identity) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity)),
% 0.57/0.75 inference(symmetry,[status(thm)],[298])).
% 0.57/0.75 tff(300,plain,
% 0.57/0.75 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity)),
% 0.57/0.75 inference(transitivity,[status(thm)],[289, 257, 253, 299])).
% 0.57/0.75 tff(301,plain,
% 0.57/0.75 (multiply(sk_c6, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c6, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[300])).
% 0.57/0.75 tff(302,plain,
% 0.57/0.75 (multiply(sk_c6, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c6, sk_c4), sk_c8)),
% 0.57/0.75 inference(symmetry,[status(thm)],[276])).
% 0.57/0.75 tff(303,plain,
% 0.57/0.75 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c6) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c6) = sk_c7))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(304,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c6) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_10')).
% 0.57/0.75 tff(305,plain,
% 0.57/0.75 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c6) = sk_c7)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.57/0.75 tff(306,plain,
% 0.57/0.75 (multiply(sk_c5, sk_c6) = sk_c7),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[305, 186])).
% 0.57/0.75 tff(307,plain,
% 0.57/0.75 (multiply(sk_c5, sk_c6) = multiply(sk_c4, sk_c8)),
% 0.57/0.75 inference(transitivity,[status(thm)],[306, 237])).
% 0.57/0.75 tff(308,plain,
% 0.57/0.75 (multiply(sk_c6, multiply(sk_c5, sk_c6)) = multiply(sk_c6, multiply(sk_c4, sk_c8))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[307])).
% 0.57/0.75 tff(309,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c5), sk_c6) = multiply(sk_c6, multiply(sk_c5, sk_c6)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(310,plain,
% 0.57/0.75 (multiply(multiply(sk_c6, sk_c5), sk_c6) = multiply(sk_c6, multiply(sk_c5, sk_c6))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[309, 39])).
% 0.57/0.75 tff(311,plain,
% 0.57/0.75 (((inverse(sk_c5) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8)) <=> ((inverse(sk_c5) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(312,plain,
% 0.57/0.75 (((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c5) = sk_c6)) <=> ((inverse(sk_c5) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(313,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c5) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_11')).
% 0.57/0.75 tff(314,plain,
% 0.57/0.75 ((inverse(sk_c5) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.57/0.75 tff(315,plain,
% 0.57/0.75 ((inverse(sk_c5) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[314, 311])).
% 0.57/0.75 tff(316,plain,
% 0.57/0.75 (inverse(sk_c5) = sk_c6),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[315, 186])).
% 0.57/0.75 tff(317,plain,
% 0.57/0.75 (sk_c6 = inverse(sk_c5)),
% 0.57/0.75 inference(symmetry,[status(thm)],[316])).
% 0.57/0.75 tff(318,plain,
% 0.57/0.75 (multiply(sk_c6, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[317])).
% 0.57/0.75 tff(319,plain,
% 0.57/0.75 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c6, sk_c5)),
% 0.57/0.75 inference(symmetry,[status(thm)],[318])).
% 0.57/0.75 tff(320,plain,
% 0.57/0.75 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c5), sk_c5) = identity)),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(321,plain,
% 0.57/0.75 (multiply(inverse(sk_c5), sk_c5) = identity),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[320, 55])).
% 0.57/0.75 tff(322,plain,
% 0.57/0.75 (identity = multiply(inverse(sk_c5), sk_c5)),
% 0.57/0.75 inference(symmetry,[status(thm)],[321])).
% 0.57/0.75 tff(323,plain,
% 0.57/0.75 (identity = multiply(sk_c6, sk_c5)),
% 0.57/0.75 inference(transitivity,[status(thm)],[322, 319])).
% 0.57/0.75 tff(324,plain,
% 0.57/0.75 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c5), sk_c6)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[323])).
% 0.57/0.75 tff(325,plain,
% 0.57/0.75 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c6) = sk_c6)),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(326,plain,
% 0.57/0.75 (multiply(identity, sk_c6) = sk_c6),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[325, 7])).
% 0.57/0.75 tff(327,plain,
% 0.57/0.75 (sk_c6 = multiply(identity, sk_c6)),
% 0.57/0.75 inference(symmetry,[status(thm)],[326])).
% 0.57/0.75 tff(328,plain,
% 0.57/0.75 (inverse(sk_c5) = sk_c8),
% 0.57/0.75 inference(transitivity,[status(thm)],[316, 327, 324, 310, 308, 302, 278, 281, 291, 301, 297, 294, 274, 272, 271, 270, 267, 261, 259, 257, 253, 250, 245, 243, 240, 134, 182, 231, 228, 226, 224, 221, 218, 185, 9])).
% 0.57/0.75 tff(329,plain,
% 0.57/0.75 (multiply(sk_c5, sk_c8) = multiply(sk_c5, identity)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[277])).
% 0.57/0.75 tff(330,plain,
% 0.57/0.75 (multiply(sk_c5, identity) = multiply(sk_c5, sk_c8)),
% 0.57/0.75 inference(symmetry,[status(thm)],[329])).
% 0.57/0.75 tff(331,plain,
% 0.57/0.75 (multiply(sk_c6, sk_c5) = identity),
% 0.57/0.75 inference(transitivity,[status(thm)],[318, 321])).
% 0.57/0.75 tff(332,plain,
% 0.57/0.75 (multiply(sk_c5, multiply(sk_c6, sk_c5)) = multiply(sk_c5, identity)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[331])).
% 0.57/0.75 tff(333,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c6), sk_c5) = multiply(sk_c5, multiply(sk_c6, sk_c5)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(334,plain,
% 0.57/0.75 (multiply(multiply(sk_c5, sk_c6), sk_c5) = multiply(sk_c5, multiply(sk_c6, sk_c5))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[333, 39])).
% 0.57/0.75 tff(335,plain,
% 0.57/0.75 (sk_c7 = multiply(sk_c5, sk_c6)),
% 0.57/0.75 inference(symmetry,[status(thm)],[306])).
% 0.57/0.75 tff(336,plain,
% 0.57/0.75 (multiply(sk_c4, sk_c8) = multiply(sk_c5, sk_c6)),
% 0.57/0.75 inference(transitivity,[status(thm)],[197, 335])).
% 0.57/0.75 tff(337,plain,
% 0.57/0.75 (multiply(multiply(sk_c4, sk_c8), sk_c5) = multiply(multiply(sk_c5, sk_c6), sk_c5)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[336])).
% 0.57/0.75 tff(338,plain,
% 0.57/0.75 (multiply(sk_c4, multiply(identity, sk_c8)) = multiply(sk_c4, sk_c8)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[9])).
% 0.57/0.75 tff(339,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, identity), sk_c8) = multiply(sk_c4, multiply(identity, sk_c8)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(340,plain,
% 0.57/0.75 (multiply(multiply(sk_c4, identity), sk_c8) = multiply(sk_c4, multiply(identity, sk_c8))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[339, 39])).
% 0.57/0.75 tff(341,plain,
% 0.57/0.75 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8) = multiply(multiply(sk_c4, identity), sk_c8)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[289])).
% 0.57/0.75 tff(342,plain,
% 0.57/0.75 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8) = multiply(sk_c4, sk_c8)),
% 0.57/0.75 inference(transitivity,[status(thm)],[341, 340, 338])).
% 0.57/0.75 tff(343,plain,
% 0.57/0.75 (multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8), sk_c5) = multiply(multiply(sk_c4, sk_c8), sk_c5)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[342])).
% 0.57/0.75 tff(344,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8), sk_c5) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c8, sk_c5)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(345,plain,
% 0.57/0.75 (multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8), sk_c5) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c8, sk_c5))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[344, 39])).
% 0.57/0.75 tff(346,plain,
% 0.57/0.75 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c8, sk_c5)) = multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8), sk_c5)),
% 0.57/0.75 inference(symmetry,[status(thm)],[345])).
% 0.57/0.75 tff(347,plain,
% 0.57/0.75 (multiply(sk_c4, sk_c8) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[248, 290])).
% 0.57/0.75 tff(348,plain,
% 0.57/0.75 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, sk_c5)) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c8, sk_c5))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[347])).
% 0.57/0.75 tff(349,plain,
% 0.57/0.75 (identity = multiply(sk_c4, sk_c8)),
% 0.57/0.75 inference(transitivity,[status(thm)],[201, 239, 242, 244, 249, 252, 256, 247])).
% 0.57/0.75 tff(350,plain,
% 0.57/0.75 (multiply(identity, multiply(sk_c8, sk_c5)) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, sk_c5))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[349])).
% 0.57/0.75 tff(351,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c8), sk_c5) = multiply(identity, multiply(sk_c8, sk_c5)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(352,plain,
% 0.57/0.75 (multiply(multiply(identity, sk_c8), sk_c5) = multiply(identity, multiply(sk_c8, sk_c5))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[351, 39])).
% 0.57/0.75 tff(353,plain,
% 0.57/0.75 (multiply(sk_c8, sk_c5) = multiply(multiply(identity, sk_c8), sk_c5)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[72])).
% 0.57/0.75 tff(354,plain,
% 0.57/0.75 (multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[213])).
% 0.57/0.75 tff(355,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), sk_c5) = multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c5)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(356,plain,
% 0.57/0.75 (multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), sk_c5) = multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c5))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[355, 39])).
% 0.57/0.75 tff(357,plain,
% 0.57/0.75 (multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c5)) = multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), sk_c5)),
% 0.57/0.75 inference(symmetry,[status(thm)],[356])).
% 0.57/0.75 tff(358,plain,
% 0.57/0.75 (multiply(multiply(sk_c5, sk_c6), sk_c5) = multiply(multiply(sk_c4, sk_c8), sk_c5)),
% 0.57/0.75 inference(symmetry,[status(thm)],[337])).
% 0.57/0.75 tff(359,plain,
% 0.57/0.75 (multiply(sk_c5, multiply(sk_c6, sk_c5)) = multiply(multiply(sk_c5, sk_c6), sk_c5)),
% 0.57/0.75 inference(symmetry,[status(thm)],[334])).
% 0.57/0.75 tff(360,plain,
% 0.57/0.75 (multiply(sk_c5, identity) = multiply(sk_c5, multiply(sk_c6, sk_c5))),
% 0.57/0.75 inference(symmetry,[status(thm)],[332])).
% 0.57/0.75 tff(361,plain,
% 0.57/0.75 (multiply(sk_c5, sk_c8) = multiply(multiply(sk_c4, sk_c8), sk_c5)),
% 0.57/0.75 inference(transitivity,[status(thm)],[329, 360, 359, 358])).
% 0.57/0.75 tff(362,plain,
% 0.57/0.75 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c5))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[361])).
% 0.57/0.75 tff(363,plain,
% 0.57/0.75 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c5, sk_c8)),
% 0.57/0.75 inference(transitivity,[status(thm)],[362, 357, 354, 353, 352, 350, 348, 346, 343, 337, 334, 332, 330])).
% 0.57/0.75 tff(364,plain,
% 0.57/0.75 ((multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7) <=> (multiply(sk_c5, sk_c8) = sk_c7)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[363])).
% 0.57/0.75 tff(365,plain,
% 0.57/0.75 ((multiply(sk_c5, sk_c8) = sk_c7) <=> (multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)),
% 0.57/0.75 inference(symmetry,[status(thm)],[364])).
% 0.57/0.75 tff(366,plain,
% 0.57/0.75 (multiply(sk_c5, sk_c6) = inverse(sk_c8)),
% 0.57/0.75 inference(transitivity,[status(thm)],[306, 193])).
% 0.57/0.75 tff(367,plain,
% 0.57/0.75 (multiply(multiply(sk_c5, sk_c6), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[366])).
% 0.57/0.75 tff(368,plain,
% 0.57/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c6), sk_c8) = multiply(sk_c5, multiply(sk_c6, sk_c8)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(369,plain,
% 0.57/0.75 (multiply(multiply(sk_c5, sk_c6), sk_c8) = multiply(sk_c5, multiply(sk_c6, sk_c8))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[368, 39])).
% 0.57/0.75 tff(370,plain,
% 0.57/0.75 (multiply(sk_c5, multiply(sk_c6, sk_c8)) = multiply(multiply(sk_c5, sk_c6), sk_c8)),
% 0.57/0.75 inference(symmetry,[status(thm)],[369])).
% 0.57/0.75 tff(371,plain,
% 0.57/0.75 (sk_c7 = multiply(sk_c6, sk_c8)),
% 0.57/0.75 inference(symmetry,[status(thm)],[265])).
% 0.57/0.75 tff(372,plain,
% 0.57/0.75 (multiply(sk_c5, sk_c7) = multiply(sk_c5, multiply(sk_c6, sk_c8))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[371])).
% 0.57/0.75 tff(373,plain,
% 0.57/0.75 (identity = sk_c7),
% 0.57/0.75 inference(transitivity,[status(thm)],[201, 239, 242, 244, 249, 252, 256, 247, 197])).
% 0.57/0.75 tff(374,plain,
% 0.57/0.75 (multiply(sk_c5, identity) = multiply(sk_c5, sk_c7)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[373])).
% 0.57/0.75 tff(375,plain,
% 0.57/0.75 (multiply(sk_c5, sk_c8) = sk_c7),
% 0.57/0.75 inference(transitivity,[status(thm)],[329, 374, 372, 370, 367, 239, 242, 244, 249, 252, 256, 247, 197])).
% 0.57/0.75 tff(376,plain,
% 0.57/0.75 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[375, 365])).
% 0.57/0.75 tff(377,plain,
% 0.57/0.75 (multiply(sk_c5, inverse(sk_c5)) = multiply(sk_c5, sk_c6)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[316])).
% 0.57/0.75 tff(378,plain,
% 0.57/0.75 (multiply(sk_c5, inverse(sk_c5)) = sk_c7),
% 0.57/0.75 inference(transitivity,[status(thm)],[377, 306])).
% 0.57/0.75 tff(379,plain,
% 0.57/0.75 (multiply(inverse(sk_c5), sk_c8) = multiply(sk_c6, sk_c8)),
% 0.57/0.75 inference(monotonicity,[status(thm)],[316])).
% 0.57/0.75 tff(380,plain,
% 0.57/0.75 (multiply(inverse(sk_c5), sk_c8) = sk_c7),
% 0.57/0.75 inference(transitivity,[status(thm)],[379, 265])).
% 0.57/0.75 tff(381,plain,
% 0.57/0.76 (multiply(sk_c5, sk_c7) = sk_c8),
% 0.57/0.76 inference(transitivity,[status(thm)],[372, 370, 367, 134, 182, 231, 228, 226, 224, 221, 218, 185, 9])).
% 0.57/0.76 tff(382,plain,
% 0.57/0.76 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c5), sk_c8) = sk_c7)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c5, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = 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(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c5), sk_c8) = sk_c7)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c5, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(383,plain,
% 0.57/0.76 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(inverse(sk_c5), sk_c8) = sk_c7)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c5), sk_c8) = sk_c7)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c5, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(384,plain,
% 0.57/0.76 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(inverse(sk_c5), sk_c8) = sk_c7)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c5), sk_c8) = sk_c7)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c5, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[383])).
% 0.57/0.76 tff(385,plain,
% 0.57/0.76 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(inverse(sk_c5), sk_c8) = sk_c7)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c5), sk_c8) = sk_c7)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c5, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[384, 382])).
% 0.57/0.76 tff(386,plain,
% 0.57/0.76 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(inverse(sk_c5), sk_c8) = sk_c7)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c5, sk_c7) = sk_c8)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(387,plain,
% 0.57/0.76 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c5), sk_c8) = sk_c7)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c5, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.57/0.76 tff(388,plain,
% 0.57/0.76 ((~(multiply(inverse(sk_c5), sk_c8) = sk_c7)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c5, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[387, 192, 197, 176, 165])).
% 0.57/0.76 tff(389,plain,
% 0.57/0.76 (~(inverse(sk_c5) = sk_c8)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[388, 381, 380, 378, 376])).
% 0.57/0.76 tff(390,plain,
% 0.57/0.76 ($false),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[389, 328])).
% 0.57/0.76 tff(391,plain,(multiply(sk_c1, sk_c7) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.57/0.76 tff(392,plain,
% 0.57/0.76 (((inverse(sk_c8) = sk_c7) | (multiply(sk_c2, sk_c8) = sk_c3)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(393,plain,
% 0.57/0.76 (((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c8) = sk_c7)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(394,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_19')).
% 0.57/0.76 tff(395,plain,
% 0.57/0.76 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.57/0.76 tff(396,plain,
% 0.57/0.76 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[395, 392])).
% 0.57/0.76 tff(397,plain,
% 0.57/0.76 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[396, 145])).
% 0.57/0.76 tff(398,plain,
% 0.57/0.76 (((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c7)) <=> ((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c7))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(399,axiom,((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_25')).
% 0.57/0.76 tff(400,plain,
% 0.57/0.76 ((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c7)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.57/0.76 tff(401,plain,
% 0.57/0.76 (inverse(sk_c2) = sk_c8),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[400, 145])).
% 0.57/0.76 tff(402,plain,
% 0.57/0.76 (((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(403,plain,
% 0.57/0.76 (((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c8) = sk_c7)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(404,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_13')).
% 0.57/0.76 tff(405,plain,
% 0.57/0.76 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.57/0.76 tff(406,plain,
% 0.57/0.76 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[405, 402])).
% 0.57/0.76 tff(407,plain,
% 0.57/0.76 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[406, 145])).
% 0.57/0.76 tff(408,plain,
% 0.57/0.76 (((inverse(sk_c1) = sk_c8) | (inverse(sk_c8) = sk_c7)) <=> ((inverse(sk_c1) = sk_c8) | (inverse(sk_c8) = sk_c7))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(409,axiom,((inverse(sk_c1) = sk_c8) | (inverse(sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_1')).
% 0.57/0.76 tff(410,plain,
% 0.57/0.76 ((inverse(sk_c1) = sk_c8) | (inverse(sk_c8) = sk_c7)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.57/0.76 tff(411,plain,
% 0.57/0.76 (inverse(sk_c1) = sk_c8),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[410, 145])).
% 0.57/0.76 tff(412,plain,
% 0.57/0.76 ((inverse(sk_c8) = sk_c7) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c3))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[147, 391])).
% 0.57/0.76 tff(413,plain,
% 0.57/0.76 ($false),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[412, 411, 145, 407, 401, 397])).
% 0.57/0.76 tff(414,plain,(inverse(sk_c8) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.57/0.76 tff(415,plain,
% 0.57/0.76 (sk_c7 = inverse(sk_c8)),
% 0.57/0.76 inference(symmetry,[status(thm)],[414])).
% 0.57/0.76 tff(416,plain,
% 0.57/0.76 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(inverse(sk_c8), sk_c8)),
% 0.57/0.76 inference(monotonicity,[status(thm)],[415, 391])).
% 0.57/0.76 tff(417,plain,
% 0.57/0.76 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(418,plain,
% 0.57/0.76 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[417, 39])).
% 0.57/0.76 tff(419,plain,
% 0.57/0.76 (multiply(multiply(sk_c7, sk_c1), sk_c7) = identity),
% 0.57/0.76 inference(transitivity,[status(thm)],[418, 416, 134])).
% 0.57/0.76 tff(420,plain,
% 0.57/0.76 (multiply(sk_c4, multiply(multiply(sk_c7, sk_c1), sk_c7)) = multiply(sk_c4, identity)),
% 0.57/0.76 inference(monotonicity,[status(thm)],[419])).
% 0.57/0.76 tff(421,plain,
% 0.57/0.76 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7) = multiply(sk_c4, multiply(multiply(sk_c7, sk_c1), sk_c7)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(422,plain,
% 0.57/0.76 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7) = multiply(sk_c4, multiply(multiply(sk_c7, sk_c1), sk_c7))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[421, 39])).
% 0.57/0.76 tff(423,plain,
% 0.57/0.76 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(424,plain,
% 0.57/0.76 (multiply(identity, sk_c7) = sk_c7),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[423, 7])).
% 0.57/0.76 tff(425,plain,
% 0.57/0.76 (multiply(sk_c7, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.57/0.76 inference(monotonicity,[status(thm)],[415])).
% 0.57/0.76 tff(426,plain,
% 0.57/0.76 (multiply(sk_c7, sk_c8) = identity),
% 0.57/0.76 inference(transitivity,[status(thm)],[425, 134])).
% 0.57/0.76 tff(427,plain,
% 0.57/0.76 (multiply(multiply(sk_c7, sk_c8), sk_c7) = multiply(identity, sk_c7)),
% 0.57/0.76 inference(monotonicity,[status(thm)],[426])).
% 0.57/0.76 tff(428,plain,
% 0.57/0.76 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), sk_c7) = multiply(sk_c7, multiply(sk_c8, sk_c7)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(429,plain,
% 0.57/0.76 (multiply(multiply(sk_c7, sk_c8), sk_c7) = multiply(sk_c7, multiply(sk_c8, sk_c7))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[428, 39])).
% 0.57/0.76 tff(430,plain,
% 0.57/0.76 (multiply(sk_c7, multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c7, sk_c8), sk_c7)),
% 0.57/0.76 inference(symmetry,[status(thm)],[429])).
% 0.57/0.76 tff(431,plain,
% 0.57/0.76 (multiply(sk_c7, multiply(sk_c8, sk_c7)) = sk_c7),
% 0.57/0.76 inference(transitivity,[status(thm)],[430, 427, 424])).
% 0.57/0.76 tff(432,plain,
% 0.57/0.76 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), multiply(sk_c7, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7)),
% 0.57/0.76 inference(monotonicity,[status(thm)],[431])).
% 0.57/0.76 tff(433,plain,
% 0.57/0.76 ((~![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_c1)), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), multiply(sk_c7, multiply(sk_c8, sk_c7))))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(434,plain,
% 0.57/0.76 (multiply(multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), multiply(sk_c7, multiply(sk_c8, sk_c7)))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[433, 39])).
% 0.57/0.76 tff(435,plain,
% 0.57/0.76 (multiply(sk_c4, multiply(multiply(sk_c7, sk_c1), sk_c7)) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7)),
% 0.57/0.76 inference(symmetry,[status(thm)],[422])).
% 0.57/0.76 tff(436,plain,
% 0.57/0.76 (multiply(sk_c4, identity) = multiply(sk_c4, multiply(multiply(sk_c7, sk_c1), sk_c7))),
% 0.57/0.76 inference(symmetry,[status(thm)],[420])).
% 0.57/0.76 tff(437,plain,
% 0.57/0.76 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c4, sk_c8)) = multiply(sk_c4, sk_c8))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(438,plain,
% 0.57/0.76 (multiply(identity, multiply(sk_c4, sk_c8)) = multiply(sk_c4, sk_c8)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[437, 7])).
% 0.57/0.76 tff(439,plain,
% 0.57/0.76 (multiply(multiply(sk_c7, sk_c8), multiply(sk_c4, sk_c8)) = multiply(identity, multiply(sk_c4, sk_c8))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[426])).
% 0.57/0.76 tff(440,plain,
% 0.57/0.76 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), multiply(sk_c4, sk_c8)) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c4, sk_c8))))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(441,plain,
% 0.57/0.76 (multiply(multiply(sk_c7, sk_c8), multiply(sk_c4, sk_c8)) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[440, 39])).
% 0.57/0.76 tff(442,plain,
% 0.57/0.76 (multiply(sk_c7, multiply(sk_c8, multiply(sk_c4, sk_c8))) = multiply(multiply(sk_c7, sk_c8), multiply(sk_c4, sk_c8))),
% 0.57/0.76 inference(symmetry,[status(thm)],[441])).
% 0.57/0.76 tff(443,plain,
% 0.57/0.76 (sk_c8 = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.57/0.76 inference(transitivity,[status(thm)],[72, 184, 211])).
% 0.57/0.76 tff(444,plain,
% 0.57/0.76 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[414, 443])).
% 0.57/0.76 tff(445,plain,
% 0.57/0.76 (multiply(sk_c7, sk_c8) = multiply(sk_c4, sk_c8)),
% 0.57/0.76 inference(transitivity,[status(thm)],[425, 444, 442, 439, 438])).
% 0.57/0.76 tff(446,plain,
% 0.57/0.76 (multiply(multiply(sk_c7, sk_c8), sk_c4) = multiply(multiply(sk_c4, sk_c8), sk_c4)),
% 0.57/0.76 inference(monotonicity,[status(thm)],[445])).
% 0.57/0.76 tff(447,plain,
% 0.57/0.76 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), sk_c4) = multiply(sk_c7, multiply(sk_c8, sk_c4)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(448,plain,
% 0.60/0.76 (multiply(multiply(sk_c7, sk_c8), sk_c4) = multiply(sk_c7, multiply(sk_c8, sk_c4))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[447, 39])).
% 0.60/0.76 tff(449,plain,
% 0.60/0.76 (multiply(sk_c7, multiply(sk_c8, sk_c4)) = multiply(multiply(sk_c7, sk_c8), sk_c4)),
% 0.60/0.76 inference(symmetry,[status(thm)],[448])).
% 0.60/0.76 tff(450,plain,
% 0.60/0.76 (multiply(sk_c7, identity) = multiply(sk_c7, multiply(sk_c8, sk_c4))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[183])).
% 0.60/0.76 tff(451,plain,
% 0.60/0.76 (multiply(sk_c7, identity) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7)),
% 0.60/0.76 inference(transitivity,[status(thm)],[450, 449, 446, 261, 259, 436, 435])).
% 0.60/0.76 tff(452,plain,
% 0.60/0.76 (multiply(multiply(sk_c7, identity), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7), multiply(sk_c8, sk_c7))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[451])).
% 0.60/0.76 tff(453,plain,
% 0.60/0.76 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, identity), sk_c8), sk_c7) = multiply(multiply(sk_c7, identity), multiply(sk_c8, sk_c7)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(454,plain,
% 0.60/0.76 (multiply(multiply(multiply(sk_c7, identity), sk_c8), sk_c7) = multiply(multiply(sk_c7, identity), multiply(sk_c8, sk_c7))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[453, 39])).
% 0.60/0.76 tff(455,plain,
% 0.60/0.76 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, identity), sk_c8) = multiply(sk_c7, multiply(identity, sk_c8)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(456,plain,
% 0.60/0.76 (multiply(multiply(sk_c7, identity), sk_c8) = multiply(sk_c7, multiply(identity, sk_c8))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[455, 39])).
% 0.60/0.76 tff(457,plain,
% 0.60/0.76 (multiply(sk_c7, multiply(identity, sk_c8)) = multiply(multiply(sk_c7, identity), sk_c8)),
% 0.60/0.76 inference(symmetry,[status(thm)],[456])).
% 0.60/0.76 tff(458,plain,
% 0.60/0.76 (multiply(sk_c7, multiply(identity, sk_c8)) = multiply(inverse(sk_c8), sk_c8)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[415, 9])).
% 0.60/0.76 tff(459,plain,
% 0.60/0.76 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, multiply(identity, sk_c8))),
% 0.60/0.76 inference(symmetry,[status(thm)],[458])).
% 0.60/0.76 tff(460,plain,
% 0.60/0.76 (identity = multiply(multiply(sk_c7, identity), sk_c8)),
% 0.60/0.76 inference(transitivity,[status(thm)],[201, 459, 457])).
% 0.60/0.76 tff(461,plain,
% 0.60/0.76 (multiply(identity, sk_c7) = multiply(multiply(multiply(sk_c7, identity), sk_c8), sk_c7)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[460])).
% 0.60/0.76 tff(462,plain,
% 0.60/0.76 (sk_c7 = multiply(identity, sk_c7)),
% 0.60/0.76 inference(symmetry,[status(thm)],[424])).
% 0.60/0.76 tff(463,assumption,(multiply(sk_c4, sk_c8) = sk_c7), introduced(assumption)).
% 0.60/0.76 tff(464,plain,
% 0.60/0.76 (multiply(sk_c8, sk_c4) = multiply(sk_c4, identity)),
% 0.60/0.76 inference(transitivity,[status(thm)],[178, 181, 201, 444, 442, 439, 438, 463, 462, 461, 454, 452, 434, 432, 422, 420])).
% 0.60/0.76 tff(465,plain,
% 0.60/0.76 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c4, identity), sk_c8)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[464])).
% 0.60/0.76 tff(466,plain,
% 0.60/0.76 (multiply(multiply(sk_c4, identity), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.60/0.76 inference(symmetry,[status(thm)],[465])).
% 0.60/0.76 tff(467,plain,
% 0.60/0.76 (multiply(sk_c4, multiply(identity, sk_c8)) = multiply(multiply(sk_c4, identity), sk_c8)),
% 0.60/0.76 inference(symmetry,[status(thm)],[340])).
% 0.60/0.76 tff(468,plain,
% 0.60/0.76 (multiply(sk_c4, sk_c8) = multiply(sk_c4, multiply(identity, sk_c8))),
% 0.60/0.76 inference(symmetry,[status(thm)],[338])).
% 0.60/0.76 tff(469,plain,
% 0.60/0.76 (multiply(sk_c7, multiply(sk_c8, multiply(sk_c4, sk_c8))) = multiply(inverse(sk_c8), sk_c8)),
% 0.60/0.76 inference(symmetry,[status(thm)],[444])).
% 0.60/0.76 tff(470,plain,
% 0.60/0.76 (multiply(identity, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c7, sk_c8), multiply(sk_c4, sk_c8))),
% 0.60/0.76 inference(symmetry,[status(thm)],[439])).
% 0.60/0.76 tff(471,plain,
% 0.60/0.76 (multiply(sk_c4, sk_c8) = multiply(identity, multiply(sk_c4, sk_c8))),
% 0.60/0.76 inference(symmetry,[status(thm)],[438])).
% 0.60/0.76 tff(472,plain,
% 0.60/0.76 (sk_c7 = multiply(sk_c4, sk_c8)),
% 0.60/0.76 inference(symmetry,[status(thm)],[463])).
% 0.60/0.76 tff(473,plain,
% 0.60/0.76 (multiply(multiply(multiply(sk_c7, identity), sk_c8), sk_c7) = multiply(identity, sk_c7)),
% 0.60/0.76 inference(symmetry,[status(thm)],[461])).
% 0.60/0.76 tff(474,plain,
% 0.60/0.76 (multiply(multiply(sk_c7, identity), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(sk_c7, identity), sk_c8), sk_c7)),
% 0.60/0.76 inference(symmetry,[status(thm)],[454])).
% 0.60/0.76 tff(475,plain,
% 0.60/0.76 (multiply(multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c7, identity), multiply(sk_c8, sk_c7))),
% 0.60/0.76 inference(symmetry,[status(thm)],[452])).
% 0.60/0.76 tff(476,plain,
% 0.60/0.76 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), multiply(sk_c7, multiply(sk_c8, sk_c7))) = multiply(multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7), multiply(sk_c8, sk_c7))),
% 0.60/0.76 inference(symmetry,[status(thm)],[434])).
% 0.60/0.76 tff(477,plain,
% 0.60/0.76 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), multiply(sk_c7, multiply(sk_c8, sk_c7)))),
% 0.60/0.76 inference(symmetry,[status(thm)],[432])).
% 0.60/0.76 tff(478,plain,
% 0.60/0.76 (multiply(sk_c7, identity) = identity),
% 0.60/0.76 inference(transitivity,[status(thm)],[450, 449, 446, 261, 259, 436, 435, 477, 476, 475, 474, 473, 424, 472, 471, 470, 441, 469, 134])).
% 0.60/0.76 tff(479,plain,
% 0.60/0.76 (multiply(inverse(sk_c4), sk_c4) = multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), sk_c4)),
% 0.60/0.76 inference(symmetry,[status(thm)],[284])).
% 0.60/0.76 tff(480,plain,
% 0.60/0.76 (identity = multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.76 inference(transitivity,[status(thm)],[182, 479, 286])).
% 0.60/0.76 tff(481,plain,
% 0.60/0.76 (multiply(sk_c4, identity) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[480])).
% 0.60/0.76 tff(482,plain,
% 0.60/0.76 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(sk_c4, identity)),
% 0.60/0.76 inference(symmetry,[status(thm)],[481])).
% 0.60/0.76 tff(483,plain,
% 0.60/0.76 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = identity),
% 0.60/0.76 inference(transitivity,[status(thm)],[482, 436, 435, 477, 476, 475, 474, 473, 424, 472, 471, 470, 441, 469, 134])).
% 0.60/0.76 tff(484,plain,
% 0.60/0.76 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c7, identity)) = multiply(identity, identity)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[483, 478])).
% 0.60/0.76 tff(485,plain,
% 0.60/0.76 (multiply(sk_c7, multiply(sk_c8, sk_c4)) = multiply(sk_c7, identity)),
% 0.60/0.76 inference(symmetry,[status(thm)],[450])).
% 0.60/0.76 tff(486,plain,
% 0.60/0.76 (multiply(multiply(sk_c4, sk_c8), sk_c4) = multiply(multiply(sk_c7, sk_c8), sk_c4)),
% 0.60/0.76 inference(symmetry,[status(thm)],[446])).
% 0.60/0.76 tff(487,plain,
% 0.60/0.76 (multiply(sk_c4, multiply(sk_c8, sk_c4)) = multiply(multiply(sk_c4, sk_c8), sk_c4)),
% 0.60/0.76 inference(symmetry,[status(thm)],[261])).
% 0.60/0.76 tff(488,plain,
% 0.60/0.76 (multiply(sk_c4, identity) = multiply(sk_c4, multiply(sk_c8, sk_c4))),
% 0.60/0.76 inference(symmetry,[status(thm)],[259])).
% 0.60/0.76 tff(489,plain,
% 0.60/0.76 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(sk_c7, identity)),
% 0.60/0.76 inference(transitivity,[status(thm)],[482, 488, 487, 486, 448, 485])).
% 0.60/0.76 tff(490,plain,
% 0.60/0.76 (multiply(sk_c4, sk_c8) = identity),
% 0.60/0.76 inference(transitivity,[status(thm)],[471, 470, 441, 469, 134])).
% 0.60/0.76 tff(491,plain,
% 0.60/0.76 (multiply(sk_c7, multiply(sk_c4, sk_c8)) = multiply(sk_c7, identity)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[490])).
% 0.60/0.76 tff(492,plain,
% 0.60/0.76 (multiply(sk_c7, multiply(sk_c4, sk_c8)) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[491, 450, 449, 446, 261, 259, 481])).
% 0.60/0.76 tff(493,plain,
% 0.60/0.76 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c7, identity))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[492, 489])).
% 0.60/0.76 tff(494,plain,
% 0.60/0.76 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(495,plain,
% 0.60/0.77 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[494, 39])).
% 0.60/0.77 tff(496,plain,
% 0.60/0.77 (multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.77 inference(symmetry,[status(thm)],[495])).
% 0.60/0.77 tff(497,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, identity))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[482])).
% 0.60/0.77 tff(498,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, identity)) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.77 inference(symmetry,[status(thm)],[497])).
% 0.60/0.77 tff(499,plain,
% 0.60/0.77 (multiply(sk_c4, identity) = multiply(multiply(sk_c4, sk_c8), sk_c4)),
% 0.60/0.77 inference(transitivity,[status(thm)],[488, 487])).
% 0.60/0.77 tff(500,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, identity)) = multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[499])).
% 0.60/0.77 tff(501,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, identity))),
% 0.60/0.77 inference(symmetry,[status(thm)],[500])).
% 0.60/0.77 tff(502,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(503,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[502, 39])).
% 0.60/0.77 tff(504,plain,
% 0.60/0.77 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.77 inference(symmetry,[status(thm)],[503])).
% 0.60/0.77 tff(505,plain,
% 0.60/0.77 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[504, 501, 498])).
% 0.60/0.77 tff(506,plain,
% 0.60/0.77 (multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[505])).
% 0.60/0.77 tff(507,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity) = multiply(multiply(sk_c4, identity), identity)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[482])).
% 0.60/0.77 tff(508,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[507, 252, 256, 481])).
% 0.60/0.77 tff(509,plain,
% 0.60/0.77 (multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity)) = multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[508])).
% 0.60/0.77 tff(510,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), identity) = multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(511,plain,
% 0.60/0.77 (multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), identity) = multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[510, 39])).
% 0.60/0.77 tff(512,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, sk_c8), sk_c4) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[261, 259, 481])).
% 0.60/0.77 tff(513,plain,
% 0.60/0.77 (multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[512])).
% 0.60/0.77 tff(514,plain,
% 0.60/0.77 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), identity)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[513, 426])).
% 0.60/0.77 tff(515,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c8) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c8)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(516,plain,
% 0.60/0.77 (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c8) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c8))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[515, 39])).
% 0.60/0.77 tff(517,plain,
% 0.60/0.77 (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), multiply(sk_c1, sk_c7)) = multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c8)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[391])).
% 0.60/0.77 tff(518,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), sk_c7) = multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), multiply(sk_c1, sk_c7)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(519,plain,
% 0.60/0.77 (multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), sk_c7) = multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), multiply(sk_c1, sk_c7))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[518, 39])).
% 0.60/0.77 tff(520,plain,
% 0.60/0.77 (multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), multiply(sk_c7, multiply(sk_c8, sk_c7))) = multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), sk_c7)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[431])).
% 0.60/0.77 tff(521,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), multiply(sk_c7, multiply(sk_c8, sk_c7))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(522,plain,
% 0.60/0.77 (multiply(multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), multiply(sk_c7, multiply(sk_c8, sk_c7)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[521, 39])).
% 0.60/0.77 tff(523,plain,
% 0.60/0.77 (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), multiply(sk_c1, sk_c7)) = multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), sk_c7)),
% 0.60/0.77 inference(symmetry,[status(thm)],[519])).
% 0.60/0.77 tff(524,plain,
% 0.60/0.77 (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c8) = multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), multiply(sk_c1, sk_c7))),
% 0.60/0.77 inference(symmetry,[status(thm)],[517])).
% 0.60/0.77 tff(525,plain,
% 0.60/0.77 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c8)) = multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c8)),
% 0.60/0.77 inference(symmetry,[status(thm)],[516])).
% 0.60/0.77 tff(526,plain,
% 0.60/0.77 (multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), identity) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c8))),
% 0.60/0.77 inference(symmetry,[status(thm)],[514])).
% 0.60/0.77 tff(527,plain,
% 0.60/0.77 (multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity)) = multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), identity)),
% 0.60/0.77 inference(symmetry,[status(thm)],[511])).
% 0.60/0.77 tff(528,plain,
% 0.60/0.77 (multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity))),
% 0.60/0.77 inference(symmetry,[status(thm)],[509])).
% 0.60/0.77 tff(529,plain,
% 0.60/0.77 (multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), sk_c7)),
% 0.60/0.77 inference(transitivity,[status(thm)],[528, 527, 526, 525, 524, 523])).
% 0.60/0.77 tff(530,plain,
% 0.60/0.77 (multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), sk_c7), multiply(sk_c8, sk_c7))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[529])).
% 0.60/0.77 tff(531,plain,
% 0.60/0.77 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), multiply(sk_c8, sk_c7))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[513])).
% 0.60/0.77 tff(532,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c8), sk_c7) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c8, sk_c7)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(533,plain,
% 0.60/0.77 (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c8), sk_c7) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c8, sk_c7))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[532, 39])).
% 0.60/0.77 tff(534,plain,
% 0.60/0.77 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c8) = multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c8)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[513])).
% 0.60/0.77 tff(535,plain,
% 0.60/0.77 (multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c8) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c8)),
% 0.60/0.77 inference(symmetry,[status(thm)],[534])).
% 0.60/0.77 tff(536,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c8) = multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(537,plain,
% 0.60/0.77 (multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c8) = multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[536, 39])).
% 0.60/0.77 tff(538,plain,
% 0.60/0.77 (multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8)) = multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c8)),
% 0.60/0.77 inference(symmetry,[status(thm)],[537])).
% 0.60/0.77 tff(539,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8) = multiply(multiply(sk_c4, identity), sk_c8)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[482])).
% 0.60/0.77 tff(540,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8) = multiply(sk_c4, sk_c8)),
% 0.60/0.77 inference(transitivity,[status(thm)],[539, 340, 338])).
% 0.60/0.77 tff(541,plain,
% 0.60/0.77 (multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8)) = multiply(sk_c7, multiply(sk_c4, sk_c8))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[540])).
% 0.60/0.77 tff(542,plain,
% 0.60/0.77 (multiply(sk_c7, multiply(sk_c4, sk_c8)) = multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8))),
% 0.60/0.77 inference(symmetry,[status(thm)],[541])).
% 0.60/0.77 tff(543,plain,
% 0.60/0.77 (multiply(sk_c7, identity) = multiply(sk_c7, multiply(sk_c4, sk_c8))),
% 0.60/0.77 inference(symmetry,[status(thm)],[491])).
% 0.60/0.77 tff(544,plain,
% 0.60/0.77 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c8)),
% 0.60/0.77 inference(transitivity,[status(thm)],[482, 488, 487, 486, 448, 485, 543, 542, 538, 535])).
% 0.60/0.77 tff(545,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7) = multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c8), sk_c7)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[544])).
% 0.60/0.77 tff(546,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, identity), sk_c7) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[481])).
% 0.60/0.77 tff(547,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, identity), sk_c7) = multiply(sk_c4, multiply(identity, sk_c7)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(548,plain,
% 0.60/0.77 (multiply(multiply(sk_c4, identity), sk_c7) = multiply(sk_c4, multiply(identity, sk_c7))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[547, 39])).
% 0.60/0.77 tff(549,plain,
% 0.60/0.77 (multiply(sk_c4, multiply(identity, sk_c7)) = multiply(multiply(sk_c4, identity), sk_c7)),
% 0.60/0.77 inference(symmetry,[status(thm)],[548])).
% 0.60/0.77 tff(550,plain,
% 0.60/0.77 (multiply(sk_c4, sk_c7) = multiply(sk_c4, multiply(identity, sk_c7))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[462])).
% 0.60/0.77 tff(551,plain,
% 0.60/0.77 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.60/0.77 inference(transitivity,[status(thm)],[550, 549, 546, 545, 533, 531, 530, 522, 520, 519, 517, 516, 514, 511, 509, 506, 496, 493, 484, 225, 254, 230, 181, 201, 444, 442, 439, 438, 468, 467, 466, 185, 9])).
% 0.60/0.77 tff(552,plain,
% 0.60/0.77 (multiply(sk_c4, inverse(sk_c4)) = multiply(sk_c4, sk_c8)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[176])).
% 0.60/0.77 tff(553,plain,
% 0.60/0.77 ((multiply(sk_c4, inverse(sk_c4)) = sk_c7) <=> (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[552])).
% 0.60/0.77 tff(554,plain,
% 0.60/0.77 ((multiply(sk_c4, sk_c8) = sk_c7) <=> (multiply(sk_c4, inverse(sk_c4)) = sk_c7)),
% 0.60/0.77 inference(symmetry,[status(thm)],[553])).
% 0.60/0.77 tff(555,plain,
% 0.60/0.77 (multiply(sk_c4, inverse(sk_c4)) = sk_c7),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[463, 554])).
% 0.60/0.77 tff(556,plain,
% 0.60/0.77 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7),
% 0.60/0.77 inference(transitivity,[status(thm)],[212, 465, 340, 338, 463])).
% 0.60/0.77 tff(557,plain,
% 0.60/0.77 (identity = multiply(sk_c4, sk_c8)),
% 0.60/0.77 inference(transitivity,[status(thm)],[201, 444, 442, 439, 438])).
% 0.60/0.77 tff(558,plain,
% 0.60/0.77 (multiply(sk_c8, identity) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[557])).
% 0.60/0.77 tff(559,plain,
% 0.60/0.77 (multiply(multiply(sk_c1, sk_c7), identity) = multiply(sk_c8, identity)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[391])).
% 0.60/0.77 tff(560,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), identity) = multiply(sk_c1, multiply(sk_c7, identity)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(561,plain,
% 0.60/0.77 (multiply(multiply(sk_c1, sk_c7), identity) = multiply(sk_c1, multiply(sk_c7, identity))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[560, 39])).
% 0.60/0.77 tff(562,plain,
% 0.60/0.77 (multiply(sk_c1, multiply(sk_c7, identity)) = multiply(multiply(sk_c1, sk_c7), identity)),
% 0.60/0.77 inference(symmetry,[status(thm)],[561])).
% 0.60/0.77 tff(563,plain,
% 0.60/0.77 (multiply(sk_c7, sk_c8) = multiply(sk_c7, identity)),
% 0.60/0.77 inference(transitivity,[status(thm)],[425, 444, 442, 439, 438, 463, 462, 461, 454, 452, 434, 432, 422, 420, 488, 487, 486, 448, 485])).
% 0.60/0.77 tff(564,plain,
% 0.60/0.77 (multiply(sk_c1, multiply(sk_c7, sk_c8)) = multiply(sk_c1, multiply(sk_c7, identity))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[563])).
% 0.60/0.77 tff(565,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), sk_c8) = multiply(sk_c1, multiply(sk_c7, sk_c8)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(566,plain,
% 0.60/0.77 (multiply(multiply(sk_c1, sk_c7), sk_c8) = multiply(sk_c1, multiply(sk_c7, sk_c8))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[565, 39])).
% 0.60/0.77 tff(567,plain,
% 0.60/0.77 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.60/0.77 inference(symmetry,[status(thm)],[391])).
% 0.60/0.77 tff(568,plain,
% 0.60/0.77 (inverse(sk_c4) = multiply(sk_c1, sk_c7)),
% 0.60/0.77 inference(transitivity,[status(thm)],[176, 567])).
% 0.60/0.77 tff(569,plain,
% 0.60/0.77 (multiply(inverse(sk_c4), sk_c8) = multiply(multiply(sk_c1, sk_c7), sk_c8)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[568])).
% 0.60/0.77 tff(570,plain,
% 0.60/0.77 (multiply(inverse(sk_c4), sk_c8) = sk_c7),
% 0.60/0.77 inference(transitivity,[status(thm)],[569, 566, 564, 562, 559, 558, 212, 465, 340, 338, 463])).
% 0.60/0.77 tff(571,plain,
% 0.60/0.77 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(572,plain,
% 0.60/0.77 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(573,plain,
% 0.60/0.78 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[572])).
% 0.60/0.78 tff(574,plain,
% 0.60/0.78 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[573, 571])).
% 0.60/0.78 tff(575,plain,
% 0.60/0.78 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(576,plain,
% 0.60/0.78 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(inverse(X3), sk_c8) = sk_c7)) | (~(multiply(X3, inverse(X3)) = sk_c7)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.60/0.78 tff(577,plain,
% 0.60/0.78 ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[576, 176, 165])).
% 0.60/0.78 tff(578,plain,
% 0.60/0.78 ((~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[577, 414])).
% 0.60/0.78 tff(579,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[578, 570, 556, 463, 555, 551])).
% 0.60/0.78 tff(580,plain,(~(multiply(sk_c4, sk_c8) = sk_c7)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(581,plain,
% 0.60/0.78 (((multiply(sk_c4, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((multiply(sk_c4, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(582,plain,
% 0.60/0.78 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c7)) <=> ((multiply(sk_c4, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(583,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_14')).
% 0.60/0.78 tff(584,plain,
% 0.60/0.78 ((multiply(sk_c4, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.60/0.78 tff(585,plain,
% 0.60/0.78 ((multiply(sk_c4, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[584, 581])).
% 0.60/0.78 tff(586,plain,
% 0.60/0.78 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[585, 580])).
% 0.60/0.78 tff(587,plain,
% 0.60/0.78 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c7)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c7))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(588,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_20')).
% 0.60/0.78 tff(589,plain,
% 0.60/0.78 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.60/0.78 tff(590,plain,
% 0.60/0.78 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[589, 580])).
% 0.60/0.78 tff(591,plain,
% 0.60/0.78 (sk_c3 = multiply(sk_c2, sk_c8)),
% 0.60/0.78 inference(symmetry,[status(thm)],[590])).
% 0.60/0.78 tff(592,plain,
% 0.60/0.78 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[591])).
% 0.60/0.78 tff(593,plain,
% 0.60/0.78 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.60/0.78 inference(symmetry,[status(thm)],[592])).
% 0.60/0.78 tff(594,plain,
% 0.60/0.78 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(595,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_26')).
% 0.60/0.78 tff(596,plain,
% 0.60/0.78 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.60/0.78 tff(597,plain,
% 0.60/0.78 (inverse(sk_c2) = sk_c8),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[596, 580])).
% 0.60/0.78 tff(598,plain,
% 0.60/0.78 (sk_c8 = inverse(sk_c2)),
% 0.60/0.78 inference(symmetry,[status(thm)],[597])).
% 0.60/0.78 tff(599,plain,
% 0.60/0.78 (multiply(sk_c8, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[598])).
% 0.60/0.78 tff(600,plain,
% 0.60/0.78 (multiply(sk_c8, sk_c2) = multiply(sk_c8, sk_c4)),
% 0.60/0.78 inference(transitivity,[status(thm)],[599, 57, 182, 179])).
% 0.60/0.78 tff(601,plain,
% 0.60/0.78 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[600])).
% 0.60/0.78 tff(602,plain,
% 0.60/0.78 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.60/0.78 inference(symmetry,[status(thm)],[601])).
% 0.60/0.78 tff(603,plain,
% 0.60/0.78 (sk_c8 = sk_c7),
% 0.60/0.78 inference(transitivity,[status(thm)],[72, 184, 602, 41, 593, 586])).
% 0.60/0.78 tff(604,plain,
% 0.60/0.78 (multiply(sk_c7, multiply(sk_c8, multiply(sk_c4, sk_c8))) = multiply(inverse(sk_c8), sk_c8)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[415, 213])).
% 0.60/0.78 tff(605,plain,
% 0.60/0.78 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, sk_c8)),
% 0.60/0.78 inference(symmetry,[status(thm)],[425])).
% 0.60/0.78 tff(606,plain,
% 0.60/0.78 (identity = multiply(sk_c7, sk_c8)),
% 0.60/0.78 inference(transitivity,[status(thm)],[201, 605])).
% 0.60/0.78 tff(607,plain,
% 0.60/0.78 (multiply(identity, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c7, sk_c8), multiply(sk_c4, sk_c8))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[606])).
% 0.60/0.78 tff(608,plain,
% 0.60/0.78 (multiply(sk_c4, multiply(sk_c1, sk_c7)) = multiply(sk_c4, sk_c8)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[391])).
% 0.60/0.78 tff(609,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c1), sk_c7) = multiply(sk_c4, multiply(sk_c1, sk_c7)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(610,plain,
% 0.60/0.78 (multiply(multiply(sk_c4, sk_c1), sk_c7) = multiply(sk_c4, multiply(sk_c1, sk_c7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[609, 39])).
% 0.60/0.78 tff(611,plain,
% 0.60/0.78 (multiply(multiply(sk_c4, sk_c1), sk_c7) = multiply(sk_c4, sk_c8)),
% 0.60/0.78 inference(transitivity,[status(thm)],[610, 608])).
% 0.60/0.78 tff(612,plain,
% 0.60/0.78 (multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c1), sk_c7)) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c8))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[611])).
% 0.60/0.78 tff(613,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c1)), sk_c7) = multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c1), sk_c7)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(614,plain,
% 0.60/0.78 (multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c1)), sk_c7) = multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c1), sk_c7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[613, 39])).
% 0.60/0.78 tff(615,plain,
% 0.60/0.78 (multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c1)), multiply(sk_c7, multiply(sk_c8, sk_c7))) = multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c1)), sk_c7)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[431])).
% 0.60/0.78 tff(616,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c1)), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c1)), multiply(sk_c7, multiply(sk_c8, sk_c7))))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(617,plain,
% 0.60/0.78 (multiply(multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c1)), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c1)), multiply(sk_c7, multiply(sk_c8, sk_c7)))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[616, 39])).
% 0.60/0.78 tff(618,plain,
% 0.60/0.78 (multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c1), sk_c7)) = multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c1)), sk_c7)),
% 0.60/0.78 inference(symmetry,[status(thm)],[614])).
% 0.60/0.78 tff(619,plain,
% 0.60/0.78 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c1), sk_c7))),
% 0.60/0.78 inference(symmetry,[status(thm)],[612])).
% 0.60/0.78 tff(620,plain,
% 0.60/0.78 (multiply(multiply(sk_c7, sk_c8), multiply(sk_c4, sk_c8)) = multiply(identity, multiply(sk_c4, sk_c8))),
% 0.60/0.78 inference(symmetry,[status(thm)],[607])).
% 0.60/0.78 tff(621,plain,
% 0.60/0.78 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.60/0.78 inference(symmetry,[status(thm)],[604])).
% 0.60/0.78 tff(622,plain,
% 0.60/0.78 (inverse(sk_c4) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.60/0.78 inference(transitivity,[status(thm)],[176, 72, 184, 211])).
% 0.60/0.78 tff(623,plain,
% 0.60/0.78 (multiply(inverse(sk_c4), sk_c4) = multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), sk_c4)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[622])).
% 0.60/0.78 tff(624,plain,
% 0.60/0.78 (multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.60/0.78 inference(symmetry,[status(thm)],[623])).
% 0.60/0.78 tff(625,plain,
% 0.60/0.78 (multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[443])).
% 0.60/0.78 tff(626,plain,
% 0.60/0.78 (multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.78 inference(symmetry,[status(thm)],[625])).
% 0.60/0.78 tff(627,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(628,plain,
% 0.60/0.78 (multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[627, 39])).
% 0.60/0.78 tff(629,plain,
% 0.60/0.78 (multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(sk_c8, multiply(sk_c4, sk_c8)), multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.78 inference(symmetry,[status(thm)],[628])).
% 0.60/0.78 tff(630,plain,
% 0.60/0.78 (multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[504])).
% 0.60/0.78 tff(631,plain,
% 0.60/0.78 (multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c1)), sk_c7)),
% 0.60/0.78 inference(transitivity,[status(thm)],[630, 629, 626, 287, 624, 181, 201, 621, 442, 620, 438, 236, 234, 619, 618])).
% 0.60/0.78 tff(632,plain,
% 0.60/0.78 (multiply(multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, sk_c1)), sk_c7), multiply(sk_c8, sk_c7))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[631])).
% 0.60/0.78 tff(633,plain,
% 0.60/0.78 (multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.78 inference(symmetry,[status(thm)],[630])).
% 0.60/0.78 tff(634,plain,
% 0.60/0.78 (identity = multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.78 inference(transitivity,[status(thm)],[182, 623, 286, 625, 628, 633])).
% 0.60/0.78 tff(635,plain,
% 0.60/0.78 (multiply(identity, multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), multiply(sk_c8, sk_c7))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[634])).
% 0.60/0.78 tff(636,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c8), sk_c7) = multiply(identity, multiply(sk_c8, sk_c7)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(637,plain,
% 0.60/0.78 (multiply(multiply(identity, sk_c8), sk_c7) = multiply(identity, multiply(sk_c8, sk_c7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[636, 39])).
% 0.60/0.78 tff(638,plain,
% 0.60/0.78 (multiply(sk_c8, sk_c7) = multiply(multiply(identity, sk_c8), sk_c7)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[72])).
% 0.60/0.78 tff(639,plain,
% 0.60/0.78 (multiply(sk_c8, sk_c7) = multiply(inverse(sk_c8), sk_c8)),
% 0.60/0.78 inference(transitivity,[status(thm)],[638, 637, 635, 632, 617, 615, 614, 612, 233, 235, 471, 607, 441, 604])).
% 0.60/0.78 tff(640,plain,
% 0.60/0.78 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (multiply(inverse(sk_c8), sk_c8) = sk_c7)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[639, 603])).
% 0.60/0.78 tff(641,plain,
% 0.60/0.78 ((multiply(inverse(sk_c8), sk_c8) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.60/0.78 inference(symmetry,[status(thm)],[640])).
% 0.60/0.78 tff(642,plain,
% 0.60/0.78 ((~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) <=> (~(multiply(sk_c8, sk_c7) = sk_c8))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[641])).
% 0.60/0.78 tff(643,plain,
% 0.60/0.78 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c4, sk_c8)),
% 0.60/0.78 inference(transitivity,[status(thm)],[621, 442, 620, 438])).
% 0.60/0.78 tff(644,plain,
% 0.60/0.78 ((multiply(inverse(sk_c8), sk_c8) = sk_c7) <=> (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[643])).
% 0.60/0.78 tff(645,plain,
% 0.60/0.78 ((multiply(sk_c4, sk_c8) = sk_c7) <=> (multiply(inverse(sk_c8), sk_c8) = sk_c7)),
% 0.60/0.78 inference(symmetry,[status(thm)],[644])).
% 0.60/0.78 tff(646,plain,
% 0.60/0.78 ((~(multiply(sk_c4, sk_c8) = sk_c7)) <=> (~(multiply(inverse(sk_c8), sk_c8) = sk_c7))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[645])).
% 0.60/0.78 tff(647,plain,
% 0.60/0.78 (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[580, 646])).
% 0.60/0.78 tff(648,plain,
% 0.60/0.78 (~(multiply(sk_c8, sk_c7) = sk_c8)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[647, 642])).
% 0.60/0.78 tff(649,plain,
% 0.60/0.78 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.60/0.78 inference(symmetry,[status(thm)],[41])).
% 0.60/0.78 tff(650,plain,
% 0.60/0.78 (sk_c7 = multiply(sk_c8, sk_c3)),
% 0.60/0.78 inference(symmetry,[status(thm)],[586])).
% 0.60/0.78 tff(651,plain,
% 0.60/0.78 (multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = identity),
% 0.60/0.78 inference(transitivity,[status(thm)],[630, 629, 626, 287, 624, 181])).
% 0.60/0.78 tff(652,plain,
% 0.60/0.78 (multiply(multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c7) = multiply(identity, sk_c7)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[651])).
% 0.60/0.78 tff(653,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c7) = multiply(sk_c8, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(654,plain,
% 0.60/0.78 (multiply(multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c7) = multiply(sk_c8, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[653, 39])).
% 0.60/0.78 tff(655,plain,
% 0.60/0.78 (multiply(sk_c8, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7)) = multiply(multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c7)),
% 0.60/0.78 inference(symmetry,[status(thm)],[654])).
% 0.60/0.78 tff(656,plain,
% 0.60/0.78 (multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)) = identity),
% 0.60/0.78 inference(transitivity,[status(thm)],[287, 624, 181])).
% 0.60/0.78 tff(657,plain,
% 0.60/0.78 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(sk_c4, identity)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[656])).
% 0.60/0.78 tff(658,plain,
% 0.60/0.78 (multiply(sk_c4, identity) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.78 inference(symmetry,[status(thm)],[657])).
% 0.60/0.78 tff(659,plain,
% 0.60/0.78 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c4, identity), identity)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[657, 426])).
% 0.60/0.78 tff(660,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), sk_c8) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c7, sk_c8)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(661,plain,
% 0.60/0.78 (multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), sk_c8) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c7, sk_c8))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[660, 39])).
% 0.60/0.79 tff(662,plain,
% 0.60/0.79 (multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), sk_c8) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[661, 659, 252, 256, 658])).
% 0.60/0.79 tff(663,plain,
% 0.60/0.79 (multiply(multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), sk_c8), sk_c7) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[662])).
% 0.60/0.79 tff(664,plain,
% 0.60/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), sk_c8), sk_c7) = multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(665,plain,
% 0.60/0.79 (multiply(multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), sk_c8), sk_c7) = multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[664, 39])).
% 0.60/0.79 tff(666,plain,
% 0.60/0.79 (multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), sk_c8), sk_c7)),
% 0.60/0.79 inference(symmetry,[status(thm)],[665])).
% 0.60/0.79 tff(667,plain,
% 0.60/0.79 (multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7)),
% 0.60/0.79 inference(transitivity,[status(thm)],[666, 663])).
% 0.60/0.79 tff(668,plain,
% 0.60/0.79 (multiply(sk_c4, sk_c8) = identity),
% 0.60/0.79 inference(transitivity,[status(thm)],[471, 607, 441, 604, 134])).
% 0.60/0.79 tff(669,plain,
% 0.60/0.79 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, identity)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[668])).
% 0.60/0.79 tff(670,plain,
% 0.60/0.79 (multiply(sk_c8, identity) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.60/0.79 inference(symmetry,[status(thm)],[669])).
% 0.60/0.79 tff(671,plain,
% 0.60/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), sk_c4) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(672,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), sk_c4) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[671, 39])).
% 0.60/0.79 tff(673,plain,
% 0.60/0.79 (multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), sk_c4)),
% 0.60/0.79 inference(symmetry,[status(thm)],[672])).
% 0.60/0.79 tff(674,plain,
% 0.60/0.79 (multiply(sk_c1, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(sk_c1, multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), sk_c4))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[673])).
% 0.60/0.79 tff(675,plain,
% 0.60/0.79 (multiply(sk_c1, multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), sk_c4)) = multiply(sk_c1, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.79 inference(symmetry,[status(thm)],[674])).
% 0.60/0.79 tff(676,plain,
% 0.60/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, multiply(sk_c7, multiply(sk_c4, sk_c8))), sk_c4) = multiply(sk_c1, multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), sk_c4)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(677,plain,
% 0.60/0.79 (multiply(multiply(sk_c1, multiply(sk_c7, multiply(sk_c4, sk_c8))), sk_c4) = multiply(sk_c1, multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), sk_c4))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[676, 39])).
% 0.60/0.79 tff(678,plain,
% 0.60/0.79 (multiply(multiply(sk_c1, sk_c7), multiply(sk_c4, sk_c8)) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[391])).
% 0.60/0.79 tff(679,plain,
% 0.60/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), multiply(sk_c4, sk_c8)) = multiply(sk_c1, multiply(sk_c7, multiply(sk_c4, sk_c8))))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(680,plain,
% 0.60/0.79 (multiply(multiply(sk_c1, sk_c7), multiply(sk_c4, sk_c8)) = multiply(sk_c1, multiply(sk_c7, multiply(sk_c4, sk_c8)))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[679, 39])).
% 0.60/0.79 tff(681,plain,
% 0.60/0.79 (multiply(sk_c1, multiply(sk_c7, multiply(sk_c4, sk_c8))) = multiply(multiply(sk_c1, sk_c7), multiply(sk_c4, sk_c8))),
% 0.60/0.79 inference(symmetry,[status(thm)],[680])).
% 0.60/0.79 tff(682,plain,
% 0.60/0.79 (multiply(sk_c1, multiply(sk_c7, multiply(sk_c4, sk_c8))) = inverse(sk_c4)),
% 0.60/0.79 inference(transitivity,[status(thm)],[681, 678, 212, 185, 9, 177])).
% 0.60/0.79 tff(683,plain,
% 0.60/0.79 (multiply(multiply(sk_c1, multiply(sk_c7, multiply(sk_c4, sk_c8))), sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[682])).
% 0.60/0.79 tff(684,plain,
% 0.60/0.79 (multiply(inverse(sk_c4), sk_c4) = multiply(multiply(sk_c1, multiply(sk_c7, multiply(sk_c4, sk_c8))), sk_c4)),
% 0.60/0.79 inference(symmetry,[status(thm)],[683])).
% 0.60/0.79 tff(685,plain,
% 0.60/0.79 (identity = multiply(sk_c1, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[182, 684, 677, 675])).
% 0.60/0.79 tff(686,plain,
% 0.60/0.79 (multiply(sk_c8, identity) = multiply(sk_c8, multiply(sk_c1, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[685])).
% 0.60/0.79 tff(687,plain,
% 0.60/0.79 (multiply(sk_c8, multiply(sk_c1, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c8, identity)),
% 0.60/0.79 inference(symmetry,[status(thm)],[686])).
% 0.60/0.79 tff(688,plain,
% 0.60/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c1), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(sk_c8, multiply(sk_c1, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(689,plain,
% 0.60/0.79 (multiply(multiply(sk_c8, sk_c1), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(sk_c8, multiply(sk_c1, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[688, 39])).
% 0.60/0.79 tff(690,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, sk_c8), sk_c1) = multiply(identity, sk_c1)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[426])).
% 0.60/0.79 tff(691,plain,
% 0.60/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), sk_c1) = multiply(sk_c7, multiply(sk_c8, sk_c1)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(692,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, sk_c8), sk_c1) = multiply(sk_c7, multiply(sk_c8, sk_c1))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[691, 39])).
% 0.60/0.79 tff(693,plain,
% 0.60/0.79 (multiply(sk_c7, multiply(sk_c8, sk_c1)) = multiply(multiply(sk_c7, sk_c8), sk_c1)),
% 0.60/0.79 inference(symmetry,[status(thm)],[692])).
% 0.60/0.79 tff(694,plain,
% 0.60/0.79 (multiply(sk_c7, multiply(sk_c8, sk_c1)) = sk_c1),
% 0.60/0.79 inference(transitivity,[status(thm)],[693, 690, 100])).
% 0.60/0.79 tff(695,plain,
% 0.60/0.79 (multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))) = multiply(sk_c8, sk_c1)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[694])).
% 0.60/0.79 tff(696,plain,
% 0.60/0.79 (multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(sk_c8, sk_c1), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[695])).
% 0.60/0.79 tff(697,plain,
% 0.60/0.79 (multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = sk_c8),
% 0.60/0.79 inference(transitivity,[status(thm)],[696, 689, 687, 670, 212, 185, 9])).
% 0.60/0.79 tff(698,plain,
% 0.60/0.79 (multiply(multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))) = multiply(sk_c8, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[697, 667])).
% 0.60/0.79 tff(699,plain,
% 0.60/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(700,plain,
% 0.60/0.79 (multiply(multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[699, 39])).
% 0.60/0.79 tff(701,plain,
% 0.60/0.79 (multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))) = multiply(multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))),
% 0.60/0.79 inference(symmetry,[status(thm)],[700])).
% 0.60/0.79 tff(702,plain,
% 0.60/0.79 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7) = multiply(multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), sk_c8), sk_c7)),
% 0.60/0.79 inference(symmetry,[status(thm)],[663])).
% 0.60/0.79 tff(703,plain,
% 0.60/0.79 (multiply(sk_c7, sk_c8) = multiply(sk_c4, sk_c8)),
% 0.60/0.79 inference(transitivity,[status(thm)],[425, 621, 442, 620, 438])).
% 0.60/0.79 tff(704,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, sk_c8), sk_c4) = multiply(multiply(sk_c4, sk_c8), sk_c4)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[703])).
% 0.60/0.79 tff(705,plain,
% 0.60/0.79 (multiply(sk_c7, identity) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[450, 449, 704, 261, 259, 658])).
% 0.60/0.79 tff(706,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, identity), sk_c7) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[705])).
% 0.60/0.79 tff(707,plain,
% 0.60/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, identity), sk_c7) = multiply(sk_c7, multiply(identity, sk_c7)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(708,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, identity), sk_c7) = multiply(sk_c7, multiply(identity, sk_c7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[707, 39])).
% 0.60/0.79 tff(709,plain,
% 0.60/0.79 (multiply(sk_c7, multiply(identity, sk_c7)) = multiply(multiply(sk_c7, identity), sk_c7)),
% 0.60/0.79 inference(symmetry,[status(thm)],[708])).
% 0.60/0.79 tff(710,plain,
% 0.60/0.79 (multiply(sk_c7, sk_c7) = multiply(sk_c7, multiply(identity, sk_c7))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[462])).
% 0.60/0.79 tff(711,plain,
% 0.60/0.79 (multiply(sk_c7, sk_c7) = multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))),
% 0.60/0.79 inference(transitivity,[status(thm)],[710, 709, 706, 702, 665])).
% 0.60/0.79 tff(712,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[711])).
% 0.60/0.79 tff(713,plain,
% 0.60/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c7) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c7)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(714,plain,
% 0.60/0.79 (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c7) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[713, 39])).
% 0.60/0.79 tff(715,plain,
% 0.60/0.79 (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c7) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[714, 712])).
% 0.60/0.79 tff(716,plain,
% 0.60/0.79 (multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c7)) = multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[715])).
% 0.60/0.79 tff(717,plain,
% 0.60/0.79 (multiply(sk_c8, sk_c1) = multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1)))),
% 0.60/0.79 inference(symmetry,[status(thm)],[695])).
% 0.60/0.79 tff(718,plain,
% 0.60/0.79 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(719,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_2')).
% 0.60/0.79 tff(720,plain,
% 0.60/0.79 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[719, 718])).
% 0.60/0.79 tff(721,plain,
% 0.60/0.79 (inverse(sk_c1) = sk_c8),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[720, 580])).
% 0.60/0.79 tff(722,plain,
% 0.60/0.79 (sk_c8 = inverse(sk_c1)),
% 0.60/0.79 inference(symmetry,[status(thm)],[721])).
% 0.60/0.79 tff(723,plain,
% 0.60/0.79 (multiply(sk_c8, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[722])).
% 0.60/0.79 tff(724,plain,
% 0.60/0.79 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c8, sk_c1)),
% 0.60/0.79 inference(symmetry,[status(thm)],[723])).
% 0.60/0.79 tff(725,plain,
% 0.60/0.79 (identity = multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[132, 724, 717])).
% 0.60/0.79 tff(726,plain,
% 0.60/0.79 (multiply(identity, multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c7)) = multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c7))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[725])).
% 0.60/0.79 tff(727,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c7)) = multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c7)),
% 0.60/0.79 inference(symmetry,[status(thm)],[714])).
% 0.60/0.79 tff(728,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c7))),
% 0.60/0.79 inference(symmetry,[status(thm)],[712])).
% 0.60/0.79 tff(729,plain,
% 0.60/0.79 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(sk_c4, sk_c8), sk_c4)),
% 0.60/0.79 inference(transitivity,[status(thm)],[657, 488, 487])).
% 0.60/0.79 tff(730,plain,
% 0.60/0.79 (multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[729])).
% 0.60/0.79 tff(731,plain,
% 0.60/0.79 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity) = multiply(multiply(sk_c4, identity), identity)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[657])).
% 0.60/0.79 tff(732,plain,
% 0.60/0.79 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[731, 252, 256, 658])).
% 0.60/0.79 tff(733,plain,
% 0.60/0.79 (multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity)) = multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[732])).
% 0.60/0.79 tff(734,plain,
% 0.60/0.79 (multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.79 inference(symmetry,[status(thm)],[730])).
% 0.60/0.79 tff(735,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), identity)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[734, 426])).
% 0.60/0.79 tff(736,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), identity) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, sk_c8))),
% 0.60/0.79 inference(symmetry,[status(thm)],[735])).
% 0.60/0.79 tff(737,plain,
% 0.60/0.79 (multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), identity))),
% 0.60/0.79 inference(symmetry,[status(thm)],[733])).
% 0.60/0.79 tff(738,plain,
% 0.60/0.79 (multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), sk_c7)),
% 0.60/0.79 inference(transitivity,[status(thm)],[737, 527, 736, 525, 524, 523])).
% 0.60/0.79 tff(739,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c1), sk_c7), multiply(sk_c8, sk_c7))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[738])).
% 0.60/0.79 tff(740,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), multiply(sk_c8, sk_c7))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[734])).
% 0.60/0.79 tff(741,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c8) = multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c8)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[734])).
% 0.60/0.79 tff(742,plain,
% 0.60/0.79 (multiply(multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c8) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c8)),
% 0.60/0.79 inference(symmetry,[status(thm)],[741])).
% 0.60/0.79 tff(743,plain,
% 0.60/0.79 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8) = multiply(multiply(sk_c4, identity), sk_c8)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[657])).
% 0.60/0.79 tff(744,plain,
% 0.60/0.79 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8) = multiply(sk_c4, sk_c8)),
% 0.60/0.79 inference(transitivity,[status(thm)],[743, 340, 338])).
% 0.60/0.79 tff(745,plain,
% 0.60/0.79 (multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8)) = multiply(sk_c7, multiply(sk_c4, sk_c8))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[744])).
% 0.60/0.80 tff(746,plain,
% 0.60/0.80 (multiply(sk_c7, multiply(sk_c4, sk_c8)) = multiply(sk_c7, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c8))),
% 0.60/0.80 inference(symmetry,[status(thm)],[745])).
% 0.60/0.80 tff(747,plain,
% 0.60/0.80 (multiply(sk_c7, multiply(sk_c4, sk_c8)) = multiply(sk_c7, identity)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[668])).
% 0.60/0.80 tff(748,plain,
% 0.60/0.80 (multiply(sk_c7, identity) = multiply(sk_c7, multiply(sk_c4, sk_c8))),
% 0.60/0.80 inference(symmetry,[status(thm)],[747])).
% 0.60/0.80 tff(749,plain,
% 0.60/0.80 (multiply(multiply(sk_c4, sk_c8), sk_c4) = multiply(multiply(sk_c7, sk_c8), sk_c4)),
% 0.60/0.80 inference(symmetry,[status(thm)],[704])).
% 0.60/0.80 tff(750,plain,
% 0.60/0.80 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c8)),
% 0.60/0.80 inference(transitivity,[status(thm)],[657, 488, 487, 749, 448, 485, 748, 746, 538, 742])).
% 0.60/0.80 tff(751,plain,
% 0.60/0.80 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7) = multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c8), sk_c7)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[750])).
% 0.60/0.80 tff(752,plain,
% 0.60/0.80 (multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.80 inference(transitivity,[status(thm)],[666, 663, 751, 533, 740, 739, 522, 520, 519, 517, 516, 735, 511, 733, 730])).
% 0.60/0.80 tff(753,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[752])).
% 0.60/0.80 tff(754,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))),
% 0.60/0.80 inference(symmetry,[status(thm)],[753])).
% 0.60/0.80 tff(755,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c7)),
% 0.60/0.80 inference(transitivity,[status(thm)],[754, 728, 727])).
% 0.60/0.80 tff(756,plain,
% 0.60/0.80 (multiply(identity, multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(identity, multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), sk_c7))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[755])).
% 0.60/0.80 tff(757,plain,
% 0.60/0.80 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(identity, multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(758,plain,
% 0.60/0.80 (multiply(multiply(identity, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(identity, multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[757, 39])).
% 0.60/0.80 tff(759,plain,
% 0.60/0.80 (multiply(identity, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(identity, multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[734])).
% 0.60/0.80 tff(760,plain,
% 0.60/0.80 (multiply(identity, multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))) = multiply(identity, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.80 inference(symmetry,[status(thm)],[759])).
% 0.60/0.80 tff(761,plain,
% 0.60/0.80 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c7), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(identity, multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(762,plain,
% 0.60/0.80 (multiply(multiply(identity, sk_c7), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(identity, multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[761, 39])).
% 0.60/0.80 tff(763,plain,
% 0.60/0.80 (multiply(multiply(identity, sk_c7), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[424])).
% 0.60/0.80 tff(764,plain,
% 0.60/0.80 (multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(identity, sk_c7), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.80 inference(symmetry,[status(thm)],[763])).
% 0.60/0.80 tff(765,plain,
% 0.60/0.80 (multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)) = multiply(identity, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[734, 764, 762, 760])).
% 0.60/0.80 tff(766,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(identity, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[765])).
% 0.60/0.80 tff(767,plain,
% 0.60/0.80 (multiply(identity, multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))) = multiply(multiply(identity, sk_c7), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.80 inference(symmetry,[status(thm)],[762])).
% 0.60/0.80 tff(768,plain,
% 0.60/0.80 (multiply(sk_c8, sk_c1) = identity),
% 0.60/0.80 inference(transitivity,[status(thm)],[723, 60])).
% 0.60/0.80 tff(769,plain,
% 0.60/0.80 (multiply(multiply(sk_c8, sk_c1), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(identity, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[768])).
% 0.60/0.80 tff(770,plain,
% 0.60/0.80 (multiply(sk_c8, multiply(sk_c1, multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(sk_c8, sk_c1), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.80 inference(symmetry,[status(thm)],[689])).
% 0.60/0.80 tff(771,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, identity), sk_c8) = identity),
% 0.60/0.80 inference(transitivity,[status(thm)],[456, 458, 134])).
% 0.60/0.80 tff(772,plain,
% 0.60/0.80 (multiply(multiply(multiply(sk_c7, identity), sk_c8), sk_c7) = multiply(identity, sk_c7)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[771])).
% 0.60/0.80 tff(773,plain,
% 0.60/0.80 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.60/0.80 inference(symmetry,[status(thm)],[418])).
% 0.60/0.80 tff(774,plain,
% 0.60/0.80 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.60/0.80 inference(symmetry,[status(thm)],[416])).
% 0.60/0.80 tff(775,plain,
% 0.60/0.80 (identity = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.60/0.80 inference(transitivity,[status(thm)],[201, 774, 773])).
% 0.60/0.80 tff(776,plain,
% 0.60/0.80 (multiply(sk_c4, identity) = multiply(sk_c4, multiply(multiply(sk_c7, sk_c1), sk_c7))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[775])).
% 0.60/0.80 tff(777,plain,
% 0.60/0.80 (multiply(sk_c4, multiply(multiply(sk_c7, sk_c1), sk_c7)) = multiply(sk_c4, identity)),
% 0.60/0.80 inference(symmetry,[status(thm)],[776])).
% 0.60/0.80 tff(778,plain,
% 0.60/0.80 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7) = multiply(sk_c7, identity)),
% 0.60/0.80 inference(transitivity,[status(thm)],[422, 777, 488, 487, 749, 448, 485])).
% 0.60/0.80 tff(779,plain,
% 0.60/0.80 (multiply(multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c7, identity), multiply(sk_c8, sk_c7))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[778])).
% 0.60/0.80 tff(780,plain,
% 0.60/0.80 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c8), sk_c7)),
% 0.60/0.80 inference(symmetry,[status(thm)],[427])).
% 0.60/0.80 tff(781,plain,
% 0.60/0.80 (sk_c7 = multiply(sk_c7, multiply(sk_c8, sk_c7))),
% 0.60/0.80 inference(transitivity,[status(thm)],[462, 780, 429])).
% 0.60/0.80 tff(782,plain,
% 0.60/0.80 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), multiply(sk_c7, multiply(sk_c8, sk_c7)))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[781])).
% 0.60/0.80 tff(783,plain,
% 0.60/0.80 (multiply(sk_c7, identity) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.80 inference(transitivity,[status(thm)],[450, 449, 704, 261, 259, 776, 435, 782, 476, 779, 474, 772, 424, 650, 592, 649, 601, 211, 669, 686, 770, 769, 759, 767, 763, 730])).
% 0.60/0.80 tff(784,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, identity)) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[783])).
% 0.60/0.80 tff(785,plain,
% 0.60/0.80 (multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), multiply(sk_c7, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7)),
% 0.60/0.80 inference(symmetry,[status(thm)],[782])).
% 0.60/0.80 tff(786,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, identity), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(sk_c4, multiply(sk_c7, sk_c1)), sk_c7), multiply(sk_c8, sk_c7))),
% 0.60/0.80 inference(symmetry,[status(thm)],[779])).
% 0.60/0.80 tff(787,plain,
% 0.60/0.80 (multiply(identity, sk_c7) = multiply(multiply(multiply(sk_c7, identity), sk_c8), sk_c7)),
% 0.60/0.80 inference(symmetry,[status(thm)],[772])).
% 0.60/0.80 tff(788,plain,
% 0.60/0.80 (sk_c7 = multiply(sk_c7, identity)),
% 0.60/0.80 inference(transitivity,[status(thm)],[462, 787, 454, 786, 434, 785, 422, 777, 488, 487, 749, 448, 485])).
% 0.60/0.80 tff(789,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, identity))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[788])).
% 0.60/0.80 tff(790,plain,
% 0.60/0.80 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, identity))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[657])).
% 0.60/0.80 tff(791,plain,
% 0.60/0.80 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[790, 500, 503])).
% 0.60/0.80 tff(792,plain,
% 0.60/0.80 (multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))) = multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[791])).
% 0.60/0.80 tff(793,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.80 inference(transitivity,[status(thm)],[495, 792, 730])).
% 0.60/0.80 tff(794,plain,
% 0.60/0.80 (multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c7) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[793])).
% 0.60/0.80 tff(795,plain,
% 0.60/0.80 ((~![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_c8)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c7) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(796,plain,
% 0.60/0.80 (multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c7) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[795, 39])).
% 0.60/0.80 tff(797,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7)) = multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c7)),
% 0.60/0.80 inference(symmetry,[status(thm)],[796])).
% 0.60/0.80 tff(798,plain,
% 0.60/0.80 (multiply(sk_c7, multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))) = multiply(sk_c7, identity)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[651])).
% 0.60/0.80 tff(799,plain,
% 0.60/0.80 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(800,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[799, 39])).
% 0.60/0.80 tff(801,plain,
% 0.60/0.80 (multiply(identity, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(sk_c7, sk_c8), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[606])).
% 0.60/0.80 tff(802,plain,
% 0.60/0.80 (multiply(identity, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(sk_c7, multiply(sk_c4, sk_c8))),
% 0.60/0.80 inference(transitivity,[status(thm)],[801, 800, 798, 748])).
% 0.60/0.80 tff(803,plain,
% 0.60/0.80 (multiply(multiply(identity, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[802, 667])).
% 0.60/0.80 tff(804,plain,
% 0.60/0.80 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))) = multiply(identity, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(805,plain,
% 0.60/0.80 (multiply(multiply(identity, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))) = multiply(identity, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[804, 39])).
% 0.60/0.80 tff(806,plain,
% 0.60/0.80 (multiply(identity, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))) = multiply(multiply(identity, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))),
% 0.60/0.80 inference(symmetry,[status(thm)],[805])).
% 0.60/0.80 tff(807,plain,
% 0.60/0.80 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(sk_c7, multiply(sk_c4, sk_c8))),
% 0.60/0.80 inference(transitivity,[status(thm)],[657, 488, 487, 749, 448, 485, 748])).
% 0.60/0.80 tff(808,plain,
% 0.60/0.80 (multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[807, 667])).
% 0.60/0.80 tff(809,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7)) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))),
% 0.60/0.80 inference(symmetry,[status(thm)],[808])).
% 0.60/0.80 tff(810,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7) = multiply(multiply(multiply(sk_c7, multiply(sk_c4, sk_c8)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))), sk_c7)),
% 0.60/0.80 inference(symmetry,[status(thm)],[794])).
% 0.60/0.80 tff(811,plain,
% 0.60/0.80 (multiply(sk_c7, multiply(sk_c4, identity)) = multiply(sk_c7, multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[658])).
% 0.60/0.80 tff(812,plain,
% 0.60/0.80 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c4), identity) = multiply(sk_c7, multiply(sk_c4, identity)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(813,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, sk_c4), identity) = multiply(sk_c7, multiply(sk_c4, identity))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[812, 39])).
% 0.60/0.80 tff(814,plain,
% 0.60/0.80 (multiply(multiply(sk_c7, sk_c4), multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c7, sk_c4), identity)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[426])).
% 0.60/0.80 tff(815,plain,
% 0.60/0.80 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), sk_c8) = multiply(multiply(sk_c7, sk_c4), multiply(sk_c7, sk_c8)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(816,plain,
% 0.60/0.80 (multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), sk_c8) = multiply(multiply(sk_c7, sk_c4), multiply(sk_c7, sk_c8))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[815, 39])).
% 0.60/0.80 tff(817,plain,
% 0.60/0.80 (multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), sk_c8) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.80 inference(transitivity,[status(thm)],[816, 814, 813, 811, 730])).
% 0.60/0.80 tff(818,plain,
% 0.60/0.80 (multiply(multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), sk_c8), sk_c7) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[817])).
% 0.60/0.80 tff(819,plain,
% 0.60/0.80 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), sk_c8), sk_c7) = multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), multiply(sk_c8, sk_c7)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(820,plain,
% 0.60/0.80 (multiply(multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), sk_c8), sk_c7) = multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), multiply(sk_c8, sk_c7))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[819, 39])).
% 0.60/0.80 tff(821,plain,
% 0.60/0.80 (multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), sk_c8), sk_c7)),
% 0.60/0.80 inference(symmetry,[status(thm)],[820])).
% 0.60/0.81 tff(822,plain,
% 0.60/0.81 (multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[821, 818, 810, 796, 809])).
% 0.60/0.81 tff(823,plain,
% 0.60/0.81 (multiply(identity, multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), multiply(sk_c8, sk_c7))) = multiply(identity, multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), multiply(multiply(multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))), sk_c7), multiply(sk_c8, sk_c7))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[822])).
% 0.60/0.81 tff(824,plain,
% 0.60/0.81 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7) = multiply(multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), sk_c8), sk_c7)),
% 0.60/0.81 inference(symmetry,[status(thm)],[818])).
% 0.60/0.81 tff(825,plain,
% 0.60/0.81 (multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, identity)) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7)),
% 0.60/0.81 inference(symmetry,[status(thm)],[789])).
% 0.60/0.81 tff(826,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), identity) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, identity)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(827,plain,
% 0.60/0.81 (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), identity) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), multiply(sk_c7, identity))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[826, 39])).
% 0.60/0.81 tff(828,plain,
% 0.60/0.81 (multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), identity) = multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), multiply(sk_c8, sk_c7))),
% 0.60/0.81 inference(transitivity,[status(thm)],[827, 825, 824, 820])).
% 0.60/0.81 tff(829,plain,
% 0.60/0.81 (multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))) = identity),
% 0.60/0.81 inference(transitivity,[status(thm)],[695, 723, 60])).
% 0.60/0.81 tff(830,plain,
% 0.60/0.81 (multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), identity)) = multiply(identity, multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), multiply(sk_c8, sk_c7)))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[829, 828])).
% 0.60/0.81 tff(831,plain,
% 0.60/0.81 (multiply(multiply(sk_c7, sk_c4), identity) = multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4))),
% 0.60/0.81 inference(transitivity,[status(thm)],[813, 811, 730])).
% 0.60/0.81 tff(832,plain,
% 0.60/0.81 (multiply(multiply(multiply(sk_c7, sk_c4), identity), sk_c7) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[831])).
% 0.60/0.81 tff(833,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c4), identity), sk_c7) = multiply(multiply(sk_c7, sk_c4), multiply(identity, sk_c7)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(834,plain,
% 0.60/0.81 (multiply(multiply(multiply(sk_c7, sk_c4), identity), sk_c7) = multiply(multiply(sk_c7, sk_c4), multiply(identity, sk_c7))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[833, 39])).
% 0.60/0.81 tff(835,plain,
% 0.60/0.81 (multiply(multiply(sk_c7, sk_c4), multiply(identity, sk_c7)) = multiply(multiply(multiply(sk_c7, sk_c4), identity), sk_c7)),
% 0.60/0.81 inference(symmetry,[status(thm)],[834])).
% 0.60/0.81 tff(836,plain,
% 0.60/0.81 (multiply(multiply(sk_c7, sk_c4), sk_c7) = multiply(multiply(sk_c7, sk_c4), multiply(identity, sk_c7))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[462])).
% 0.60/0.81 tff(837,plain,
% 0.60/0.81 (multiply(multiply(sk_c7, sk_c4), sk_c7) = multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7)),
% 0.60/0.81 inference(transitivity,[status(thm)],[836, 835, 832])).
% 0.60/0.81 tff(838,plain,
% 0.60/0.81 (multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), identity) = multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), identity)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[837])).
% 0.60/0.81 tff(839,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), identity) = multiply(multiply(sk_c7, sk_c4), multiply(sk_c7, identity)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(840,plain,
% 0.60/0.81 (multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), identity) = multiply(multiply(sk_c7, sk_c4), multiply(sk_c7, identity))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[839, 39])).
% 0.60/0.81 tff(841,plain,
% 0.60/0.81 (multiply(multiply(sk_c7, sk_c4), multiply(sk_c7, identity)) = multiply(multiply(multiply(sk_c7, sk_c4), sk_c7), identity)),
% 0.60/0.81 inference(symmetry,[status(thm)],[840])).
% 0.60/0.81 tff(842,plain,
% 0.60/0.81 (multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(sk_c7, identity)),
% 0.60/0.81 inference(transitivity,[status(thm)],[657, 488, 487, 749, 448, 485])).
% 0.60/0.81 tff(843,plain,
% 0.60/0.81 (multiply(multiply(sk_c7, sk_c4), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(sk_c7, sk_c4), multiply(sk_c7, identity))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[842])).
% 0.60/0.81 tff(844,plain,
% 0.60/0.81 (multiply(multiply(sk_c7, sk_c4), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), identity)),
% 0.60/0.81 inference(transitivity,[status(thm)],[843, 841, 838])).
% 0.60/0.81 tff(845,plain,
% 0.60/0.81 (multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(multiply(sk_c7, sk_c4), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))) = multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(multiply(multiply(sk_c7, multiply(multiply(sk_c4, sk_c8), sk_c4)), sk_c7), identity))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[844])).
% 0.60/0.81 tff(846,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, sk_c4)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(multiply(sk_c7, sk_c4), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(847,plain,
% 0.60/0.81 (multiply(multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, sk_c4)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))) = multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(multiply(sk_c7, sk_c4), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4)))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[846, 39])).
% 0.60/0.81 tff(848,plain,
% 0.60/0.81 (multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, sk_c4)) = multiply(multiply(sk_c8, sk_c1), multiply(sk_c7, sk_c4))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[695])).
% 0.60/0.81 tff(849,plain,
% 0.60/0.81 (multiply(multiply(sk_c8, sk_c1), multiply(sk_c7, sk_c4)) = multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, sk_c4))),
% 0.60/0.81 inference(symmetry,[status(thm)],[848])).
% 0.60/0.81 tff(850,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c1), multiply(sk_c7, sk_c4)) = multiply(sk_c8, multiply(sk_c1, multiply(sk_c7, sk_c4))))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(851,plain,
% 0.60/0.81 (multiply(multiply(sk_c8, sk_c1), multiply(sk_c7, sk_c4)) = multiply(sk_c8, multiply(sk_c1, multiply(sk_c7, sk_c4)))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[850, 39])).
% 0.60/0.81 tff(852,plain,
% 0.60/0.81 (multiply(sk_c8, multiply(sk_c1, multiply(sk_c7, sk_c4))) = multiply(multiply(sk_c8, sk_c1), multiply(sk_c7, sk_c4))),
% 0.60/0.81 inference(symmetry,[status(thm)],[851])).
% 0.60/0.81 tff(853,plain,
% 0.60/0.81 (multiply(sk_c1, sk_c7) = inverse(sk_c4)),
% 0.60/0.81 inference(transitivity,[status(thm)],[391, 177])).
% 0.60/0.81 tff(854,plain,
% 0.60/0.81 (multiply(multiply(sk_c1, sk_c7), sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[853])).
% 0.60/0.81 tff(855,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), sk_c4) = multiply(sk_c1, multiply(sk_c7, sk_c4)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(856,plain,
% 0.60/0.81 (multiply(multiply(sk_c1, sk_c7), sk_c4) = multiply(sk_c1, multiply(sk_c7, sk_c4))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[855, 39])).
% 0.60/0.81 tff(857,plain,
% 0.60/0.81 (multiply(sk_c1, multiply(sk_c7, sk_c4)) = multiply(multiply(sk_c1, sk_c7), sk_c4)),
% 0.60/0.81 inference(symmetry,[status(thm)],[856])).
% 0.60/0.81 tff(858,plain,
% 0.60/0.81 (multiply(sk_c1, multiply(sk_c7, sk_c4)) = identity),
% 0.60/0.81 inference(transitivity,[status(thm)],[857, 854, 181])).
% 0.60/0.81 tff(859,plain,
% 0.60/0.81 (multiply(sk_c8, multiply(sk_c1, multiply(sk_c7, sk_c4))) = multiply(sk_c8, identity)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[858])).
% 0.60/0.81 tff(860,plain,
% 0.60/0.81 (multiply(sk_c8, identity) = multiply(sk_c8, multiply(sk_c1, multiply(sk_c7, sk_c4)))),
% 0.60/0.81 inference(symmetry,[status(thm)],[859])).
% 0.60/0.81 tff(861,plain,
% 0.60/0.81 (sk_c8 = multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, sk_c4))),
% 0.60/0.81 inference(transitivity,[status(thm)],[72, 184, 211, 669, 860, 852, 849])).
% 0.60/0.81 tff(862,plain,
% 0.60/0.81 (multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), multiply(multiply(sk_c4, sk_c8), sk_c4))) = multiply(multiply(multiply(sk_c8, multiply(sk_c7, multiply(sk_c8, sk_c1))), multiply(sk_c7, sk_c4)), multiply(sk_c4, multiply(sk_c8, multiply(multiply(sk_c4, sk_c8), sk_c4))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[861, 503])).
% 0.60/0.81 tff(863,plain,
% 0.60/0.81 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.60/0.81 inference(transitivity,[status(thm)],[638, 637, 635, 632, 617, 615, 614, 612, 233, 235, 471, 607, 441, 604, 134, 182, 623, 286, 625, 628, 862, 847, 845, 830, 823, 806, 803, 797, 794, 789, 784, 766, 758, 756, 726, 716, 701, 698, 655, 652, 424, 650, 592, 649, 601, 185, 9])).
% 0.60/0.81 tff(864,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[863, 648])).
% 0.60/0.81 % SZS output end Proof
% 0.60/0.81 % E exiting
%------------------------------------------------------------------------------