%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP219-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP219-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 300
% 0.18/0.33 % DateTime : Thu Jun 19 15:48:03 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.19/0.51 % SZS status Unsatisfiable
% 0.19/0.51 % SZS output start Proof
% 0.19/0.51 tff(sk_c8_type, type, (
% 0.19/0.51 sk_c8: $i)).
% 0.19/0.51 tff(multiply_type, type, (
% 0.19/0.51 multiply: ( $i * $i ) > $i)).
% 0.19/0.51 tff(sk_c9_type, type, (
% 0.19/0.51 sk_c9: $i)).
% 0.19/0.51 tff(inverse_type, type, (
% 0.19/0.51 inverse: $i > $i)).
% 0.19/0.51 tff(sk_c4_type, type, (
% 0.19/0.51 sk_c4: $i)).
% 0.19/0.51 tff(sk_c7_type, type, (
% 0.19/0.51 sk_c7: $i)).
% 0.19/0.51 tff(sk_c6_type, type, (
% 0.19/0.51 sk_c6: $i)).
% 0.19/0.51 tff(identity_type, type, (
% 0.19/0.51 identity: $i)).
% 0.19/0.51 tff(sk_c5_type, type, (
% 0.19/0.51 sk_c5: $i)).
% 0.19/0.51 tff(sk_c1_type, type, (
% 0.19/0.51 sk_c1: $i)).
% 0.19/0.51 tff(sk_c2_type, type, (
% 0.19/0.51 sk_c2: $i)).
% 0.19/0.51 tff(sk_c3_type, type, (
% 0.19/0.51 sk_c3: $i)).
% 0.19/0.51 tff(1,assumption,(~(inverse(sk_c4) = sk_c9)), introduced(assumption)).
% 0.19/0.51 tff(2,plain,
% 0.19/0.51 (((inverse(sk_c4) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9)) <=> ((inverse(sk_c4) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(3,axiom,((inverse(sk_c4) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_30')).
% 0.19/0.51 tff(4,plain,
% 0.19/0.51 ((inverse(sk_c4) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.51 tff(5,plain,
% 0.19/0.51 (multiply(sk_c6, sk_c8) = sk_c9),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.51 tff(6,plain,
% 0.19/0.51 (((inverse(sk_c4) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9)) <=> ((inverse(sk_c4) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(7,axiom,((inverse(sk_c4) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_31')).
% 0.19/0.51 tff(8,plain,
% 0.19/0.51 ((inverse(sk_c4) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.51 tff(9,plain,
% 0.19/0.51 (multiply(sk_c7, sk_c8) = sk_c9),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[8, 1])).
% 0.19/0.51 tff(10,plain,
% 0.19/0.51 (((inverse(sk_c4) = sk_c9) | (inverse(sk_c6) = sk_c9)) <=> ((inverse(sk_c4) = sk_c9) | (inverse(sk_c6) = sk_c9))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(11,axiom,((inverse(sk_c4) = sk_c9) | (inverse(sk_c6) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_29')).
% 0.19/0.51 tff(12,plain,
% 0.19/0.51 ((inverse(sk_c4) = sk_c9) | (inverse(sk_c6) = sk_c9)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.51 tff(13,plain,
% 0.19/0.51 (inverse(sk_c6) = sk_c9),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.19/0.51 tff(14,plain,
% 0.19/0.51 (((inverse(sk_c4) = sk_c9) | (inverse(sk_c7) = sk_c8)) <=> ((inverse(sk_c4) = sk_c9) | (inverse(sk_c7) = sk_c8))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(15,axiom,((inverse(sk_c4) = sk_c9) | (inverse(sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_32')).
% 0.19/0.51 tff(16,plain,
% 0.19/0.51 ((inverse(sk_c4) = sk_c9) | (inverse(sk_c7) = sk_c8)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.51 tff(17,plain,
% 0.19/0.51 (inverse(sk_c7) = sk_c8),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[16, 1])).
% 0.19/0.51 tff(18,assumption,(inverse(sk_c7) = sk_c8), introduced(assumption)).
% 0.19/0.51 tff(19,plain,
% 0.19/0.51 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(20,plain,
% 0.19/0.51 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.19/0.51 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.51 tff(21,plain,
% 0.19/0.51 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(22,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.19/0.51 tff(23,plain,
% 0.19/0.51 (![X: $i] : (multiply(identity, X) = X)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.51 tff(24,plain,(
% 0.19/0.51 ![X: $i] : (multiply(identity, X) = X)),
% 0.19/0.51 inference(skolemize,[status(sab)],[23])).
% 0.19/0.51 tff(25,plain,
% 0.19/0.51 (![X: $i] : (multiply(identity, X) = X)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.51 tff(26,plain,
% 0.19/0.51 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c6) = sk_c6)),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(27,plain,
% 0.19/0.51 (multiply(identity, sk_c6) = sk_c6),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.19/0.51 tff(28,plain,
% 0.19/0.51 (^[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))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(29,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.51 tff(30,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(31,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')).
% 0.19/0.51 tff(32,plain,
% 0.19/0.51 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.51 tff(33,plain,(
% 0.19/0.51 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[32])).
% 0.19/0.51 tff(34,plain,
% 0.19/0.51 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.51 tff(35,plain,
% 0.19/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), sk_c6) = multiply(sk_c6, multiply(sk_c8, sk_c6)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(36,plain,
% 0.19/0.51 (multiply(multiply(sk_c6, sk_c8), sk_c6) = multiply(sk_c6, multiply(sk_c8, sk_c6))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.51 tff(37,assumption,(inverse(sk_c6) = sk_c9), introduced(assumption)).
% 0.19/0.51 tff(38,plain,
% 0.19/0.51 (sk_c9 = inverse(sk_c6)),
% 0.19/0.51 inference(symmetry,[status(thm)],[37])).
% 0.19/0.51 tff(39,assumption,(multiply(sk_c6, sk_c8) = sk_c9), introduced(assumption)).
% 0.19/0.51 tff(40,plain,
% 0.19/0.51 (multiply(sk_c6, sk_c8) = inverse(sk_c6)),
% 0.19/0.51 inference(transitivity,[status(thm)],[39, 38])).
% 0.19/0.51 tff(41,plain,
% 0.19/0.51 (multiply(multiply(sk_c6, sk_c8), sk_c6) = multiply(inverse(sk_c6), sk_c6)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.51 tff(42,plain,
% 0.19/0.51 (multiply(inverse(sk_c6), sk_c6) = multiply(multiply(sk_c6, sk_c8), sk_c6)),
% 0.19/0.51 inference(symmetry,[status(thm)],[41])).
% 0.19/0.51 tff(43,plain,
% 0.19/0.51 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(44,plain,
% 0.19/0.51 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.19/0.51 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.51 tff(45,plain,
% 0.19/0.51 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(46,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.19/0.51 tff(47,plain,
% 0.19/0.51 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.51 tff(48,plain,(
% 0.19/0.51 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.19/0.51 inference(skolemize,[status(sab)],[47])).
% 0.19/0.51 tff(49,plain,
% 0.19/0.51 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.51 tff(50,plain,
% 0.19/0.51 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c6), sk_c6) = identity)),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(51,plain,
% 0.19/0.51 (multiply(inverse(sk_c6), sk_c6) = identity),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.51 tff(52,plain,
% 0.19/0.51 (identity = multiply(inverse(sk_c6), sk_c6)),
% 0.19/0.51 inference(symmetry,[status(thm)],[51])).
% 0.19/0.51 tff(53,plain,
% 0.19/0.51 (identity = multiply(sk_c6, multiply(sk_c8, sk_c6))),
% 0.19/0.51 inference(transitivity,[status(thm)],[52, 42, 36])).
% 0.19/0.51 tff(54,plain,
% 0.19/0.51 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, multiply(sk_c8, sk_c6)), sk_c6)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.51 tff(55,plain,
% 0.19/0.51 (multiply(multiply(sk_c6, multiply(sk_c8, sk_c6)), sk_c6) = multiply(identity, sk_c6)),
% 0.19/0.52 inference(symmetry,[status(thm)],[54])).
% 0.19/0.52 tff(56,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, multiply(sk_c8, sk_c6)), sk_c6) = multiply(sk_c6, multiply(multiply(sk_c8, sk_c6), sk_c6)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(57,plain,
% 0.19/0.52 (multiply(multiply(sk_c6, multiply(sk_c8, sk_c6)), sk_c6) = multiply(sk_c6, multiply(multiply(sk_c8, sk_c6), sk_c6))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[56, 34])).
% 0.19/0.52 tff(58,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(multiply(sk_c8, sk_c6), sk_c6)) = multiply(multiply(sk_c6, multiply(sk_c8, sk_c6)), sk_c6)),
% 0.19/0.52 inference(symmetry,[status(thm)],[57])).
% 0.19/0.52 tff(59,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c6), sk_c6) = multiply(sk_c8, multiply(sk_c6, sk_c6)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(60,plain,
% 0.19/0.52 (multiply(multiply(sk_c8, sk_c6), sk_c6) = multiply(sk_c8, multiply(sk_c6, sk_c6))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[59, 34])).
% 0.19/0.52 tff(61,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(multiply(sk_c8, sk_c6), sk_c6)) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c6, sk_c6)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.52 tff(62,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c6, sk_c6))) = multiply(sk_c6, multiply(multiply(sk_c8, sk_c6), sk_c6))),
% 0.19/0.52 inference(symmetry,[status(thm)],[61])).
% 0.19/0.52 tff(63,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), multiply(sk_c6, sk_c6)) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c6, sk_c6))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(64,plain,
% 0.19/0.52 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c6, sk_c6)) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c6, sk_c6)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[63, 34])).
% 0.19/0.52 tff(65,plain,
% 0.19/0.52 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c6, sk_c6)) = multiply(sk_c9, multiply(sk_c6, sk_c6))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.52 tff(66,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(sk_c6, sk_c6)) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c6, sk_c6))),
% 0.19/0.52 inference(symmetry,[status(thm)],[65])).
% 0.19/0.52 tff(67,plain,
% 0.19/0.52 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c9) = sk_c9)),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(68,plain,
% 0.19/0.52 (multiply(identity, sk_c9) = sk_c9),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[67, 25])).
% 0.19/0.52 tff(69,plain,
% 0.19/0.52 (multiply(sk_c9, sk_c6) = multiply(inverse(sk_c6), sk_c6)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.52 tff(70,plain,
% 0.19/0.52 (multiply(inverse(sk_c6), sk_c6) = multiply(sk_c9, sk_c6)),
% 0.19/0.52 inference(symmetry,[status(thm)],[69])).
% 0.19/0.52 tff(71,plain,
% 0.19/0.52 (identity = multiply(sk_c9, sk_c6)),
% 0.19/0.52 inference(transitivity,[status(thm)],[52, 70])).
% 0.19/0.52 tff(72,plain,
% 0.19/0.52 (multiply(identity, sk_c9) = multiply(multiply(sk_c9, sk_c6), sk_c9)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[71])).
% 0.19/0.52 tff(73,plain,
% 0.19/0.52 (multiply(multiply(sk_c9, sk_c6), sk_c9) = multiply(identity, sk_c9)),
% 0.19/0.52 inference(symmetry,[status(thm)],[72])).
% 0.19/0.52 tff(74,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c9, sk_c6), sk_c9) = multiply(sk_c9, multiply(sk_c6, sk_c9)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(75,plain,
% 0.19/0.52 (multiply(multiply(sk_c9, sk_c6), sk_c9) = multiply(sk_c9, multiply(sk_c6, sk_c9))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[74, 34])).
% 0.19/0.52 tff(76,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(sk_c6, sk_c9)) = multiply(multiply(sk_c9, sk_c6), sk_c9)),
% 0.19/0.52 inference(symmetry,[status(thm)],[75])).
% 0.19/0.52 tff(77,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c9),
% 0.19/0.52 inference(transitivity,[status(thm)],[76, 73, 68])).
% 0.19/0.52 tff(78,plain,
% 0.19/0.52 (multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c9)) = multiply(sk_c9, multiply(sk_c6, sk_c9))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.52 tff(79,plain,
% 0.19/0.52 (multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c9)) = sk_c9),
% 0.19/0.52 inference(transitivity,[status(thm)],[78, 76, 73, 68])).
% 0.19/0.52 tff(80,plain,
% 0.19/0.52 (multiply(multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c6)) = multiply(sk_c9, multiply(sk_c6, sk_c6))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.52 tff(81,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c6)) = multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c6))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(82,plain,
% 0.19/0.52 (multiply(multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c6)) = multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c6)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[81, 34])).
% 0.19/0.52 tff(83,plain,
% 0.19/0.52 (multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c6))) = multiply(multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c6))),
% 0.19/0.52 inference(symmetry,[status(thm)],[82])).
% 0.19/0.52 tff(84,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c7), sk_c9) = multiply(sk_c8, multiply(sk_c7, sk_c9)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(85,plain,
% 0.19/0.52 (multiply(multiply(sk_c8, sk_c7), sk_c9) = multiply(sk_c8, multiply(sk_c7, sk_c9))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[84, 34])).
% 0.19/0.52 tff(86,plain,
% 0.19/0.52 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c7), sk_c7) = identity)),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(87,plain,
% 0.19/0.52 (multiply(inverse(sk_c7), sk_c7) = identity),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[86, 49])).
% 0.19/0.52 tff(88,plain,
% 0.19/0.52 (sk_c8 = inverse(sk_c7)),
% 0.19/0.52 inference(symmetry,[status(thm)],[18])).
% 0.19/0.52 tff(89,plain,
% 0.19/0.52 (multiply(sk_c8, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.52 tff(90,plain,
% 0.19/0.52 (multiply(sk_c8, sk_c7) = multiply(sk_c9, sk_c6)),
% 0.19/0.52 inference(transitivity,[status(thm)],[89, 87, 52, 70])).
% 0.19/0.52 tff(91,plain,
% 0.19/0.52 (multiply(multiply(sk_c8, sk_c7), sk_c9) = multiply(multiply(sk_c9, sk_c6), sk_c9)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.52 tff(92,plain,
% 0.19/0.52 (multiply(multiply(sk_c9, sk_c6), sk_c9) = multiply(multiply(sk_c8, sk_c7), sk_c9)),
% 0.19/0.52 inference(symmetry,[status(thm)],[91])).
% 0.19/0.52 tff(93,plain,
% 0.19/0.52 (sk_c9 = multiply(identity, sk_c9)),
% 0.19/0.52 inference(symmetry,[status(thm)],[68])).
% 0.19/0.52 tff(94,plain,
% 0.19/0.52 (sk_c9 = multiply(sk_c8, multiply(sk_c7, sk_c9))),
% 0.19/0.52 inference(transitivity,[status(thm)],[93, 72, 92, 85])).
% 0.19/0.52 tff(95,plain,
% 0.19/0.52 (multiply(sk_c7, sk_c9) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c7, sk_c9)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.52 tff(96,plain,
% 0.19/0.52 (multiply(sk_c7, multiply(sk_c8, multiply(sk_c7, sk_c9))) = multiply(sk_c7, sk_c9)),
% 0.19/0.52 inference(symmetry,[status(thm)],[95])).
% 0.19/0.52 tff(97,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), multiply(sk_c7, sk_c9)) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c7, sk_c9))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(98,plain,
% 0.19/0.52 (multiply(multiply(sk_c7, sk_c8), multiply(sk_c7, sk_c9)) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c7, sk_c9)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[97, 34])).
% 0.19/0.52 tff(99,assumption,(multiply(sk_c7, sk_c8) = sk_c9), introduced(assumption)).
% 0.19/0.52 tff(100,plain,
% 0.19/0.52 (multiply(multiply(sk_c7, sk_c8), multiply(sk_c7, sk_c9)) = multiply(sk_c9, multiply(sk_c7, sk_c9))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.52 tff(101,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(sk_c7, sk_c9)) = multiply(multiply(sk_c7, sk_c8), multiply(sk_c7, sk_c9))),
% 0.19/0.52 inference(symmetry,[status(thm)],[100])).
% 0.19/0.52 tff(102,plain,
% 0.19/0.52 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c7, sk_c9)) = multiply(sk_c9, multiply(sk_c7, sk_c9))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.52 tff(103,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), multiply(sk_c7, sk_c9)) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c7, sk_c9))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(104,plain,
% 0.19/0.52 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c7, sk_c9)) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c7, sk_c9)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[103, 34])).
% 0.19/0.52 tff(105,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c7, sk_c9))) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c7, sk_c9))),
% 0.19/0.52 inference(symmetry,[status(thm)],[104])).
% 0.19/0.52 tff(106,plain,
% 0.19/0.52 (multiply(sk_c6, sk_c9) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c7, sk_c9)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.52 tff(107,plain,
% 0.19/0.52 (multiply(sk_c6, sk_c9) = multiply(sk_c7, sk_c9)),
% 0.19/0.52 inference(transitivity,[status(thm)],[106, 105, 102, 101, 98, 96])).
% 0.19/0.52 tff(108,plain,
% 0.19/0.52 (multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c6)) = multiply(multiply(sk_c7, sk_c9), multiply(sk_c6, sk_c6))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.52 tff(109,plain,
% 0.19/0.52 (multiply(multiply(sk_c7, sk_c9), multiply(sk_c6, sk_c6)) = multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c6))),
% 0.19/0.52 inference(symmetry,[status(thm)],[108])).
% 0.19/0.52 tff(110,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c7, sk_c9))) = multiply(sk_c6, sk_c9)),
% 0.19/0.52 inference(symmetry,[status(thm)],[106])).
% 0.19/0.52 tff(111,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(sk_c7, sk_c9)) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c7, sk_c9))),
% 0.19/0.52 inference(symmetry,[status(thm)],[102])).
% 0.19/0.52 tff(112,plain,
% 0.19/0.52 (multiply(sk_c7, multiply(sk_c8, multiply(sk_c7, sk_c9))) = multiply(multiply(sk_c7, sk_c8), multiply(sk_c7, sk_c9))),
% 0.19/0.52 inference(symmetry,[status(thm)],[98])).
% 0.19/0.52 tff(113,plain,
% 0.19/0.52 (multiply(sk_c7, sk_c9) = multiply(sk_c6, sk_c9)),
% 0.19/0.52 inference(transitivity,[status(thm)],[95, 112, 100, 111, 104, 110])).
% 0.19/0.52 tff(114,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(sk_c7, sk_c9)) = multiply(sk_c9, multiply(sk_c6, sk_c9))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[113])).
% 0.19/0.52 tff(115,plain,
% 0.19/0.52 (multiply(sk_c7, sk_c9) = sk_c9),
% 0.19/0.52 inference(transitivity,[status(thm)],[95, 112, 100, 114, 76, 73, 68])).
% 0.19/0.52 tff(116,plain,
% 0.19/0.52 (multiply(multiply(sk_c7, sk_c9), multiply(sk_c6, sk_c6)) = multiply(sk_c9, multiply(sk_c6, sk_c6))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.52 tff(117,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(sk_c6, sk_c6)) = multiply(multiply(sk_c7, sk_c9), multiply(sk_c6, sk_c6))),
% 0.19/0.52 inference(symmetry,[status(thm)],[116])).
% 0.19/0.52 tff(118,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c6, sk_c6))) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c6, sk_c6))),
% 0.19/0.52 inference(symmetry,[status(thm)],[64])).
% 0.19/0.52 tff(119,plain,
% 0.19/0.52 (sk_c6 = multiply(identity, sk_c6)),
% 0.19/0.52 inference(symmetry,[status(thm)],[27])).
% 0.19/0.52 tff(120,plain,
% 0.19/0.52 (sk_c6 = multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c6))),
% 0.19/0.52 inference(transitivity,[status(thm)],[119, 54, 57, 61, 118, 65, 117, 109])).
% 0.19/0.52 tff(121,plain,
% 0.19/0.52 (inverse(sk_c6) = multiply(sk_c9, multiply(sk_c6, sk_c9))),
% 0.19/0.52 inference(transitivity,[status(thm)],[37, 93, 72, 75])).
% 0.19/0.52 tff(122,plain,
% 0.19/0.52 (multiply(inverse(sk_c6), sk_c6) = multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c6)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[121, 120])).
% 0.19/0.52 tff(123,plain,
% 0.19/0.52 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(124,plain,
% 0.19/0.52 (multiply(identity, sk_c7) = sk_c7),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[123, 25])).
% 0.19/0.52 tff(125,plain,
% 0.19/0.52 (multiply(identity, sk_c7) = multiply(multiply(sk_c6, multiply(sk_c8, sk_c6)), sk_c7)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.52 tff(126,plain,
% 0.19/0.52 (multiply(multiply(sk_c6, multiply(sk_c8, sk_c6)), sk_c7) = multiply(identity, sk_c7)),
% 0.19/0.52 inference(symmetry,[status(thm)],[125])).
% 0.19/0.52 tff(127,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, multiply(sk_c8, sk_c6)), sk_c7) = multiply(sk_c6, multiply(multiply(sk_c8, sk_c6), sk_c7)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(128,plain,
% 0.19/0.52 (multiply(multiply(sk_c6, multiply(sk_c8, sk_c6)), sk_c7) = multiply(sk_c6, multiply(multiply(sk_c8, sk_c6), sk_c7))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[127, 34])).
% 0.19/0.52 tff(129,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(multiply(sk_c8, sk_c6), sk_c7)) = multiply(multiply(sk_c6, multiply(sk_c8, sk_c6)), sk_c7)),
% 0.19/0.52 inference(symmetry,[status(thm)],[128])).
% 0.19/0.52 tff(130,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c6), sk_c7) = multiply(sk_c8, multiply(sk_c6, sk_c7)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(131,plain,
% 0.19/0.52 (multiply(multiply(sk_c8, sk_c6), sk_c7) = multiply(sk_c8, multiply(sk_c6, sk_c7))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[130, 34])).
% 0.19/0.52 tff(132,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(multiply(sk_c8, sk_c6), sk_c7)) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c6, sk_c7)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[131])).
% 0.19/0.52 tff(133,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c6, sk_c7))) = multiply(sk_c6, multiply(multiply(sk_c8, sk_c6), sk_c7))),
% 0.19/0.52 inference(symmetry,[status(thm)],[132])).
% 0.19/0.52 tff(134,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), multiply(sk_c6, sk_c7)) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c6, sk_c7))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(135,plain,
% 0.19/0.52 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c6, sk_c7)) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c6, sk_c7)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[134, 34])).
% 0.19/0.52 tff(136,plain,
% 0.19/0.52 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c6, sk_c7)) = multiply(sk_c9, multiply(sk_c6, sk_c7))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.52 tff(137,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c6, sk_c7))),
% 0.19/0.52 inference(symmetry,[status(thm)],[136])).
% 0.19/0.52 tff(138,plain,
% 0.19/0.52 (multiply(multiply(sk_c7, sk_c9), multiply(sk_c6, sk_c7)) = multiply(sk_c9, multiply(sk_c6, sk_c7))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.52 tff(139,plain,
% 0.19/0.52 (multiply(multiply(sk_c7, sk_c9), multiply(sk_c6, sk_c7)) = sk_c7),
% 0.19/0.52 inference(transitivity,[status(thm)],[138, 137, 135, 133, 129, 126, 124])).
% 0.19/0.52 tff(140,plain,
% 0.19/0.52 (multiply(sk_c8, multiply(multiply(sk_c7, sk_c9), multiply(sk_c6, sk_c7))) = multiply(inverse(sk_c7), sk_c7)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[88, 139])).
% 0.19/0.52 tff(141,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c7, sk_c9)), multiply(sk_c6, sk_c7)) = multiply(sk_c8, multiply(multiply(sk_c7, sk_c9), multiply(sk_c6, sk_c7))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(142,plain,
% 0.19/0.52 (multiply(multiply(sk_c8, multiply(sk_c7, sk_c9)), multiply(sk_c6, sk_c7)) = multiply(sk_c8, multiply(multiply(sk_c7, sk_c9), multiply(sk_c6, sk_c7)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[141, 34])).
% 0.19/0.52 tff(143,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c8, multiply(sk_c7, sk_c9)), multiply(sk_c6, sk_c7))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.52 tff(144,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c6, sk_c7))) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c6, sk_c7))),
% 0.19/0.52 inference(symmetry,[status(thm)],[135])).
% 0.19/0.52 tff(145,plain,
% 0.19/0.52 (sk_c7 = multiply(identity, sk_c7)),
% 0.19/0.52 inference(symmetry,[status(thm)],[124])).
% 0.19/0.52 tff(146,plain,
% 0.19/0.52 (sk_c7 = sk_c6),
% 0.19/0.52 inference(transitivity,[status(thm)],[145, 125, 128, 132, 144, 136, 143, 142, 140, 87, 52, 122, 83, 80, 66, 64, 62, 58, 55, 27])).
% 0.19/0.52 tff(147,plain,
% 0.19/0.52 (inverse(sk_c7) = inverse(sk_c6)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[146])).
% 0.19/0.52 tff(148,plain,
% 0.19/0.52 (inverse(sk_c6) = inverse(sk_c7)),
% 0.19/0.52 inference(symmetry,[status(thm)],[147])).
% 0.19/0.52 tff(149,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8),
% 0.19/0.52 inference(transitivity,[status(thm)],[76, 73, 68, 38, 148, 18])).
% 0.19/0.52 tff(150,assumption,(~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)), introduced(assumption)).
% 0.19/0.52 tff(151,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.19/0.52 tff(152,plain,((multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(153,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[152, 17, 13, 9, 5])).
% 0.19/0.52 tff(154,plain,
% 0.19/0.52 (sk_c9 = inverse(sk_c6)),
% 0.19/0.52 inference(symmetry,[status(thm)],[13])).
% 0.19/0.52 tff(155,plain,
% 0.19/0.52 (multiply(sk_c9, sk_c6) = multiply(inverse(sk_c6), sk_c6)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[154])).
% 0.19/0.52 tff(156,plain,
% 0.19/0.52 (multiply(inverse(sk_c6), sk_c6) = multiply(sk_c9, sk_c6)),
% 0.19/0.52 inference(symmetry,[status(thm)],[155])).
% 0.19/0.52 tff(157,plain,
% 0.19/0.52 (identity = multiply(sk_c9, sk_c6)),
% 0.19/0.52 inference(transitivity,[status(thm)],[52, 156])).
% 0.19/0.52 tff(158,plain,
% 0.19/0.52 (multiply(identity, sk_c9) = multiply(multiply(sk_c9, sk_c6), sk_c9)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[157])).
% 0.19/0.52 tff(159,plain,
% 0.19/0.52 (sk_c9 = sk_c8),
% 0.19/0.52 inference(transitivity,[status(thm)],[93, 158, 75, 153])).
% 0.19/0.52 tff(160,plain,
% 0.19/0.52 (multiply(sk_c6, sk_c9) = multiply(sk_c6, sk_c8)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.52 tff(161,plain,
% 0.19/0.52 (multiply(sk_c6, inverse(sk_c6)) = multiply(sk_c6, sk_c9)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[13])).
% 0.19/0.52 tff(162,plain,
% 0.19/0.52 (multiply(sk_c6, inverse(sk_c6)) = sk_c8),
% 0.19/0.52 inference(transitivity,[status(thm)],[161, 160, 5, 93, 158, 75, 153])).
% 0.19/0.52 tff(163,plain,
% 0.19/0.52 (inverse(sk_c6) = sk_c8),
% 0.19/0.52 inference(transitivity,[status(thm)],[13, 93, 158, 75, 153])).
% 0.19/0.52 tff(164,plain,
% 0.19/0.52 (multiply(multiply(sk_c9, sk_c6), sk_c9) = multiply(identity, sk_c9)),
% 0.19/0.52 inference(symmetry,[status(thm)],[158])).
% 0.19/0.52 tff(165,plain,
% 0.19/0.52 (sk_c8 = multiply(sk_c9, multiply(sk_c6, sk_c9))),
% 0.19/0.52 inference(symmetry,[status(thm)],[153])).
% 0.19/0.52 tff(166,plain,
% 0.19/0.52 (sk_c8 = sk_c9),
% 0.19/0.52 inference(transitivity,[status(thm)],[165, 76, 164, 68])).
% 0.19/0.52 tff(167,plain,
% 0.19/0.52 (multiply(sk_c8, multiply(sk_c6, sk_c9)) = multiply(sk_c9, multiply(sk_c6, sk_c9))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[166])).
% 0.19/0.52 tff(168,plain,
% 0.19/0.52 (multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c9)) = multiply(sk_c8, multiply(sk_c6, sk_c9))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[153])).
% 0.19/0.52 tff(169,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c9)) = multiply(sk_c9, multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c9))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(170,plain,
% 0.19/0.52 (multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c9)) = multiply(sk_c9, multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c9)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[169, 34])).
% 0.19/0.52 tff(171,plain,
% 0.19/0.52 (multiply(sk_c9, multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c9))) = multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c9))),
% 0.19/0.52 inference(symmetry,[status(thm)],[170])).
% 0.19/0.52 tff(172,plain,
% 0.19/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c9)) = multiply(sk_c6, multiply(sk_c9, multiply(sk_c6, sk_c9))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(173,plain,
% 0.19/0.52 (multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c9)) = multiply(sk_c6, multiply(sk_c9, multiply(sk_c6, sk_c9)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[172, 34])).
% 0.19/0.52 tff(174,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(sk_c9, multiply(sk_c6, sk_c9))) = multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c9))),
% 0.19/0.52 inference(symmetry,[status(thm)],[173])).
% 0.19/0.52 tff(175,plain,
% 0.19/0.52 (multiply(sk_c6, multiply(sk_c9, multiply(sk_c6, sk_c9))) = multiply(sk_c6, sk_c8)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[153])).
% 0.19/0.52 tff(176,plain,
% 0.19/0.52 (multiply(sk_c6, sk_c8) = multiply(sk_c6, multiply(sk_c9, multiply(sk_c6, sk_c9)))),
% 0.19/0.52 inference(symmetry,[status(thm)],[175])).
% 0.19/0.52 tff(177,plain,
% 0.19/0.52 (sk_c9 = multiply(sk_c6, sk_c8)),
% 0.19/0.52 inference(symmetry,[status(thm)],[5])).
% 0.19/0.52 tff(178,plain,
% 0.19/0.52 (sk_c9 = multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c9))),
% 0.19/0.52 inference(transitivity,[status(thm)],[177, 176, 174])).
% 0.19/0.52 tff(179,plain,
% 0.19/0.52 (multiply(inverse(sk_c6), sk_c9) = multiply(sk_c9, multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c9)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[13, 178])).
% 0.19/0.52 tff(180,plain,
% 0.19/0.52 (multiply(inverse(sk_c6), sk_c9) = sk_c8),
% 0.19/0.52 inference(transitivity,[status(thm)],[179, 171, 168, 167, 153])).
% 0.19/0.52 tff(181,plain,
% 0.19/0.52 (^[X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : refl(((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8))) <=> ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(182,plain,
% 0.19/0.52 (![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8))) <=> ![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.52 tff(183,plain,
% 0.19/0.52 (![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8))) <=> ![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(184,plain,
% 0.19/0.52 (^[X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : rewrite(((~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9))) <=> ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(185,plain,
% 0.19/0.53 (![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9))) <=> ![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[184])).
% 0.19/0.53 tff(186,plain,
% 0.19/0.53 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9))) <=> ![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)))),
% 0.19/0.53 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.53 tff(187,plain,
% 0.19/0.53 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)))),
% 0.19/0.53 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.53 tff(188,plain,
% 0.19/0.53 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) <=> ![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)))),
% 0.19/0.53 inference(transitivity,[status(thm)],[187, 186])).
% 0.19/0.53 tff(189,plain,
% 0.19/0.53 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) <=> ![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))),
% 0.19/0.53 inference(transitivity,[status(thm)],[188, 185])).
% 0.19/0.53 tff(190,plain,
% 0.19/0.53 (^[X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) <=> ((~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))), (((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) <=> (((~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(inverse(X4) = X5))))), rewrite((((~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(inverse(X4) = X5))) <=> ((~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))), (((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) <=> ((~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))))), ((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) <=> (((~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(multiply(X5, sk_c9) = sk_c8))))), rewrite((((~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(multiply(X5, sk_c9) = sk_c8))) <=> ((~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))), ((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) <=> ((~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))))), (((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) <=> (((~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(multiply(sk_c9, X6) = sk_c8))))), rewrite((((~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(multiply(sk_c9, X6) = sk_c8))) <=> ((~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))), (((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) <=> ((~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))))), ((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) <=> (((~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(multiply(X7, sk_c9) = X6))))), rewrite((((~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(multiply(X7, sk_c9) = X6))) <=> ((~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))), ((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) <=> ((~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))))), (((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) <=> (((~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(inverse(X7) = sk_c9))))), rewrite((((~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(inverse(X7) = sk_c9))) <=> ((~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))), (((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) <=> ((~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))))), ((((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) | (~(inverse(X1) = sk_c9))) <=> (((~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(inverse(X1) = sk_c9))))), rewrite((((~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(inverse(X1) = sk_c9))) <=> ((~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))), ((((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) | (~(inverse(X1) = sk_c9))) <=> ((~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))))), (((((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) | (~(inverse(X1) = sk_c9))) | (~(multiply(X1, sk_c8) = sk_c9))) <=> (((~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(multiply(X1, sk_c8) = sk_c9))))), rewrite((((~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(multiply(X1, sk_c8) = sk_c9))) <=> ((~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))), (((((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) | (~(inverse(X1) = sk_c9))) | (~(multiply(X1, sk_c8) = sk_c9))) <=> ((~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))))), ((((((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) | (~(inverse(X1) = sk_c9))) | (~(multiply(X1, sk_c8) = sk_c9))) | (~(multiply(X2, sk_c8) = sk_c9))) <=> (((~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(multiply(X2, sk_c8) = sk_c9))))), rewrite((((~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(multiply(X2, sk_c8) = sk_c9))) <=> ((~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))), ((((((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) | (~(inverse(X1) = sk_c9))) | (~(multiply(X1, sk_c8) = sk_c9))) | (~(multiply(X2, sk_c8) = sk_c9))) <=> ((~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))))), (((((((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) | (~(inverse(X1) = sk_c9))) | (~(multiply(X1, sk_c8) = sk_c9))) | (~(multiply(X2, sk_c8) = sk_c9))) | (~(inverse(X2) = sk_c8))) <=> (((~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(inverse(X2) = sk_c8))))), rewrite((((~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9))) | (~(inverse(X2) = sk_c8))) <=> ((~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))), (((((((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) | (~(inverse(X1) = sk_c9))) | (~(multiply(X1, sk_c8) = sk_c9))) | (~(multiply(X2, sk_c8) = sk_c9))) | (~(inverse(X2) = sk_c8))) <=> ((~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(191,plain,
% 0.19/0.53 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((((((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) | (~(inverse(X1) = sk_c9))) | (~(multiply(X1, sk_c8) = sk_c9))) | (~(multiply(X2, sk_c8) = sk_c9))) | (~(inverse(X2) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(X7, sk_c9) = X6)) | (~(multiply(sk_c9, X6) = sk_c8)) | (~(multiply(X5, sk_c9) = sk_c8)) | (~(inverse(X4) = X5)) | (~(multiply(X4, X5) = sk_c8)) | (~(multiply(X3, sk_c8) = sk_c9)) | (~(inverse(X3) = sk_c9)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[190])).
% 0.19/0.53 tff(192,plain,
% 0.19/0.53 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((((((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) | (~(inverse(X1) = sk_c9))) | (~(multiply(X1, sk_c8) = sk_c9))) | (~(multiply(X2, sk_c8) = sk_c9))) | (~(inverse(X2) = sk_c8))) <=> ![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))),
% 0.19/0.54 inference(transitivity,[status(thm)],[191, 189])).
% 0.19/0.54 tff(193,axiom,(![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((((((((((((~(inverse(X3) = sk_c9)) | (~(multiply(X3, sk_c8) = sk_c9))) | (~(multiply(X4, X5) = sk_c8))) | (~(inverse(X4) = X5))) | (~(multiply(X5, sk_c9) = sk_c8))) | (~(multiply(sk_c9, X6) = sk_c8))) | (~(multiply(X7, sk_c9) = X6))) | (~(inverse(X7) = sk_c9))) | (~(inverse(X1) = sk_c9))) | (~(multiply(X1, sk_c8) = sk_c9))) | (~(multiply(X2, sk_c8) = sk_c9))) | (~(inverse(X2) = sk_c8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_33')).
% 0.19/0.54 tff(194,plain,
% 0.19/0.54 (![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.19/0.54 tff(195,plain,
% 0.19/0.54 (![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[194, 183])).
% 0.19/0.54 tff(196,plain,(
% 0.19/0.54 ![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))),
% 0.19/0.54 inference(skolemize,[status(sab)],[195])).
% 0.19/0.54 tff(197,plain,
% 0.19/0.54 (![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[196, 182])).
% 0.19/0.54 tff(198,plain,
% 0.19/0.54 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(199,plain,
% 0.19/0.54 (((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8))) <=> ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(200,plain,
% 0.19/0.54 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[199])).
% 0.19/0.54 tff(201,plain,
% 0.19/0.54 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)))),
% 0.19/0.54 inference(transitivity,[status(thm)],[200, 198])).
% 0.19/0.54 tff(202,plain,
% 0.19/0.54 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(203,plain,
% 0.19/0.54 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.19/0.54 tff(204,plain,
% 0.19/0.54 ((~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[203, 13, 5, 197])).
% 0.19/0.54 tff(205,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[204, 180, 163, 153, 162])).
% 0.19/0.54 tff(206,plain,(inverse(sk_c4) = sk_c9), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(207,plain,
% 0.19/0.54 (sk_c9 = inverse(sk_c4)),
% 0.19/0.54 inference(symmetry,[status(thm)],[206])).
% 0.19/0.54 tff(208,plain,
% 0.19/0.54 (multiply(sk_c9, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.19/0.54 inference(monotonicity,[status(thm)],[207])).
% 0.19/0.54 tff(209,plain,
% 0.19/0.54 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c9, sk_c4)),
% 0.19/0.54 inference(symmetry,[status(thm)],[208])).
% 0.19/0.54 tff(210,plain,
% 0.19/0.54 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(211,plain,
% 0.19/0.54 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[210, 49])).
% 0.19/0.54 tff(212,plain,
% 0.19/0.54 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.19/0.54 inference(symmetry,[status(thm)],[211])).
% 0.19/0.54 tff(213,plain,
% 0.19/0.54 (identity = multiply(sk_c9, sk_c4)),
% 0.19/0.54 inference(transitivity,[status(thm)],[212, 209])).
% 0.19/0.54 tff(214,plain,
% 0.19/0.54 (multiply(identity, sk_c9) = multiply(multiply(sk_c9, sk_c4), sk_c9)),
% 0.19/0.54 inference(monotonicity,[status(thm)],[213])).
% 0.19/0.54 tff(215,plain,
% 0.19/0.54 (multiply(multiply(sk_c9, sk_c4), sk_c9) = multiply(identity, sk_c9)),
% 0.19/0.54 inference(symmetry,[status(thm)],[214])).
% 0.19/0.54 tff(216,plain,
% 0.19/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c9, sk_c4), sk_c9) = multiply(sk_c9, multiply(sk_c4, sk_c9)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(217,plain,
% 0.19/0.54 (multiply(multiply(sk_c9, sk_c4), sk_c9) = multiply(sk_c9, multiply(sk_c4, sk_c9))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[216, 34])).
% 0.19/0.54 tff(218,plain,
% 0.19/0.54 (multiply(sk_c9, multiply(sk_c4, sk_c9)) = multiply(multiply(sk_c9, sk_c4), sk_c9)),
% 0.19/0.54 inference(symmetry,[status(thm)],[217])).
% 0.19/0.54 tff(219,assumption,(~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)), introduced(assumption)).
% 0.19/0.54 tff(220,assumption,(~(inverse(sk_c6) = sk_c9)), introduced(assumption)).
% 0.19/0.54 tff(221,plain,
% 0.19/0.54 (((inverse(sk_c6) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8)) <=> ((inverse(sk_c6) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(222,plain,
% 0.19/0.54 (((multiply(sk_c9, sk_c5) = sk_c8) | (inverse(sk_c6) = sk_c9)) <=> ((inverse(sk_c6) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(223,axiom,((multiply(sk_c9, sk_c5) = sk_c8) | (inverse(sk_c6) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_21')).
% 0.19/0.54 tff(224,plain,
% 0.19/0.54 ((inverse(sk_c6) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.19/0.54 tff(225,plain,
% 0.19/0.54 ((inverse(sk_c6) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[224, 221])).
% 0.19/0.54 tff(226,plain,
% 0.19/0.54 (multiply(sk_c9, sk_c5) = sk_c8),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[225, 220])).
% 0.19/0.54 tff(227,plain,
% 0.19/0.54 (((inverse(sk_c6) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c5)) <=> ((inverse(sk_c6) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c5))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(228,plain,
% 0.19/0.54 (((multiply(sk_c4, sk_c9) = sk_c5) | (inverse(sk_c6) = sk_c9)) <=> ((inverse(sk_c6) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c5))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(229,axiom,((multiply(sk_c4, sk_c9) = sk_c5) | (inverse(sk_c6) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_25')).
% 0.19/0.54 tff(230,plain,
% 0.19/0.54 ((inverse(sk_c6) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c5)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.19/0.54 tff(231,plain,
% 0.19/0.54 ((inverse(sk_c6) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c5)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[230, 227])).
% 0.19/0.54 tff(232,plain,
% 0.19/0.54 (multiply(sk_c4, sk_c9) = sk_c5),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[231, 220])).
% 0.19/0.54 tff(233,plain,
% 0.19/0.54 (sk_c5 = multiply(sk_c4, sk_c9)),
% 0.19/0.54 inference(symmetry,[status(thm)],[232])).
% 0.19/0.54 tff(234,plain,
% 0.19/0.54 (multiply(sk_c9, sk_c5) = multiply(sk_c9, multiply(sk_c4, sk_c9))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[233])).
% 0.19/0.54 tff(235,plain,
% 0.19/0.54 (multiply(sk_c9, multiply(sk_c4, sk_c9)) = multiply(sk_c9, sk_c5)),
% 0.19/0.54 inference(symmetry,[status(thm)],[234])).
% 0.19/0.54 tff(236,plain,
% 0.19/0.54 (multiply(sk_c9, sk_c4) = identity),
% 0.19/0.54 inference(transitivity,[status(thm)],[208, 211])).
% 0.19/0.54 tff(237,plain,
% 0.19/0.54 (multiply(multiply(sk_c9, sk_c4), sk_c9) = multiply(identity, sk_c9)),
% 0.19/0.54 inference(monotonicity,[status(thm)],[236])).
% 0.19/0.54 tff(238,plain,
% 0.19/0.54 (multiply(identity, sk_c9) = multiply(multiply(sk_c9, sk_c4), sk_c9)),
% 0.19/0.54 inference(symmetry,[status(thm)],[237])).
% 0.19/0.54 tff(239,plain,
% 0.19/0.54 (inverse(sk_c4) = sk_c8),
% 0.19/0.54 inference(transitivity,[status(thm)],[206, 93, 238, 217, 235, 226])).
% 0.19/0.54 tff(240,plain,
% 0.19/0.54 (((inverse(sk_c1) = sk_c9) | (inverse(sk_c6) = sk_c9)) <=> ((inverse(sk_c1) = sk_c9) | (inverse(sk_c6) = sk_c9))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(241,axiom,((inverse(sk_c1) = sk_c9) | (inverse(sk_c6) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_1')).
% 0.19/0.54 tff(242,plain,
% 0.19/0.54 ((inverse(sk_c1) = sk_c9) | (inverse(sk_c6) = sk_c9)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.19/0.54 tff(243,plain,
% 0.19/0.54 (inverse(sk_c1) = sk_c9),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[242, 220])).
% 0.19/0.54 tff(244,plain,
% 0.19/0.54 (inverse(sk_c1) = inverse(sk_c4)),
% 0.19/0.54 inference(transitivity,[status(thm)],[243, 207])).
% 0.19/0.54 tff(245,plain,
% 0.19/0.54 ((inverse(sk_c1) = sk_c8) <=> (inverse(sk_c4) = sk_c8)),
% 0.19/0.54 inference(monotonicity,[status(thm)],[244])).
% 0.19/0.54 tff(246,plain,
% 0.19/0.54 ((~(inverse(sk_c1) = sk_c8)) <=> (~(inverse(sk_c4) = sk_c8))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[245])).
% 0.19/0.54 tff(247,plain,
% 0.19/0.54 (((inverse(sk_c6) = sk_c9) | (multiply(sk_c2, sk_c3) = sk_c8)) <=> ((inverse(sk_c6) = sk_c9) | (multiply(sk_c2, sk_c3) = sk_c8))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(248,plain,
% 0.19/0.54 (((multiply(sk_c2, sk_c3) = sk_c8) | (inverse(sk_c6) = sk_c9)) <=> ((inverse(sk_c6) = sk_c9) | (multiply(sk_c2, sk_c3) = sk_c8))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(249,axiom,((multiply(sk_c2, sk_c3) = sk_c8) | (inverse(sk_c6) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_9')).
% 0.19/0.54 tff(250,plain,
% 0.19/0.54 ((inverse(sk_c6) = sk_c9) | (multiply(sk_c2, sk_c3) = sk_c8)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.19/0.54 tff(251,plain,
% 0.19/0.54 ((inverse(sk_c6) = sk_c9) | (multiply(sk_c2, sk_c3) = sk_c8)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[250, 247])).
% 0.19/0.54 tff(252,plain,
% 0.19/0.54 (multiply(sk_c2, sk_c3) = sk_c8),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[251, 220])).
% 0.19/0.54 tff(253,plain,
% 0.19/0.54 (((inverse(sk_c2) = sk_c3) | (inverse(sk_c6) = sk_c9)) <=> ((inverse(sk_c2) = sk_c3) | (inverse(sk_c6) = sk_c9))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(254,axiom,((inverse(sk_c2) = sk_c3) | (inverse(sk_c6) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_13')).
% 0.19/0.54 tff(255,plain,
% 0.19/0.54 ((inverse(sk_c2) = sk_c3) | (inverse(sk_c6) = sk_c9)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.19/0.54 tff(256,plain,
% 0.19/0.54 (inverse(sk_c2) = sk_c3),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[255, 220])).
% 0.19/0.54 tff(257,plain,
% 0.19/0.54 (multiply(sk_c2, inverse(sk_c2)) = multiply(sk_c2, sk_c3)),
% 0.19/0.54 inference(monotonicity,[status(thm)],[256])).
% 0.19/0.54 tff(258,plain,
% 0.19/0.54 (multiply(sk_c2, inverse(sk_c2)) = sk_c8),
% 0.19/0.54 inference(transitivity,[status(thm)],[257, 252])).
% 0.19/0.54 tff(259,plain,
% 0.19/0.54 (((inverse(sk_c6) = sk_c9) | (multiply(sk_c3, sk_c9) = sk_c8)) <=> ((inverse(sk_c6) = sk_c9) | (multiply(sk_c3, sk_c9) = sk_c8))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(260,plain,
% 0.19/0.54 (((multiply(sk_c3, sk_c9) = sk_c8) | (inverse(sk_c6) = sk_c9)) <=> ((inverse(sk_c6) = sk_c9) | (multiply(sk_c3, sk_c9) = sk_c8))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(261,axiom,((multiply(sk_c3, sk_c9) = sk_c8) | (inverse(sk_c6) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_17')).
% 0.19/0.54 tff(262,plain,
% 0.19/0.54 ((inverse(sk_c6) = sk_c9) | (multiply(sk_c3, sk_c9) = sk_c8)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.19/0.54 tff(263,plain,
% 0.19/0.54 ((inverse(sk_c6) = sk_c9) | (multiply(sk_c3, sk_c9) = sk_c8)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[262, 259])).
% 0.19/0.54 tff(264,plain,
% 0.19/0.54 (multiply(sk_c3, sk_c9) = sk_c8),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[263, 220])).
% 0.19/0.54 tff(265,plain,
% 0.19/0.54 (multiply(inverse(sk_c2), sk_c9) = multiply(sk_c3, sk_c9)),
% 0.19/0.54 inference(monotonicity,[status(thm)],[256])).
% 0.19/0.54 tff(266,plain,
% 0.19/0.54 (multiply(inverse(sk_c2), sk_c9) = sk_c8),
% 0.19/0.54 inference(transitivity,[status(thm)],[265, 264])).
% 0.19/0.54 tff(267,plain,
% 0.19/0.54 (multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8),
% 0.19/0.54 inference(transitivity,[status(thm)],[235, 226])).
% 0.19/0.54 tff(268,plain,
% 0.19/0.54 (((inverse(sk_c6) = sk_c9) | (multiply(sk_c1, sk_c8) = sk_c9)) <=> ((inverse(sk_c6) = sk_c9) | (multiply(sk_c1, sk_c8) = sk_c9))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(269,plain,
% 0.19/0.54 (((multiply(sk_c1, sk_c8) = sk_c9) | (inverse(sk_c6) = sk_c9)) <=> ((inverse(sk_c6) = sk_c9) | (multiply(sk_c1, sk_c8) = sk_c9))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(270,axiom,((multiply(sk_c1, sk_c8) = sk_c9) | (inverse(sk_c6) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_5')).
% 0.19/0.54 tff(271,plain,
% 0.19/0.54 ((inverse(sk_c6) = sk_c9) | (multiply(sk_c1, sk_c8) = sk_c9)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.19/0.54 tff(272,plain,
% 0.19/0.54 ((inverse(sk_c6) = sk_c9) | (multiply(sk_c1, sk_c8) = sk_c9)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[271, 268])).
% 0.19/0.54 tff(273,plain,
% 0.19/0.54 (multiply(sk_c1, sk_c8) = sk_c9),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[272, 220])).
% 0.19/0.54 tff(274,plain,
% 0.19/0.54 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)) | (~(inverse(sk_c4) = sk_c9)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)) | (~(inverse(sk_c4) = sk_c9)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(275,plain,
% 0.19/0.55 (((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8))) <=> ((~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)) | (~(inverse(sk_c4) = sk_c9)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(276,plain,
% 0.19/0.55 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)) | (~(inverse(sk_c4) = sk_c9))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[275])).
% 0.19/0.55 tff(277,plain,
% 0.19/0.55 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)) | (~(inverse(sk_c4) = sk_c9)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[276, 274])).
% 0.19/0.55 tff(278,plain,
% 0.19/0.55 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(279,plain,
% 0.19/0.55 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)) | (~(inverse(sk_c4) = sk_c9))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.19/0.55 tff(280,plain,
% 0.19/0.55 ((~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[279, 243, 273, 206, 197, 267])).
% 0.19/0.55 tff(281,plain,
% 0.19/0.55 (~(inverse(sk_c1) = sk_c8)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[280, 266, 258])).
% 0.19/0.55 tff(282,plain,
% 0.19/0.55 (~(inverse(sk_c4) = sk_c8)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[281, 246])).
% 0.19/0.55 tff(283,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[282, 239])).
% 0.19/0.55 tff(284,plain,(inverse(sk_c6) = sk_c9), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(285,plain,
% 0.19/0.55 (sk_c9 = inverse(sk_c6)),
% 0.19/0.55 inference(symmetry,[status(thm)],[284])).
% 0.19/0.55 tff(286,plain,
% 0.19/0.55 (multiply(sk_c9, sk_c6) = multiply(inverse(sk_c6), sk_c6)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[285])).
% 0.19/0.55 tff(287,plain,
% 0.19/0.55 (multiply(sk_c9, sk_c6) = multiply(sk_c9, sk_c4)),
% 0.19/0.55 inference(transitivity,[status(thm)],[286, 51, 212, 209])).
% 0.19/0.55 tff(288,plain,
% 0.19/0.55 (multiply(multiply(sk_c9, sk_c6), sk_c9) = multiply(multiply(sk_c9, sk_c4), sk_c9)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[287])).
% 0.19/0.55 tff(289,plain,
% 0.19/0.55 (multiply(sk_c9, multiply(sk_c6, sk_c9)) = multiply(sk_c9, multiply(sk_c4, sk_c9))),
% 0.19/0.55 inference(transitivity,[status(thm)],[76, 288, 217])).
% 0.19/0.55 tff(290,plain,
% 0.19/0.55 ((multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8) <=> (multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[289])).
% 0.19/0.55 tff(291,plain,
% 0.19/0.55 ((multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8) <=> (multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)),
% 0.19/0.55 inference(symmetry,[status(thm)],[290])).
% 0.19/0.55 tff(292,plain,
% 0.19/0.55 ((~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) <=> (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[291])).
% 0.19/0.55 tff(293,plain,
% 0.19/0.55 (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[219, 292])).
% 0.19/0.55 tff(294,assumption,(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8), introduced(assumption)).
% 0.19/0.55 tff(295,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[294, 293])).
% 0.19/0.55 tff(296,plain,((multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(297,plain,
% 0.19/0.55 (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[296, 219])).
% 0.19/0.55 tff(298,plain,
% 0.19/0.55 (inverse(sk_c6) = inverse(sk_c4)),
% 0.19/0.55 inference(transitivity,[status(thm)],[284, 207])).
% 0.19/0.55 tff(299,plain,
% 0.19/0.55 (multiply(inverse(sk_c6), sk_c9) = multiply(inverse(sk_c4), sk_c9)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[298])).
% 0.19/0.55 tff(300,plain,
% 0.19/0.55 ((multiply(inverse(sk_c6), sk_c9) = sk_c8) <=> (multiply(inverse(sk_c4), sk_c9) = sk_c8)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[299])).
% 0.19/0.55 tff(301,plain,
% 0.19/0.55 ((~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) <=> (~(multiply(inverse(sk_c4), sk_c9) = sk_c8))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[300])).
% 0.19/0.55 tff(302,assumption,(~(multiply(sk_c4, sk_c9) = sk_c5)), introduced(assumption)).
% 0.19/0.55 tff(303,plain,
% 0.19/0.55 (((multiply(sk_c4, sk_c9) = sk_c5) | (multiply(sk_c7, sk_c8) = sk_c9)) <=> ((multiply(sk_c4, sk_c9) = sk_c5) | (multiply(sk_c7, sk_c8) = sk_c9))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(304,axiom,((multiply(sk_c4, sk_c9) = sk_c5) | (multiply(sk_c7, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_27')).
% 0.19/0.55 tff(305,plain,
% 0.19/0.55 ((multiply(sk_c4, sk_c9) = sk_c5) | (multiply(sk_c7, sk_c8) = sk_c9)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.19/0.55 tff(306,plain,
% 0.19/0.55 (multiply(sk_c7, sk_c8) = sk_c9),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[305, 302])).
% 0.19/0.55 tff(307,plain,
% 0.19/0.55 (((multiply(sk_c4, sk_c9) = sk_c5) | (multiply(sk_c6, sk_c8) = sk_c9)) <=> ((multiply(sk_c4, sk_c9) = sk_c5) | (multiply(sk_c6, sk_c8) = sk_c9))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(308,axiom,((multiply(sk_c4, sk_c9) = sk_c5) | (multiply(sk_c6, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_26')).
% 0.19/0.55 tff(309,plain,
% 0.19/0.55 ((multiply(sk_c4, sk_c9) = sk_c5) | (multiply(sk_c6, sk_c8) = sk_c9)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.19/0.55 tff(310,plain,
% 0.19/0.55 (multiply(sk_c6, sk_c8) = sk_c9),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[309, 302])).
% 0.19/0.55 tff(311,assumption,(~(inverse(sk_c7) = sk_c8)), introduced(assumption)).
% 0.19/0.55 tff(312,plain,
% 0.19/0.55 (((inverse(sk_c7) = sk_c8) | (multiply(sk_c9, sk_c5) = sk_c8)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c9, sk_c5) = sk_c8))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(313,plain,
% 0.19/0.55 (((multiply(sk_c9, sk_c5) = sk_c8) | (inverse(sk_c7) = sk_c8)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c9, sk_c5) = sk_c8))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(314,axiom,((multiply(sk_c9, sk_c5) = sk_c8) | (inverse(sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_24')).
% 0.19/0.55 tff(315,plain,
% 0.19/0.55 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c9, sk_c5) = sk_c8)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.19/0.55 tff(316,plain,
% 0.19/0.55 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c9, sk_c5) = sk_c8)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[315, 312])).
% 0.19/0.55 tff(317,plain,
% 0.19/0.55 (multiply(sk_c9, sk_c5) = sk_c8),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[316, 311])).
% 0.19/0.55 tff(318,plain,
% 0.19/0.55 (((inverse(sk_c7) = sk_c8) | (multiply(sk_c4, sk_c9) = sk_c5)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c4, sk_c9) = sk_c5))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(319,plain,
% 0.19/0.55 (((multiply(sk_c4, sk_c9) = sk_c5) | (inverse(sk_c7) = sk_c8)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c4, sk_c9) = sk_c5))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(320,axiom,((multiply(sk_c4, sk_c9) = sk_c5) | (inverse(sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_28')).
% 0.19/0.55 tff(321,plain,
% 0.19/0.55 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c4, sk_c9) = sk_c5)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.19/0.55 tff(322,plain,
% 0.19/0.55 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c4, sk_c9) = sk_c5)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[321, 318])).
% 0.19/0.55 tff(323,plain,
% 0.19/0.55 (multiply(sk_c4, sk_c9) = sk_c5),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[322, 311])).
% 0.19/0.55 tff(324,plain,
% 0.19/0.55 (sk_c5 = multiply(sk_c4, sk_c9)),
% 0.19/0.55 inference(symmetry,[status(thm)],[323])).
% 0.19/0.55 tff(325,plain,
% 0.19/0.55 (multiply(sk_c9, sk_c5) = multiply(sk_c9, multiply(sk_c4, sk_c9))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[324])).
% 0.19/0.55 tff(326,plain,
% 0.19/0.55 (multiply(sk_c9, multiply(sk_c4, sk_c9)) = multiply(sk_c9, sk_c5)),
% 0.19/0.55 inference(symmetry,[status(thm)],[325])).
% 0.19/0.55 tff(327,plain,
% 0.19/0.55 (inverse(sk_c4) = sk_c8),
% 0.19/0.55 inference(transitivity,[status(thm)],[206, 93, 238, 217, 326, 317])).
% 0.19/0.55 tff(328,plain,
% 0.19/0.55 (((inverse(sk_c1) = sk_c9) | (inverse(sk_c7) = sk_c8)) <=> ((inverse(sk_c1) = sk_c9) | (inverse(sk_c7) = sk_c8))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(329,axiom,((inverse(sk_c1) = sk_c9) | (inverse(sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_4')).
% 0.19/0.55 tff(330,plain,
% 0.19/0.55 ((inverse(sk_c1) = sk_c9) | (inverse(sk_c7) = sk_c8)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.19/0.55 tff(331,plain,
% 0.19/0.55 (inverse(sk_c1) = sk_c9),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[330, 311])).
% 0.19/0.55 tff(332,plain,
% 0.19/0.55 (inverse(sk_c1) = inverse(sk_c4)),
% 0.19/0.55 inference(transitivity,[status(thm)],[331, 207])).
% 0.19/0.55 tff(333,plain,
% 0.19/0.55 ((inverse(sk_c1) = sk_c8) <=> (inverse(sk_c4) = sk_c8)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[332])).
% 0.19/0.55 tff(334,plain,
% 0.19/0.55 ((~(inverse(sk_c1) = sk_c8)) <=> (~(inverse(sk_c4) = sk_c8))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[333])).
% 0.19/0.55 tff(335,plain,
% 0.19/0.55 (((inverse(sk_c7) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c8)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c8))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(336,plain,
% 0.19/0.55 (((multiply(sk_c2, sk_c3) = sk_c8) | (inverse(sk_c7) = sk_c8)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c8))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(337,axiom,((multiply(sk_c2, sk_c3) = sk_c8) | (inverse(sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_12')).
% 0.19/0.55 tff(338,plain,
% 0.19/0.55 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c8)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.19/0.55 tff(339,plain,
% 0.19/0.55 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c8)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[338, 335])).
% 0.19/0.55 tff(340,plain,
% 0.19/0.55 (multiply(sk_c2, sk_c3) = sk_c8),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[339, 311])).
% 0.19/0.55 tff(341,plain,
% 0.19/0.55 (((inverse(sk_c2) = sk_c3) | (inverse(sk_c7) = sk_c8)) <=> ((inverse(sk_c2) = sk_c3) | (inverse(sk_c7) = sk_c8))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(342,axiom,((inverse(sk_c2) = sk_c3) | (inverse(sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_16')).
% 0.19/0.55 tff(343,plain,
% 0.19/0.55 ((inverse(sk_c2) = sk_c3) | (inverse(sk_c7) = sk_c8)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.19/0.55 tff(344,plain,
% 0.19/0.55 (inverse(sk_c2) = sk_c3),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[343, 311])).
% 0.19/0.55 tff(345,plain,
% 0.19/0.55 (multiply(sk_c2, inverse(sk_c2)) = multiply(sk_c2, sk_c3)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[344])).
% 0.19/0.55 tff(346,plain,
% 0.19/0.55 (multiply(sk_c2, inverse(sk_c2)) = sk_c8),
% 0.19/0.55 inference(transitivity,[status(thm)],[345, 340])).
% 0.19/0.55 tff(347,plain,
% 0.19/0.55 (((inverse(sk_c7) = sk_c8) | (multiply(sk_c3, sk_c9) = sk_c8)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c3, sk_c9) = sk_c8))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(348,plain,
% 0.19/0.55 (((multiply(sk_c3, sk_c9) = sk_c8) | (inverse(sk_c7) = sk_c8)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c3, sk_c9) = sk_c8))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(349,axiom,((multiply(sk_c3, sk_c9) = sk_c8) | (inverse(sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_20')).
% 0.19/0.55 tff(350,plain,
% 0.19/0.55 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c3, sk_c9) = sk_c8)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.19/0.55 tff(351,plain,
% 0.19/0.55 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c3, sk_c9) = sk_c8)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[350, 347])).
% 0.19/0.55 tff(352,plain,
% 0.19/0.55 (multiply(sk_c3, sk_c9) = sk_c8),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[351, 311])).
% 0.19/0.55 tff(353,plain,
% 0.19/0.55 (multiply(inverse(sk_c2), sk_c9) = multiply(sk_c3, sk_c9)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[344])).
% 0.19/0.55 tff(354,plain,
% 0.19/0.55 (multiply(inverse(sk_c2), sk_c9) = sk_c8),
% 0.19/0.55 inference(transitivity,[status(thm)],[353, 352])).
% 0.19/0.55 tff(355,plain,
% 0.19/0.55 (multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8),
% 0.19/0.55 inference(transitivity,[status(thm)],[326, 317])).
% 0.19/0.55 tff(356,plain,
% 0.19/0.55 (((inverse(sk_c7) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c9)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c9))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(357,plain,
% 0.19/0.55 (((multiply(sk_c1, sk_c8) = sk_c9) | (inverse(sk_c7) = sk_c8)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c9))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(358,axiom,((multiply(sk_c1, sk_c8) = sk_c9) | (inverse(sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_8')).
% 0.19/0.55 tff(359,plain,
% 0.19/0.55 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c9)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.19/0.55 tff(360,plain,
% 0.19/0.55 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c9)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[359, 356])).
% 0.19/0.55 tff(361,plain,
% 0.19/0.55 (multiply(sk_c1, sk_c8) = sk_c9),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[360, 311])).
% 0.19/0.55 tff(362,plain,
% 0.19/0.55 ((~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[279, 331, 361, 206, 197, 355])).
% 0.19/0.55 tff(363,plain,
% 0.19/0.55 (~(inverse(sk_c1) = sk_c8)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[362, 354, 346])).
% 0.19/0.55 tff(364,plain,
% 0.19/0.55 (~(inverse(sk_c4) = sk_c8)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[363, 334])).
% 0.19/0.55 tff(365,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[364, 327])).
% 0.19/0.55 tff(366,plain,(inverse(sk_c7) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(367,plain,
% 0.19/0.55 ((multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[152, 366])).
% 0.19/0.55 tff(368,plain,
% 0.19/0.55 (multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[367, 310, 284, 306])).
% 0.19/0.55 tff(369,plain,
% 0.19/0.55 (multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[296, 368])).
% 0.19/0.55 tff(370,plain,
% 0.19/0.55 (sk_c9 = sk_c8),
% 0.19/0.55 inference(transitivity,[status(thm)],[93, 214, 217, 369])).
% 0.19/0.55 tff(371,plain,
% 0.19/0.55 (multiply(sk_c6, sk_c9) = multiply(sk_c6, sk_c8)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[370])).
% 0.19/0.55 tff(372,plain,
% 0.19/0.55 (multiply(sk_c6, inverse(sk_c6)) = multiply(sk_c6, sk_c9)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[284])).
% 0.19/0.55 tff(373,plain,
% 0.19/0.55 (multiply(sk_c6, inverse(sk_c6)) = sk_c8),
% 0.19/0.55 inference(transitivity,[status(thm)],[372, 371, 310, 93, 214, 217, 369])).
% 0.19/0.55 tff(374,plain,
% 0.19/0.55 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(375,plain,
% 0.19/0.55 (((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8))) <=> ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(376,plain,
% 0.19/0.56 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[375])).
% 0.19/0.56 tff(377,plain,
% 0.19/0.56 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)))),
% 0.19/0.56 inference(transitivity,[status(thm)],[376, 374])).
% 0.19/0.56 tff(378,plain,
% 0.19/0.56 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(379,plain,
% 0.19/0.56 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.19/0.56 tff(380,plain,
% 0.19/0.56 ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)) | (~(multiply(sk_c6, inverse(sk_c6)) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[379, 284, 366, 197])).
% 0.19/0.56 tff(381,plain,
% 0.19/0.56 (~(multiply(inverse(sk_c6), sk_c9) = sk_c8)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[380, 373, 368, 310, 306])).
% 0.19/0.56 tff(382,plain,
% 0.19/0.56 (~(multiply(inverse(sk_c4), sk_c9) = sk_c8)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[381, 301])).
% 0.19/0.56 tff(383,plain,
% 0.19/0.56 (sk_c8 = multiply(sk_c9, multiply(sk_c4, sk_c9))),
% 0.19/0.56 inference(symmetry,[status(thm)],[369])).
% 0.19/0.56 tff(384,plain,
% 0.19/0.56 (sk_c8 = sk_c9),
% 0.19/0.56 inference(transitivity,[status(thm)],[383, 218, 215, 68])).
% 0.19/0.56 tff(385,plain,
% 0.19/0.56 (multiply(sk_c8, multiply(sk_c6, sk_c9)) = multiply(sk_c9, multiply(sk_c6, sk_c9))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[384])).
% 0.19/0.56 tff(386,plain,
% 0.19/0.56 (multiply(multiply(sk_c9, multiply(sk_c6, sk_c9)), multiply(sk_c6, sk_c9)) = multiply(sk_c8, multiply(sk_c6, sk_c9))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[368])).
% 0.19/0.56 tff(387,plain,
% 0.19/0.56 (multiply(sk_c6, multiply(sk_c9, multiply(sk_c6, sk_c9))) = multiply(sk_c6, sk_c8)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[368])).
% 0.19/0.56 tff(388,plain,
% 0.19/0.56 (multiply(sk_c6, sk_c8) = multiply(sk_c6, multiply(sk_c9, multiply(sk_c6, sk_c9)))),
% 0.19/0.56 inference(symmetry,[status(thm)],[387])).
% 0.19/0.56 tff(389,plain,
% 0.19/0.56 (sk_c9 = multiply(sk_c6, sk_c8)),
% 0.19/0.56 inference(symmetry,[status(thm)],[310])).
% 0.19/0.56 tff(390,plain,
% 0.19/0.56 (sk_c9 = multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c9))),
% 0.19/0.56 inference(transitivity,[status(thm)],[389, 388, 174])).
% 0.19/0.56 tff(391,plain,
% 0.19/0.56 (multiply(inverse(sk_c4), sk_c9) = multiply(sk_c9, multiply(multiply(sk_c6, sk_c9), multiply(sk_c6, sk_c9)))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[206, 390])).
% 0.19/0.56 tff(392,plain,
% 0.19/0.56 (multiply(inverse(sk_c4), sk_c9) = sk_c8),
% 0.19/0.56 inference(transitivity,[status(thm)],[391, 171, 386, 385, 368])).
% 0.19/0.56 tff(393,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[392, 382])).
% 0.19/0.56 tff(394,plain,(multiply(sk_c4, sk_c9) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(395,plain,
% 0.19/0.56 (sk_c5 = multiply(sk_c4, sk_c9)),
% 0.19/0.56 inference(symmetry,[status(thm)],[394])).
% 0.19/0.56 tff(396,plain,
% 0.19/0.56 (multiply(sk_c9, sk_c5) = multiply(sk_c9, multiply(sk_c4, sk_c9))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[395])).
% 0.19/0.56 tff(397,plain,
% 0.19/0.56 ((multiply(sk_c9, sk_c5) = sk_c8) <=> (multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[396])).
% 0.19/0.56 tff(398,plain,
% 0.19/0.56 ((multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8) <=> (multiply(sk_c9, sk_c5) = sk_c8)),
% 0.19/0.56 inference(symmetry,[status(thm)],[397])).
% 0.19/0.56 tff(399,plain,
% 0.19/0.56 ((~(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8)) <=> (~(multiply(sk_c9, sk_c5) = sk_c8))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[398])).
% 0.19/0.56 tff(400,plain,
% 0.19/0.56 (~(multiply(sk_c9, sk_c5) = sk_c8)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[219, 399])).
% 0.19/0.56 tff(401,plain,
% 0.19/0.56 (((multiply(sk_c6, sk_c8) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8)) <=> ((multiply(sk_c6, sk_c8) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(402,plain,
% 0.19/0.56 (((multiply(sk_c9, sk_c5) = sk_c8) | (multiply(sk_c6, sk_c8) = sk_c9)) <=> ((multiply(sk_c6, sk_c8) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(403,axiom,((multiply(sk_c9, sk_c5) = sk_c8) | (multiply(sk_c6, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_22')).
% 0.19/0.56 tff(404,plain,
% 0.19/0.56 ((multiply(sk_c6, sk_c8) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.19/0.56 tff(405,plain,
% 0.19/0.56 ((multiply(sk_c6, sk_c8) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[404, 401])).
% 0.19/0.56 tff(406,plain,
% 0.19/0.56 (multiply(sk_c6, sk_c8) = sk_c9),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[405, 400])).
% 0.19/0.56 tff(407,plain,
% 0.19/0.56 (((multiply(sk_c7, sk_c8) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8)) <=> ((multiply(sk_c7, sk_c8) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(408,plain,
% 0.19/0.56 (((multiply(sk_c9, sk_c5) = sk_c8) | (multiply(sk_c7, sk_c8) = sk_c9)) <=> ((multiply(sk_c7, sk_c8) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(409,axiom,((multiply(sk_c9, sk_c5) = sk_c8) | (multiply(sk_c7, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_23')).
% 0.19/0.56 tff(410,plain,
% 0.19/0.56 ((multiply(sk_c7, sk_c8) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.19/0.56 tff(411,plain,
% 0.19/0.56 ((multiply(sk_c7, sk_c8) = sk_c9) | (multiply(sk_c9, sk_c5) = sk_c8)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[410, 407])).
% 0.19/0.56 tff(412,plain,
% 0.19/0.56 (multiply(sk_c7, sk_c8) = sk_c9),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[411, 400])).
% 0.19/0.56 tff(413,plain,
% 0.19/0.56 ((multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[367, 284])).
% 0.19/0.56 tff(414,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[413, 412, 406, 297])).
% 0.19/0.56 tff(415,plain,(multiply(sk_c9, multiply(sk_c4, sk_c9)) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(416,plain,
% 0.19/0.56 (sk_c8 = multiply(sk_c9, multiply(sk_c4, sk_c9))),
% 0.19/0.56 inference(symmetry,[status(thm)],[415])).
% 0.19/0.56 tff(417,plain,
% 0.19/0.56 (inverse(sk_c7) = inverse(sk_c4)),
% 0.19/0.56 inference(transitivity,[status(thm)],[366, 416, 218, 215, 68, 207])).
% 0.19/0.56 tff(418,plain,
% 0.19/0.56 (multiply(inverse(sk_c7), sk_c9) = multiply(inverse(sk_c4), sk_c9)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[417])).
% 0.19/0.56 tff(419,plain,
% 0.19/0.56 ((multiply(inverse(sk_c7), sk_c9) = sk_c8) <=> (multiply(inverse(sk_c4), sk_c9) = sk_c8)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[418])).
% 0.19/0.56 tff(420,plain,
% 0.19/0.56 ((~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) <=> (~(multiply(inverse(sk_c4), sk_c9) = sk_c8))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[419])).
% 0.19/0.56 tff(421,assumption,(~(multiply(sk_c7, sk_c8) = sk_c9)), introduced(assumption)).
% 0.19/0.56 tff(422,plain,
% 0.19/0.56 (((multiply(sk_c3, sk_c9) = sk_c8) | (multiply(sk_c7, sk_c8) = sk_c9)) <=> ((multiply(sk_c3, sk_c9) = sk_c8) | (multiply(sk_c7, sk_c8) = sk_c9))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(423,axiom,((multiply(sk_c3, sk_c9) = sk_c8) | (multiply(sk_c7, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_19')).
% 0.19/0.56 tff(424,plain,
% 0.19/0.56 ((multiply(sk_c3, sk_c9) = sk_c8) | (multiply(sk_c7, sk_c8) = sk_c9)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.19/0.56 tff(425,plain,
% 0.19/0.56 (multiply(sk_c3, sk_c9) = sk_c8),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[424, 421])).
% 0.19/0.56 tff(426,plain,
% 0.19/0.56 (((inverse(sk_c2) = sk_c3) | (multiply(sk_c7, sk_c8) = sk_c9)) <=> ((inverse(sk_c2) = sk_c3) | (multiply(sk_c7, sk_c8) = sk_c9))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(427,axiom,((inverse(sk_c2) = sk_c3) | (multiply(sk_c7, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_15')).
% 0.19/0.56 tff(428,plain,
% 0.19/0.56 ((inverse(sk_c2) = sk_c3) | (multiply(sk_c7, sk_c8) = sk_c9)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.19/0.56 tff(429,plain,
% 0.19/0.56 (inverse(sk_c2) = sk_c3),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[428, 421])).
% 0.19/0.56 tff(430,plain,
% 0.19/0.56 (multiply(inverse(sk_c2), sk_c9) = multiply(sk_c3, sk_c9)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[429])).
% 0.19/0.56 tff(431,plain,
% 0.19/0.56 (multiply(inverse(sk_c2), sk_c9) = sk_c8),
% 0.19/0.56 inference(transitivity,[status(thm)],[430, 425])).
% 0.19/0.56 tff(432,plain,
% 0.19/0.56 (((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c7, sk_c8) = sk_c9)) <=> ((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c7, sk_c8) = sk_c9))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(433,axiom,((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c7, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_11')).
% 0.19/0.56 tff(434,plain,
% 0.19/0.56 ((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c7, sk_c8) = sk_c9)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.19/0.56 tff(435,plain,
% 0.19/0.56 (multiply(sk_c2, sk_c3) = sk_c8),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[434, 421])).
% 0.19/0.56 tff(436,plain,
% 0.19/0.56 (multiply(sk_c2, inverse(sk_c2)) = multiply(sk_c2, sk_c3)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[429])).
% 0.19/0.56 tff(437,plain,
% 0.19/0.56 (multiply(sk_c2, inverse(sk_c2)) = sk_c8),
% 0.19/0.56 inference(transitivity,[status(thm)],[436, 435])).
% 0.19/0.56 tff(438,plain,
% 0.19/0.56 (((inverse(sk_c1) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9)) <=> ((inverse(sk_c1) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(439,axiom,((inverse(sk_c1) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_3')).
% 0.19/0.56 tff(440,plain,
% 0.19/0.56 ((inverse(sk_c1) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.19/0.56 tff(441,plain,
% 0.19/0.56 (inverse(sk_c1) = sk_c9),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[440, 421])).
% 0.19/0.56 tff(442,plain,
% 0.19/0.56 (inverse(sk_c1) = sk_c8),
% 0.19/0.56 inference(transitivity,[status(thm)],[441, 93, 214, 217, 415])).
% 0.19/0.56 tff(443,plain,
% 0.19/0.56 (multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8),
% 0.19/0.56 inference(transitivity,[status(thm)],[76, 288, 217, 415])).
% 0.19/0.56 tff(444,plain,
% 0.19/0.56 (((multiply(sk_c1, sk_c8) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9)) <=> ((multiply(sk_c1, sk_c8) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(445,axiom,((multiply(sk_c1, sk_c8) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_7')).
% 0.19/0.56 tff(446,plain,
% 0.19/0.56 ((multiply(sk_c1, sk_c8) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c9)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.19/0.56 tff(447,plain,
% 0.19/0.56 (multiply(sk_c1, sk_c8) = sk_c9),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[446, 421])).
% 0.19/0.56 tff(448,plain,
% 0.19/0.56 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(449,plain,
% 0.19/0.56 (((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8))) <=> ((~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(450,plain,
% 0.19/0.56 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[449])).
% 0.19/0.56 tff(451,plain,
% 0.19/0.56 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)))),
% 0.19/0.56 inference(transitivity,[status(thm)],[450, 448])).
% 0.19/0.56 tff(452,plain,
% 0.19/0.56 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(453,plain,
% 0.19/0.57 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.19/0.57 tff(454,plain,
% 0.19/0.57 ((~(multiply(inverse(sk_c2), sk_c9) = sk_c8)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c8))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[453, 441, 284, 447, 197, 443, 442])).
% 0.19/0.57 tff(455,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[454, 437, 431])).
% 0.19/0.57 tff(456,plain,(multiply(sk_c7, sk_c8) = sk_c9), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(457,plain,
% 0.19/0.57 (sk_c9 = sk_c8),
% 0.19/0.57 inference(transitivity,[status(thm)],[93, 214, 217, 415])).
% 0.19/0.57 tff(458,plain,
% 0.19/0.57 (multiply(sk_c7, inverse(sk_c7)) = multiply(sk_c7, sk_c8)),
% 0.19/0.57 inference(monotonicity,[status(thm)],[366])).
% 0.19/0.57 tff(459,plain,
% 0.19/0.57 (multiply(sk_c7, sk_c8) = multiply(sk_c7, inverse(sk_c7))),
% 0.19/0.57 inference(symmetry,[status(thm)],[458])).
% 0.19/0.57 tff(460,plain,
% 0.19/0.57 ((multiply(sk_c7, sk_c8) = sk_c9) <=> (multiply(sk_c7, inverse(sk_c7)) = sk_c8)),
% 0.19/0.57 inference(monotonicity,[status(thm)],[459, 457])).
% 0.19/0.57 tff(461,plain,
% 0.19/0.57 (multiply(sk_c7, inverse(sk_c7)) = sk_c8),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[456, 460])).
% 0.19/0.57 tff(462,plain,
% 0.19/0.57 (sk_c8 = inverse(sk_c7)),
% 0.19/0.57 inference(symmetry,[status(thm)],[366])).
% 0.19/0.57 tff(463,plain,
% 0.19/0.57 (multiply(sk_c8, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.19/0.57 inference(monotonicity,[status(thm)],[462])).
% 0.19/0.57 tff(464,plain,
% 0.19/0.57 (multiply(sk_c8, sk_c7) = multiply(sk_c9, sk_c4)),
% 0.19/0.57 inference(transitivity,[status(thm)],[463, 87, 212, 209])).
% 0.19/0.57 tff(465,plain,
% 0.19/0.57 (multiply(multiply(sk_c8, sk_c7), sk_c9) = multiply(multiply(sk_c9, sk_c4), sk_c9)),
% 0.19/0.57 inference(monotonicity,[status(thm)],[464])).
% 0.19/0.57 tff(466,plain,
% 0.19/0.57 (multiply(sk_c8, multiply(sk_c7, sk_c9)) = multiply(multiply(sk_c8, sk_c7), sk_c9)),
% 0.19/0.57 inference(symmetry,[status(thm)],[85])).
% 0.19/0.57 tff(467,plain,
% 0.19/0.57 (multiply(sk_c7, sk_c9) = multiply(sk_c7, sk_c8)),
% 0.19/0.57 inference(monotonicity,[status(thm)],[457])).
% 0.19/0.57 tff(468,plain,
% 0.19/0.57 (multiply(sk_c7, sk_c8) = multiply(sk_c7, sk_c9)),
% 0.19/0.57 inference(symmetry,[status(thm)],[467])).
% 0.19/0.57 tff(469,plain,
% 0.19/0.57 (sk_c9 = multiply(sk_c7, sk_c8)),
% 0.19/0.57 inference(symmetry,[status(thm)],[456])).
% 0.19/0.57 tff(470,plain,
% 0.19/0.57 (sk_c9 = multiply(sk_c7, sk_c9)),
% 0.19/0.57 inference(transitivity,[status(thm)],[469, 468])).
% 0.19/0.57 tff(471,plain,
% 0.19/0.57 (inverse(sk_c4) = sk_c8),
% 0.19/0.57 inference(transitivity,[status(thm)],[206, 93, 214, 217, 415])).
% 0.19/0.57 tff(472,plain,
% 0.19/0.57 (multiply(inverse(sk_c4), sk_c9) = multiply(sk_c8, multiply(sk_c7, sk_c9))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[471, 470])).
% 0.19/0.57 tff(473,assumption,(~(multiply(sk_c6, sk_c8) = sk_c9)), introduced(assumption)).
% 0.19/0.57 tff(474,plain,
% 0.19/0.57 (((inverse(sk_c1) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9)) <=> ((inverse(sk_c1) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(475,axiom,((inverse(sk_c1) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_2')).
% 0.19/0.57 tff(476,plain,
% 0.19/0.57 ((inverse(sk_c1) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.19/0.57 tff(477,plain,
% 0.19/0.57 (inverse(sk_c1) = sk_c9),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[476, 473])).
% 0.19/0.57 tff(478,plain,
% 0.19/0.57 (inverse(sk_c1) = inverse(sk_c4)),
% 0.19/0.57 inference(transitivity,[status(thm)],[477, 207])).
% 0.19/0.57 tff(479,plain,
% 0.19/0.57 (multiply(inverse(sk_c1), sk_c9) = multiply(inverse(sk_c4), sk_c9)),
% 0.19/0.57 inference(monotonicity,[status(thm)],[478])).
% 0.19/0.57 tff(480,plain,
% 0.19/0.57 (multiply(inverse(sk_c1), sk_c9) = sk_c8),
% 0.19/0.57 inference(transitivity,[status(thm)],[479, 472, 466, 465, 217, 415])).
% 0.19/0.57 tff(481,plain,
% 0.19/0.57 (((multiply(sk_c1, sk_c8) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9)) <=> ((multiply(sk_c1, sk_c8) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(482,axiom,((multiply(sk_c1, sk_c8) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_6')).
% 0.19/0.57 tff(483,plain,
% 0.19/0.57 ((multiply(sk_c1, sk_c8) = sk_c9) | (multiply(sk_c6, sk_c8) = sk_c9)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.19/0.57 tff(484,plain,
% 0.19/0.57 (multiply(sk_c1, sk_c8) = sk_c9),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[483, 473])).
% 0.19/0.57 tff(485,plain,
% 0.19/0.57 (inverse(sk_c1) = sk_c8),
% 0.19/0.57 inference(transitivity,[status(thm)],[477, 93, 214, 217, 415])).
% 0.19/0.57 tff(486,plain,
% 0.19/0.57 (multiply(sk_c1, inverse(sk_c1)) = multiply(sk_c1, sk_c8)),
% 0.19/0.57 inference(monotonicity,[status(thm)],[485])).
% 0.19/0.57 tff(487,plain,
% 0.19/0.57 (multiply(sk_c1, inverse(sk_c1)) = sk_c8),
% 0.19/0.57 inference(transitivity,[status(thm)],[486, 484, 93, 214, 217, 415])).
% 0.19/0.57 tff(488,plain,
% 0.19/0.57 (multiply(sk_c1, sk_c9) = multiply(sk_c1, sk_c8)),
% 0.19/0.57 inference(monotonicity,[status(thm)],[457])).
% 0.19/0.57 tff(489,plain,
% 0.19/0.57 (multiply(sk_c1, sk_c9) = sk_c9),
% 0.19/0.57 inference(transitivity,[status(thm)],[488, 484])).
% 0.19/0.57 tff(490,plain,
% 0.19/0.57 (multiply(sk_c9, multiply(sk_c1, sk_c9)) = multiply(inverse(sk_c4), sk_c9)),
% 0.19/0.57 inference(monotonicity,[status(thm)],[207, 489])).
% 0.19/0.57 tff(491,plain,
% 0.19/0.57 (multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8),
% 0.19/0.57 inference(transitivity,[status(thm)],[490, 472, 466, 465, 217, 415])).
% 0.19/0.57 tff(492,plain,
% 0.19/0.57 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c9) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c9) = sk_c8)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(493,plain,
% 0.19/0.57 (((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c9) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8))) <=> ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c9) = sk_c8)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(494,plain,
% 0.19/0.57 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c9) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c9) = sk_c8))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[493])).
% 0.19/0.57 tff(495,plain,
% 0.19/0.57 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c9) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c9) = sk_c8)))),
% 0.19/0.57 inference(transitivity,[status(thm)],[494, 492])).
% 0.19/0.57 tff(496,plain,
% 0.19/0.57 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c9) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(497,plain,
% 0.19/0.57 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c1, sk_c8) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c9) = sk_c8))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.19/0.57 tff(498,plain,
% 0.19/0.57 ((~(multiply(sk_c9, multiply(sk_c1, sk_c9)) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(inverse(sk_c1), sk_c9) = sk_c8))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[497, 477, 484, 197, 485])).
% 0.19/0.57 tff(499,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[498, 491, 487, 480])).
% 0.19/0.57 tff(500,plain,(multiply(sk_c6, sk_c8) = sk_c9), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(501,plain,
% 0.19/0.57 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) | (~(multiply(sk_c7, inverse(sk_c7)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) | (~(multiply(sk_c7, inverse(sk_c7)) = sk_c8)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(502,plain,
% 0.19/0.57 (((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) | (~(multiply(sk_c7, inverse(sk_c7)) = sk_c8))) <=> ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) | (~(multiply(sk_c7, inverse(sk_c7)) = sk_c8)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(503,plain,
% 0.19/0.57 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) | (~(multiply(sk_c7, inverse(sk_c7)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) | (~(multiply(sk_c7, inverse(sk_c7)) = sk_c8))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[502])).
% 0.19/0.58 tff(504,plain,
% 0.19/0.58 (((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) | (~(multiply(sk_c7, inverse(sk_c7)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) | (~(multiply(sk_c7, inverse(sk_c7)) = sk_c8)))),
% 0.19/0.58 inference(transitivity,[status(thm)],[503, 501])).
% 0.19/0.58 tff(505,plain,
% 0.19/0.58 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) | (~(multiply(sk_c7, inverse(sk_c7)) = sk_c8)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(506,plain,
% 0.19/0.58 ((~![X4: $i, X3: $i, X2: $i, X7: $i, X1: $i] : ((~(multiply(X3, sk_c8) = sk_c9)) | (~(multiply(X1, sk_c8) = sk_c9)) | (~(inverse(X1) = sk_c9)) | (~(inverse(X3) = sk_c9)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = sk_c9)) | (~(inverse(X7) = sk_c9)) | (~(multiply(sk_c9, multiply(X7, sk_c9)) = sk_c8)) | (~(multiply(inverse(X4), sk_c9) = sk_c8)) | (~(multiply(X4, inverse(X4)) = sk_c8)))) | (~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(inverse(sk_c6) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) | (~(multiply(sk_c7, inverse(sk_c7)) = sk_c8))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.19/0.58 tff(507,plain,
% 0.19/0.58 ((~(multiply(sk_c6, sk_c8) = sk_c9)) | (~(multiply(sk_c9, multiply(sk_c6, sk_c9)) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c9)) | (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)) | (~(multiply(sk_c7, inverse(sk_c7)) = sk_c8))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[506, 284, 366, 197])).
% 0.19/0.58 tff(508,plain,
% 0.19/0.58 (~(multiply(inverse(sk_c7), sk_c9) = sk_c8)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[507, 500, 443, 461, 456])).
% 0.19/0.58 tff(509,plain,
% 0.19/0.58 (~(multiply(inverse(sk_c4), sk_c9) = sk_c8)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[508, 420])).
% 0.19/0.58 tff(510,plain,
% 0.19/0.58 (multiply(inverse(sk_c4), sk_c9) = sk_c8),
% 0.19/0.58 inference(transitivity,[status(thm)],[472, 466, 465, 217, 415])).
% 0.19/0.58 tff(511,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[510, 509])).
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58 % E exiting
%------------------------------------------------------------------------------