TSTP Solution File: GRP324-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP324-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 : Fri Sep 16 22:27:08 EDT 2022
% Result : Unsatisfiable 0.56s 0.61s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP324-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 16:14:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.56/0.61 % SZS status Unsatisfiable
% 0.56/0.61 % SZS output start Proof
% 0.56/0.61 tff(sk_c7_type, type, (
% 0.56/0.61 sk_c7: $i)).
% 0.56/0.61 tff(multiply_type, type, (
% 0.56/0.61 multiply: ( $i * $i ) > $i)).
% 0.56/0.61 tff(sk_c8_type, type, (
% 0.56/0.61 sk_c8: $i)).
% 0.56/0.61 tff(sk_c4_type, type, (
% 0.56/0.61 sk_c4: $i)).
% 0.56/0.61 tff(identity_type, type, (
% 0.56/0.61 identity: $i)).
% 0.56/0.61 tff(sk_c3_type, type, (
% 0.56/0.61 sk_c3: $i)).
% 0.56/0.61 tff(sk_c6_type, type, (
% 0.56/0.61 sk_c6: $i)).
% 0.56/0.61 tff(inverse_type, type, (
% 0.56/0.61 inverse: $i > $i)).
% 0.56/0.61 tff(sk_c5_type, type, (
% 0.56/0.61 sk_c5: $i)).
% 0.56/0.61 tff(sk_c2_type, type, (
% 0.56/0.61 sk_c2: $i)).
% 0.56/0.61 tff(sk_c1_type, type, (
% 0.56/0.61 sk_c1: $i)).
% 0.56/0.61 tff(1,plain,
% 0.56/0.61 ((sk_c7 = multiply(sk_c8, sk_c7)) <=> (multiply(sk_c8, sk_c7) = sk_c7)),
% 0.56/0.61 inference(commutativity,[status(thm)],[])).
% 0.56/0.61 tff(2,assumption,(~(multiply(sk_c7, sk_c8) = sk_c6)), introduced(assumption)).
% 0.56/0.61 tff(3,plain,
% 0.56/0.61 (((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(4,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_1')).
% 0.56/0.61 tff(5,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.56/0.61 tff(6,plain,
% 0.56/0.61 (multiply(sk_c8, sk_c7) = sk_c6),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.56/0.61 tff(7,plain,
% 0.56/0.61 (((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(8,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_4')).
% 0.56/0.61 tff(9,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.56/0.61 tff(10,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[9, 7])).
% 0.56/0.61 tff(11,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.56/0.61 tff(12,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.56/0.61 tff(13,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.56/0.61 tff(14,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.56/0.61 tff(15,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.56/0.61 tff(16,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.56/0.61 tff(17,plain,
% 0.56/0.61 (inverse(sk_c8) = sk_c6),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[16, 2])).
% 0.56/0.61 tff(18,plain,
% 0.56/0.61 (sk_c6 = inverse(sk_c8)),
% 0.56/0.61 inference(symmetry,[status(thm)],[17])).
% 0.56/0.61 tff(19,plain,
% 0.56/0.61 (((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c7)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c7))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(20,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_2')).
% 0.56/0.61 tff(21,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.56/0.61 tff(22,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[21, 19])).
% 0.56/0.61 tff(23,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.56/0.61 tff(24,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.56/0.61 tff(25,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.56/0.61 tff(26,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.56/0.61 tff(27,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.56/0.61 tff(28,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.56/0.61 tff(29,plain,
% 0.56/0.61 (multiply(sk_c4, sk_c8) = sk_c7),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[28, 2])).
% 0.56/0.61 tff(30,plain,
% 0.56/0.61 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.56/0.61 inference(monotonicity,[status(thm)],[29])).
% 0.56/0.61 tff(31,plain,
% 0.56/0.61 (^[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))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(32,plain,
% 0.56/0.61 (![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)))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[31])).
% 0.56/0.61 tff(33,plain,
% 0.56/0.61 (![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)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(34,axiom,(![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','associativity')).
% 0.56/0.61 tff(35,plain,
% 0.56/0.61 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.56/0.61 tff(36,plain,(
% 0.56/0.61 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.56/0.61 inference(skolemize,[status(sab)],[35])).
% 0.56/0.61 tff(37,plain,
% 0.56/0.61 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.56/0.61 tff(38,plain,
% 0.56/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(39,plain,
% 0.56/0.61 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.56/0.61 tff(40,plain,
% 0.56/0.61 (((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(41,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_3')).
% 0.56/0.61 tff(42,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.56/0.61 tff(43,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[42, 40])).
% 0.56/0.61 tff(44,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.56/0.61 tff(45,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.56/0.61 tff(46,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.56/0.61 tff(47,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.56/0.61 tff(48,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.56/0.61 tff(49,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[48, 40])).
% 0.56/0.61 tff(50,plain,
% 0.56/0.61 (inverse(sk_c4) = sk_c8),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[49, 2])).
% 0.56/0.61 tff(51,plain,
% 0.56/0.61 (sk_c8 = inverse(sk_c4)),
% 0.56/0.61 inference(symmetry,[status(thm)],[50])).
% 0.56/0.61 tff(52,plain,
% 0.56/0.61 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.56/0.61 inference(monotonicity,[status(thm)],[51])).
% 0.56/0.61 tff(53,plain,
% 0.56/0.61 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.56/0.61 inference(symmetry,[status(thm)],[52])).
% 0.56/0.61 tff(54,plain,
% 0.56/0.61 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(55,plain,
% 0.56/0.61 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.56/0.61 inference(quant_intro,[status(thm)],[54])).
% 0.56/0.61 tff(56,plain,
% 0.56/0.61 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(57,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.56/0.61 tff(58,plain,
% 0.56/0.61 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.56/0.61 tff(59,plain,(
% 0.56/0.61 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.56/0.61 inference(skolemize,[status(sab)],[58])).
% 0.56/0.61 tff(60,plain,
% 0.56/0.61 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.56/0.61 tff(61,plain,
% 0.56/0.61 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(62,plain,
% 0.56/0.61 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.56/0.61 tff(63,plain,
% 0.56/0.61 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.56/0.61 inference(symmetry,[status(thm)],[62])).
% 0.56/0.61 tff(64,plain,
% 0.56/0.61 (identity = multiply(sk_c8, sk_c4)),
% 0.56/0.61 inference(transitivity,[status(thm)],[63, 53])).
% 0.56/0.61 tff(65,plain,
% 0.56/0.61 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.56/0.61 inference(monotonicity,[status(thm)],[64])).
% 0.56/0.61 tff(66,plain,
% 0.56/0.61 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(67,plain,
% 0.56/0.61 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.56/0.61 inference(quant_intro,[status(thm)],[66])).
% 0.56/0.61 tff(68,plain,
% 0.56/0.61 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(69,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.56/0.61 tff(70,plain,
% 0.56/0.61 (![X: $i] : (multiply(identity, X) = X)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.56/0.61 tff(71,plain,(
% 0.56/0.61 ![X: $i] : (multiply(identity, X) = X)),
% 0.56/0.61 inference(skolemize,[status(sab)],[70])).
% 0.56/0.61 tff(72,plain,
% 0.56/0.61 (![X: $i] : (multiply(identity, X) = X)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.56/0.61 tff(73,plain,
% 0.56/0.61 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c8) = sk_c8)),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(74,plain,
% 0.56/0.61 (multiply(identity, sk_c8) = sk_c8),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.56/0.61 tff(75,plain,
% 0.56/0.61 (sk_c8 = multiply(identity, sk_c8)),
% 0.56/0.61 inference(symmetry,[status(thm)],[74])).
% 0.56/0.61 tff(76,plain,
% 0.56/0.61 (sk_c8 = inverse(sk_c8)),
% 0.56/0.61 inference(transitivity,[status(thm)],[75, 65, 39, 30, 6, 18])).
% 0.56/0.61 tff(77,plain,
% 0.56/0.61 (multiply(sk_c8, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.61 inference(monotonicity,[status(thm)],[76])).
% 0.56/0.61 tff(78,plain,
% 0.56/0.61 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.56/0.61 inference(symmetry,[status(thm)],[77])).
% 0.56/0.61 tff(79,plain,
% 0.56/0.61 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c8), sk_c8) = identity)),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(80,plain,
% 0.56/0.61 (multiply(inverse(sk_c8), sk_c8) = identity),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[79, 60])).
% 0.56/0.61 tff(81,plain,
% 0.56/0.61 (identity = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.61 inference(symmetry,[status(thm)],[80])).
% 0.56/0.61 tff(82,plain,
% 0.56/0.61 (identity = multiply(sk_c8, sk_c8)),
% 0.56/0.61 inference(transitivity,[status(thm)],[81, 78])).
% 0.56/0.61 tff(83,plain,
% 0.56/0.61 (multiply(sk_c6, identity) = multiply(sk_c6, multiply(sk_c8, sk_c8))),
% 0.56/0.61 inference(monotonicity,[status(thm)],[82])).
% 0.56/0.61 tff(84,plain,
% 0.56/0.61 (multiply(sk_c6, multiply(sk_c8, sk_c8)) = multiply(sk_c6, identity)),
% 0.56/0.61 inference(symmetry,[status(thm)],[83])).
% 0.56/0.61 tff(85,plain,
% 0.56/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), sk_c8) = multiply(sk_c6, multiply(sk_c8, sk_c8)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(86,plain,
% 0.56/0.61 (multiply(multiply(sk_c6, sk_c8), sk_c8) = multiply(sk_c6, multiply(sk_c8, sk_c8))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[85, 37])).
% 0.56/0.61 tff(87,plain,
% 0.56/0.61 (multiply(sk_c6, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.61 inference(monotonicity,[status(thm)],[18])).
% 0.56/0.61 tff(88,plain,
% 0.56/0.61 (multiply(sk_c6, sk_c8) = multiply(sk_c8, sk_c4)),
% 0.56/0.61 inference(transitivity,[status(thm)],[87, 80, 63, 53])).
% 0.56/0.61 tff(89,plain,
% 0.56/0.61 (multiply(multiply(sk_c6, sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.56/0.61 inference(monotonicity,[status(thm)],[88])).
% 0.56/0.61 tff(90,plain,
% 0.56/0.61 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c6, sk_c8), sk_c8)),
% 0.56/0.61 inference(symmetry,[status(thm)],[89])).
% 0.56/0.61 tff(91,plain,
% 0.56/0.61 (sk_c8 = multiply(sk_c6, identity)),
% 0.56/0.61 inference(transitivity,[status(thm)],[75, 65, 90, 86, 84])).
% 0.56/0.61 tff(92,plain,
% 0.56/0.61 (multiply(sk_c8, sk_c7) = multiply(multiply(sk_c6, identity), sk_c7)),
% 0.56/0.61 inference(monotonicity,[status(thm)],[91])).
% 0.56/0.61 tff(93,plain,
% 0.56/0.61 (multiply(multiply(sk_c6, identity), sk_c7) = multiply(sk_c8, sk_c7)),
% 0.56/0.61 inference(symmetry,[status(thm)],[92])).
% 0.56/0.61 tff(94,plain,
% 0.56/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, identity), sk_c7) = multiply(sk_c6, multiply(identity, sk_c7)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(95,plain,
% 0.56/0.61 (multiply(multiply(sk_c6, identity), sk_c7) = multiply(sk_c6, multiply(identity, sk_c7))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[94, 37])).
% 0.56/0.61 tff(96,plain,
% 0.56/0.61 (multiply(sk_c6, multiply(identity, sk_c7)) = multiply(multiply(sk_c6, identity), sk_c7)),
% 0.56/0.61 inference(symmetry,[status(thm)],[95])).
% 0.56/0.61 tff(97,plain,
% 0.56/0.61 (((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(98,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_5')).
% 0.56/0.61 tff(99,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.56/0.61 tff(100,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[99, 97])).
% 0.56/0.61 tff(101,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[100, 97])).
% 0.56/0.61 tff(102,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.56/0.61 tff(103,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[102, 97])).
% 0.56/0.61 tff(104,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[103, 97])).
% 0.56/0.61 tff(105,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.56/0.61 tff(106,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[105, 97])).
% 0.56/0.61 tff(107,plain,
% 0.56/0.61 (multiply(sk_c5, sk_c7) = sk_c6),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[106, 2])).
% 0.56/0.61 tff(108,plain,
% 0.56/0.61 (sk_c6 = multiply(sk_c5, sk_c7)),
% 0.56/0.61 inference(symmetry,[status(thm)],[107])).
% 0.56/0.61 tff(109,plain,
% 0.56/0.61 (sk_c8 = multiply(sk_c5, sk_c7)),
% 0.56/0.61 inference(transitivity,[status(thm)],[75, 65, 39, 30, 6, 108])).
% 0.56/0.61 tff(110,plain,
% 0.56/0.61 (multiply(sk_c7, sk_c8) = multiply(sk_c7, multiply(sk_c5, sk_c7))),
% 0.56/0.61 inference(monotonicity,[status(thm)],[109])).
% 0.56/0.61 tff(111,plain,
% 0.56/0.61 (multiply(sk_c7, multiply(sk_c5, sk_c7)) = multiply(sk_c7, sk_c8)),
% 0.56/0.61 inference(symmetry,[status(thm)],[110])).
% 0.56/0.61 tff(112,plain,
% 0.56/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c5), sk_c7) = multiply(sk_c7, multiply(sk_c5, sk_c7)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(113,plain,
% 0.56/0.61 (multiply(multiply(sk_c7, sk_c5), sk_c7) = multiply(sk_c7, multiply(sk_c5, sk_c7))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[112, 37])).
% 0.56/0.61 tff(114,plain,
% 0.56/0.61 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c5), sk_c5) = identity)),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(115,plain,
% 0.56/0.61 (multiply(inverse(sk_c5), sk_c5) = identity),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[114, 60])).
% 0.56/0.61 tff(116,plain,
% 0.56/0.61 (((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c5) = sk_c7)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c5) = sk_c7))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(117,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c5) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_6')).
% 0.56/0.61 tff(118,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c5) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.56/0.61 tff(119,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c5) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[118, 116])).
% 0.56/0.61 tff(120,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c5) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[119, 116])).
% 0.56/0.61 tff(121,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c5) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.56/0.61 tff(122,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c5) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[121, 116])).
% 0.56/0.61 tff(123,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c5) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[122, 116])).
% 0.56/0.61 tff(124,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c5) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.56/0.61 tff(125,plain,
% 0.56/0.61 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c5) = sk_c7)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[124, 116])).
% 0.56/0.61 tff(126,plain,
% 0.56/0.61 (inverse(sk_c5) = sk_c7),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[125, 2])).
% 0.56/0.61 tff(127,plain,
% 0.56/0.61 (sk_c7 = inverse(sk_c5)),
% 0.56/0.61 inference(symmetry,[status(thm)],[126])).
% 0.56/0.61 tff(128,plain,
% 0.56/0.61 (multiply(sk_c7, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.56/0.61 inference(monotonicity,[status(thm)],[127])).
% 0.56/0.61 tff(129,plain,
% 0.56/0.61 (multiply(sk_c7, sk_c5) = identity),
% 0.56/0.61 inference(transitivity,[status(thm)],[128, 115])).
% 0.56/0.61 tff(130,plain,
% 0.56/0.61 (multiply(multiply(sk_c7, sk_c5), sk_c7) = multiply(identity, sk_c7)),
% 0.56/0.61 inference(monotonicity,[status(thm)],[129])).
% 0.56/0.61 tff(131,plain,
% 0.56/0.61 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c5), sk_c7)),
% 0.56/0.61 inference(symmetry,[status(thm)],[130])).
% 0.56/0.61 tff(132,plain,
% 0.56/0.61 (multiply(identity, sk_c7) = multiply(sk_c7, sk_c8)),
% 0.56/0.61 inference(transitivity,[status(thm)],[131, 113, 111])).
% 0.56/0.61 tff(133,plain,
% 0.56/0.61 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, sk_c8)),
% 0.56/0.61 inference(symmetry,[status(thm)],[65])).
% 0.56/0.61 tff(134,plain,
% 0.56/0.61 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.56/0.61 inference(symmetry,[status(thm)],[39])).
% 0.56/0.61 tff(135,plain,
% 0.56/0.61 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.56/0.61 inference(symmetry,[status(thm)],[30])).
% 0.56/0.61 tff(136,plain,
% 0.56/0.61 (sk_c6 = multiply(sk_c8, sk_c7)),
% 0.56/0.61 inference(symmetry,[status(thm)],[6])).
% 0.56/0.61 tff(137,plain,
% 0.56/0.61 (sk_c6 = sk_c8),
% 0.56/0.61 inference(transitivity,[status(thm)],[136, 135, 134, 133, 74])).
% 0.56/0.61 tff(138,plain,
% 0.56/0.61 (multiply(sk_c6, multiply(identity, sk_c7)) = multiply(sk_c8, multiply(sk_c7, sk_c8))),
% 0.56/0.61 inference(monotonicity,[status(thm)],[137, 132])).
% 0.56/0.61 tff(139,plain,
% 0.56/0.61 (multiply(sk_c8, multiply(sk_c7, sk_c8)) = multiply(sk_c6, multiply(identity, sk_c7))),
% 0.56/0.61 inference(symmetry,[status(thm)],[138])).
% 0.56/0.61 tff(140,plain,
% 0.56/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c7), sk_c8) = multiply(sk_c8, multiply(sk_c7, sk_c8)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(141,plain,
% 0.56/0.62 (multiply(multiply(sk_c8, sk_c7), sk_c8) = multiply(sk_c8, multiply(sk_c7, sk_c8))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[140, 37])).
% 0.56/0.62 tff(142,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c7) = inverse(sk_c8)),
% 0.56/0.62 inference(transitivity,[status(thm)],[6, 18])).
% 0.56/0.62 tff(143,plain,
% 0.56/0.62 (multiply(multiply(sk_c8, sk_c7), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[142])).
% 0.56/0.62 tff(144,plain,
% 0.56/0.62 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c7), sk_c8)),
% 0.56/0.62 inference(symmetry,[status(thm)],[143])).
% 0.56/0.62 tff(145,plain,
% 0.56/0.62 (multiply(sk_c6, sk_c7) = multiply(sk_c8, sk_c7)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[137])).
% 0.56/0.62 tff(146,plain,
% 0.56/0.62 (multiply(sk_c6, sk_c7) = sk_c8),
% 0.56/0.62 inference(transitivity,[status(thm)],[145, 135, 134, 133, 74])).
% 0.56/0.62 tff(147,plain,
% 0.56/0.62 (multiply(sk_c6, multiply(sk_c6, sk_c7)) = multiply(sk_c8, sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[137, 146])).
% 0.56/0.62 tff(148,plain,
% 0.56/0.62 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c6), sk_c7) = multiply(sk_c6, multiply(sk_c6, sk_c7)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(149,plain,
% 0.56/0.62 (multiply(multiply(sk_c6, sk_c6), sk_c7) = multiply(sk_c6, multiply(sk_c6, sk_c7))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[148, 37])).
% 0.56/0.62 tff(150,plain,
% 0.56/0.62 (multiply(sk_c6, sk_c6) = multiply(sk_c8, sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[137, 137])).
% 0.56/0.62 tff(151,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c8) = multiply(sk_c6, sk_c6)),
% 0.56/0.62 inference(symmetry,[status(thm)],[150])).
% 0.56/0.62 tff(152,plain,
% 0.56/0.62 (identity = multiply(sk_c6, sk_c6)),
% 0.56/0.62 inference(transitivity,[status(thm)],[81, 78, 151])).
% 0.56/0.62 tff(153,plain,
% 0.56/0.62 (multiply(identity, sk_c7) = multiply(multiply(sk_c6, sk_c6), sk_c7)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[152])).
% 0.56/0.62 tff(154,plain,
% 0.56/0.62 (multiply(sk_c7, multiply(sk_c5, sk_c7)) = multiply(multiply(sk_c7, sk_c5), sk_c7)),
% 0.56/0.62 inference(symmetry,[status(thm)],[113])).
% 0.56/0.62 tff(155,plain,
% 0.56/0.62 (multiply(sk_c7, sk_c8) = sk_c6),
% 0.56/0.62 inference(transitivity,[status(thm)],[110, 154, 130, 153, 149, 147, 77, 144, 141, 139, 96, 93, 6])).
% 0.56/0.62 tff(156,plain,
% 0.56/0.62 ($false),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[2, 155])).
% 0.56/0.62 tff(157,plain,(multiply(sk_c7, sk_c8) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.56/0.62 tff(158,assumption,(~(inverse(sk_c2) = sk_c8)), introduced(assumption)).
% 0.56/0.62 tff(159,plain,
% 0.56/0.62 (((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(160,axiom,((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_33')).
% 0.56/0.62 tff(161,plain,
% 0.56/0.62 ((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.56/0.62 tff(162,plain,
% 0.56/0.62 (inverse(sk_c4) = sk_c8),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[161, 158])).
% 0.56/0.62 tff(163,plain,
% 0.56/0.62 (sk_c8 = inverse(sk_c4)),
% 0.56/0.62 inference(symmetry,[status(thm)],[162])).
% 0.56/0.62 tff(164,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[163])).
% 0.56/0.62 tff(165,plain,
% 0.56/0.62 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.56/0.62 inference(symmetry,[status(thm)],[164])).
% 0.56/0.62 tff(166,plain,
% 0.56/0.62 (identity = multiply(sk_c8, sk_c4)),
% 0.56/0.62 inference(transitivity,[status(thm)],[63, 165])).
% 0.56/0.62 tff(167,plain,
% 0.56/0.62 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[166])).
% 0.56/0.62 tff(168,plain,
% 0.56/0.62 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, sk_c8)),
% 0.56/0.62 inference(symmetry,[status(thm)],[167])).
% 0.56/0.62 tff(169,plain,
% 0.56/0.62 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(170,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_32')).
% 0.56/0.62 tff(171,plain,
% 0.56/0.62 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.56/0.62 tff(172,plain,
% 0.56/0.62 (multiply(sk_c4, sk_c8) = sk_c7),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[171, 158])).
% 0.56/0.62 tff(173,plain,
% 0.56/0.62 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[172])).
% 0.56/0.62 tff(174,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.56/0.62 inference(symmetry,[status(thm)],[173])).
% 0.56/0.62 tff(175,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.56/0.62 inference(transitivity,[status(thm)],[174, 134, 168, 74])).
% 0.56/0.62 tff(176,plain,
% 0.56/0.62 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c7) = sk_c6)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c7) = sk_c6))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(177,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_31')).
% 0.56/0.62 tff(178,plain,
% 0.56/0.62 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c7) = sk_c6)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.56/0.62 tff(179,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c7) = sk_c6),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[178, 158])).
% 0.56/0.62 tff(180,plain,
% 0.56/0.62 (sk_c6 = multiply(sk_c8, sk_c7)),
% 0.56/0.62 inference(symmetry,[status(thm)],[179])).
% 0.56/0.62 tff(181,plain,
% 0.56/0.62 (((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c6)) <=> ((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c6))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(182,axiom,((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_34')).
% 0.56/0.62 tff(183,plain,
% 0.56/0.62 ((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c6)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.56/0.62 tff(184,plain,
% 0.56/0.62 (inverse(sk_c8) = sk_c6),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[183, 158])).
% 0.56/0.62 tff(185,plain,
% 0.56/0.62 (inverse(sk_c8) = multiply(sk_c8, sk_c7)),
% 0.56/0.62 inference(transitivity,[status(thm)],[184, 180])).
% 0.56/0.62 tff(186,plain,
% 0.56/0.62 ((inverse(sk_c8) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c7)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[185])).
% 0.56/0.62 tff(187,plain,
% 0.56/0.62 ((multiply(sk_c8, sk_c7) = sk_c7) <=> (inverse(sk_c8) = sk_c7)),
% 0.56/0.62 inference(symmetry,[status(thm)],[186])).
% 0.56/0.62 tff(188,plain,
% 0.56/0.62 (sk_c6 = inverse(sk_c8)),
% 0.56/0.62 inference(symmetry,[status(thm)],[184])).
% 0.56/0.62 tff(189,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c7) = inverse(sk_c8)),
% 0.56/0.62 inference(transitivity,[status(thm)],[179, 188])).
% 0.56/0.62 tff(190,plain,
% 0.56/0.62 (multiply(multiply(sk_c8, sk_c7), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[189])).
% 0.56/0.62 tff(191,plain,
% 0.56/0.62 (multiply(sk_c8, multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c8, sk_c7), sk_c8)),
% 0.56/0.62 inference(symmetry,[status(thm)],[141])).
% 0.56/0.62 tff(192,plain,
% 0.56/0.62 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c7) = sk_c6)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c7) = sk_c6))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(193,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_35')).
% 0.56/0.62 tff(194,plain,
% 0.56/0.62 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.56/0.62 tff(195,plain,
% 0.56/0.62 (multiply(sk_c5, sk_c7) = sk_c6),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[194, 158])).
% 0.56/0.62 tff(196,plain,
% 0.56/0.62 (sk_c6 = multiply(sk_c5, sk_c7)),
% 0.56/0.62 inference(symmetry,[status(thm)],[195])).
% 0.56/0.62 tff(197,plain,
% 0.56/0.62 (sk_c8 = multiply(sk_c5, sk_c7)),
% 0.56/0.62 inference(transitivity,[status(thm)],[75, 167, 39, 173, 179, 196])).
% 0.56/0.62 tff(198,plain,
% 0.56/0.62 (multiply(sk_c7, sk_c8) = multiply(sk_c7, multiply(sk_c5, sk_c7))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[197])).
% 0.56/0.62 tff(199,plain,
% 0.56/0.62 (multiply(sk_c7, multiply(sk_c5, sk_c7)) = multiply(sk_c7, sk_c8)),
% 0.56/0.62 inference(symmetry,[status(thm)],[198])).
% 0.56/0.62 tff(200,plain,
% 0.56/0.62 (((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c7)) <=> ((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c7))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(201,axiom,((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_36')).
% 0.56/0.62 tff(202,plain,
% 0.56/0.62 ((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c7)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.56/0.62 tff(203,plain,
% 0.56/0.62 (inverse(sk_c5) = sk_c7),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[202, 158])).
% 0.56/0.62 tff(204,plain,
% 0.56/0.62 (sk_c7 = inverse(sk_c5)),
% 0.56/0.62 inference(symmetry,[status(thm)],[203])).
% 0.56/0.62 tff(205,plain,
% 0.56/0.62 (multiply(sk_c7, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[204])).
% 0.56/0.62 tff(206,plain,
% 0.56/0.62 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c7, sk_c5)),
% 0.56/0.62 inference(symmetry,[status(thm)],[205])).
% 0.56/0.62 tff(207,plain,
% 0.56/0.62 (identity = multiply(inverse(sk_c5), sk_c5)),
% 0.56/0.62 inference(symmetry,[status(thm)],[115])).
% 0.56/0.62 tff(208,plain,
% 0.56/0.62 (identity = multiply(sk_c7, sk_c5)),
% 0.56/0.62 inference(transitivity,[status(thm)],[207, 206])).
% 0.56/0.62 tff(209,plain,
% 0.56/0.62 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c5), sk_c7)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[208])).
% 0.56/0.62 tff(210,plain,
% 0.56/0.62 (multiply(identity, sk_c7) = multiply(sk_c7, sk_c8)),
% 0.56/0.62 inference(transitivity,[status(thm)],[209, 113, 199])).
% 0.56/0.62 tff(211,plain,
% 0.56/0.62 (sk_c6 = sk_c8),
% 0.56/0.62 inference(transitivity,[status(thm)],[180, 174, 134, 168, 74])).
% 0.56/0.62 tff(212,plain,
% 0.56/0.62 (multiply(sk_c6, multiply(identity, sk_c7)) = multiply(sk_c8, multiply(sk_c7, sk_c8))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[211, 210])).
% 0.56/0.62 tff(213,plain,
% 0.56/0.62 (sk_c8 = inverse(sk_c8)),
% 0.56/0.62 inference(transitivity,[status(thm)],[75, 167, 39, 173, 179, 188])).
% 0.56/0.62 tff(214,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[213])).
% 0.56/0.62 tff(215,plain,
% 0.56/0.62 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.56/0.62 inference(symmetry,[status(thm)],[214])).
% 0.56/0.62 tff(216,plain,
% 0.56/0.62 (identity = multiply(sk_c8, sk_c8)),
% 0.56/0.62 inference(transitivity,[status(thm)],[81, 215])).
% 0.56/0.62 tff(217,plain,
% 0.56/0.62 (multiply(sk_c6, identity) = multiply(sk_c6, multiply(sk_c8, sk_c8))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[216])).
% 0.56/0.62 tff(218,plain,
% 0.56/0.62 (multiply(sk_c6, multiply(sk_c8, sk_c8)) = multiply(sk_c6, identity)),
% 0.56/0.62 inference(symmetry,[status(thm)],[217])).
% 0.56/0.62 tff(219,plain,
% 0.56/0.62 (multiply(sk_c6, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[188])).
% 0.56/0.62 tff(220,plain,
% 0.56/0.62 (multiply(sk_c6, sk_c8) = multiply(sk_c8, sk_c4)),
% 0.56/0.62 inference(transitivity,[status(thm)],[219, 80, 63, 165])).
% 0.56/0.62 tff(221,plain,
% 0.56/0.62 (multiply(multiply(sk_c6, sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[220])).
% 0.56/0.62 tff(222,plain,
% 0.56/0.62 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c6, sk_c8), sk_c8)),
% 0.56/0.62 inference(symmetry,[status(thm)],[221])).
% 0.56/0.62 tff(223,plain,
% 0.56/0.62 (sk_c8 = multiply(sk_c6, identity)),
% 0.56/0.62 inference(transitivity,[status(thm)],[75, 167, 222, 86, 218])).
% 0.56/0.62 tff(224,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c7) = multiply(multiply(sk_c6, identity), sk_c7)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[223])).
% 0.56/0.62 tff(225,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c7) = multiply(sk_c8, sk_c4)),
% 0.56/0.62 inference(transitivity,[status(thm)],[224, 95, 212, 191, 190, 80, 63, 165])).
% 0.56/0.62 tff(226,plain,
% 0.56/0.62 ((multiply(sk_c8, sk_c7) = sk_c7) <=> (multiply(sk_c8, sk_c4) = sk_c7)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[225])).
% 0.56/0.62 tff(227,plain,
% 0.56/0.62 ((multiply(sk_c8, sk_c4) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c7)),
% 0.56/0.62 inference(symmetry,[status(thm)],[226])).
% 0.56/0.62 tff(228,plain,
% 0.56/0.62 ((multiply(sk_c8, sk_c4) = sk_c7) <=> (inverse(sk_c8) = sk_c7)),
% 0.56/0.62 inference(transitivity,[status(thm)],[227, 187])).
% 0.56/0.62 tff(229,plain,
% 0.56/0.62 (multiply(sk_c6, sk_c7) = multiply(sk_c8, sk_c7)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[211])).
% 0.56/0.62 tff(230,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c7) = multiply(sk_c6, sk_c7)),
% 0.56/0.62 inference(symmetry,[status(thm)],[229])).
% 0.56/0.62 tff(231,plain,
% 0.56/0.62 (sk_c8 = multiply(sk_c6, sk_c7)),
% 0.56/0.62 inference(transitivity,[status(thm)],[75, 167, 39, 173, 230])).
% 0.56/0.62 tff(232,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c5) = multiply(multiply(sk_c6, sk_c7), sk_c5)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[231])).
% 0.56/0.62 tff(233,plain,
% 0.56/0.62 (multiply(multiply(sk_c6, sk_c7), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.56/0.62 inference(symmetry,[status(thm)],[232])).
% 0.56/0.62 tff(234,plain,
% 0.56/0.62 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c7), sk_c5) = multiply(sk_c6, multiply(sk_c7, sk_c5)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(235,plain,
% 0.56/0.62 (multiply(multiply(sk_c6, sk_c7), sk_c5) = multiply(sk_c6, multiply(sk_c7, sk_c5))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[234, 37])).
% 0.56/0.62 tff(236,plain,
% 0.56/0.62 (multiply(sk_c6, multiply(sk_c7, sk_c5)) = multiply(multiply(sk_c6, sk_c7), sk_c5)),
% 0.56/0.62 inference(symmetry,[status(thm)],[235])).
% 0.56/0.62 tff(237,plain,
% 0.56/0.62 (multiply(sk_c7, sk_c5) = multiply(sk_c8, sk_c8)),
% 0.56/0.62 inference(transitivity,[status(thm)],[205, 115, 81, 215])).
% 0.56/0.62 tff(238,plain,
% 0.56/0.62 (multiply(sk_c6, multiply(sk_c7, sk_c5)) = multiply(sk_c6, multiply(sk_c8, sk_c8))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[237])).
% 0.56/0.62 tff(239,plain,
% 0.56/0.62 (multiply(sk_c6, multiply(sk_c8, sk_c8)) = multiply(sk_c6, multiply(sk_c7, sk_c5))),
% 0.56/0.62 inference(symmetry,[status(thm)],[238])).
% 0.56/0.62 tff(240,plain,
% 0.56/0.62 (sk_c8 = multiply(sk_c8, sk_c5)),
% 0.56/0.62 inference(transitivity,[status(thm)],[75, 167, 222, 86, 239, 236, 233])).
% 0.56/0.62 tff(241,plain,
% 0.56/0.62 (multiply(sk_c4, sk_c8) = multiply(sk_c4, multiply(sk_c8, sk_c5))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[240])).
% 0.56/0.62 tff(242,plain,
% 0.56/0.62 (multiply(sk_c4, multiply(sk_c8, sk_c5)) = multiply(sk_c4, sk_c8)),
% 0.56/0.62 inference(symmetry,[status(thm)],[241])).
% 0.56/0.62 tff(243,plain,
% 0.56/0.62 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c8), sk_c5) = multiply(sk_c4, multiply(sk_c8, sk_c5)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(244,plain,
% 0.56/0.62 (multiply(multiply(sk_c4, sk_c8), sk_c5) = multiply(sk_c4, multiply(sk_c8, sk_c5))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[243, 37])).
% 0.56/0.62 tff(245,plain,
% 0.56/0.62 (multiply(sk_c4, sk_c8) = inverse(sk_c5)),
% 0.56/0.62 inference(transitivity,[status(thm)],[172, 204])).
% 0.56/0.62 tff(246,plain,
% 0.56/0.62 (multiply(multiply(sk_c4, sk_c8), sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[245])).
% 0.56/0.62 tff(247,plain,
% 0.56/0.62 (multiply(inverse(sk_c5), sk_c5) = multiply(multiply(sk_c4, sk_c8), sk_c5)),
% 0.56/0.62 inference(symmetry,[status(thm)],[246])).
% 0.56/0.62 tff(248,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c4) = sk_c7),
% 0.56/0.62 inference(transitivity,[status(thm)],[164, 62, 207, 247, 244, 242, 172])).
% 0.56/0.62 tff(249,plain,
% 0.56/0.62 (inverse(sk_c8) = sk_c7),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[248, 228])).
% 0.56/0.62 tff(250,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c7) = sk_c7),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[248, 227])).
% 0.56/0.62 tff(251,plain,
% 0.56/0.62 (multiply(multiply(sk_c6, identity), sk_c7) = multiply(sk_c8, sk_c7)),
% 0.56/0.62 inference(symmetry,[status(thm)],[224])).
% 0.56/0.62 tff(252,plain,
% 0.56/0.62 (multiply(sk_c8, multiply(sk_c7, sk_c8)) = multiply(sk_c6, multiply(identity, sk_c7))),
% 0.56/0.62 inference(symmetry,[status(thm)],[212])).
% 0.56/0.62 tff(253,plain,
% 0.56/0.62 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c7), sk_c8)),
% 0.56/0.62 inference(symmetry,[status(thm)],[190])).
% 0.56/0.62 tff(254,plain,
% 0.56/0.62 (multiply(sk_c6, sk_c7) = sk_c8),
% 0.56/0.62 inference(transitivity,[status(thm)],[229, 174, 134, 168, 74])).
% 0.56/0.62 tff(255,plain,
% 0.56/0.62 (multiply(sk_c6, multiply(sk_c6, sk_c7)) = multiply(sk_c8, sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[211, 254])).
% 0.56/0.62 tff(256,plain,
% 0.56/0.62 (multiply(sk_c6, sk_c6) = multiply(sk_c8, sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[211, 211])).
% 0.56/0.62 tff(257,plain,
% 0.56/0.62 (multiply(sk_c8, sk_c8) = multiply(sk_c6, sk_c6)),
% 0.56/0.62 inference(symmetry,[status(thm)],[256])).
% 0.56/0.62 tff(258,plain,
% 0.56/0.62 (multiply(sk_c7, sk_c5) = multiply(sk_c6, sk_c6)),
% 0.56/0.62 inference(transitivity,[status(thm)],[205, 115, 81, 215, 257])).
% 0.56/0.62 tff(259,plain,
% 0.56/0.62 (multiply(multiply(sk_c7, sk_c5), sk_c7) = multiply(multiply(sk_c6, sk_c6), sk_c7)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[258])).
% 0.56/0.62 tff(260,plain,
% 0.56/0.62 (multiply(sk_c4, sk_c6) = multiply(sk_c4, sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[211])).
% 0.56/0.62 tff(261,plain,
% 0.56/0.62 (multiply(sk_c4, sk_c6) = sk_c7),
% 0.56/0.62 inference(transitivity,[status(thm)],[260, 172])).
% 0.56/0.62 tff(262,plain,
% 0.56/0.62 (multiply(multiply(sk_c4, sk_c6), sk_c6) = multiply(sk_c7, sk_c8)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[261, 211])).
% 0.56/0.62 tff(263,plain,
% 0.56/0.62 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c6), sk_c6) = multiply(sk_c4, multiply(sk_c6, sk_c6)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(264,plain,
% 0.56/0.62 (multiply(multiply(sk_c4, sk_c6), sk_c6) = multiply(sk_c4, multiply(sk_c6, sk_c6))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[263, 37])).
% 0.56/0.62 tff(265,plain,
% 0.56/0.62 (multiply(sk_c4, multiply(sk_c6, sk_c6)) = multiply(multiply(sk_c4, sk_c6), sk_c6)),
% 0.56/0.62 inference(symmetry,[status(thm)],[264])).
% 0.56/0.62 tff(266,plain,
% 0.56/0.62 (identity = multiply(sk_c6, sk_c6)),
% 0.56/0.62 inference(transitivity,[status(thm)],[81, 215, 257])).
% 0.56/0.62 tff(267,plain,
% 0.56/0.62 (multiply(sk_c4, identity) = multiply(sk_c4, multiply(sk_c6, sk_c6))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[266])).
% 0.56/0.62 tff(268,plain,
% 0.56/0.62 (multiply(sk_c4, multiply(sk_c8, sk_c5)) = multiply(multiply(sk_c4, sk_c8), sk_c5)),
% 0.56/0.62 inference(symmetry,[status(thm)],[244])).
% 0.56/0.62 tff(269,plain,
% 0.56/0.62 (sk_c7 = multiply(sk_c4, sk_c8)),
% 0.56/0.62 inference(symmetry,[status(thm)],[172])).
% 0.56/0.62 tff(270,plain,
% 0.56/0.62 (sk_c7 = identity),
% 0.56/0.62 inference(transitivity,[status(thm)],[269, 241, 268, 246, 115])).
% 0.56/0.62 tff(271,plain,
% 0.56/0.62 (multiply(sk_c4, sk_c7) = multiply(sk_c4, identity)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[270])).
% 0.56/0.62 tff(272,plain,
% 0.56/0.62 (multiply(sk_c4, sk_c7) = sk_c6),
% 0.56/0.62 inference(transitivity,[status(thm)],[271, 267, 265, 262, 198, 154, 259, 149, 255, 214, 253, 141, 252, 96, 251, 179])).
% 0.56/0.62 tff(273,plain,
% 0.56/0.62 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c6, sk_c8)),
% 0.56/0.62 inference(symmetry,[status(thm)],[219])).
% 0.56/0.62 tff(274,plain,
% 0.56/0.62 (multiply(sk_c7, sk_c8) = multiply(sk_c6, sk_c8)),
% 0.56/0.62 inference(transitivity,[status(thm)],[198, 154, 259, 149, 255, 214, 273])).
% 0.56/0.62 tff(275,plain,
% 0.56/0.62 ((multiply(sk_c7, sk_c8) = sk_c6) <=> (multiply(sk_c6, sk_c8) = sk_c6)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[274])).
% 0.56/0.62 tff(276,plain,
% 0.56/0.62 ((multiply(sk_c6, sk_c8) = sk_c6) <=> (multiply(sk_c7, sk_c8) = sk_c6)),
% 0.56/0.62 inference(symmetry,[status(thm)],[275])).
% 0.56/0.62 tff(277,plain,
% 0.56/0.62 (multiply(sk_c6, sk_c8) = sk_c6),
% 0.56/0.62 inference(transitivity,[status(thm)],[219, 253, 141, 252, 96, 251, 179])).
% 0.56/0.62 tff(278,plain,
% 0.56/0.62 (multiply(sk_c7, sk_c8) = sk_c6),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.56/0.62 tff(279,plain,
% 0.56/0.62 (inverse(sk_c4) = multiply(sk_c8, sk_c7)),
% 0.56/0.62 inference(transitivity,[status(thm)],[162, 75, 167, 39, 173])).
% 0.56/0.62 tff(280,plain,
% 0.56/0.62 ((inverse(sk_c4) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c7)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[279])).
% 0.56/0.62 tff(281,plain,
% 0.56/0.62 ((multiply(sk_c8, sk_c7) = sk_c7) <=> (inverse(sk_c4) = sk_c7)),
% 0.56/0.62 inference(symmetry,[status(thm)],[280])).
% 0.56/0.62 tff(282,plain,
% 0.56/0.62 ((multiply(sk_c8, sk_c4) = sk_c7) <=> (inverse(sk_c4) = sk_c7)),
% 0.56/0.62 inference(transitivity,[status(thm)],[227, 281])).
% 0.56/0.62 tff(283,plain,
% 0.56/0.62 (inverse(sk_c4) = sk_c7),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[248, 282])).
% 0.56/0.62 tff(284,plain,
% 0.56/0.62 (^[X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : refl(((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(285,plain,
% 0.56/0.62 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) <=> ![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))),
% 0.56/0.63 inference(quant_intro,[status(thm)],[284])).
% 0.56/0.63 tff(286,plain,
% 0.56/0.63 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) <=> ![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(287,plain,
% 0.56/0.63 (^[X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), (((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X4) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X4) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), (((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), ((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(X5, sk_c8) = X4))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(X5, sk_c8) = X4))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), ((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), (((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X5) = sk_c8))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X5) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), (((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), ((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), ((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), (((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), (((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), ((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X1) = sk_c8))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X1) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), ((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), ((((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(X2, sk_c7) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(X2, sk_c7) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(X2, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), ((((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(X2, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), (((((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(X2, sk_c7) = sk_c6))) | (~(inverse(X2) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X2) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X2) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), (((((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(X2, sk_c7) = sk_c6))) | (~(inverse(X2) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))))),
% 0.62/0.63 inference(bind,[status(th)],[])).
% 0.62/0.63 tff(288,plain,
% 0.62/0.63 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(X2, sk_c7) = sk_c6))) | (~(inverse(X2) = sk_c7))) <=> ![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))),
% 0.62/0.63 inference(quant_intro,[status(thm)],[287])).
% 0.62/0.63 tff(289,axiom,(![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(X2, sk_c7) = sk_c6))) | (~(inverse(X2) = sk_c7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_37')).
% 0.62/0.63 tff(290,plain,
% 0.62/0.63 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))),
% 0.62/0.63 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.62/0.63 tff(291,plain,
% 0.62/0.63 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))),
% 0.62/0.63 inference(modus_ponens,[status(thm)],[290, 286])).
% 0.62/0.63 tff(292,plain,(
% 0.62/0.63 ![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))),
% 0.62/0.63 inference(skolemize,[status(sab)],[291])).
% 0.62/0.63 tff(293,plain,
% 0.62/0.63 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))),
% 0.62/0.63 inference(modus_ponens,[status(thm)],[292, 285])).
% 0.62/0.63 tff(294,plain,
% 0.62/0.63 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(295,plain,
% 0.62/0.64 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(296,plain,
% 0.62/0.64 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8))))),
% 0.62/0.64 inference(monotonicity,[status(thm)],[295])).
% 0.62/0.64 tff(297,plain,
% 0.62/0.64 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))),
% 0.63/0.64 inference(transitivity,[status(thm)],[296, 294])).
% 0.63/0.64 tff(298,plain,
% 0.63/0.64 ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(299,plain,
% 0.63/0.64 ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.63/0.64 tff(300,plain,
% 0.63/0.64 ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[299, 179, 172, 162, 184, 293])).
% 0.63/0.64 tff(301,plain,
% 0.63/0.64 ($false),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[300, 283, 278, 272, 250, 249, 175])).
% 0.63/0.64 tff(302,plain,(inverse(sk_c2) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.63/0.64 tff(303,plain,
% 0.63/0.64 (sk_c8 = inverse(sk_c2)),
% 0.63/0.64 inference(symmetry,[status(thm)],[302])).
% 0.63/0.64 tff(304,plain,
% 0.63/0.64 (multiply(sk_c8, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.63/0.64 inference(monotonicity,[status(thm)],[303])).
% 0.63/0.64 tff(305,plain,
% 0.63/0.64 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c8, sk_c2)),
% 0.63/0.64 inference(symmetry,[status(thm)],[304])).
% 0.63/0.64 tff(306,plain,
% 0.63/0.64 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(307,plain,
% 0.63/0.64 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[306, 60])).
% 0.63/0.64 tff(308,plain,
% 0.63/0.64 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.63/0.64 inference(symmetry,[status(thm)],[307])).
% 0.63/0.64 tff(309,plain,
% 0.63/0.64 (identity = multiply(sk_c8, sk_c2)),
% 0.63/0.64 inference(transitivity,[status(thm)],[308, 305])).
% 0.63/0.64 tff(310,plain,
% 0.63/0.64 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.63/0.64 inference(monotonicity,[status(thm)],[309])).
% 0.63/0.64 tff(311,plain,
% 0.63/0.64 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(identity, sk_c8)),
% 0.63/0.64 inference(symmetry,[status(thm)],[310])).
% 0.63/0.64 tff(312,plain,
% 0.63/0.64 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(313,plain,
% 0.63/0.64 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[312, 37])).
% 0.63/0.64 tff(314,plain,
% 0.63/0.64 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.63/0.64 inference(symmetry,[status(thm)],[313])).
% 0.63/0.64 tff(315,assumption,(~(multiply(sk_c8, sk_c7) = sk_c6)), introduced(assumption)).
% 0.63/0.64 tff(316,plain,
% 0.63/0.64 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c7) = sk_c6)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c7) = sk_c6))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(317,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_25')).
% 0.63/0.64 tff(318,plain,
% 0.63/0.64 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c7) = sk_c6)),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.63/0.64 tff(319,plain,
% 0.63/0.64 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[318, 315])).
% 0.63/0.64 tff(320,plain,
% 0.63/0.64 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.63/0.64 inference(monotonicity,[status(thm)],[319])).
% 0.63/0.64 tff(321,plain,
% 0.63/0.64 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.63/0.64 inference(symmetry,[status(thm)],[320])).
% 0.63/0.64 tff(322,plain,
% 0.63/0.64 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6)) <=> ((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(323,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_19')).
% 0.63/0.64 tff(324,plain,
% 0.63/0.64 ((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6)),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.63/0.64 tff(325,plain,
% 0.63/0.64 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[324, 315])).
% 0.63/0.64 tff(326,plain,
% 0.63/0.64 (sk_c7 = multiply(sk_c8, sk_c3)),
% 0.63/0.64 inference(symmetry,[status(thm)],[325])).
% 0.63/0.64 tff(327,plain,
% 0.63/0.64 (sk_c7 = sk_c8),
% 0.63/0.64 inference(transitivity,[status(thm)],[326, 321, 314, 311, 74])).
% 0.63/0.64 tff(328,plain,
% 0.63/0.64 (multiply(sk_c7, sk_c7) = multiply(sk_c7, sk_c8)),
% 0.63/0.64 inference(monotonicity,[status(thm)],[327])).
% 0.63/0.64 tff(329,plain,
% 0.63/0.64 (sk_c8 = sk_c7),
% 0.63/0.64 inference(transitivity,[status(thm)],[75, 310, 313, 320, 325])).
% 0.63/0.64 tff(330,plain,
% 0.63/0.64 (multiply(sk_c8, sk_c7) = multiply(sk_c7, sk_c7)),
% 0.63/0.64 inference(monotonicity,[status(thm)],[329])).
% 0.63/0.64 tff(331,plain,
% 0.63/0.64 (multiply(sk_c8, sk_c7) = sk_c6),
% 0.63/0.64 inference(transitivity,[status(thm)],[330, 328, 157])).
% 0.63/0.64 tff(332,plain,
% 0.63/0.64 ($false),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[315, 331])).
% 0.63/0.64 tff(333,plain,(multiply(sk_c8, sk_c7) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.63/0.64 tff(334,plain,
% 0.63/0.64 (sk_c6 = multiply(sk_c8, sk_c7)),
% 0.63/0.64 inference(symmetry,[status(thm)],[333])).
% 0.63/0.64 tff(335,plain,
% 0.63/0.64 ((sk_c8 = multiply(sk_c8, sk_c7)) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.63/0.64 inference(commutativity,[status(thm)],[])).
% 0.63/0.64 tff(336,assumption,(~(multiply(sk_c4, sk_c8) = sk_c7)), introduced(assumption)).
% 0.63/0.64 tff(337,plain,
% 0.63/0.64 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(338,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_8')).
% 0.63/0.64 tff(339,plain,
% 0.63/0.64 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.63/0.64 tff(340,plain,
% 0.63/0.64 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[339, 336])).
% 0.63/0.64 tff(341,plain,
% 0.63/0.64 ((multiply(sk_c1, sk_c7) = sk_c6) <=> (sk_c8 = multiply(sk_c8, sk_c7))),
% 0.63/0.64 inference(monotonicity,[status(thm)],[340, 334])).
% 0.63/0.64 tff(342,plain,
% 0.63/0.64 ((multiply(sk_c1, sk_c7) = sk_c6) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.63/0.64 inference(transitivity,[status(thm)],[341, 335])).
% 0.63/0.64 tff(343,plain,
% 0.63/0.64 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.63/0.64 inference(symmetry,[status(thm)],[342])).
% 0.63/0.64 tff(344,plain,
% 0.63/0.64 (((multiply(sk_c4, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((multiply(sk_c4, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(345,plain,
% 0.63/0.64 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c7)) <=> ((multiply(sk_c4, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(346,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_20')).
% 0.63/0.64 tff(347,plain,
% 0.63/0.64 ((multiply(sk_c4, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.63/0.64 tff(348,plain,
% 0.63/0.64 ((multiply(sk_c4, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[347, 344])).
% 0.63/0.64 tff(349,plain,
% 0.63/0.64 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[348, 336])).
% 0.63/0.64 tff(350,plain,
% 0.63/0.64 (multiply(sk_c8, sk_c8) = multiply(multiply(identity, sk_c8), sk_c8)),
% 0.63/0.64 inference(monotonicity,[status(thm)],[75])).
% 0.63/0.64 tff(351,plain,
% 0.63/0.64 (multiply(multiply(identity, sk_c8), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.63/0.64 inference(symmetry,[status(thm)],[350])).
% 0.63/0.64 tff(352,plain,
% 0.63/0.64 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c8), sk_c8) = multiply(identity, multiply(sk_c8, sk_c8)))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(353,plain,
% 0.63/0.64 (multiply(multiply(identity, sk_c8), sk_c8) = multiply(identity, multiply(sk_c8, sk_c8))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[352, 37])).
% 0.63/0.64 tff(354,plain,
% 0.63/0.64 (multiply(identity, multiply(sk_c8, sk_c8)) = multiply(multiply(identity, sk_c8), sk_c8)),
% 0.63/0.64 inference(symmetry,[status(thm)],[353])).
% 0.63/0.64 tff(355,assumption,(~(multiply(sk_c2, sk_c8) = sk_c3)), introduced(assumption)).
% 0.63/0.64 tff(356,plain,
% 0.63/0.64 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(357,plain,
% 0.63/0.64 (((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(358,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_27')).
% 0.63/0.64 tff(359,plain,
% 0.63/0.64 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.63/0.64 tff(360,plain,
% 0.63/0.64 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[359, 356])).
% 0.63/0.64 tff(361,plain,
% 0.63/0.64 (inverse(sk_c4) = sk_c8),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[360, 355])).
% 0.63/0.64 tff(362,plain,
% 0.63/0.64 (sk_c8 = inverse(sk_c4)),
% 0.63/0.64 inference(symmetry,[status(thm)],[361])).
% 0.63/0.65 tff(363,plain,
% 0.63/0.65 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[362])).
% 0.63/0.65 tff(364,plain,
% 0.63/0.65 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.63/0.65 inference(symmetry,[status(thm)],[363])).
% 0.63/0.65 tff(365,plain,
% 0.63/0.65 (identity = multiply(sk_c8, sk_c4)),
% 0.63/0.65 inference(transitivity,[status(thm)],[63, 364])).
% 0.63/0.65 tff(366,plain,
% 0.63/0.65 (multiply(identity, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, sk_c8))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[365])).
% 0.63/0.65 tff(367,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, sk_c8)) = multiply(identity, multiply(sk_c8, sk_c8))),
% 0.63/0.65 inference(symmetry,[status(thm)],[366])).
% 0.63/0.65 tff(368,plain,
% 0.63/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, sk_c8)) = multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, sk_c8))))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(369,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, sk_c8)) = multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, sk_c8)))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[368, 37])).
% 0.63/0.65 tff(370,plain,
% 0.63/0.65 (multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, sk_c8))) = multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, sk_c8))),
% 0.63/0.65 inference(symmetry,[status(thm)],[369])).
% 0.63/0.65 tff(371,plain,
% 0.63/0.65 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c7)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c7))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(372,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_26')).
% 0.63/0.65 tff(373,plain,
% 0.63/0.65 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.63/0.65 tff(374,plain,
% 0.63/0.65 (multiply(sk_c4, sk_c8) = sk_c7),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[373, 355])).
% 0.63/0.65 tff(375,plain,
% 0.63/0.65 (multiply(multiply(sk_c4, sk_c8), sk_c8) = multiply(sk_c7, sk_c8)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[374])).
% 0.63/0.65 tff(376,plain,
% 0.63/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c8), sk_c8) = multiply(sk_c4, multiply(sk_c8, sk_c8)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(377,plain,
% 0.63/0.65 (multiply(multiply(sk_c4, sk_c8), sk_c8) = multiply(sk_c4, multiply(sk_c8, sk_c8))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[376, 37])).
% 0.63/0.65 tff(378,plain,
% 0.63/0.65 (multiply(sk_c4, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c4, sk_c8), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[377])).
% 0.63/0.65 tff(379,plain,
% 0.63/0.65 (multiply(sk_c4, multiply(sk_c8, sk_c8)) = multiply(sk_c7, sk_c8)),
% 0.63/0.65 inference(transitivity,[status(thm)],[378, 375])).
% 0.63/0.65 tff(380,plain,
% 0.63/0.65 (multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, sk_c8))) = multiply(sk_c8, multiply(sk_c7, sk_c8))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[379])).
% 0.63/0.65 tff(381,plain,
% 0.63/0.65 (multiply(sk_c8, multiply(sk_c7, sk_c8)) = multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, sk_c8)))),
% 0.63/0.65 inference(symmetry,[status(thm)],[380])).
% 0.63/0.65 tff(382,assumption,(~(inverse(sk_c8) = sk_c6)), introduced(assumption)).
% 0.63/0.65 tff(383,plain,
% 0.63/0.65 (((inverse(sk_c8) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(384,plain,
% 0.63/0.65 (((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c8) = sk_c6)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(385,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_10')).
% 0.63/0.65 tff(386,plain,
% 0.63/0.65 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.63/0.65 tff(387,plain,
% 0.63/0.65 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[386, 383])).
% 0.63/0.65 tff(388,plain,
% 0.63/0.65 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[387, 382])).
% 0.63/0.65 tff(389,plain,
% 0.63/0.65 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.63/0.65 inference(symmetry,[status(thm)],[388])).
% 0.63/0.65 tff(390,plain,
% 0.63/0.65 (multiply(sk_c7, sk_c8) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[389])).
% 0.63/0.65 tff(391,plain,
% 0.63/0.65 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[390])).
% 0.63/0.65 tff(392,plain,
% 0.63/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(393,plain,
% 0.63/0.65 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[392, 37])).
% 0.63/0.65 tff(394,plain,
% 0.63/0.65 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(395,plain,
% 0.63/0.65 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[394, 60])).
% 0.63/0.65 tff(396,plain,
% 0.63/0.65 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c8) = sk_c6)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c8) = sk_c6))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(397,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_16')).
% 0.63/0.65 tff(398,plain,
% 0.63/0.65 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c8) = sk_c6)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.63/0.65 tff(399,plain,
% 0.63/0.65 (inverse(sk_c1) = sk_c7),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[398, 382])).
% 0.63/0.65 tff(400,plain,
% 0.63/0.65 (sk_c7 = inverse(sk_c1)),
% 0.63/0.65 inference(symmetry,[status(thm)],[399])).
% 0.63/0.65 tff(401,plain,
% 0.63/0.65 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[400])).
% 0.63/0.65 tff(402,plain,
% 0.63/0.65 (multiply(sk_c7, sk_c1) = identity),
% 0.63/0.65 inference(transitivity,[status(thm)],[401, 395])).
% 0.63/0.65 tff(403,plain,
% 0.63/0.65 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[402])).
% 0.63/0.65 tff(404,plain,
% 0.63/0.65 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.63/0.65 inference(symmetry,[status(thm)],[403])).
% 0.63/0.65 tff(405,plain,
% 0.63/0.65 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(406,plain,
% 0.63/0.65 (multiply(identity, sk_c7) = sk_c7),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[405, 72])).
% 0.63/0.65 tff(407,plain,
% 0.63/0.65 (sk_c7 = multiply(identity, sk_c7)),
% 0.63/0.65 inference(symmetry,[status(thm)],[406])).
% 0.63/0.65 tff(408,plain,
% 0.63/0.65 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c1) = sk_c1)),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(409,plain,
% 0.63/0.65 (multiply(identity, sk_c1) = sk_c1),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[408, 72])).
% 0.63/0.65 tff(410,plain,
% 0.63/0.65 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.63/0.65 inference(symmetry,[status(thm)],[401])).
% 0.63/0.65 tff(411,plain,
% 0.63/0.65 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.63/0.65 inference(symmetry,[status(thm)],[395])).
% 0.63/0.65 tff(412,plain,
% 0.63/0.65 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, sk_c1)),
% 0.63/0.65 inference(transitivity,[status(thm)],[80, 411, 410])).
% 0.63/0.65 tff(413,plain,
% 0.63/0.65 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[412])).
% 0.63/0.65 tff(414,plain,
% 0.63/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c8), sk_c8), sk_c7) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c7)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(415,plain,
% 0.63/0.65 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c7) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c7))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[414, 37])).
% 0.63/0.65 tff(416,plain,
% 0.63/0.65 (multiply(inverse(sk_c8), multiply(sk_c8, sk_c7)) = multiply(multiply(inverse(sk_c8), sk_c8), sk_c7)),
% 0.63/0.65 inference(symmetry,[status(thm)],[415])).
% 0.63/0.65 tff(417,plain,
% 0.63/0.65 (((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(418,plain,
% 0.63/0.65 (((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c8) = sk_c6)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(419,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_22')).
% 0.63/0.65 tff(420,plain,
% 0.63/0.65 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.63/0.65 tff(421,plain,
% 0.63/0.65 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[420, 417])).
% 0.63/0.65 tff(422,plain,
% 0.63/0.65 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[421, 382])).
% 0.63/0.65 tff(423,plain,
% 0.63/0.65 (((inverse(sk_c8) = sk_c6) | (multiply(sk_c2, sk_c8) = sk_c3)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(424,plain,
% 0.63/0.65 (((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c8) = sk_c6)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(425,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_28')).
% 0.63/0.65 tff(426,plain,
% 0.63/0.65 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.63/0.65 tff(427,plain,
% 0.63/0.65 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[426, 423])).
% 0.63/0.65 tff(428,plain,
% 0.63/0.65 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[427, 382])).
% 0.63/0.65 tff(429,plain,
% 0.63/0.65 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[428])).
% 0.63/0.65 tff(430,plain,
% 0.63/0.65 (sk_c8 = multiply(sk_c8, sk_c7)),
% 0.63/0.65 inference(transitivity,[status(thm)],[75, 310, 313, 429, 422, 407, 404, 393, 391, 157, 334])).
% 0.63/0.65 tff(431,plain,
% 0.63/0.65 (multiply(inverse(sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c7))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[430])).
% 0.63/0.65 tff(432,plain,
% 0.63/0.65 (identity = inverse(sk_c1)),
% 0.63/0.65 inference(transitivity,[status(thm)],[81, 431, 416, 413, 403, 406, 400])).
% 0.63/0.65 tff(433,plain,
% 0.63/0.65 (multiply(identity, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[432])).
% 0.63/0.65 tff(434,plain,
% 0.63/0.65 (multiply(inverse(sk_c1), sk_c1) = multiply(identity, sk_c1)),
% 0.63/0.65 inference(symmetry,[status(thm)],[433])).
% 0.63/0.65 tff(435,plain,
% 0.63/0.65 (multiply(inverse(sk_c8), multiply(sk_c8, sk_c7)) = multiply(inverse(sk_c8), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[431])).
% 0.63/0.65 tff(436,plain,
% 0.63/0.65 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(inverse(sk_c8), sk_c8), sk_c7)),
% 0.63/0.65 inference(symmetry,[status(thm)],[413])).
% 0.63/0.65 tff(437,plain,
% 0.63/0.65 (sk_c8 = sk_c1),
% 0.63/0.65 inference(transitivity,[status(thm)],[75, 310, 313, 429, 422, 407, 404, 436, 415, 435, 80, 411, 434, 409])).
% 0.63/0.65 tff(438,plain,
% 0.63/0.65 (inverse(sk_c8) = inverse(sk_c1)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[437])).
% 0.63/0.65 tff(439,plain,
% 0.63/0.65 (inverse(sk_c8) = sk_c6),
% 0.63/0.65 inference(transitivity,[status(thm)],[438, 399, 407, 404, 393, 391, 157])).
% 0.63/0.65 tff(440,plain,
% 0.63/0.65 ($false),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[382, 439])).
% 0.63/0.65 tff(441,plain,(inverse(sk_c8) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.63/0.65 tff(442,plain,
% 0.63/0.65 (sk_c6 = inverse(sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[441])).
% 0.63/0.65 tff(443,plain,
% 0.63/0.65 (multiply(sk_c8, sk_c7) = inverse(sk_c8)),
% 0.63/0.65 inference(transitivity,[status(thm)],[333, 442])).
% 0.63/0.65 tff(444,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c7), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[443])).
% 0.63/0.65 tff(445,plain,
% 0.63/0.65 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c7), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[444])).
% 0.63/0.65 tff(446,plain,
% 0.63/0.65 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c7) = sk_c6)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c7) = sk_c6))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(447,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_29')).
% 0.63/0.65 tff(448,plain,
% 0.63/0.65 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c7) = sk_c6)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.63/0.65 tff(449,plain,
% 0.63/0.65 (multiply(sk_c5, sk_c7) = sk_c6),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[448, 355])).
% 0.63/0.65 tff(450,plain,
% 0.63/0.65 (multiply(sk_c5, sk_c7) = inverse(sk_c8)),
% 0.63/0.65 inference(transitivity,[status(thm)],[449, 442])).
% 0.63/0.65 tff(451,plain,
% 0.63/0.65 (multiply(multiply(sk_c5, sk_c7), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[450])).
% 0.63/0.65 tff(452,plain,
% 0.63/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c7), sk_c8) = multiply(sk_c5, multiply(sk_c7, sk_c8)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(453,plain,
% 0.63/0.65 (multiply(multiply(sk_c5, sk_c7), sk_c8) = multiply(sk_c5, multiply(sk_c7, sk_c8))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[452, 37])).
% 0.63/0.65 tff(454,plain,
% 0.63/0.65 (multiply(sk_c5, multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c5, sk_c7), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[453])).
% 0.63/0.65 tff(455,plain,
% 0.63/0.65 (sk_c6 = multiply(sk_c7, sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[157])).
% 0.63/0.65 tff(456,plain,
% 0.63/0.65 (sk_c7 = multiply(sk_c4, sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[374])).
% 0.63/0.65 tff(457,plain,
% 0.63/0.65 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[456])).
% 0.63/0.65 tff(458,plain,
% 0.63/0.65 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.63/0.65 inference(symmetry,[status(thm)],[457])).
% 0.63/0.65 tff(459,plain,
% 0.63/0.65 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[365])).
% 0.63/0.65 tff(460,plain,
% 0.63/0.65 (sk_c8 = multiply(sk_c7, sk_c8)),
% 0.63/0.65 inference(transitivity,[status(thm)],[75, 459, 39, 458, 333, 455])).
% 0.63/0.65 tff(461,plain,
% 0.63/0.65 (multiply(sk_c5, sk_c8) = multiply(sk_c5, multiply(sk_c7, sk_c8))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[460])).
% 0.63/0.65 tff(462,plain,
% 0.63/0.65 (multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8)),
% 0.63/0.65 inference(transitivity,[status(thm)],[461, 454, 451, 445, 141, 381, 370, 367, 354, 351])).
% 0.63/0.65 tff(463,plain,
% 0.63/0.65 (multiply(sk_c8, sk_c7) = multiply(sk_c7, sk_c8)),
% 0.63/0.65 inference(transitivity,[status(thm)],[333, 455])).
% 0.63/0.65 tff(464,plain,
% 0.63/0.65 (multiply(sk_c8, multiply(sk_c8, sk_c7)) = multiply(sk_c8, multiply(sk_c7, sk_c8))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[463])).
% 0.63/0.65 tff(465,plain,
% 0.63/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), sk_c7) = multiply(sk_c8, multiply(sk_c8, sk_c7)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(466,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c8), sk_c7) = multiply(sk_c8, multiply(sk_c8, sk_c7))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[465, 37])).
% 0.63/0.65 tff(467,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c8), sk_c7) = multiply(sk_c8, sk_c4)),
% 0.63/0.65 inference(transitivity,[status(thm)],[466, 464, 191, 444, 80, 63, 364])).
% 0.63/0.65 tff(468,plain,
% 0.63/0.65 (multiply(multiply(multiply(sk_c8, sk_c8), sk_c7), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[467])).
% 0.63/0.65 tff(469,plain,
% 0.63/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, sk_c8), sk_c7), sk_c8) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c7, sk_c8)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(470,plain,
% 0.63/0.65 (multiply(multiply(multiply(sk_c8, sk_c8), sk_c7), sk_c8) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c7, sk_c8))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[469, 37])).
% 0.63/0.65 tff(471,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c7, sk_c8)) = multiply(multiply(multiply(sk_c8, sk_c8), sk_c7), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[470])).
% 0.63/0.65 tff(472,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c7, sk_c8))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[460])).
% 0.63/0.65 tff(473,plain,
% 0.63/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), sk_c8) = multiply(sk_c8, multiply(sk_c8, sk_c8)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(474,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c8), sk_c8) = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[473, 37])).
% 0.63/0.65 tff(475,plain,
% 0.63/0.65 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c8, sk_c8), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[474])).
% 0.63/0.65 tff(476,plain,
% 0.63/0.65 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.63/0.65 inference(transitivity,[status(thm)],[475, 472, 471, 468, 39, 458])).
% 0.63/0.65 tff(477,plain,
% 0.63/0.65 ((multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c7)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[476])).
% 0.63/0.65 tff(478,plain,
% 0.63/0.65 ((multiply(sk_c8, sk_c7) = sk_c7) <=> (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)),
% 0.63/0.65 inference(symmetry,[status(thm)],[477])).
% 0.63/0.65 tff(479,plain,
% 0.63/0.65 (((inverse(sk_c5) = sk_c7) | (multiply(sk_c2, sk_c8) = sk_c3)) <=> ((inverse(sk_c5) = sk_c7) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(480,plain,
% 0.63/0.65 (((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c5) = sk_c7)) <=> ((inverse(sk_c5) = sk_c7) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(481,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c5) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_30')).
% 0.63/0.65 tff(482,plain,
% 0.63/0.65 ((inverse(sk_c5) = sk_c7) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[481, 480])).
% 0.63/0.65 tff(483,plain,
% 0.63/0.65 ((inverse(sk_c5) = sk_c7) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[482, 479])).
% 0.63/0.65 tff(484,plain,
% 0.63/0.65 (inverse(sk_c5) = sk_c7),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[483, 355])).
% 0.63/0.65 tff(485,plain,
% 0.63/0.65 (sk_c7 = inverse(sk_c5)),
% 0.63/0.65 inference(symmetry,[status(thm)],[484])).
% 0.63/0.65 tff(486,plain,
% 0.63/0.65 (multiply(sk_c7, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[485])).
% 0.63/0.65 tff(487,plain,
% 0.63/0.65 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c7, sk_c5)),
% 0.63/0.65 inference(symmetry,[status(thm)],[486])).
% 0.63/0.65 tff(488,plain,
% 0.63/0.65 (multiply(sk_c8, sk_c4) = multiply(sk_c7, sk_c5)),
% 0.63/0.65 inference(transitivity,[status(thm)],[363, 62, 207, 487])).
% 0.63/0.65 tff(489,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c7, sk_c5), sk_c8)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[488])).
% 0.63/0.65 tff(490,plain,
% 0.63/0.65 (multiply(multiply(sk_c7, sk_c5), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[489])).
% 0.63/0.65 tff(491,plain,
% 0.63/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c5), sk_c8) = multiply(sk_c7, multiply(sk_c5, sk_c8)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(492,plain,
% 0.63/0.65 (multiply(multiply(sk_c7, sk_c5), sk_c8) = multiply(sk_c7, multiply(sk_c5, sk_c8))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[491, 37])).
% 0.63/0.65 tff(493,plain,
% 0.63/0.65 (multiply(sk_c7, multiply(sk_c5, sk_c8)) = multiply(multiply(sk_c7, sk_c5), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[492])).
% 0.63/0.65 tff(494,plain,
% 0.63/0.65 (multiply(sk_c7, multiply(sk_c5, sk_c8)) = multiply(sk_c7, multiply(sk_c8, sk_c8))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[462])).
% 0.63/0.65 tff(495,plain,
% 0.63/0.65 (multiply(sk_c7, multiply(sk_c8, sk_c8)) = multiply(sk_c7, multiply(sk_c5, sk_c8))),
% 0.63/0.65 inference(symmetry,[status(thm)],[494])).
% 0.63/0.65 tff(496,plain,
% 0.63/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), sk_c8) = multiply(sk_c7, multiply(sk_c8, sk_c8)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(497,plain,
% 0.63/0.65 (multiply(multiply(sk_c7, sk_c8), sk_c8) = multiply(sk_c7, multiply(sk_c8, sk_c8))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[496, 37])).
% 0.63/0.65 tff(498,plain,
% 0.63/0.65 (multiply(sk_c7, sk_c8) = inverse(sk_c8)),
% 0.63/0.65 inference(transitivity,[status(thm)],[157, 442])).
% 0.63/0.65 tff(499,plain,
% 0.63/0.65 (multiply(multiply(sk_c7, sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[498])).
% 0.63/0.65 tff(500,plain,
% 0.63/0.65 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c7, sk_c8), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[499])).
% 0.63/0.65 tff(501,plain,
% 0.63/0.65 (multiply(sk_c8, sk_c2) = multiply(sk_c8, sk_c7)),
% 0.63/0.65 inference(transitivity,[status(thm)],[304, 307, 81, 500, 497, 495, 493, 490, 39, 458])).
% 0.63/0.65 tff(502,plain,
% 0.63/0.65 ((multiply(sk_c8, sk_c2) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c7)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[501])).
% 0.63/0.65 tff(503,plain,
% 0.63/0.65 ((multiply(sk_c8, sk_c2) = sk_c7) <=> (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)),
% 0.63/0.65 inference(transitivity,[status(thm)],[502, 478])).
% 0.63/0.65 tff(504,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c8, sk_c8), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[472])).
% 0.63/0.65 tff(505,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(multiply(sk_c8, sk_c8), sk_c7), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[468])).
% 0.63/0.65 tff(506,plain,
% 0.63/0.65 (sk_c8 = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.63/0.65 inference(transitivity,[status(thm)],[75, 459, 505, 470, 504, 474])).
% 0.63/0.65 tff(507,plain,
% 0.63/0.65 (multiply(sk_c4, sk_c8) = multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8)))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[506])).
% 0.63/0.65 tff(508,plain,
% 0.63/0.65 (multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8))) = multiply(sk_c4, sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[507])).
% 0.63/0.65 tff(509,plain,
% 0.63/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, sk_c8)) = multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8))))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(510,plain,
% 0.63/0.65 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, sk_c8)) = multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8)))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[509, 37])).
% 0.63/0.65 tff(511,plain,
% 0.63/0.65 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, sk_c8)) = multiply(sk_c7, multiply(sk_c8, sk_c8))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[374])).
% 0.63/0.65 tff(512,plain,
% 0.63/0.65 (multiply(sk_c7, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, sk_c8))),
% 0.63/0.65 inference(symmetry,[status(thm)],[511])).
% 0.63/0.65 tff(513,plain,
% 0.63/0.65 (multiply(sk_c8, sk_c2) = sk_c7),
% 0.63/0.65 inference(transitivity,[status(thm)],[304, 307, 81, 500, 497, 512, 510, 508, 374])).
% 0.63/0.65 tff(514,plain,
% 0.63/0.65 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[513, 503])).
% 0.63/0.65 tff(515,plain,
% 0.63/0.65 ((sk_c7 = inverse(sk_c2)) <=> (inverse(sk_c2) = sk_c7)),
% 0.63/0.65 inference(commutativity,[status(thm)],[])).
% 0.63/0.65 tff(516,plain,
% 0.63/0.65 ((inverse(sk_c5) = sk_c8) <=> (sk_c7 = inverse(sk_c2))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[484, 303])).
% 0.63/0.65 tff(517,plain,
% 0.63/0.65 ((inverse(sk_c5) = sk_c8) <=> (inverse(sk_c2) = sk_c7)),
% 0.63/0.65 inference(transitivity,[status(thm)],[516, 515])).
% 0.63/0.65 tff(518,plain,
% 0.63/0.65 ((inverse(sk_c2) = sk_c7) <=> (inverse(sk_c5) = sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[517])).
% 0.63/0.65 tff(519,plain,
% 0.63/0.65 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[459])).
% 0.63/0.65 tff(520,plain,
% 0.63/0.65 (multiply(sk_c8, sk_c7) = inverse(sk_c2)),
% 0.63/0.65 inference(transitivity,[status(thm)],[457, 134, 519, 74, 303])).
% 0.63/0.65 tff(521,plain,
% 0.63/0.65 ((multiply(sk_c8, sk_c7) = sk_c7) <=> (inverse(sk_c2) = sk_c7)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[520])).
% 0.63/0.65 tff(522,plain,
% 0.63/0.65 ((multiply(sk_c8, sk_c2) = sk_c7) <=> (inverse(sk_c5) = sk_c8)),
% 0.63/0.65 inference(transitivity,[status(thm)],[502, 521, 518])).
% 0.63/0.65 tff(523,plain,
% 0.63/0.65 (inverse(sk_c5) = sk_c8),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[513, 522])).
% 0.63/0.65 tff(524,plain,
% 0.63/0.65 (multiply(sk_c7, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c7, sk_c8), sk_c8)),
% 0.63/0.65 inference(symmetry,[status(thm)],[497])).
% 0.63/0.65 tff(525,plain,
% 0.63/0.65 (multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8))) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, sk_c8))),
% 0.63/0.66 inference(symmetry,[status(thm)],[510])).
% 0.63/0.66 tff(526,plain,
% 0.63/0.66 (sk_c7 = multiply(sk_c8, sk_c8)),
% 0.63/0.66 inference(transitivity,[status(thm)],[456, 507, 525, 511, 524, 499, 445, 141, 381, 370, 367, 354, 351])).
% 0.63/0.66 tff(527,plain,
% 0.63/0.66 (multiply(sk_c4, sk_c7) = multiply(sk_c4, multiply(sk_c8, sk_c8))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[526])).
% 0.63/0.66 tff(528,plain,
% 0.63/0.66 (multiply(sk_c4, sk_c7) = sk_c6),
% 0.63/0.66 inference(transitivity,[status(thm)],[527, 378, 375, 157])).
% 0.63/0.66 tff(529,plain,
% 0.63/0.66 (inverse(sk_c4) = inverse(sk_c2)),
% 0.63/0.66 inference(transitivity,[status(thm)],[361, 303])).
% 0.63/0.66 tff(530,plain,
% 0.63/0.66 ((inverse(sk_c4) = sk_c7) <=> (inverse(sk_c2) = sk_c7)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[529])).
% 0.63/0.66 tff(531,plain,
% 0.63/0.66 ((inverse(sk_c2) = sk_c7) <=> (inverse(sk_c4) = sk_c7)),
% 0.63/0.66 inference(symmetry,[status(thm)],[530])).
% 0.63/0.66 tff(532,plain,
% 0.63/0.66 ((multiply(sk_c8, sk_c2) = sk_c7) <=> (inverse(sk_c4) = sk_c7)),
% 0.63/0.66 inference(transitivity,[status(thm)],[502, 521, 531])).
% 0.63/0.66 tff(533,plain,
% 0.63/0.66 (inverse(sk_c4) = sk_c7),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[513, 532])).
% 0.63/0.66 tff(534,plain,
% 0.63/0.66 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.63/0.66 inference(transitivity,[status(thm)],[457, 134, 519, 74])).
% 0.63/0.66 tff(535,plain,
% 0.63/0.66 (inverse(sk_c8) = multiply(sk_c8, sk_c7)),
% 0.63/0.66 inference(transitivity,[status(thm)],[441, 334])).
% 0.63/0.66 tff(536,plain,
% 0.63/0.66 ((inverse(sk_c8) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c7)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[535])).
% 0.63/0.66 tff(537,plain,
% 0.63/0.66 ((multiply(sk_c8, sk_c7) = sk_c7) <=> (inverse(sk_c8) = sk_c7)),
% 0.63/0.66 inference(symmetry,[status(thm)],[536])).
% 0.63/0.66 tff(538,plain,
% 0.63/0.66 ((multiply(sk_c8, sk_c2) = sk_c7) <=> (inverse(sk_c8) = sk_c7)),
% 0.63/0.66 inference(transitivity,[status(thm)],[502, 537])).
% 0.63/0.66 tff(539,plain,
% 0.63/0.66 (inverse(sk_c8) = sk_c7),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[513, 538])).
% 0.63/0.66 tff(540,plain,
% 0.63/0.66 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8))))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8))))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(541,plain,
% 0.63/0.66 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8))) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8))))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(542,plain,
% 0.63/0.66 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8))) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8)))))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[541])).
% 0.63/0.66 tff(543,plain,
% 0.63/0.66 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8))) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8))))),
% 0.63/0.66 inference(transitivity,[status(thm)],[542, 540])).
% 0.63/0.66 tff(544,plain,
% 0.63/0.66 ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8))) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))),
% 0.63/0.66 inference(quant_inst,[status(thm)],[])).
% 0.63/0.66 tff(545,plain,
% 0.63/0.66 ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8)))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.63/0.66 tff(546,plain,
% 0.63/0.66 ((~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) | (~(multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8)))),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[545, 157, 333, 374, 361, 441, 293])).
% 0.63/0.66 tff(547,plain,
% 0.63/0.66 ($false),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[546, 539, 534, 533, 528, 523, 514, 462])).
% 0.63/0.66 tff(548,plain,(multiply(sk_c2, sk_c8) = sk_c3), inference(lemma,lemma(discharge,[]))).
% 0.63/0.66 tff(549,plain,
% 0.63/0.66 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[548])).
% 0.63/0.66 tff(550,plain,
% 0.63/0.66 (sk_c8 = sk_c7),
% 0.63/0.66 inference(transitivity,[status(thm)],[75, 310, 313, 549, 349])).
% 0.63/0.66 tff(551,plain,
% 0.63/0.66 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (multiply(sk_c8, sk_c7) = sk_c7)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[550])).
% 0.63/0.66 tff(552,plain,
% 0.63/0.66 ((multiply(sk_c8, sk_c7) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.63/0.66 inference(symmetry,[status(thm)],[551])).
% 0.63/0.66 tff(553,plain,
% 0.63/0.66 ((multiply(sk_c8, sk_c7) = sk_c7) <=> (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.63/0.66 inference(transitivity,[status(thm)],[552, 343])).
% 0.63/0.66 tff(554,plain,
% 0.63/0.66 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c7))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(555,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_14')).
% 0.63/0.66 tff(556,plain,
% 0.63/0.66 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.63/0.66 tff(557,plain,
% 0.63/0.66 (inverse(sk_c1) = sk_c7),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[556, 336])).
% 0.63/0.66 tff(558,plain,
% 0.63/0.66 (sk_c7 = inverse(sk_c1)),
% 0.63/0.66 inference(symmetry,[status(thm)],[557])).
% 0.63/0.66 tff(559,plain,
% 0.63/0.66 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[558])).
% 0.63/0.66 tff(560,plain,
% 0.63/0.66 (multiply(sk_c7, sk_c1) = identity),
% 0.63/0.66 inference(transitivity,[status(thm)],[559, 395])).
% 0.63/0.66 tff(561,plain,
% 0.63/0.66 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[560])).
% 0.63/0.66 tff(562,plain,
% 0.63/0.66 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.63/0.66 inference(symmetry,[status(thm)],[393])).
% 0.63/0.66 tff(563,plain,
% 0.63/0.66 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.63/0.66 inference(symmetry,[status(thm)],[340])).
% 0.63/0.66 tff(564,plain,
% 0.63/0.66 (multiply(sk_c7, sk_c8) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[563])).
% 0.63/0.66 tff(565,plain,
% 0.63/0.66 (multiply(sk_c8, sk_c7) = sk_c7),
% 0.63/0.66 inference(transitivity,[status(thm)],[333, 455, 564, 562, 561, 406])).
% 0.63/0.66 tff(566,plain,
% 0.63/0.66 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[565, 553])).
% 0.63/0.66 tff(567,plain,
% 0.63/0.66 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.63/0.66 inference(symmetry,[status(thm)],[549])).
% 0.63/0.66 tff(568,plain,
% 0.63/0.66 (sk_c7 = multiply(sk_c8, sk_c3)),
% 0.63/0.66 inference(symmetry,[status(thm)],[349])).
% 0.63/0.66 tff(569,plain,
% 0.63/0.66 (sk_c7 = sk_c8),
% 0.63/0.66 inference(transitivity,[status(thm)],[568, 567, 314, 311, 74])).
% 0.63/0.66 tff(570,plain,
% 0.63/0.66 (multiply(sk_c7, sk_c7) = multiply(sk_c7, sk_c8)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[569])).
% 0.63/0.66 tff(571,plain,
% 0.63/0.66 (multiply(sk_c8, sk_c8) = multiply(sk_c7, sk_c7)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[550, 550])).
% 0.63/0.66 tff(572,plain,
% 0.63/0.66 (multiply(sk_c8, sk_c8) = sk_c7),
% 0.63/0.66 inference(transitivity,[status(thm)],[571, 570, 564, 562, 561, 406])).
% 0.63/0.66 tff(573,plain,
% 0.63/0.66 ((inverse(sk_c8) = sk_c8) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[535])).
% 0.63/0.66 tff(574,plain,
% 0.63/0.66 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (inverse(sk_c8) = sk_c8)),
% 0.63/0.66 inference(symmetry,[status(thm)],[573])).
% 0.63/0.66 tff(575,plain,
% 0.63/0.66 ((multiply(sk_c8, sk_c7) = sk_c7) <=> (inverse(sk_c8) = sk_c8)),
% 0.63/0.66 inference(transitivity,[status(thm)],[552, 574])).
% 0.63/0.66 tff(576,plain,
% 0.63/0.66 (inverse(sk_c8) = sk_c8),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[565, 575])).
% 0.63/0.66 tff(577,plain,
% 0.63/0.66 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(578,plain,
% 0.63/0.66 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(579,plain,
% 0.63/0.67 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6))))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[578])).
% 0.63/0.67 tff(580,plain,
% 0.63/0.67 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.63/0.67 inference(transitivity,[status(thm)],[579, 577])).
% 0.63/0.67 tff(581,plain,
% 0.63/0.67 ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(582,plain,
% 0.63/0.67 ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.63/0.67 tff(583,plain,
% 0.63/0.67 ((~(multiply(sk_c8, sk_c7) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[582, 157, 333, 441, 340, 557, 293])).
% 0.63/0.67 tff(584,plain,
% 0.63/0.67 ($false),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[583, 576, 565, 572, 566])).
% 0.63/0.67 tff(585,plain,(multiply(sk_c4, sk_c8) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.63/0.67 tff(586,plain,
% 0.63/0.67 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c8, sk_c8)) = multiply(sk_c8, sk_c8))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(587,plain,
% 0.63/0.67 (multiply(identity, multiply(sk_c8, sk_c8)) = multiply(sk_c8, sk_c8)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[586, 72])).
% 0.63/0.67 tff(588,plain,
% 0.63/0.67 (multiply(sk_c8, sk_c8) = multiply(identity, multiply(sk_c8, sk_c8))),
% 0.63/0.67 inference(symmetry,[status(thm)],[587])).
% 0.63/0.67 tff(589,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c8), sk_c8) = multiply(multiply(identity, multiply(sk_c8, sk_c8)), sk_c8)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[588])).
% 0.63/0.67 tff(590,plain,
% 0.63/0.67 (multiply(multiply(identity, multiply(sk_c8, sk_c8)), sk_c8) = multiply(multiply(sk_c8, sk_c8), sk_c8)),
% 0.63/0.67 inference(symmetry,[status(thm)],[589])).
% 0.63/0.67 tff(591,plain,
% 0.63/0.67 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, multiply(sk_c8, sk_c8)), sk_c8) = multiply(identity, multiply(multiply(sk_c8, sk_c8), sk_c8)))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(592,plain,
% 0.63/0.67 (multiply(multiply(identity, multiply(sk_c8, sk_c8)), sk_c8) = multiply(identity, multiply(multiply(sk_c8, sk_c8), sk_c8))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[591, 37])).
% 0.63/0.67 tff(593,plain,
% 0.63/0.67 (multiply(identity, multiply(multiply(sk_c8, sk_c8), sk_c8)) = multiply(multiply(identity, multiply(sk_c8, sk_c8)), sk_c8)),
% 0.63/0.67 inference(symmetry,[status(thm)],[592])).
% 0.63/0.67 tff(594,assumption,(~(multiply(sk_c8, sk_c3) = sk_c7)), introduced(assumption)).
% 0.63/0.67 tff(595,plain,
% 0.63/0.67 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(596,plain,
% 0.63/0.67 (((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(597,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_21')).
% 0.63/0.67 tff(598,plain,
% 0.63/0.67 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.63/0.67 tff(599,plain,
% 0.63/0.67 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[598, 595])).
% 0.63/0.67 tff(600,plain,
% 0.63/0.67 (inverse(sk_c4) = sk_c8),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[599, 594])).
% 0.63/0.67 tff(601,plain,
% 0.63/0.67 (sk_c8 = inverse(sk_c4)),
% 0.63/0.67 inference(symmetry,[status(thm)],[600])).
% 0.63/0.67 tff(602,plain,
% 0.63/0.67 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[601])).
% 0.63/0.67 tff(603,plain,
% 0.63/0.67 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.63/0.67 inference(symmetry,[status(thm)],[602])).
% 0.63/0.67 tff(604,plain,
% 0.63/0.67 (identity = multiply(sk_c8, sk_c4)),
% 0.63/0.67 inference(transitivity,[status(thm)],[63, 603])).
% 0.63/0.67 tff(605,plain,
% 0.63/0.67 (multiply(identity, multiply(multiply(sk_c8, sk_c8), sk_c8)) = multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, multiply(sk_c8, sk_c8)))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[604, 474])).
% 0.63/0.67 tff(606,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, multiply(sk_c8, sk_c8))) = multiply(identity, multiply(multiply(sk_c8, sk_c8), sk_c8))),
% 0.63/0.67 inference(symmetry,[status(thm)],[605])).
% 0.63/0.67 tff(607,plain,
% 0.63/0.67 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, multiply(sk_c8, sk_c8))) = multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8)))))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(608,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, multiply(sk_c8, sk_c8))) = multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8))))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[607, 37])).
% 0.63/0.67 tff(609,plain,
% 0.63/0.67 (multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8)))) = multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, multiply(sk_c8, sk_c8)))),
% 0.63/0.67 inference(symmetry,[status(thm)],[608])).
% 0.63/0.67 tff(610,plain,
% 0.63/0.67 (multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, sk_c8)) = multiply(sk_c7, multiply(sk_c8, sk_c8))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[585])).
% 0.63/0.67 tff(611,plain,
% 0.63/0.67 (multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8))) = multiply(sk_c8, sk_c4)),
% 0.63/0.67 inference(transitivity,[status(thm)],[525, 610, 524, 499, 80, 63, 603])).
% 0.63/0.67 tff(612,plain,
% 0.63/0.67 (multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8)))) = multiply(sk_c8, multiply(sk_c8, sk_c4))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[611])).
% 0.63/0.67 tff(613,plain,
% 0.63/0.67 (multiply(sk_c8, multiply(sk_c8, sk_c4)) = multiply(sk_c8, multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8))))),
% 0.63/0.67 inference(symmetry,[status(thm)],[612])).
% 0.63/0.67 tff(614,plain,
% 0.63/0.67 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c7, sk_c8))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[455])).
% 0.63/0.67 tff(615,plain,
% 0.63/0.67 (multiply(sk_c8, multiply(sk_c7, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.63/0.67 inference(symmetry,[status(thm)],[614])).
% 0.63/0.67 tff(616,plain,
% 0.63/0.67 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c6)),
% 0.63/0.67 inference(transitivity,[status(thm)],[602, 62, 81, 445, 141, 615])).
% 0.63/0.67 tff(617,plain,
% 0.63/0.67 (multiply(sk_c8, multiply(sk_c8, sk_c4)) = multiply(sk_c8, multiply(sk_c8, sk_c6))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[616])).
% 0.63/0.67 tff(618,plain,
% 0.63/0.67 (multiply(sk_c8, multiply(sk_c8, sk_c6)) = multiply(sk_c8, multiply(sk_c8, sk_c4))),
% 0.63/0.67 inference(symmetry,[status(thm)],[617])).
% 0.63/0.67 tff(619,plain,
% 0.63/0.67 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), sk_c6) = multiply(sk_c8, multiply(sk_c8, sk_c6)))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(620,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c8), sk_c6) = multiply(sk_c8, multiply(sk_c8, sk_c6))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[619, 37])).
% 0.63/0.67 tff(621,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c8), sk_c6) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c7, sk_c8))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[455])).
% 0.63/0.67 tff(622,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c8, sk_c8), sk_c6)),
% 0.63/0.67 inference(symmetry,[status(thm)],[621])).
% 0.63/0.67 tff(623,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c8), sk_c7) = multiply(sk_c8, sk_c4)),
% 0.63/0.67 inference(transitivity,[status(thm)],[466, 464, 191, 444, 80, 63, 603])).
% 0.63/0.67 tff(624,plain,
% 0.63/0.67 (multiply(multiply(multiply(sk_c8, sk_c8), sk_c7), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[623])).
% 0.63/0.67 tff(625,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(multiply(sk_c8, sk_c8), sk_c7), sk_c8)),
% 0.63/0.67 inference(symmetry,[status(thm)],[624])).
% 0.63/0.67 tff(626,plain,
% 0.63/0.67 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[604])).
% 0.63/0.67 tff(627,plain,
% 0.63/0.67 (sk_c8 = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.63/0.67 inference(transitivity,[status(thm)],[75, 626, 625, 470, 622, 620, 618, 613, 609, 606, 593, 590, 474])).
% 0.63/0.67 tff(628,plain,
% 0.63/0.67 (multiply(sk_c4, sk_c8) = multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8)))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[627])).
% 0.63/0.67 tff(629,plain,
% 0.63/0.67 (multiply(sk_c4, multiply(sk_c8, multiply(sk_c8, sk_c8))) = multiply(sk_c4, sk_c8)),
% 0.63/0.67 inference(symmetry,[status(thm)],[628])).
% 0.63/0.67 tff(630,plain,
% 0.63/0.67 (multiply(sk_c7, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c4, sk_c8), multiply(sk_c8, sk_c8))),
% 0.63/0.67 inference(symmetry,[status(thm)],[610])).
% 0.63/0.67 tff(631,plain,
% 0.63/0.67 (sk_c7 = multiply(sk_c4, sk_c8)),
% 0.63/0.67 inference(symmetry,[status(thm)],[585])).
% 0.63/0.67 tff(632,plain,
% 0.63/0.67 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[631])).
% 0.63/0.67 tff(633,plain,
% 0.63/0.67 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.63/0.67 inference(symmetry,[status(thm)],[632])).
% 0.63/0.67 tff(634,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c4), sk_c8) = inverse(sk_c8)),
% 0.63/0.67 inference(transitivity,[status(thm)],[39, 633, 333, 442])).
% 0.63/0.67 tff(635,plain,
% 0.63/0.67 (multiply(multiply(multiply(sk_c8, sk_c4), sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[634])).
% 0.63/0.67 tff(636,plain,
% 0.63/0.67 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, sk_c4), sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, sk_c8)))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(637,plain,
% 0.63/0.67 (multiply(multiply(multiply(sk_c8, sk_c4), sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, sk_c8))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[636, 37])).
% 0.63/0.67 tff(638,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, sk_c8)) = multiply(multiply(multiply(sk_c8, sk_c4), sk_c8), sk_c8)),
% 0.63/0.67 inference(symmetry,[status(thm)],[637])).
% 0.63/0.67 tff(639,plain,
% 0.63/0.67 (multiply(identity, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, sk_c8))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[604])).
% 0.63/0.67 tff(640,plain,
% 0.63/0.67 (multiply(sk_c8, sk_c8) = sk_c7),
% 0.63/0.67 inference(transitivity,[status(thm)],[588, 639, 638, 635, 500, 497, 630, 510, 629, 585])).
% 0.63/0.67 tff(641,plain,
% 0.63/0.67 ((multiply(sk_c8, sk_c8) = sk_c6) <=> (sk_c7 = multiply(sk_c8, sk_c7))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[640, 334])).
% 0.63/0.67 tff(642,plain,
% 0.63/0.67 ((multiply(sk_c8, sk_c8) = sk_c6) <=> (multiply(sk_c8, sk_c7) = sk_c7)),
% 0.63/0.67 inference(transitivity,[status(thm)],[641, 1])).
% 0.63/0.67 tff(643,plain,
% 0.63/0.67 ((multiply(sk_c8, sk_c7) = sk_c7) <=> (multiply(sk_c8, sk_c8) = sk_c6)),
% 0.63/0.67 inference(symmetry,[status(thm)],[642])).
% 0.63/0.67 tff(644,plain,
% 0.63/0.67 ((~(multiply(sk_c8, sk_c7) = sk_c7)) <=> (~(multiply(sk_c8, sk_c8) = sk_c6))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[643])).
% 0.63/0.67 tff(645,plain,
% 0.63/0.67 (multiply(sk_c8, sk_c2) = multiply(sk_c8, sk_c4)),
% 0.63/0.67 inference(transitivity,[status(thm)],[304, 307, 63, 603])).
% 0.63/0.67 tff(646,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[645])).
% 0.63/0.67 tff(647,plain,
% 0.63/0.67 (sk_c3 = multiply(sk_c2, sk_c8)),
% 0.63/0.67 inference(symmetry,[status(thm)],[548])).
% 0.63/0.67 tff(648,plain,
% 0.63/0.67 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[647])).
% 0.63/0.67 tff(649,plain,
% 0.63/0.67 (multiply(sk_c8, sk_c3) = multiply(sk_c8, sk_c7)),
% 0.63/0.67 inference(transitivity,[status(thm)],[648, 314, 646, 39, 633])).
% 0.63/0.67 tff(650,plain,
% 0.63/0.67 ((multiply(sk_c8, sk_c3) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c7)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[649])).
% 0.63/0.67 tff(651,plain,
% 0.63/0.67 ((~(multiply(sk_c8, sk_c3) = sk_c7)) <=> (~(multiply(sk_c8, sk_c7) = sk_c7))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[650])).
% 0.63/0.67 tff(652,plain,
% 0.63/0.67 (~(multiply(sk_c8, sk_c7) = sk_c7)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[594, 651])).
% 0.63/0.67 tff(653,plain,
% 0.63/0.67 (~(multiply(sk_c8, sk_c8) = sk_c6)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[652, 644])).
% 0.63/0.67 tff(654,plain,
% 0.63/0.67 (((inverse(sk_c5) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((inverse(sk_c5) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(655,plain,
% 0.63/0.67 (((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c5) = sk_c7)) <=> ((inverse(sk_c5) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(656,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c5) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_24')).
% 0.63/0.67 tff(657,plain,
% 0.63/0.67 ((inverse(sk_c5) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.63/0.67 tff(658,plain,
% 0.63/0.67 ((inverse(sk_c5) = sk_c7) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[657, 654])).
% 0.63/0.67 tff(659,plain,
% 0.63/0.67 (inverse(sk_c5) = sk_c7),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[658, 594])).
% 0.63/0.67 tff(660,plain,
% 0.63/0.67 (sk_c7 = inverse(sk_c5)),
% 0.63/0.67 inference(symmetry,[status(thm)],[659])).
% 0.63/0.67 tff(661,plain,
% 0.63/0.67 (multiply(sk_c7, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[660])).
% 0.63/0.67 tff(662,plain,
% 0.63/0.67 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c7, sk_c5)),
% 0.63/0.67 inference(symmetry,[status(thm)],[661])).
% 0.63/0.67 tff(663,plain,
% 0.63/0.67 (multiply(sk_c8, sk_c4) = multiply(sk_c7, sk_c5)),
% 0.63/0.67 inference(transitivity,[status(thm)],[602, 62, 207, 662])).
% 0.63/0.67 tff(664,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c7, sk_c5), sk_c8)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[663])).
% 0.63/0.67 tff(665,plain,
% 0.63/0.67 (multiply(multiply(sk_c7, sk_c5), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.63/0.67 inference(symmetry,[status(thm)],[664])).
% 0.63/0.67 tff(666,plain,
% 0.63/0.67 (multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, sk_c8)) = multiply(identity, multiply(sk_c8, sk_c8))),
% 0.63/0.67 inference(symmetry,[status(thm)],[639])).
% 0.63/0.67 tff(667,plain,
% 0.63/0.67 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(multiply(sk_c8, sk_c4), sk_c8), sk_c8)),
% 0.63/0.67 inference(symmetry,[status(thm)],[635])).
% 0.63/0.67 tff(668,plain,
% 0.63/0.67 (((multiply(sk_c5, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((multiply(sk_c5, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(669,plain,
% 0.63/0.67 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)) <=> ((multiply(sk_c5, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(670,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c5, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_23')).
% 0.63/0.67 tff(671,plain,
% 0.63/0.67 ((multiply(sk_c5, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.63/0.67 tff(672,plain,
% 0.63/0.67 ((multiply(sk_c5, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[671, 668])).
% 0.63/0.67 tff(673,plain,
% 0.63/0.67 (multiply(sk_c5, sk_c7) = sk_c6),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[672, 594])).
% 0.63/0.67 tff(674,plain,
% 0.63/0.67 (multiply(sk_c5, sk_c7) = inverse(sk_c8)),
% 0.63/0.67 inference(transitivity,[status(thm)],[673, 442])).
% 0.63/0.67 tff(675,plain,
% 0.63/0.67 (multiply(multiply(sk_c5, sk_c7), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[674])).
% 0.63/0.67 tff(676,plain,
% 0.63/0.67 (sk_c8 = multiply(sk_c7, sk_c8)),
% 0.63/0.67 inference(transitivity,[status(thm)],[75, 626, 39, 633, 333, 455])).
% 0.63/0.67 tff(677,plain,
% 0.63/0.67 (multiply(sk_c5, sk_c8) = multiply(sk_c5, multiply(sk_c7, sk_c8))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[676])).
% 0.63/0.68 tff(678,plain,
% 0.63/0.68 (multiply(sk_c5, sk_c8) = multiply(sk_c8, sk_c8)),
% 0.63/0.68 inference(transitivity,[status(thm)],[677, 454, 675, 667, 637, 666, 587])).
% 0.63/0.68 tff(679,plain,
% 0.63/0.68 (multiply(sk_c7, multiply(sk_c5, sk_c8)) = multiply(sk_c7, multiply(sk_c8, sk_c8))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[678])).
% 0.63/0.68 tff(680,plain,
% 0.63/0.68 (multiply(sk_c7, multiply(sk_c8, sk_c8)) = multiply(sk_c7, multiply(sk_c5, sk_c8))),
% 0.63/0.68 inference(symmetry,[status(thm)],[679])).
% 0.63/0.68 tff(681,plain,
% 0.63/0.68 (multiply(sk_c8, sk_c8) = sk_c6),
% 0.63/0.68 inference(transitivity,[status(thm)],[588, 639, 638, 635, 500, 497, 680, 493, 665, 39, 633, 333])).
% 0.63/0.68 tff(682,plain,
% 0.63/0.68 ($false),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[681, 653])).
% 0.63/0.68 tff(683,plain,(multiply(sk_c8, sk_c3) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.63/0.68 tff(684,plain,
% 0.63/0.68 (sk_c7 = multiply(sk_c8, sk_c3)),
% 0.63/0.68 inference(symmetry,[status(thm)],[683])).
% 0.63/0.68 tff(685,plain,
% 0.63/0.68 (sk_c7 = sk_c8),
% 0.63/0.68 inference(transitivity,[status(thm)],[684, 567, 314, 311, 74])).
% 0.63/0.68 tff(686,plain,
% 0.63/0.68 (multiply(sk_c4, sk_c7) = multiply(sk_c4, sk_c8)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[685])).
% 0.63/0.68 tff(687,plain,
% 0.63/0.68 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.63/0.68 inference(transitivity,[status(thm)],[686, 585, 684, 567, 314, 311, 74])).
% 0.63/0.68 tff(688,plain,
% 0.63/0.68 (multiply(identity, multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[309, 687])).
% 0.63/0.68 tff(689,plain,
% 0.63/0.68 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c4), sk_c7) = multiply(identity, multiply(sk_c4, sk_c7)))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(690,plain,
% 0.63/0.68 (multiply(multiply(identity, sk_c4), sk_c7) = multiply(identity, multiply(sk_c4, sk_c7))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[689, 37])).
% 0.63/0.68 tff(691,plain,
% 0.63/0.68 (sk_c8 = sk_c7),
% 0.63/0.68 inference(transitivity,[status(thm)],[75, 310, 313, 549, 683])).
% 0.63/0.68 tff(692,plain,
% 0.63/0.68 (multiply(multiply(identity, sk_c4), sk_c8) = multiply(multiply(identity, sk_c4), sk_c7)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[691])).
% 0.63/0.68 tff(693,plain,
% 0.63/0.68 (multiply(multiply(identity, sk_c4), sk_c8) = sk_c7),
% 0.63/0.68 inference(transitivity,[status(thm)],[692, 690, 688, 313, 549, 683])).
% 0.63/0.68 tff(694,plain,
% 0.63/0.68 ((inverse(multiply(identity, sk_c4)) = sk_c8) <=> (inverse(multiply(identity, sk_c4)) = sk_c7)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[691])).
% 0.63/0.68 tff(695,plain,
% 0.63/0.68 ((inverse(multiply(identity, sk_c4)) = sk_c7) <=> (inverse(multiply(identity, sk_c4)) = sk_c8)),
% 0.63/0.68 inference(symmetry,[status(thm)],[694])).
% 0.63/0.68 tff(696,assumption,(~(inverse(sk_c4) = sk_c8)), introduced(assumption)).
% 0.63/0.68 tff(697,plain,
% 0.63/0.68 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(698,plain,
% 0.63/0.68 (((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(699,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_9')).
% 0.63/0.68 tff(700,plain,
% 0.63/0.68 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[699, 698])).
% 0.63/0.68 tff(701,plain,
% 0.63/0.68 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[700, 697])).
% 0.63/0.68 tff(702,plain,
% 0.63/0.68 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[701, 696])).
% 0.63/0.68 tff(703,plain,
% 0.63/0.68 (multiply(sk_c1, sk_c8) = multiply(sk_c1, sk_c7)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[691])).
% 0.63/0.68 tff(704,plain,
% 0.63/0.68 (multiply(sk_c1, sk_c8) = sk_c7),
% 0.63/0.68 inference(transitivity,[status(thm)],[703, 702, 75, 310, 313, 549, 683])).
% 0.63/0.68 tff(705,plain,
% 0.63/0.68 ((identity = multiply(sk_c7, sk_c8)) <=> (multiply(sk_c7, sk_c8) = identity)),
% 0.63/0.68 inference(commutativity,[status(thm)],[])).
% 0.63/0.68 tff(706,plain,
% 0.63/0.68 (multiply(sk_c6, sk_c7) = multiply(inverse(sk_c8), sk_c8)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[442, 685])).
% 0.63/0.68 tff(707,plain,
% 0.63/0.68 (multiply(sk_c6, sk_c7) = identity),
% 0.63/0.68 inference(transitivity,[status(thm)],[706, 80])).
% 0.63/0.68 tff(708,plain,
% 0.63/0.68 ((multiply(sk_c6, sk_c7) = sk_c6) <=> (identity = multiply(sk_c7, sk_c8))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[707, 455])).
% 0.63/0.68 tff(709,plain,
% 0.63/0.68 ((multiply(sk_c6, sk_c7) = sk_c6) <=> (multiply(sk_c7, sk_c8) = identity)),
% 0.63/0.68 inference(transitivity,[status(thm)],[708, 705])).
% 0.63/0.68 tff(710,plain,
% 0.63/0.68 ((multiply(sk_c7, sk_c8) = identity) <=> (multiply(sk_c6, sk_c7) = sk_c6)),
% 0.63/0.68 inference(symmetry,[status(thm)],[709])).
% 0.63/0.68 tff(711,plain,
% 0.63/0.68 ((sk_c7 = multiply(sk_c8, sk_c2)) <=> (multiply(sk_c8, sk_c2) = sk_c7)),
% 0.63/0.68 inference(commutativity,[status(thm)],[])).
% 0.63/0.68 tff(712,plain,
% 0.63/0.68 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(713,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_15')).
% 0.63/0.68 tff(714,plain,
% 0.63/0.68 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[713, 712])).
% 0.63/0.68 tff(715,plain,
% 0.63/0.68 (inverse(sk_c1) = sk_c7),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[714, 696])).
% 0.63/0.68 tff(716,plain,
% 0.63/0.68 (sk_c7 = inverse(sk_c1)),
% 0.63/0.68 inference(symmetry,[status(thm)],[715])).
% 0.63/0.68 tff(717,plain,
% 0.63/0.68 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[716])).
% 0.63/0.68 tff(718,plain,
% 0.63/0.68 (multiply(sk_c7, sk_c1) = multiply(sk_c8, sk_c2)),
% 0.63/0.68 inference(transitivity,[status(thm)],[717, 395, 308, 305])).
% 0.63/0.68 tff(719,plain,
% 0.63/0.68 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[718, 685])).
% 0.63/0.68 tff(720,plain,
% 0.63/0.68 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.63/0.68 inference(symmetry,[status(thm)],[702])).
% 0.63/0.68 tff(721,plain,
% 0.63/0.68 (multiply(sk_c7, sk_c8) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[720])).
% 0.63/0.68 tff(722,plain,
% 0.63/0.68 (multiply(sk_c7, sk_c8) = sk_c7),
% 0.63/0.68 inference(transitivity,[status(thm)],[721, 562, 719, 313, 549, 683])).
% 0.63/0.68 tff(723,plain,
% 0.63/0.68 ((multiply(sk_c7, sk_c8) = identity) <=> (sk_c7 = multiply(sk_c8, sk_c2))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[722, 309])).
% 0.63/0.68 tff(724,plain,
% 0.63/0.68 ((multiply(sk_c7, sk_c8) = identity) <=> (multiply(sk_c8, sk_c2) = sk_c7)),
% 0.63/0.68 inference(transitivity,[status(thm)],[723, 711])).
% 0.63/0.68 tff(725,plain,
% 0.63/0.68 ((multiply(sk_c8, sk_c2) = sk_c7) <=> (multiply(sk_c7, sk_c8) = identity)),
% 0.63/0.68 inference(symmetry,[status(thm)],[724])).
% 0.63/0.68 tff(726,plain,
% 0.63/0.68 ((multiply(sk_c8, sk_c2) = sk_c7) <=> (multiply(sk_c6, sk_c7) = sk_c6)),
% 0.63/0.68 inference(transitivity,[status(thm)],[725, 710])).
% 0.63/0.68 tff(727,plain,
% 0.63/0.68 (inverse(sk_c8) = sk_c7),
% 0.63/0.68 inference(transitivity,[status(thm)],[441, 455, 721, 562, 719, 313, 549, 683])).
% 0.63/0.68 tff(728,plain,
% 0.63/0.68 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, sk_c8)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[727])).
% 0.63/0.68 tff(729,plain,
% 0.63/0.68 (multiply(sk_c8, sk_c2) = sk_c7),
% 0.63/0.68 inference(transitivity,[status(thm)],[304, 307, 81, 728, 721, 562, 719, 313, 549, 683])).
% 0.63/0.68 tff(730,plain,
% 0.63/0.68 (multiply(sk_c6, sk_c7) = sk_c6),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[729, 726])).
% 0.63/0.68 tff(731,plain,
% 0.63/0.68 (multiply(sk_c6, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[442])).
% 0.63/0.68 tff(732,plain,
% 0.63/0.68 (multiply(sk_c6, sk_c8) = identity),
% 0.63/0.68 inference(transitivity,[status(thm)],[731, 80])).
% 0.63/0.68 tff(733,plain,
% 0.63/0.68 (inverse(sk_c1) = sk_c8),
% 0.63/0.68 inference(transitivity,[status(thm)],[715, 684, 567, 314, 311, 74])).
% 0.63/0.68 tff(734,plain,
% 0.63/0.68 ((inverse(sk_c6) = sk_c8) <=> (inverse(sk_c6) = sk_c7)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[691])).
% 0.63/0.68 tff(735,plain,
% 0.63/0.68 ((inverse(sk_c6) = sk_c7) <=> (inverse(sk_c6) = sk_c8)),
% 0.63/0.68 inference(symmetry,[status(thm)],[734])).
% 0.63/0.68 tff(736,plain,
% 0.63/0.68 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c2) = sk_c2)),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(737,plain,
% 0.63/0.68 (multiply(identity, sk_c2) = sk_c2),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[736, 72])).
% 0.63/0.68 tff(738,plain,
% 0.63/0.68 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = multiply(sk_c7, multiply(sk_c8, sk_c8))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[691])).
% 0.63/0.68 tff(739,plain,
% 0.63/0.68 (multiply(sk_c7, multiply(sk_c8, sk_c8)) = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.63/0.68 inference(symmetry,[status(thm)],[738])).
% 0.63/0.68 tff(740,plain,
% 0.63/0.68 (identity = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.63/0.68 inference(transitivity,[status(thm)],[81, 500, 497, 739])).
% 0.63/0.68 tff(741,plain,
% 0.63/0.68 (multiply(identity, sk_c2) = multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[740])).
% 0.63/0.68 tff(742,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2) = multiply(identity, sk_c2)),
% 0.63/0.68 inference(symmetry,[status(thm)],[741])).
% 0.63/0.68 tff(743,plain,
% 0.63/0.68 (multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c7) = multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c8)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[685])).
% 0.63/0.68 tff(744,plain,
% 0.63/0.68 (multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c8) = multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c7)),
% 0.63/0.68 inference(symmetry,[status(thm)],[743])).
% 0.63/0.68 tff(745,plain,
% 0.63/0.68 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c8) = multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), multiply(sk_c2, sk_c8)))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(746,plain,
% 0.63/0.68 (multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c8) = multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), multiply(sk_c2, sk_c8))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[745, 37])).
% 0.63/0.68 tff(747,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), multiply(sk_c2, sk_c8)) = multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c8)),
% 0.63/0.68 inference(symmetry,[status(thm)],[746])).
% 0.63/0.68 tff(748,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), multiply(sk_c2, sk_c8)) = multiply(multiply(multiply(sk_c8, sk_c8), sk_c8), sk_c3)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[475, 548])).
% 0.63/0.68 tff(749,plain,
% 0.63/0.68 (multiply(multiply(multiply(sk_c8, sk_c8), sk_c8), sk_c3) = multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), multiply(sk_c2, sk_c8))),
% 0.63/0.68 inference(symmetry,[status(thm)],[748])).
% 0.63/0.68 tff(750,plain,
% 0.63/0.68 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, sk_c8), sk_c8), sk_c3) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c8, sk_c3)))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(751,plain,
% 0.63/0.68 (multiply(multiply(multiply(sk_c8, sk_c8), sk_c8), sk_c3) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c8, sk_c3))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[750, 37])).
% 0.63/0.68 tff(752,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c8, sk_c3)) = multiply(multiply(multiply(sk_c8, sk_c8), sk_c8), sk_c3)),
% 0.63/0.68 inference(symmetry,[status(thm)],[751])).
% 0.63/0.68 tff(753,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c8, sk_c3)) = multiply(multiply(sk_c8, sk_c8), sk_c7)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[683])).
% 0.63/0.68 tff(754,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, sk_c8), sk_c7) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c8, sk_c3))),
% 0.63/0.68 inference(symmetry,[status(thm)],[753])).
% 0.63/0.68 tff(755,plain,
% 0.63/0.68 (multiply(sk_c8, multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c8, sk_c8), sk_c7)),
% 0.63/0.68 inference(symmetry,[status(thm)],[466])).
% 0.63/0.68 tff(756,plain,
% 0.63/0.68 (multiply(sk_c8, multiply(sk_c7, sk_c8)) = multiply(sk_c8, multiply(sk_c8, sk_c7))),
% 0.63/0.68 inference(symmetry,[status(thm)],[464])).
% 0.63/0.68 tff(757,plain,
% 0.63/0.68 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c7)),
% 0.63/0.68 inference(transitivity,[status(thm)],[738, 524, 499, 445, 141, 756, 755, 754, 752, 749, 747, 744])).
% 0.63/0.68 tff(758,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2) = multiply(multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c7), sk_c2)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[757])).
% 0.63/0.68 tff(759,plain,
% 0.63/0.68 (multiply(multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c7), sk_c2) = multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2)),
% 0.63/0.68 inference(symmetry,[status(thm)],[758])).
% 0.63/0.68 tff(760,plain,
% 0.63/0.68 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c7), sk_c2) = multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), multiply(sk_c7, sk_c2)))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(761,plain,
% 0.63/0.68 (multiply(multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c7), sk_c2) = multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), multiply(sk_c7, sk_c2))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[760, 37])).
% 0.63/0.68 tff(762,plain,
% 0.63/0.68 (multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), multiply(sk_c7, sk_c2)) = multiply(multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), sk_c7), sk_c2)),
% 0.63/0.68 inference(symmetry,[status(thm)],[761])).
% 0.63/0.68 tff(763,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2) = sk_c2),
% 0.63/0.68 inference(transitivity,[status(thm)],[742, 737])).
% 0.63/0.68 tff(764,plain,
% 0.63/0.68 (multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), multiply(sk_c7, sk_c2)) = multiply(sk_c2, multiply(sk_c7, sk_c2))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[763])).
% 0.63/0.68 tff(765,plain,
% 0.63/0.68 (multiply(sk_c2, multiply(sk_c7, sk_c2)) = multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c2), multiply(sk_c7, sk_c2))),
% 0.63/0.68 inference(symmetry,[status(thm)],[764])).
% 0.63/0.68 tff(766,plain,
% 0.63/0.68 (sk_c7 = inverse(sk_c2)),
% 0.63/0.68 inference(transitivity,[status(thm)],[684, 567, 314, 311, 74, 303])).
% 0.63/0.68 tff(767,plain,
% 0.63/0.68 (multiply(sk_c7, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[766])).
% 0.63/0.68 tff(768,plain,
% 0.63/0.68 (multiply(sk_c7, sk_c2) = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.63/0.68 inference(transitivity,[status(thm)],[767, 307, 81, 500, 497, 739])).
% 0.63/0.68 tff(769,plain,
% 0.63/0.68 (multiply(sk_c2, multiply(sk_c7, sk_c2)) = multiply(sk_c2, multiply(sk_c8, multiply(sk_c8, sk_c8)))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[768])).
% 0.63/0.68 tff(770,plain,
% 0.63/0.68 (multiply(sk_c2, multiply(sk_c8, multiply(sk_c8, sk_c8))) = multiply(sk_c2, multiply(sk_c7, sk_c2))),
% 0.63/0.68 inference(symmetry,[status(thm)],[769])).
% 0.63/0.68 tff(771,plain,
% 0.63/0.68 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c8), multiply(sk_c8, sk_c8)) = multiply(sk_c2, multiply(sk_c8, multiply(sk_c8, sk_c8))))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(772,plain,
% 0.63/0.68 (multiply(multiply(sk_c2, sk_c8), multiply(sk_c8, sk_c8)) = multiply(sk_c2, multiply(sk_c8, multiply(sk_c8, sk_c8)))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[771, 37])).
% 0.63/0.68 tff(773,plain,
% 0.63/0.68 (multiply(multiply(sk_c2, sk_c8), multiply(sk_c8, sk_c8)) = multiply(sk_c3, multiply(sk_c8, sk_c8))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[548])).
% 0.63/0.68 tff(774,plain,
% 0.63/0.68 (multiply(sk_c3, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c2, sk_c8), multiply(sk_c8, sk_c8))),
% 0.63/0.68 inference(symmetry,[status(thm)],[773])).
% 0.63/0.68 tff(775,plain,
% 0.63/0.68 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c8), sk_c8) = multiply(sk_c3, multiply(sk_c8, sk_c8)))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(776,plain,
% 0.63/0.68 (multiply(multiply(sk_c3, sk_c8), sk_c8) = multiply(sk_c3, multiply(sk_c8, sk_c8))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[775, 37])).
% 0.63/0.68 tff(777,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c3) = multiply(multiply(multiply(sk_c8, sk_c8), sk_c8), sk_c3)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[475])).
% 0.63/0.68 tff(778,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c3) = multiply(sk_c8, sk_c2)),
% 0.63/0.68 inference(transitivity,[status(thm)],[777, 751, 753, 466, 464, 191, 444, 80, 308, 305])).
% 0.63/0.68 tff(779,plain,
% 0.63/0.68 (multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c3), sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[778])).
% 0.63/0.68 tff(780,plain,
% 0.63/0.68 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c3), sk_c8) = multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), multiply(sk_c3, sk_c8)))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(781,plain,
% 0.63/0.68 (multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c3), sk_c8) = multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), multiply(sk_c3, sk_c8))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[780, 37])).
% 0.63/0.68 tff(782,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), multiply(sk_c3, sk_c8)) = multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c3), sk_c8)),
% 0.63/0.68 inference(symmetry,[status(thm)],[781])).
% 0.63/0.68 tff(783,plain,
% 0.63/0.68 (multiply(sk_c3, sk_c8) = multiply(multiply(sk_c2, sk_c8), sk_c8)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[647])).
% 0.63/0.68 tff(784,plain,
% 0.63/0.68 (multiply(multiply(sk_c2, sk_c8), sk_c8) = multiply(sk_c3, sk_c8)),
% 0.63/0.68 inference(symmetry,[status(thm)],[783])).
% 0.63/0.68 tff(785,plain,
% 0.63/0.68 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c8), sk_c8) = multiply(sk_c2, multiply(sk_c8, sk_c8)))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(786,plain,
% 0.63/0.68 (multiply(multiply(sk_c2, sk_c8), sk_c8) = multiply(sk_c2, multiply(sk_c8, sk_c8))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[785, 37])).
% 0.63/0.68 tff(787,plain,
% 0.63/0.68 (multiply(sk_c2, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c2, sk_c8), sk_c8)),
% 0.63/0.68 inference(symmetry,[status(thm)],[786])).
% 0.63/0.68 tff(788,plain,
% 0.63/0.68 (multiply(sk_c2, multiply(sk_c8, sk_c8)) = multiply(sk_c3, sk_c8)),
% 0.63/0.68 inference(transitivity,[status(thm)],[787, 784])).
% 0.63/0.68 tff(789,plain,
% 0.63/0.68 (multiply(identity, multiply(sk_c2, multiply(sk_c8, sk_c8))) = multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), multiply(sk_c3, sk_c8))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[740, 788])).
% 0.63/0.68 tff(790,plain,
% 0.63/0.68 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c2, multiply(sk_c8, sk_c8))) = multiply(sk_c2, multiply(sk_c8, sk_c8)))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(791,plain,
% 0.63/0.68 (multiply(identity, multiply(sk_c2, multiply(sk_c8, sk_c8))) = multiply(sk_c2, multiply(sk_c8, sk_c8))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[790, 72])).
% 0.63/0.68 tff(792,plain,
% 0.63/0.68 (multiply(sk_c2, multiply(sk_c8, sk_c8)) = multiply(identity, multiply(sk_c2, multiply(sk_c8, sk_c8)))),
% 0.63/0.68 inference(symmetry,[status(thm)],[791])).
% 0.63/0.68 tff(793,plain,
% 0.63/0.68 (multiply(sk_c3, sk_c8) = sk_c7),
% 0.63/0.68 inference(transitivity,[status(thm)],[783, 786, 792, 789, 782, 779, 313, 549, 683])).
% 0.63/0.68 tff(794,plain,
% 0.63/0.68 (multiply(multiply(sk_c3, sk_c8), sk_c8) = multiply(sk_c7, sk_c8)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[793])).
% 0.63/0.68 tff(795,plain,
% 0.63/0.68 (multiply(sk_c7, sk_c8) = multiply(multiply(sk_c3, sk_c8), sk_c8)),
% 0.63/0.68 inference(symmetry,[status(thm)],[794])).
% 0.63/0.68 tff(796,plain,
% 0.63/0.68 (sk_c6 = sk_c2),
% 0.63/0.68 inference(transitivity,[status(thm)],[455, 795, 776, 774, 772, 770, 765, 762, 759, 742, 737])).
% 0.63/0.68 tff(797,plain,
% 0.63/0.68 (inverse(sk_c6) = inverse(sk_c2)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[796])).
% 0.63/0.68 tff(798,plain,
% 0.63/0.68 (inverse(sk_c6) = sk_c7),
% 0.63/0.68 inference(transitivity,[status(thm)],[797, 302, 75, 310, 313, 549, 683])).
% 0.63/0.68 tff(799,plain,
% 0.63/0.68 (inverse(sk_c6) = sk_c8),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[798, 735])).
% 0.63/0.68 tff(800,plain,
% 0.63/0.68 (multiply(sk_c8, sk_c6) = multiply(sk_c8, sk_c2)),
% 0.63/0.68 inference(transitivity,[status(thm)],[614, 191, 444, 80, 308, 305])).
% 0.63/0.68 tff(801,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, sk_c6), sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[800])).
% 0.63/0.68 tff(802,plain,
% 0.63/0.68 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c6), sk_c8) = multiply(sk_c8, multiply(sk_c6, sk_c8)))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(803,plain,
% 0.63/0.68 (multiply(multiply(sk_c8, sk_c6), sk_c8) = multiply(sk_c8, multiply(sk_c6, sk_c8))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[802, 37])).
% 0.63/0.68 tff(804,plain,
% 0.63/0.68 (multiply(sk_c8, multiply(sk_c6, sk_c8)) = multiply(multiply(sk_c8, sk_c6), sk_c8)),
% 0.63/0.68 inference(symmetry,[status(thm)],[803])).
% 0.63/0.68 tff(805,plain,
% 0.63/0.68 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c6, sk_c8)),
% 0.63/0.68 inference(symmetry,[status(thm)],[731])).
% 0.63/0.68 tff(806,plain,
% 0.63/0.68 (identity = multiply(sk_c6, sk_c8)),
% 0.63/0.68 inference(transitivity,[status(thm)],[81, 805])).
% 0.63/0.68 tff(807,plain,
% 0.63/0.68 (multiply(sk_c8, identity) = multiply(sk_c8, multiply(sk_c6, sk_c8))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[806])).
% 0.63/0.68 tff(808,plain,
% 0.63/0.68 (multiply(sk_c8, identity) = sk_c7),
% 0.63/0.68 inference(transitivity,[status(thm)],[807, 804, 801, 313, 549, 683])).
% 0.63/0.68 tff(809,plain,
% 0.63/0.68 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(810,plain,
% 0.63/0.69 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(811,plain,
% 0.63/0.69 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6))))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[810])).
% 0.63/0.69 tff(812,plain,
% 0.63/0.69 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6)))),
% 0.63/0.69 inference(transitivity,[status(thm)],[811, 809])).
% 0.63/0.69 tff(813,plain,
% 0.63/0.69 ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(814,plain,
% 0.63/0.69 ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[813, 812])).
% 0.63/0.69 tff(815,plain,
% 0.63/0.69 ((~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c6))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[814, 157, 333, 441, 702, 715, 293, 808, 798, 799, 733, 732])).
% 0.63/0.69 tff(816,plain,
% 0.63/0.69 ($false),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[815, 730, 704])).
% 0.63/0.69 tff(817,plain,(inverse(sk_c4) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.63/0.69 tff(818,plain,
% 0.63/0.69 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c4) = sk_c4)),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(819,plain,
% 0.63/0.69 (multiply(identity, sk_c4) = sk_c4),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[818, 72])).
% 0.63/0.69 tff(820,plain,
% 0.63/0.69 (inverse(multiply(identity, sk_c4)) = inverse(sk_c4)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[819])).
% 0.63/0.69 tff(821,plain,
% 0.63/0.69 (inverse(multiply(identity, sk_c4)) = sk_c7),
% 0.63/0.69 inference(transitivity,[status(thm)],[820, 817, 75, 310, 313, 549, 683])).
% 0.63/0.69 tff(822,plain,
% 0.63/0.69 (inverse(multiply(identity, sk_c4)) = sk_c8),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[821, 695])).
% 0.63/0.69 tff(823,plain,
% 0.63/0.69 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(multiply(identity, sk_c4)), multiply(identity, sk_c4)) = identity)),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(824,plain,
% 0.63/0.69 (multiply(inverse(multiply(identity, sk_c4)), multiply(identity, sk_c4)) = identity),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[823, 60])).
% 0.63/0.69 tff(825,plain,
% 0.63/0.69 (inverse(sk_c4) = inverse(multiply(identity, sk_c4))),
% 0.63/0.69 inference(symmetry,[status(thm)],[820])).
% 0.63/0.69 tff(826,plain,
% 0.63/0.69 (sk_c8 = inverse(sk_c4)),
% 0.63/0.69 inference(symmetry,[status(thm)],[817])).
% 0.63/0.69 tff(827,plain,
% 0.63/0.69 (sk_c7 = inverse(multiply(identity, sk_c4))),
% 0.63/0.69 inference(transitivity,[status(thm)],[684, 567, 314, 311, 74, 826, 825])).
% 0.63/0.69 tff(828,plain,
% 0.63/0.69 (multiply(sk_c7, multiply(identity, sk_c4)) = multiply(inverse(multiply(identity, sk_c4)), multiply(identity, sk_c4))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[827])).
% 0.63/0.69 tff(829,plain,
% 0.63/0.69 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, identity), sk_c4) = multiply(sk_c7, multiply(identity, sk_c4)))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(830,plain,
% 0.63/0.69 (multiply(multiply(sk_c7, identity), sk_c4) = multiply(sk_c7, multiply(identity, sk_c4))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[829, 37])).
% 0.63/0.69 tff(831,plain,
% 0.63/0.69 (multiply(sk_c7, identity) = multiply(sk_c8, identity)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[685])).
% 0.63/0.69 tff(832,plain,
% 0.63/0.69 (multiply(sk_c8, identity) = multiply(sk_c7, identity)),
% 0.63/0.69 inference(symmetry,[status(thm)],[831])).
% 0.63/0.69 tff(833,plain,
% 0.63/0.69 (multiply(sk_c8, multiply(sk_c6, sk_c8)) = multiply(sk_c8, identity)),
% 0.63/0.69 inference(symmetry,[status(thm)],[807])).
% 0.63/0.69 tff(834,plain,
% 0.63/0.69 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(multiply(sk_c8, sk_c6), sk_c8)),
% 0.63/0.69 inference(symmetry,[status(thm)],[801])).
% 0.63/0.69 tff(835,plain,
% 0.63/0.69 (sk_c8 = multiply(sk_c7, identity)),
% 0.63/0.69 inference(transitivity,[status(thm)],[75, 310, 834, 803, 833, 832])).
% 0.63/0.69 tff(836,plain,
% 0.63/0.69 (multiply(sk_c8, sk_c4) = multiply(multiply(sk_c7, identity), sk_c4)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[835])).
% 0.63/0.69 tff(837,plain,
% 0.63/0.69 (multiply(sk_c2, multiply(sk_c8, sk_c8)) = sk_c8),
% 0.63/0.69 inference(transitivity,[status(thm)],[792, 789, 782, 779, 311, 74])).
% 0.63/0.69 tff(838,plain,
% 0.63/0.69 (multiply(multiply(sk_c2, multiply(sk_c8, sk_c8)), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[837])).
% 0.63/0.69 tff(839,plain,
% 0.63/0.69 (multiply(multiply(sk_c2, multiply(sk_c8, sk_c8)), sk_c4) = multiply(sk_c8, sk_c2)),
% 0.63/0.69 inference(transitivity,[status(thm)],[838, 836, 830, 828, 824, 308, 305])).
% 0.63/0.69 tff(840,plain,
% 0.63/0.69 (multiply(multiply(multiply(sk_c2, multiply(sk_c8, sk_c8)), sk_c4), sk_c7) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[839, 685])).
% 0.63/0.69 tff(841,plain,
% 0.63/0.69 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c2, multiply(sk_c8, sk_c8)), sk_c4), sk_c7) = multiply(multiply(sk_c2, multiply(sk_c8, sk_c8)), multiply(sk_c4, sk_c7)))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(842,plain,
% 0.63/0.69 (multiply(multiply(multiply(sk_c2, multiply(sk_c8, sk_c8)), sk_c4), sk_c7) = multiply(multiply(sk_c2, multiply(sk_c8, sk_c8)), multiply(sk_c4, sk_c7))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[841, 37])).
% 0.63/0.69 tff(843,plain,
% 0.63/0.69 (multiply(multiply(sk_c2, multiply(sk_c8, sk_c8)), multiply(sk_c4, sk_c7)) = multiply(multiply(multiply(sk_c2, multiply(sk_c8, sk_c8)), sk_c4), sk_c7)),
% 0.63/0.69 inference(symmetry,[status(thm)],[842])).
% 0.63/0.69 tff(844,plain,
% 0.63/0.69 (multiply(sk_c4, sk_c8) = multiply(sk_c4, sk_c7)),
% 0.63/0.69 inference(symmetry,[status(thm)],[686])).
% 0.63/0.69 tff(845,plain,
% 0.63/0.69 (sk_c8 = multiply(sk_c4, sk_c7)),
% 0.63/0.69 inference(transitivity,[status(thm)],[75, 310, 313, 549, 683, 631, 844])).
% 0.63/0.69 tff(846,plain,
% 0.63/0.69 (multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), multiply(sk_c3, sk_c8)) = multiply(identity, multiply(sk_c2, multiply(sk_c8, sk_c8)))),
% 0.63/0.69 inference(symmetry,[status(thm)],[789])).
% 0.63/0.69 tff(847,plain,
% 0.63/0.69 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(multiply(multiply(sk_c8, multiply(sk_c8, sk_c8)), sk_c3), sk_c8)),
% 0.63/0.69 inference(symmetry,[status(thm)],[779])).
% 0.63/0.69 tff(848,plain,
% 0.63/0.69 (sk_c7 = multiply(sk_c2, multiply(sk_c8, sk_c8))),
% 0.63/0.69 inference(transitivity,[status(thm)],[684, 567, 314, 847, 781, 846, 791])).
% 0.63/0.69 tff(849,plain,
% 0.63/0.69 (multiply(sk_c7, sk_c8) = multiply(multiply(sk_c2, multiply(sk_c8, sk_c8)), multiply(sk_c4, sk_c7))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[848, 845])).
% 0.63/0.69 tff(850,plain,
% 0.63/0.69 (multiply(sk_c7, sk_c8) = sk_c7),
% 0.63/0.69 inference(transitivity,[status(thm)],[849, 843, 840, 313, 549, 683])).
% 0.63/0.69 tff(851,plain,
% 0.63/0.69 ((multiply(sk_c7, sk_c8) = identity) <=> (sk_c7 = multiply(sk_c8, sk_c2))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[850, 309])).
% 0.63/0.69 tff(852,plain,
% 0.63/0.69 ((multiply(sk_c7, sk_c8) = identity) <=> (multiply(sk_c8, sk_c2) = sk_c7)),
% 0.63/0.69 inference(transitivity,[status(thm)],[851, 711])).
% 0.63/0.69 tff(853,plain,
% 0.63/0.69 ((multiply(sk_c8, sk_c2) = sk_c7) <=> (multiply(sk_c7, sk_c8) = identity)),
% 0.63/0.69 inference(symmetry,[status(thm)],[852])).
% 0.63/0.69 tff(854,plain,
% 0.63/0.69 ((multiply(sk_c8, sk_c2) = sk_c7) <=> (multiply(sk_c6, sk_c7) = sk_c6)),
% 0.63/0.69 inference(transitivity,[status(thm)],[853, 710])).
% 0.63/0.69 tff(855,plain,
% 0.63/0.69 (multiply(sk_c8, sk_c8) = multiply(sk_c7, sk_c8)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[691])).
% 0.63/0.69 tff(856,plain,
% 0.63/0.69 (multiply(multiply(identity, sk_c8), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[74])).
% 0.63/0.69 tff(857,plain,
% 0.63/0.69 (multiply(sk_c8, sk_c4) = identity),
% 0.63/0.69 inference(transitivity,[status(thm)],[836, 830, 828, 824])).
% 0.63/0.69 tff(858,plain,
% 0.63/0.69 (multiply(multiply(sk_c8, sk_c4), multiply(sk_c8, sk_c8)) = multiply(identity, multiply(sk_c8, sk_c8))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[857])).
% 0.63/0.69 tff(859,plain,
% 0.63/0.69 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[585])).
% 0.63/0.69 tff(860,plain,
% 0.63/0.69 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.63/0.69 inference(symmetry,[status(thm)],[859])).
% 0.63/0.69 tff(861,plain,
% 0.63/0.69 (inverse(sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.63/0.69 inference(transitivity,[status(thm)],[441, 334, 860, 134])).
% 0.63/0.69 tff(862,plain,
% 0.63/0.69 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(multiply(sk_c8, sk_c4), sk_c8), sk_c8)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[861])).
% 0.63/0.69 tff(863,plain,
% 0.63/0.69 (multiply(sk_c8, sk_c2) = sk_c7),
% 0.63/0.69 inference(transitivity,[status(thm)],[304, 307, 81, 862, 637, 858, 354, 856, 855, 849, 843, 840, 313, 549, 683])).
% 0.63/0.69 tff(864,plain,
% 0.63/0.69 (multiply(sk_c6, sk_c7) = sk_c6),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[863, 854])).
% 0.63/0.69 tff(865,plain,
% 0.63/0.69 (multiply(multiply(identity, sk_c4), sk_c7) = sk_c8),
% 0.63/0.69 inference(transitivity,[status(thm)],[690, 688, 311, 74])).
% 0.63/0.69 tff(866,plain,
% 0.63/0.69 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(multiply(identity, sk_c4)) = sk_c7)) | (~(inverse(multiply(identity, sk_c4)) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c7) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c8) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(multiply(identity, sk_c4)) = sk_c7)) | (~(inverse(multiply(identity, sk_c4)) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c7) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c8) = sk_c7)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(867,plain,
% 0.63/0.69 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(multiply(identity, sk_c4)) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c8) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(multiply(identity, sk_c4)) = sk_c7)) | (~(multiply(multiply(identity, sk_c4), sk_c7) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(multiply(identity, sk_c4)) = sk_c7)) | (~(inverse(multiply(identity, sk_c4)) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c7) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c8) = sk_c7)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(868,plain,
% 0.63/0.69 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(multiply(identity, sk_c4)) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c8) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(multiply(identity, sk_c4)) = sk_c7)) | (~(multiply(multiply(identity, sk_c4), sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(multiply(identity, sk_c4)) = sk_c7)) | (~(inverse(multiply(identity, sk_c4)) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c7) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c8) = sk_c7))))),
% 0.63/0.70 inference(monotonicity,[status(thm)],[867])).
% 0.63/0.70 tff(869,plain,
% 0.63/0.70 (((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(multiply(identity, sk_c4)) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c8) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(multiply(identity, sk_c4)) = sk_c7)) | (~(multiply(multiply(identity, sk_c4), sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(multiply(identity, sk_c4)) = sk_c7)) | (~(inverse(multiply(identity, sk_c4)) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c7) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c8) = sk_c7)))),
% 0.63/0.70 inference(transitivity,[status(thm)],[868, 866])).
% 0.63/0.70 tff(870,plain,
% 0.63/0.70 ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(multiply(identity, sk_c4)) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c8) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(multiply(identity, sk_c4)) = sk_c7)) | (~(multiply(multiply(identity, sk_c4), sk_c7) = sk_c8)))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(871,plain,
% 0.63/0.70 ((~![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c7)) | (~(multiply(X2, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, identity) = sk_c7)) | (~(inverse(sk_c6) = sk_c7)) | (~(inverse(sk_c6) = sk_c8)) | (~(multiply(sk_c6, sk_c8) = identity)) | (~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(multiply(identity, sk_c4)) = sk_c7)) | (~(inverse(multiply(identity, sk_c4)) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c7) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c8) = sk_c7))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[870, 869])).
% 0.63/0.70 tff(872,plain,
% 0.63/0.70 ((~(multiply(sk_c6, sk_c7) = sk_c6)) | (~(inverse(multiply(identity, sk_c4)) = sk_c7)) | (~(inverse(multiply(identity, sk_c4)) = sk_c8)) | (~(multiply(multiply(identity, sk_c4), sk_c8) = sk_c7))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[871, 157, 333, 441, 293, 808, 798, 799, 865, 732])).
% 0.63/0.70 tff(873,plain,
% 0.63/0.70 ($false),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[872, 864, 821, 822, 693])).
% 0.63/0.70 % SZS output end Proof
%------------------------------------------------------------------------------