TSTP Solution File: GRP288-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP288-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 22:27:02 EDT 2022
% Result : Unsatisfiable 0.21s 0.52s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP288-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 31 16:10:50 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 0.21/0.52 % SZS status Unsatisfiable
% 0.21/0.52 % SZS output start Proof
% 0.21/0.52 tff(sk_c7_type, type, (
% 0.21/0.52 sk_c7: $i)).
% 0.21/0.52 tff(multiply_type, type, (
% 0.21/0.52 multiply: ( $i * $i ) > $i)).
% 0.21/0.52 tff(sk_c6_type, type, (
% 0.21/0.52 sk_c6: $i)).
% 0.21/0.52 tff(sk_c2_type, type, (
% 0.21/0.52 sk_c2: $i)).
% 0.21/0.52 tff(identity_type, type, (
% 0.21/0.52 identity: $i)).
% 0.21/0.52 tff(sk_c1_type, type, (
% 0.21/0.52 sk_c1: $i)).
% 0.21/0.52 tff(inverse_type, type, (
% 0.21/0.52 inverse: $i > $i)).
% 0.21/0.52 tff(sk_c4_type, type, (
% 0.21/0.52 sk_c4: $i)).
% 0.21/0.52 tff(sk_c3_type, type, (
% 0.21/0.52 sk_c3: $i)).
% 0.21/0.52 tff(sk_c5_type, type, (
% 0.21/0.52 sk_c5: $i)).
% 0.21/0.52 tff(1,plain,
% 0.21/0.52 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(2,plain,
% 0.21/0.52 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.52 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.52 tff(3,plain,
% 0.21/0.52 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(4,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.21/0.52 tff(5,plain,
% 0.21/0.52 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.52 tff(6,plain,(
% 0.21/0.52 ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.52 inference(skolemize,[status(sab)],[5])).
% 0.21/0.52 tff(7,plain,
% 0.21/0.52 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.52 tff(8,plain,
% 0.21/0.52 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(9,plain,
% 0.21/0.52 (multiply(identity, sk_c7) = sk_c7),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.52 tff(10,plain,
% 0.21/0.52 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c6) = sk_c6)),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(11,plain,
% 0.21/0.52 (multiply(identity, sk_c6) = sk_c6),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.21/0.52 tff(12,assumption,(~(inverse(sk_c4) = sk_c6)), introduced(assumption)).
% 0.21/0.52 tff(13,plain,
% 0.21/0.52 (((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)) <=> ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(14,axiom,((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_5')).
% 0.21/0.52 tff(15,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.52 tff(16,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.21/0.52 tff(17,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.21/0.52 tff(18,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.21/0.52 tff(19,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.21/0.52 tff(20,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.21/0.52 tff(21,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.52 tff(22,plain,
% 0.21/0.52 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.21/0.52 tff(23,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c6) = sk_c5),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[22, 12])).
% 0.21/0.52 tff(24,plain,
% 0.21/0.52 (((inverse(sk_c4) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c6)) <=> ((inverse(sk_c4) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(25,plain,
% 0.21/0.52 (((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c4) = sk_c6)) <=> ((inverse(sk_c4) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(26,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_10')).
% 0.21/0.52 tff(27,plain,
% 0.21/0.52 ((inverse(sk_c4) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.52 tff(28,plain,
% 0.21/0.52 ((inverse(sk_c4) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.21/0.52 tff(29,plain,
% 0.21/0.52 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[28, 12])).
% 0.21/0.52 tff(30,plain,
% 0.21/0.52 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[29])).
% 0.21/0.52 tff(31,plain,
% 0.21/0.52 (^[Z: $i, Y: $i, X: $i] : refl((multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(32,plain,
% 0.21/0.52 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.52 tff(33,plain,
% 0.21/0.52 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(34,axiom,(![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','associativity')).
% 0.21/0.52 tff(35,plain,
% 0.21/0.52 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.52 tff(36,plain,(
% 0.21/0.52 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[35])).
% 0.21/0.52 tff(37,plain,
% 0.21/0.52 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.21/0.52 tff(38,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(39,plain,
% 0.21/0.52 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.52 tff(40,plain,
% 0.21/0.52 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c6)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c6))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(41,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_15')).
% 0.21/0.52 tff(42,plain,
% 0.21/0.52 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.52 tff(43,plain,
% 0.21/0.52 (inverse(sk_c1) = sk_c7),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[42, 12])).
% 0.21/0.52 tff(44,plain,
% 0.21/0.52 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.52 tff(45,plain,
% 0.21/0.52 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(46,plain,
% 0.21/0.52 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.52 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.52 tff(47,plain,
% 0.21/0.52 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(48,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.21/0.52 tff(49,plain,
% 0.21/0.52 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.52 tff(50,plain,(
% 0.21/0.52 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.52 inference(skolemize,[status(sab)],[49])).
% 0.21/0.52 tff(51,plain,
% 0.21/0.52 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.52 tff(52,plain,
% 0.21/0.52 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(53,plain,
% 0.21/0.52 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.21/0.52 tff(54,plain,
% 0.21/0.52 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.52 inference(symmetry,[status(thm)],[53])).
% 0.21/0.52 tff(55,plain,
% 0.21/0.52 (identity = multiply(sk_c7, sk_c1)),
% 0.21/0.52 inference(transitivity,[status(thm)],[54, 44])).
% 0.21/0.52 tff(56,plain,
% 0.21/0.52 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.52 tff(57,plain,
% 0.21/0.52 (sk_c7 = multiply(identity, sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[9])).
% 0.21/0.52 tff(58,plain,
% 0.21/0.52 (sk_c7 = sk_c5),
% 0.21/0.52 inference(transitivity,[status(thm)],[57, 56, 39, 30, 23])).
% 0.21/0.52 tff(59,plain,
% 0.21/0.52 ((multiply(sk_c1, sk_c6) = sk_c7) <=> (multiply(sk_c1, sk_c6) = sk_c5)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.52 tff(60,plain,
% 0.21/0.52 ((~(multiply(sk_c1, sk_c6) = sk_c7)) <=> (~(multiply(sk_c1, sk_c6) = sk_c5))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[59])).
% 0.21/0.52 tff(61,plain,
% 0.21/0.52 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(62,plain,
% 0.21/0.52 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[61, 51])).
% 0.21/0.52 tff(63,plain,
% 0.21/0.52 (((inverse(sk_c2) = sk_c6) | (inverse(sk_c4) = sk_c6)) <=> ((inverse(sk_c2) = sk_c6) | (inverse(sk_c4) = sk_c6))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(64,axiom,((inverse(sk_c2) = sk_c6) | (inverse(sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_25')).
% 0.21/0.52 tff(65,plain,
% 0.21/0.52 ((inverse(sk_c2) = sk_c6) | (inverse(sk_c4) = sk_c6)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.52 tff(66,plain,
% 0.21/0.52 (inverse(sk_c2) = sk_c6),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[65, 12])).
% 0.21/0.52 tff(67,plain,
% 0.21/0.52 (sk_c6 = inverse(sk_c2)),
% 0.21/0.52 inference(symmetry,[status(thm)],[66])).
% 0.21/0.52 tff(68,plain,
% 0.21/0.52 (multiply(sk_c6, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.52 tff(69,plain,
% 0.21/0.52 (multiply(sk_c6, sk_c2) = multiply(sk_c7, sk_c1)),
% 0.21/0.52 inference(transitivity,[status(thm)],[68, 62, 54, 44])).
% 0.21/0.52 tff(70,plain,
% 0.21/0.52 (multiply(multiply(sk_c6, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.52 tff(71,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c2), sk_c7) = multiply(sk_c6, multiply(sk_c2, sk_c7)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(72,plain,
% 0.21/0.52 (multiply(multiply(sk_c6, sk_c2), sk_c7) = multiply(sk_c6, multiply(sk_c2, sk_c7))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[71, 37])).
% 0.21/0.52 tff(73,plain,
% 0.21/0.52 (multiply(sk_c6, multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c6, sk_c2), sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[72])).
% 0.21/0.52 tff(74,plain,
% 0.21/0.52 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[56])).
% 0.21/0.52 tff(75,plain,
% 0.21/0.52 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.52 inference(symmetry,[status(thm)],[39])).
% 0.21/0.52 tff(76,plain,
% 0.21/0.52 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.52 inference(symmetry,[status(thm)],[30])).
% 0.21/0.52 tff(77,plain,
% 0.21/0.52 (sk_c5 = multiply(sk_c7, sk_c6)),
% 0.21/0.52 inference(symmetry,[status(thm)],[23])).
% 0.21/0.52 tff(78,plain,
% 0.21/0.52 (((inverse(sk_c4) = sk_c6) | (multiply(sk_c2, sk_c6) = sk_c5)) <=> ((inverse(sk_c4) = sk_c6) | (multiply(sk_c2, sk_c6) = sk_c5))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(79,plain,
% 0.21/0.52 (((multiply(sk_c2, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)) <=> ((inverse(sk_c4) = sk_c6) | (multiply(sk_c2, sk_c6) = sk_c5))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(80,axiom,((multiply(sk_c2, sk_c6) = sk_c5) | (inverse(sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_20')).
% 0.21/0.52 tff(81,plain,
% 0.21/0.52 ((inverse(sk_c4) = sk_c6) | (multiply(sk_c2, sk_c6) = sk_c5)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.52 tff(82,plain,
% 0.21/0.52 ((inverse(sk_c4) = sk_c6) | (multiply(sk_c2, sk_c6) = sk_c5)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.21/0.52 tff(83,plain,
% 0.21/0.52 (multiply(sk_c2, sk_c6) = sk_c5),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[82, 12])).
% 0.21/0.52 tff(84,plain,
% 0.21/0.52 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.21/0.52 inference(transitivity,[status(thm)],[83, 77, 76, 75, 74, 9])).
% 0.21/0.52 tff(85,plain,
% 0.21/0.52 (multiply(sk_c2, multiply(sk_c2, sk_c6)) = multiply(sk_c2, sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.52 tff(86,plain,
% 0.21/0.52 (sk_c5 = sk_c7),
% 0.21/0.52 inference(transitivity,[status(thm)],[77, 76, 75, 74, 9])).
% 0.21/0.52 tff(87,plain,
% 0.21/0.52 (multiply(sk_c5, sk_c6) = multiply(sk_c7, sk_c6)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[86])).
% 0.21/0.52 tff(88,plain,
% 0.21/0.52 (multiply(sk_c5, sk_c6) = sk_c7),
% 0.21/0.52 inference(transitivity,[status(thm)],[87, 76, 75, 74, 9])).
% 0.21/0.52 tff(89,plain,
% 0.21/0.52 (multiply(sk_c1, multiply(sk_c5, sk_c6)) = multiply(sk_c1, sk_c7)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[88])).
% 0.21/0.52 tff(90,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c5), sk_c6) = multiply(sk_c1, multiply(sk_c5, sk_c6)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(91,plain,
% 0.21/0.53 (multiply(multiply(sk_c1, sk_c5), sk_c6) = multiply(sk_c1, multiply(sk_c5, sk_c6))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[90, 37])).
% 0.21/0.53 tff(92,plain,
% 0.21/0.53 (multiply(sk_c1, sk_c5) = multiply(sk_c1, sk_c7)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[86])).
% 0.21/0.53 tff(93,plain,
% 0.21/0.53 (multiply(sk_c1, sk_c7) = multiply(sk_c1, sk_c5)),
% 0.21/0.53 inference(symmetry,[status(thm)],[92])).
% 0.21/0.53 tff(94,plain,
% 0.21/0.53 (sk_c6 = multiply(sk_c1, sk_c7)),
% 0.21/0.53 inference(symmetry,[status(thm)],[29])).
% 0.21/0.53 tff(95,plain,
% 0.21/0.53 (sk_c6 = multiply(sk_c1, sk_c5)),
% 0.21/0.53 inference(transitivity,[status(thm)],[94, 93])).
% 0.21/0.53 tff(96,plain,
% 0.21/0.53 (multiply(sk_c6, sk_c6) = multiply(multiply(sk_c1, sk_c5), sk_c6)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[95])).
% 0.21/0.53 tff(97,plain,
% 0.21/0.53 (multiply(sk_c6, sk_c6) = sk_c6),
% 0.21/0.53 inference(transitivity,[status(thm)],[96, 91, 89, 29])).
% 0.21/0.53 tff(98,plain,
% 0.21/0.53 (multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c2, sk_c6))) = multiply(sk_c6, multiply(sk_c2, sk_c7))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[97, 85])).
% 0.21/0.53 tff(99,plain,
% 0.21/0.53 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c2, sk_c6))) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6)))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(100,plain,
% 0.21/0.53 (multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c2, sk_c6))) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[99, 37])).
% 0.21/0.53 tff(101,plain,
% 0.21/0.53 (multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6)))) = multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c2, sk_c6)))),
% 0.21/0.53 inference(symmetry,[status(thm)],[100])).
% 0.21/0.53 tff(102,plain,
% 0.21/0.53 (multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6))) = multiply(sk_c6, multiply(sk_c2, sk_c7))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[85])).
% 0.21/0.53 tff(103,plain,
% 0.21/0.53 (multiply(sk_c6, multiply(sk_c2, sk_c7)) = multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6)))),
% 0.21/0.53 inference(symmetry,[status(thm)],[102])).
% 0.21/0.53 tff(104,plain,
% 0.21/0.53 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c6, sk_c2), sk_c7)),
% 0.21/0.53 inference(symmetry,[status(thm)],[70])).
% 0.21/0.53 tff(105,plain,
% 0.21/0.53 (sk_c7 = multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[57, 56, 104, 72, 103])).
% 0.21/0.53 tff(106,plain,
% 0.21/0.53 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[105])).
% 0.21/0.53 tff(107,plain,
% 0.21/0.53 (multiply(sk_c6, multiply(sk_c2, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.53 tff(108,plain,
% 0.21/0.53 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c2), sk_c6) = multiply(sk_c6, multiply(sk_c2, sk_c6)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(109,plain,
% 0.21/0.53 (multiply(multiply(sk_c6, sk_c2), sk_c6) = multiply(sk_c6, multiply(sk_c2, sk_c6))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[108, 37])).
% 0.21/0.53 tff(110,plain,
% 0.21/0.53 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c6, sk_c2)),
% 0.21/0.53 inference(symmetry,[status(thm)],[68])).
% 0.21/0.53 tff(111,plain,
% 0.21/0.53 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.53 inference(symmetry,[status(thm)],[62])).
% 0.21/0.53 tff(112,plain,
% 0.21/0.53 (identity = multiply(sk_c6, sk_c2)),
% 0.21/0.53 inference(transitivity,[status(thm)],[111, 110])).
% 0.21/0.53 tff(113,plain,
% 0.21/0.53 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c2), sk_c6)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[112])).
% 0.21/0.53 tff(114,plain,
% 0.21/0.53 (sk_c6 = multiply(identity, sk_c6)),
% 0.21/0.53 inference(symmetry,[status(thm)],[11])).
% 0.21/0.53 tff(115,plain,
% 0.21/0.53 (sk_c6 = sk_c7),
% 0.21/0.53 inference(transitivity,[status(thm)],[114, 113, 109, 107, 106, 101, 98, 73, 70, 74, 9])).
% 0.21/0.53 tff(116,plain,
% 0.21/0.53 (multiply(sk_c1, sk_c6) = multiply(sk_c1, sk_c7)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[115])).
% 0.21/0.53 tff(117,plain,
% 0.21/0.53 (multiply(sk_c1, sk_c6) = sk_c5),
% 0.21/0.53 inference(transitivity,[status(thm)],[116, 29, 114, 113, 109, 107, 106, 101, 98, 73, 70, 39, 30, 23])).
% 0.21/0.53 tff(118,plain,
% 0.21/0.53 (multiply(multiply(sk_c6, sk_c2), sk_c6) = multiply(identity, sk_c6)),
% 0.21/0.53 inference(symmetry,[status(thm)],[113])).
% 0.21/0.53 tff(119,plain,
% 0.21/0.53 (multiply(sk_c6, multiply(sk_c2, sk_c6)) = multiply(multiply(sk_c6, sk_c2), sk_c6)),
% 0.21/0.53 inference(symmetry,[status(thm)],[109])).
% 0.21/0.53 tff(120,plain,
% 0.21/0.53 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c2, sk_c6))),
% 0.21/0.53 inference(symmetry,[status(thm)],[107])).
% 0.21/0.53 tff(121,plain,
% 0.21/0.53 (multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c2, sk_c6)))) = multiply(sk_c6, sk_c7)),
% 0.21/0.53 inference(symmetry,[status(thm)],[106])).
% 0.21/0.53 tff(122,plain,
% 0.21/0.53 (multiply(sk_c6, multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c2, sk_c6)))),
% 0.21/0.53 inference(symmetry,[status(thm)],[98])).
% 0.21/0.53 tff(123,plain,
% 0.21/0.53 (inverse(sk_c1) = sk_c6),
% 0.21/0.53 inference(transitivity,[status(thm)],[43, 57, 56, 104, 72, 122, 100, 121, 120, 119, 118, 11])).
% 0.21/0.53 tff(124,plain,
% 0.21/0.53 ((sk_c6 = inverse(sk_c1)) <=> (inverse(sk_c1) = sk_c6)),
% 0.21/0.53 inference(commutativity,[status(thm)],[])).
% 0.21/0.53 tff(125,plain,
% 0.21/0.53 (sk_c7 = inverse(sk_c1)),
% 0.21/0.53 inference(symmetry,[status(thm)],[43])).
% 0.21/0.53 tff(126,plain,
% 0.21/0.53 (sk_c5 = inverse(sk_c1)),
% 0.21/0.53 inference(transitivity,[status(thm)],[77, 76, 75, 74, 9, 125])).
% 0.21/0.53 tff(127,plain,
% 0.21/0.53 (multiply(sk_c6, sk_c7) = sk_c6),
% 0.21/0.53 inference(transitivity,[status(thm)],[120, 119, 118, 11])).
% 0.21/0.53 tff(128,plain,
% 0.21/0.53 ((multiply(sk_c6, sk_c7) = sk_c5) <=> (sk_c6 = inverse(sk_c1))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[127, 126])).
% 0.21/0.53 tff(129,plain,
% 0.21/0.53 ((multiply(sk_c6, sk_c7) = sk_c5) <=> (inverse(sk_c1) = sk_c6)),
% 0.21/0.53 inference(transitivity,[status(thm)],[128, 124])).
% 0.21/0.53 tff(130,plain,
% 0.21/0.53 ((inverse(sk_c1) = sk_c6) <=> (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.21/0.53 inference(symmetry,[status(thm)],[129])).
% 0.21/0.53 tff(131,plain,
% 0.21/0.53 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[123, 130])).
% 0.21/0.53 tff(132,plain,
% 0.21/0.53 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(133,plain,
% 0.21/0.53 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.53 tff(134,plain,
% 0.21/0.53 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(135,plain,
% 0.21/0.53 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X4, sk_c6) = sk_c5))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X4, sk_c6) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), ((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X4) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X4) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), ((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), (((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), ((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), ((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), (((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c6) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X2, sk_c6) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), (((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X2) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X2) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(136,plain,
% 0.21/0.53 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.45/0.54 inference(quant_intro,[status(thm)],[135])).
% 0.45/0.54 tff(137,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c6) = sk_c5))) | (~(inverse(X4) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(X1) = sk_c7))) | (~(multiply(X1, sk_c6) = sk_c7))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_26')).
% 0.45/0.54 tff(138,plain,
% 0.45/0.54 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.45/0.54 tff(139,plain,
% 0.45/0.54 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.45/0.54 tff(140,plain,(
% 0.45/0.54 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.45/0.54 inference(skolemize,[status(sab)],[139])).
% 0.45/0.54 tff(141,plain,
% 0.45/0.54 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.45/0.54 tff(142,plain,
% 0.45/0.54 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(143,plain,
% 0.45/0.54 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(144,plain,
% 0.45/0.54 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6))))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[143])).
% 0.45/0.54 tff(145,plain,
% 0.45/0.54 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.45/0.54 inference(transitivity,[status(thm)],[144, 142])).
% 0.45/0.54 tff(146,plain,
% 0.45/0.54 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(147,plain,
% 0.45/0.54 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5)) | (~(multiply(sk_c1, sk_c7) = sk_c6))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.45/0.54 tff(148,plain,
% 0.45/0.54 ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c5))),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[147, 23, 29, 43, 141])).
% 0.45/0.54 tff(149,plain,
% 0.45/0.54 (~(multiply(sk_c1, sk_c6) = sk_c7)),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[148, 131, 123, 117])).
% 0.45/0.54 tff(150,plain,
% 0.45/0.54 (~(multiply(sk_c1, sk_c6) = sk_c5)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[149, 60])).
% 0.45/0.54 tff(151,plain,
% 0.45/0.54 ($false),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[117, 150])).
% 0.45/0.54 tff(152,plain,(inverse(sk_c4) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.45/0.54 tff(153,plain,
% 0.45/0.54 (sk_c6 = inverse(sk_c4)),
% 0.45/0.54 inference(symmetry,[status(thm)],[152])).
% 0.45/0.54 tff(154,plain,
% 0.45/0.54 (multiply(sk_c6, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.45/0.54 inference(monotonicity,[status(thm)],[153])).
% 0.45/0.54 tff(155,plain,
% 0.45/0.54 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c6, sk_c4)),
% 0.45/0.54 inference(symmetry,[status(thm)],[154])).
% 0.45/0.54 tff(156,plain,
% 0.45/0.54 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(157,plain,
% 0.45/0.54 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[156, 51])).
% 0.45/0.54 tff(158,plain,
% 0.45/0.54 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.45/0.54 inference(symmetry,[status(thm)],[157])).
% 0.45/0.54 tff(159,plain,
% 0.45/0.54 (identity = multiply(sk_c6, sk_c4)),
% 0.45/0.54 inference(transitivity,[status(thm)],[158, 155])).
% 0.45/0.54 tff(160,plain,
% 0.45/0.54 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.45/0.54 inference(monotonicity,[status(thm)],[159])).
% 0.45/0.54 tff(161,plain,
% 0.45/0.54 (multiply(multiply(sk_c6, sk_c4), sk_c6) = multiply(identity, sk_c6)),
% 0.45/0.54 inference(symmetry,[status(thm)],[160])).
% 0.45/0.54 tff(162,plain,
% 0.45/0.54 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c3), sk_c3) = identity)),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(163,plain,
% 0.45/0.54 (multiply(inverse(sk_c3), sk_c3) = identity),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[162, 51])).
% 0.45/0.54 tff(164,assumption,(~(inverse(sk_c3) = sk_c7)), introduced(assumption)).
% 0.45/0.54 tff(165,plain,
% 0.45/0.54 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(166,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_12')).
% 0.45/0.54 tff(167,plain,
% 0.45/0.54 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c7)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.45/0.54 tff(168,plain,
% 0.45/0.54 (inverse(sk_c1) = sk_c7),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[167, 164])).
% 0.45/0.54 tff(169,plain,
% 0.45/0.54 (sk_c7 = inverse(sk_c1)),
% 0.45/0.54 inference(symmetry,[status(thm)],[168])).
% 0.45/0.54 tff(170,plain,
% 0.45/0.54 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.45/0.54 inference(monotonicity,[status(thm)],[169])).
% 0.45/0.54 tff(171,plain,
% 0.45/0.54 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.45/0.54 inference(symmetry,[status(thm)],[170])).
% 0.45/0.54 tff(172,plain,
% 0.45/0.54 (identity = multiply(sk_c7, sk_c1)),
% 0.45/0.54 inference(transitivity,[status(thm)],[54, 171])).
% 0.45/0.54 tff(173,plain,
% 0.45/0.54 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.45/0.54 inference(monotonicity,[status(thm)],[172])).
% 0.45/0.54 tff(174,plain,
% 0.45/0.54 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.45/0.54 inference(symmetry,[status(thm)],[173])).
% 0.45/0.54 tff(175,plain,
% 0.45/0.54 (((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c6)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(176,plain,
% 0.45/0.54 (((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(177,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_7')).
% 0.45/0.54 tff(178,plain,
% 0.45/0.54 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.45/0.54 tff(179,plain,
% 0.45/0.54 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[178, 175])).
% 0.45/0.54 tff(180,plain,
% 0.45/0.54 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[179, 164])).
% 0.45/0.54 tff(181,plain,
% 0.45/0.54 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.45/0.54 inference(monotonicity,[status(thm)],[180])).
% 0.45/0.54 tff(182,plain,
% 0.45/0.54 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.45/0.54 inference(symmetry,[status(thm)],[181])).
% 0.45/0.54 tff(183,assumption,(~(multiply(sk_c7, sk_c6) = sk_c5)), introduced(assumption)).
% 0.45/0.54 tff(184,plain,
% 0.45/0.54 (((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(185,axiom,((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_1')).
% 0.45/0.54 tff(186,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.45/0.54 tff(187,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[186, 184])).
% 0.45/0.54 tff(188,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[187, 184])).
% 0.45/0.54 tff(189,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.45/0.54 tff(190,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[189, 184])).
% 0.45/0.54 tff(191,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[190, 184])).
% 0.45/0.54 tff(192,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.45/0.54 tff(193,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[192, 184])).
% 0.45/0.54 tff(194,plain,
% 0.45/0.54 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[193, 183])).
% 0.45/0.54 tff(195,plain,
% 0.45/0.54 (((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)) <=> ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(196,axiom,((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_2')).
% 0.45/0.54 tff(197,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.45/0.54 tff(198,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[197, 195])).
% 0.45/0.54 tff(199,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[198, 195])).
% 0.45/0.54 tff(200,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.45/0.54 tff(201,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[200, 195])).
% 0.45/0.54 tff(202,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[201, 195])).
% 0.45/0.54 tff(203,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[202, 195])).
% 0.45/0.54 tff(204,plain,
% 0.45/0.54 ((multiply(sk_c7, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[203, 195])).
% 0.45/0.54 tff(205,plain,
% 0.45/0.54 (inverse(sk_c3) = sk_c7),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[204, 183])).
% 0.45/0.54 tff(206,plain,
% 0.45/0.54 (sk_c7 = inverse(sk_c3)),
% 0.45/0.54 inference(symmetry,[status(thm)],[205])).
% 0.45/0.54 tff(207,plain,
% 0.45/0.54 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.45/0.54 inference(monotonicity,[status(thm)],[206])).
% 0.45/0.54 tff(208,plain,
% 0.45/0.54 (multiply(sk_c7, sk_c3) = multiply(sk_c6, sk_c4)),
% 0.45/0.54 inference(transitivity,[status(thm)],[207, 163, 158, 155])).
% 0.45/0.54 tff(209,plain,
% 0.45/0.54 (multiply(multiply(sk_c7, sk_c3), sk_c6) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.45/0.54 inference(monotonicity,[status(thm)],[208])).
% 0.45/0.54 tff(210,plain,
% 0.45/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c3), sk_c6) = multiply(sk_c7, multiply(sk_c3, sk_c6)))),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(211,plain,
% 0.45/0.54 (multiply(multiply(sk_c7, sk_c3), sk_c6) = multiply(sk_c7, multiply(sk_c3, sk_c6))),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[210, 37])).
% 0.45/0.54 tff(212,plain,
% 0.45/0.55 (multiply(sk_c7, multiply(sk_c3, sk_c6)) = multiply(multiply(sk_c7, sk_c3), sk_c6)),
% 0.45/0.55 inference(symmetry,[status(thm)],[211])).
% 0.45/0.55 tff(213,plain,
% 0.45/0.55 (((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(214,axiom,((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_3')).
% 0.45/0.55 tff(215,plain,
% 0.45/0.55 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.45/0.55 tff(216,plain,
% 0.45/0.55 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[215, 213])).
% 0.45/0.55 tff(217,plain,
% 0.45/0.55 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[216, 213])).
% 0.45/0.55 tff(218,plain,
% 0.45/0.55 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.45/0.55 tff(219,plain,
% 0.45/0.55 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[218, 213])).
% 0.45/0.55 tff(220,plain,
% 0.45/0.55 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[219, 213])).
% 0.45/0.55 tff(221,plain,
% 0.45/0.55 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.45/0.55 tff(222,plain,
% 0.45/0.55 ((multiply(sk_c7, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[221, 213])).
% 0.45/0.55 tff(223,plain,
% 0.45/0.55 (multiply(sk_c3, sk_c6) = sk_c7),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[222, 183])).
% 0.45/0.55 tff(224,plain,
% 0.45/0.55 (sk_c7 = multiply(sk_c3, sk_c6)),
% 0.45/0.55 inference(symmetry,[status(thm)],[223])).
% 0.45/0.55 tff(225,plain,
% 0.45/0.55 (multiply(sk_c7, sk_c7) = multiply(sk_c7, multiply(sk_c3, sk_c6))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[224])).
% 0.45/0.55 tff(226,plain,
% 0.45/0.55 (multiply(sk_c7, sk_c7) = sk_c6),
% 0.45/0.55 inference(transitivity,[status(thm)],[225, 212, 209, 161, 11])).
% 0.45/0.55 tff(227,plain,
% 0.45/0.55 (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[226])).
% 0.45/0.55 tff(228,plain,
% 0.45/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(sk_c7, multiply(sk_c7, sk_c7)))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(229,plain,
% 0.45/0.55 (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[228, 37])).
% 0.45/0.55 tff(230,plain,
% 0.45/0.55 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c7), sk_c7)),
% 0.45/0.55 inference(symmetry,[status(thm)],[229])).
% 0.45/0.55 tff(231,plain,
% 0.45/0.55 (multiply(sk_c7, multiply(sk_c3, sk_c6)) = multiply(sk_c7, sk_c7)),
% 0.45/0.55 inference(symmetry,[status(thm)],[225])).
% 0.45/0.55 tff(232,plain,
% 0.45/0.55 (multiply(multiply(sk_c6, sk_c4), sk_c6) = multiply(multiply(sk_c7, sk_c3), sk_c6)),
% 0.45/0.55 inference(symmetry,[status(thm)],[209])).
% 0.45/0.55 tff(233,plain,
% 0.45/0.55 (sk_c6 = multiply(sk_c7, sk_c7)),
% 0.45/0.55 inference(transitivity,[status(thm)],[114, 160, 232, 211, 231])).
% 0.45/0.55 tff(234,plain,
% 0.45/0.55 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[233])).
% 0.45/0.55 tff(235,plain,
% 0.45/0.55 (multiply(sk_c7, sk_c6) = sk_c5),
% 0.45/0.55 inference(transitivity,[status(thm)],[234, 230, 227, 194])).
% 0.45/0.55 tff(236,plain,
% 0.45/0.55 ($false),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[183, 235])).
% 0.45/0.55 tff(237,plain,(multiply(sk_c7, sk_c6) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.45/0.55 tff(238,plain,
% 0.45/0.55 (sk_c5 = multiply(sk_c7, sk_c6)),
% 0.45/0.55 inference(symmetry,[status(thm)],[237])).
% 0.45/0.55 tff(239,assumption,(~(multiply(sk_c6, sk_c7) = sk_c5)), introduced(assumption)).
% 0.45/0.55 tff(240,plain,
% 0.45/0.55 (((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(241,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_6')).
% 0.45/0.55 tff(242,plain,
% 0.45/0.55 ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.45/0.55 tff(243,plain,
% 0.45/0.55 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[242, 239])).
% 0.45/0.55 tff(244,plain,
% 0.45/0.55 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[243])).
% 0.45/0.55 tff(245,plain,
% 0.45/0.55 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(246,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_11')).
% 0.45/0.55 tff(247,plain,
% 0.45/0.55 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.45/0.55 tff(248,plain,
% 0.45/0.55 (inverse(sk_c1) = sk_c7),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[247, 239])).
% 0.45/0.55 tff(249,plain,
% 0.45/0.55 (sk_c7 = inverse(sk_c1)),
% 0.45/0.55 inference(symmetry,[status(thm)],[248])).
% 0.45/0.55 tff(250,plain,
% 0.45/0.55 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[249])).
% 0.45/0.55 tff(251,plain,
% 0.45/0.55 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.45/0.55 inference(symmetry,[status(thm)],[250])).
% 0.45/0.55 tff(252,plain,
% 0.45/0.55 (((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(253,axiom,((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_21')).
% 0.45/0.55 tff(254,plain,
% 0.45/0.55 ((inverse(sk_c2) = sk_c6) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.45/0.55 tff(255,plain,
% 0.45/0.55 (inverse(sk_c2) = sk_c6),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[254, 239])).
% 0.45/0.55 tff(256,plain,
% 0.45/0.55 (sk_c6 = inverse(sk_c2)),
% 0.45/0.55 inference(symmetry,[status(thm)],[255])).
% 0.45/0.55 tff(257,plain,
% 0.45/0.55 (multiply(sk_c6, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[256])).
% 0.45/0.55 tff(258,plain,
% 0.45/0.55 (multiply(sk_c6, sk_c2) = multiply(sk_c7, sk_c1)),
% 0.45/0.55 inference(transitivity,[status(thm)],[257, 62, 54, 251])).
% 0.45/0.55 tff(259,plain,
% 0.45/0.55 (multiply(multiply(sk_c6, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[258])).
% 0.45/0.55 tff(260,plain,
% 0.45/0.55 (identity = multiply(sk_c7, sk_c1)),
% 0.45/0.55 inference(transitivity,[status(thm)],[54, 251])).
% 0.45/0.55 tff(261,plain,
% 0.45/0.55 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[260])).
% 0.45/0.55 tff(262,plain,
% 0.45/0.55 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.45/0.55 inference(symmetry,[status(thm)],[261])).
% 0.45/0.55 tff(263,plain,
% 0.45/0.55 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.45/0.55 inference(symmetry,[status(thm)],[244])).
% 0.45/0.55 tff(264,plain,
% 0.45/0.55 (sk_c5 = sk_c7),
% 0.45/0.55 inference(transitivity,[status(thm)],[238, 263, 75, 262, 9])).
% 0.45/0.55 tff(265,plain,
% 0.45/0.55 (multiply(sk_c1, sk_c5) = multiply(sk_c1, sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[264])).
% 0.45/0.55 tff(266,plain,
% 0.45/0.55 (multiply(sk_c1, sk_c5) = sk_c6),
% 0.45/0.55 inference(transitivity,[status(thm)],[265, 243])).
% 0.45/0.55 tff(267,plain,
% 0.45/0.55 (multiply(multiply(sk_c1, sk_c5), multiply(sk_c2, sk_c7)) = multiply(sk_c6, multiply(sk_c2, sk_c7))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[266])).
% 0.45/0.55 tff(268,plain,
% 0.45/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c5), multiply(sk_c2, sk_c7)) = multiply(sk_c1, multiply(sk_c5, multiply(sk_c2, sk_c7))))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(269,plain,
% 0.45/0.55 (multiply(multiply(sk_c1, sk_c5), multiply(sk_c2, sk_c7)) = multiply(sk_c1, multiply(sk_c5, multiply(sk_c2, sk_c7)))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[268, 37])).
% 0.45/0.55 tff(270,plain,
% 0.45/0.55 (multiply(sk_c1, multiply(sk_c5, multiply(sk_c2, sk_c7))) = multiply(multiply(sk_c1, sk_c5), multiply(sk_c2, sk_c7))),
% 0.45/0.55 inference(symmetry,[status(thm)],[269])).
% 0.45/0.55 tff(271,plain,
% 0.45/0.55 (((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)) <=> ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(272,axiom,((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_16')).
% 0.45/0.55 tff(273,plain,
% 0.45/0.55 ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c6, sk_c7) = sk_c5)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.45/0.55 tff(274,plain,
% 0.45/0.55 (multiply(sk_c2, sk_c6) = sk_c5),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[273, 239])).
% 0.45/0.55 tff(275,plain,
% 0.45/0.55 (sk_c5 = multiply(sk_c2, sk_c6)),
% 0.45/0.55 inference(symmetry,[status(thm)],[274])).
% 0.45/0.55 tff(276,plain,
% 0.45/0.55 (multiply(sk_c5, multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c2, sk_c6), multiply(sk_c2, sk_c7))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[275])).
% 0.45/0.55 tff(277,plain,
% 0.45/0.55 (multiply(multiply(sk_c2, sk_c6), multiply(sk_c2, sk_c7)) = multiply(sk_c5, multiply(sk_c2, sk_c7))),
% 0.45/0.55 inference(symmetry,[status(thm)],[276])).
% 0.45/0.55 tff(278,plain,
% 0.45/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c6), multiply(sk_c2, sk_c7)) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c2, sk_c7))))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(279,plain,
% 0.45/0.55 (multiply(multiply(sk_c2, sk_c6), multiply(sk_c2, sk_c7)) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c2, sk_c7)))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[278, 37])).
% 0.45/0.55 tff(280,plain,
% 0.45/0.55 (multiply(sk_c2, multiply(sk_c6, multiply(sk_c2, sk_c7))) = multiply(multiply(sk_c2, sk_c6), multiply(sk_c2, sk_c7))),
% 0.45/0.55 inference(symmetry,[status(thm)],[279])).
% 0.45/0.55 tff(281,plain,
% 0.45/0.55 (multiply(sk_c6, multiply(sk_c2, sk_c7)) = sk_c7),
% 0.45/0.55 inference(transitivity,[status(thm)],[73, 259, 262, 9])).
% 0.45/0.55 tff(282,plain,
% 0.45/0.55 (multiply(sk_c2, multiply(sk_c6, multiply(sk_c2, sk_c7))) = multiply(sk_c2, sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[281])).
% 0.45/0.55 tff(283,plain,
% 0.45/0.55 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c2, sk_c7)))),
% 0.45/0.55 inference(symmetry,[status(thm)],[282])).
% 0.45/0.55 tff(284,plain,
% 0.45/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c4), sk_c7) = multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(285,plain,
% 0.45/0.55 (multiply(multiply(sk_c6, sk_c4), sk_c7) = multiply(sk_c6, multiply(sk_c4, sk_c7))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[284, 37])).
% 0.45/0.55 tff(286,plain,
% 0.45/0.55 (multiply(sk_c6, sk_c4) = multiply(sk_c7, sk_c1)),
% 0.45/0.55 inference(transitivity,[status(thm)],[154, 157, 54, 251])).
% 0.45/0.55 tff(287,plain,
% 0.45/0.55 (multiply(multiply(sk_c6, sk_c4), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[286])).
% 0.45/0.55 tff(288,plain,
% 0.45/0.55 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c6, sk_c4), sk_c7)),
% 0.45/0.55 inference(symmetry,[status(thm)],[287])).
% 0.45/0.55 tff(289,plain,
% 0.45/0.55 (sk_c7 = multiply(sk_c6, multiply(sk_c4, sk_c7))),
% 0.45/0.55 inference(transitivity,[status(thm)],[57, 261, 288, 285])).
% 0.45/0.55 tff(290,plain,
% 0.45/0.55 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[289])).
% 0.45/0.55 tff(291,plain,
% 0.45/0.55 (multiply(sk_c2, multiply(sk_c6, multiply(sk_c4, sk_c7))) = multiply(sk_c2, sk_c7)),
% 0.45/0.55 inference(symmetry,[status(thm)],[290])).
% 0.45/0.55 tff(292,plain,
% 0.45/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c6), multiply(sk_c4, sk_c7)) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c4, sk_c7))))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(293,plain,
% 0.45/0.55 (multiply(multiply(sk_c2, sk_c6), multiply(sk_c4, sk_c7)) = multiply(sk_c2, multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[292, 37])).
% 0.45/0.55 tff(294,plain,
% 0.45/0.55 (multiply(sk_c5, sk_c6) = multiply(sk_c7, sk_c6)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[264])).
% 0.45/0.55 tff(295,plain,
% 0.45/0.55 (multiply(sk_c7, sk_c6) = multiply(sk_c5, sk_c6)),
% 0.45/0.55 inference(symmetry,[status(thm)],[294])).
% 0.45/0.55 tff(296,plain,
% 0.45/0.55 (multiply(sk_c2, sk_c6) = multiply(sk_c5, sk_c6)),
% 0.45/0.55 inference(transitivity,[status(thm)],[274, 238, 295])).
% 0.45/0.55 tff(297,plain,
% 0.45/0.55 (multiply(multiply(sk_c2, sk_c6), multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c4, sk_c7))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[296])).
% 0.45/0.55 tff(298,plain,
% 0.45/0.55 (multiply(multiply(sk_c5, sk_c6), multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c2, sk_c6), multiply(sk_c4, sk_c7))),
% 0.45/0.55 inference(symmetry,[status(thm)],[297])).
% 0.45/0.55 tff(299,plain,
% 0.45/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c6), multiply(sk_c4, sk_c7)) = multiply(sk_c5, multiply(sk_c6, multiply(sk_c4, sk_c7))))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(300,plain,
% 0.45/0.55 (multiply(multiply(sk_c5, sk_c6), multiply(sk_c4, sk_c7)) = multiply(sk_c5, multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[299, 37])).
% 0.45/0.55 tff(301,plain,
% 0.45/0.55 (multiply(sk_c5, multiply(sk_c6, multiply(sk_c4, sk_c7))) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c4, sk_c7))),
% 0.45/0.55 inference(symmetry,[status(thm)],[300])).
% 0.45/0.55 tff(302,plain,
% 0.45/0.55 (multiply(sk_c6, multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c6, sk_c4), sk_c7)),
% 0.45/0.55 inference(symmetry,[status(thm)],[285])).
% 0.45/0.55 tff(303,plain,
% 0.45/0.55 (multiply(sk_c6, multiply(sk_c4, sk_c7)) = sk_c7),
% 0.45/0.55 inference(transitivity,[status(thm)],[302, 287, 262, 9])).
% 0.45/0.55 tff(304,plain,
% 0.45/0.55 (multiply(sk_c5, multiply(sk_c6, multiply(sk_c4, sk_c7))) = multiply(sk_c7, sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[264, 303])).
% 0.45/0.55 tff(305,plain,
% 0.45/0.55 (multiply(sk_c7, sk_c7) = multiply(sk_c5, multiply(sk_c6, multiply(sk_c4, sk_c7)))),
% 0.45/0.55 inference(symmetry,[status(thm)],[304])).
% 0.45/0.55 tff(306,plain,
% 0.45/0.55 (multiply(sk_c7, sk_c7) = multiply(sk_c5, multiply(sk_c2, sk_c7))),
% 0.45/0.55 inference(transitivity,[status(thm)],[305, 301, 298, 293, 291, 283, 280, 277])).
% 0.45/0.55 tff(307,plain,
% 0.45/0.55 (multiply(sk_c1, multiply(sk_c7, sk_c7)) = multiply(sk_c1, multiply(sk_c5, multiply(sk_c2, sk_c7)))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[306])).
% 0.45/0.55 tff(308,plain,
% 0.45/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), sk_c7) = multiply(sk_c1, multiply(sk_c7, sk_c7)))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(309,plain,
% 0.45/0.55 (multiply(multiply(sk_c1, sk_c7), sk_c7) = multiply(sk_c1, multiply(sk_c7, sk_c7))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[308, 37])).
% 0.45/0.55 tff(310,plain,
% 0.45/0.55 (sk_c6 = multiply(sk_c1, sk_c7)),
% 0.45/0.55 inference(symmetry,[status(thm)],[243])).
% 0.45/0.55 tff(311,plain,
% 0.45/0.55 (multiply(sk_c6, sk_c7) = multiply(multiply(sk_c1, sk_c7), sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[310])).
% 0.45/0.55 tff(312,plain,
% 0.45/0.55 (multiply(sk_c6, sk_c7) = sk_c5),
% 0.45/0.55 inference(transitivity,[status(thm)],[311, 309, 307, 270, 267, 73, 259, 39, 244, 237])).
% 0.45/0.55 tff(313,plain,
% 0.45/0.55 ($false),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[239, 312])).
% 0.45/0.55 tff(314,plain,(multiply(sk_c6, sk_c7) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.45/0.55 tff(315,plain,
% 0.45/0.55 (sk_c5 = sk_c7),
% 0.45/0.55 inference(transitivity,[status(thm)],[238, 182, 75, 174, 9])).
% 0.45/0.55 tff(316,plain,
% 0.45/0.55 (sk_c7 = multiply(sk_c7, sk_c6)),
% 0.45/0.55 inference(transitivity,[status(thm)],[57, 173, 39, 181])).
% 0.45/0.55 tff(317,plain,
% 0.45/0.55 (multiply(sk_c1, sk_c7) = multiply(sk_c1, multiply(sk_c7, sk_c6))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[316])).
% 0.45/0.55 tff(318,plain,
% 0.45/0.55 (multiply(sk_c1, multiply(sk_c7, sk_c6)) = multiply(sk_c1, sk_c7)),
% 0.45/0.55 inference(symmetry,[status(thm)],[317])).
% 0.45/0.55 tff(319,plain,
% 0.45/0.55 (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)),
% 0.45/0.55 inference(transitivity,[status(thm)],[314, 238])).
% 0.45/0.55 tff(320,plain,
% 0.45/0.55 (multiply(sk_c1, multiply(sk_c6, sk_c7)) = multiply(sk_c1, multiply(sk_c7, sk_c6))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[319])).
% 0.45/0.55 tff(321,plain,
% 0.45/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c6), sk_c7) = multiply(sk_c1, multiply(sk_c6, sk_c7)))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(322,plain,
% 0.45/0.55 (multiply(multiply(sk_c1, sk_c6), sk_c7) = multiply(sk_c1, multiply(sk_c6, sk_c7))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[321, 37])).
% 0.45/0.55 tff(323,plain,
% 0.45/0.55 (multiply(multiply(sk_c1, sk_c6), sk_c5) = multiply(multiply(sk_c1, sk_c6), sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[315])).
% 0.45/0.55 tff(324,plain,
% 0.45/0.55 (multiply(multiply(sk_c1, sk_c6), sk_c5) = sk_c6),
% 0.45/0.55 inference(transitivity,[status(thm)],[323, 322, 320, 318, 180])).
% 0.45/0.55 tff(325,plain,
% 0.45/0.55 (multiply(multiply(multiply(sk_c1, sk_c6), sk_c5), sk_c5) = multiply(sk_c6, sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[324, 315])).
% 0.45/0.55 tff(326,plain,
% 0.45/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c1, sk_c6), sk_c5), sk_c5) = multiply(multiply(sk_c1, sk_c6), multiply(sk_c5, sk_c5)))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(327,plain,
% 0.45/0.55 (multiply(multiply(multiply(sk_c1, sk_c6), sk_c5), sk_c5) = multiply(multiply(sk_c1, sk_c6), multiply(sk_c5, sk_c5))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[326, 37])).
% 0.45/0.55 tff(328,plain,
% 0.45/0.55 (multiply(multiply(sk_c1, sk_c6), multiply(sk_c5, sk_c5)) = multiply(multiply(multiply(sk_c1, sk_c6), sk_c5), sk_c5)),
% 0.45/0.55 inference(symmetry,[status(thm)],[327])).
% 0.45/0.55 tff(329,plain,
% 0.45/0.55 (multiply(sk_c5, sk_c5) = multiply(sk_c7, sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[315, 315])).
% 0.45/0.55 tff(330,plain,
% 0.45/0.55 (multiply(sk_c7, sk_c7) = multiply(sk_c5, sk_c5)),
% 0.45/0.55 inference(symmetry,[status(thm)],[329])).
% 0.45/0.55 tff(331,assumption,(~(multiply(sk_c2, sk_c6) = sk_c5)), introduced(assumption)).
% 0.45/0.55 tff(332,plain,
% 0.45/0.55 (((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c4, sk_c6) = sk_c7)) <=> ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c4, sk_c6) = sk_c7))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(333,axiom,((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c4, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_19')).
% 0.45/0.55 tff(334,plain,
% 0.45/0.55 ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c4, sk_c6) = sk_c7)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.45/0.55 tff(335,plain,
% 0.45/0.55 (multiply(sk_c4, sk_c6) = sk_c7),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[334, 331])).
% 0.45/0.55 tff(336,plain,
% 0.45/0.55 (multiply(sk_c6, multiply(sk_c4, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.45/0.55 inference(monotonicity,[status(thm)],[335])).
% 0.45/0.55 tff(337,plain,
% 0.45/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c4), sk_c6) = multiply(sk_c6, multiply(sk_c4, sk_c6)))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(338,plain,
% 0.45/0.55 (multiply(multiply(sk_c6, sk_c4), sk_c6) = multiply(sk_c6, multiply(sk_c4, sk_c6))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[337, 37])).
% 0.45/0.55 tff(339,plain,
% 0.45/0.55 (((inverse(sk_c3) = sk_c7) | (multiply(sk_c2, sk_c6) = sk_c5)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c2, sk_c6) = sk_c5))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(340,plain,
% 0.47/0.55 (((multiply(sk_c2, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c2, sk_c6) = sk_c5))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(341,axiom,((multiply(sk_c2, sk_c6) = sk_c5) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_17')).
% 0.47/0.55 tff(342,plain,
% 0.47/0.55 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c2, sk_c6) = sk_c5)),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.47/0.55 tff(343,plain,
% 0.47/0.55 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c2, sk_c6) = sk_c5)),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[342, 339])).
% 0.47/0.55 tff(344,plain,
% 0.47/0.55 (inverse(sk_c3) = sk_c7),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[343, 331])).
% 0.47/0.55 tff(345,plain,
% 0.47/0.55 (sk_c7 = inverse(sk_c3)),
% 0.47/0.55 inference(symmetry,[status(thm)],[344])).
% 0.47/0.55 tff(346,plain,
% 0.47/0.55 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.47/0.55 inference(monotonicity,[status(thm)],[345])).
% 0.47/0.55 tff(347,plain,
% 0.47/0.55 (multiply(sk_c7, sk_c3) = multiply(sk_c6, sk_c4)),
% 0.47/0.55 inference(transitivity,[status(thm)],[346, 163, 158, 155])).
% 0.47/0.55 tff(348,plain,
% 0.47/0.55 (multiply(multiply(sk_c7, sk_c3), sk_c6) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.47/0.55 inference(monotonicity,[status(thm)],[347])).
% 0.47/0.55 tff(349,plain,
% 0.47/0.55 ((sk_c7 = inverse(sk_c4)) <=> (inverse(sk_c4) = sk_c7)),
% 0.47/0.55 inference(commutativity,[status(thm)],[])).
% 0.47/0.55 tff(350,assumption,(~(multiply(sk_c3, sk_c6) = sk_c7)), introduced(assumption)).
% 0.47/0.55 tff(351,plain,
% 0.47/0.55 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c7))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(352,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_13')).
% 0.47/0.55 tff(353,plain,
% 0.47/0.55 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.47/0.55 tff(354,plain,
% 0.47/0.55 (inverse(sk_c1) = sk_c7),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[353, 350])).
% 0.47/0.55 tff(355,plain,
% 0.47/0.55 (sk_c7 = inverse(sk_c1)),
% 0.47/0.55 inference(symmetry,[status(thm)],[354])).
% 0.47/0.55 tff(356,plain,
% 0.47/0.55 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.47/0.55 inference(monotonicity,[status(thm)],[355])).
% 0.47/0.55 tff(357,plain,
% 0.47/0.55 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.47/0.55 inference(symmetry,[status(thm)],[356])).
% 0.47/0.55 tff(358,plain,
% 0.47/0.55 (identity = multiply(sk_c7, sk_c1)),
% 0.47/0.55 inference(transitivity,[status(thm)],[54, 357])).
% 0.47/0.55 tff(359,plain,
% 0.47/0.55 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.47/0.55 inference(monotonicity,[status(thm)],[358])).
% 0.47/0.55 tff(360,plain,
% 0.47/0.55 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.47/0.55 inference(symmetry,[status(thm)],[359])).
% 0.47/0.55 tff(361,plain,
% 0.47/0.55 (((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(362,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_8')).
% 0.47/0.55 tff(363,plain,
% 0.47/0.55 ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.47/0.55 tff(364,plain,
% 0.47/0.55 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[363, 350])).
% 0.47/0.55 tff(365,plain,
% 0.47/0.55 (sk_c6 = multiply(sk_c1, sk_c7)),
% 0.47/0.55 inference(symmetry,[status(thm)],[364])).
% 0.47/0.55 tff(366,plain,
% 0.47/0.55 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.47/0.55 inference(monotonicity,[status(thm)],[365])).
% 0.47/0.55 tff(367,plain,
% 0.47/0.55 (sk_c5 = sk_c7),
% 0.47/0.55 inference(transitivity,[status(thm)],[238, 366, 75, 360, 9])).
% 0.47/0.55 tff(368,plain,
% 0.47/0.55 (multiply(sk_c6, sk_c5) = multiply(sk_c6, sk_c7)),
% 0.47/0.55 inference(monotonicity,[status(thm)],[367])).
% 0.47/0.55 tff(369,plain,
% 0.47/0.55 (multiply(sk_c6, sk_c7) = multiply(sk_c6, sk_c5)),
% 0.47/0.55 inference(symmetry,[status(thm)],[368])).
% 0.47/0.55 tff(370,plain,
% 0.47/0.55 (sk_c5 = multiply(sk_c6, sk_c7)),
% 0.47/0.55 inference(symmetry,[status(thm)],[314])).
% 0.47/0.55 tff(371,plain,
% 0.47/0.55 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.47/0.56 inference(symmetry,[status(thm)],[366])).
% 0.47/0.56 tff(372,plain,
% 0.47/0.56 (sk_c7 = multiply(sk_c6, sk_c5)),
% 0.47/0.56 inference(transitivity,[status(thm)],[57, 359, 39, 371, 237, 370, 369])).
% 0.47/0.56 tff(373,plain,
% 0.47/0.56 (multiply(sk_c7, sk_c1) = identity),
% 0.47/0.56 inference(transitivity,[status(thm)],[356, 53])).
% 0.47/0.56 tff(374,plain,
% 0.47/0.56 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, multiply(sk_c6, sk_c5))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[373, 372])).
% 0.47/0.56 tff(375,plain,
% 0.47/0.56 (multiply(identity, multiply(sk_c6, sk_c5)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.47/0.56 inference(symmetry,[status(thm)],[374])).
% 0.47/0.56 tff(376,plain,
% 0.47/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c6), sk_c5) = multiply(identity, multiply(sk_c6, sk_c5)))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(377,plain,
% 0.47/0.56 (multiply(multiply(identity, sk_c6), sk_c5) = multiply(identity, multiply(sk_c6, sk_c5))),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[376, 37])).
% 0.47/0.56 tff(378,plain,
% 0.47/0.56 (((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(379,axiom,((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_18')).
% 0.47/0.56 tff(380,plain,
% 0.47/0.56 ((multiply(sk_c2, sk_c6) = sk_c5) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.47/0.56 tff(381,plain,
% 0.47/0.56 (multiply(sk_c2, sk_c6) = sk_c5),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[380, 350])).
% 0.47/0.56 tff(382,plain,
% 0.47/0.56 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.47/0.56 inference(transitivity,[status(thm)],[381, 238, 366, 75, 360, 9])).
% 0.47/0.56 tff(383,plain,
% 0.47/0.56 (multiply(sk_c6, multiply(sk_c2, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.47/0.56 inference(monotonicity,[status(thm)],[382])).
% 0.47/0.56 tff(384,assumption,(~(inverse(sk_c2) = sk_c6)), introduced(assumption)).
% 0.47/0.56 tff(385,plain,
% 0.47/0.56 (((inverse(sk_c2) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)) <=> ((inverse(sk_c2) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(386,axiom,((inverse(sk_c2) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_24')).
% 0.47/0.56 tff(387,plain,
% 0.47/0.56 ((inverse(sk_c2) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.47/0.56 tff(388,plain,
% 0.47/0.56 (multiply(sk_c4, sk_c6) = sk_c7),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[387, 384])).
% 0.47/0.56 tff(389,plain,
% 0.47/0.56 (multiply(sk_c6, multiply(sk_c4, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.47/0.56 inference(monotonicity,[status(thm)],[388])).
% 0.47/0.56 tff(390,plain,
% 0.47/0.56 (((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c7))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(391,axiom,((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_22')).
% 0.47/0.56 tff(392,plain,
% 0.47/0.56 ((inverse(sk_c2) = sk_c6) | (inverse(sk_c3) = sk_c7)),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.47/0.56 tff(393,plain,
% 0.47/0.56 (inverse(sk_c3) = sk_c7),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[392, 384])).
% 0.47/0.56 tff(394,plain,
% 0.47/0.56 (sk_c7 = inverse(sk_c3)),
% 0.47/0.56 inference(symmetry,[status(thm)],[393])).
% 0.47/0.56 tff(395,plain,
% 0.47/0.56 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.47/0.56 inference(monotonicity,[status(thm)],[394])).
% 0.47/0.56 tff(396,plain,
% 0.47/0.56 (multiply(sk_c7, sk_c3) = multiply(sk_c6, sk_c4)),
% 0.47/0.56 inference(transitivity,[status(thm)],[395, 163, 158, 155])).
% 0.47/0.56 tff(397,plain,
% 0.47/0.56 (multiply(multiply(sk_c7, sk_c3), sk_c6) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.47/0.56 inference(monotonicity,[status(thm)],[396])).
% 0.47/0.56 tff(398,plain,
% 0.47/0.56 (((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)) <=> ((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(399,axiom,((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_23')).
% 0.47/0.56 tff(400,plain,
% 0.47/0.56 ((inverse(sk_c2) = sk_c6) | (multiply(sk_c3, sk_c6) = sk_c7)),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.47/0.56 tff(401,plain,
% 0.47/0.56 (multiply(sk_c3, sk_c6) = sk_c7),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[400, 384])).
% 0.47/0.56 tff(402,plain,
% 0.47/0.56 (sk_c7 = multiply(sk_c3, sk_c6)),
% 0.47/0.56 inference(symmetry,[status(thm)],[401])).
% 0.47/0.56 tff(403,plain,
% 0.47/0.56 (multiply(sk_c6, multiply(sk_c4, sk_c6)) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.47/0.56 inference(symmetry,[status(thm)],[338])).
% 0.47/0.56 tff(404,plain,
% 0.47/0.56 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c4, sk_c6))),
% 0.47/0.56 inference(symmetry,[status(thm)],[389])).
% 0.47/0.56 tff(405,plain,
% 0.47/0.56 (sk_c5 = sk_c6),
% 0.47/0.56 inference(transitivity,[status(thm)],[370, 404, 403, 161, 11])).
% 0.47/0.56 tff(406,plain,
% 0.47/0.56 (multiply(sk_c4, sk_c5) = multiply(sk_c4, sk_c6)),
% 0.47/0.56 inference(monotonicity,[status(thm)],[405])).
% 0.47/0.56 tff(407,plain,
% 0.47/0.56 (multiply(sk_c4, sk_c5) = sk_c7),
% 0.47/0.56 inference(transitivity,[status(thm)],[406, 388])).
% 0.47/0.56 tff(408,plain,
% 0.47/0.56 (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c7, multiply(sk_c3, sk_c6))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[407, 402])).
% 0.47/0.56 tff(409,plain,
% 0.47/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c4, multiply(sk_c5, sk_c7)))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(410,plain,
% 0.47/0.56 (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c4, multiply(sk_c5, sk_c7))),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[409, 37])).
% 0.47/0.56 tff(411,plain,
% 0.47/0.56 (multiply(sk_c4, multiply(sk_c5, sk_c7)) = multiply(multiply(sk_c4, sk_c5), sk_c7)),
% 0.47/0.56 inference(symmetry,[status(thm)],[410])).
% 0.47/0.56 tff(412,plain,
% 0.47/0.56 (multiply(sk_c5, sk_c7) = multiply(sk_c6, sk_c7)),
% 0.47/0.56 inference(monotonicity,[status(thm)],[405])).
% 0.47/0.56 tff(413,plain,
% 0.47/0.56 (multiply(sk_c6, sk_c7) = multiply(sk_c5, sk_c7)),
% 0.47/0.56 inference(symmetry,[status(thm)],[412])).
% 0.47/0.56 tff(414,plain,
% 0.47/0.56 (sk_c6 = multiply(sk_c5, sk_c7)),
% 0.47/0.56 inference(transitivity,[status(thm)],[114, 160, 338, 389, 413])).
% 0.47/0.56 tff(415,plain,
% 0.47/0.56 (multiply(sk_c4, sk_c6) = multiply(sk_c4, multiply(sk_c5, sk_c7))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[414])).
% 0.47/0.56 tff(416,plain,
% 0.47/0.56 (multiply(sk_c4, sk_c6) = sk_c5),
% 0.47/0.56 inference(transitivity,[status(thm)],[415, 411, 408, 212, 397, 338, 389, 314])).
% 0.47/0.56 tff(417,plain,
% 0.47/0.56 (sk_c7 = multiply(sk_c4, sk_c6)),
% 0.47/0.56 inference(symmetry,[status(thm)],[388])).
% 0.47/0.56 tff(418,plain,
% 0.47/0.56 (sk_c7 = sk_c6),
% 0.47/0.56 inference(transitivity,[status(thm)],[417, 415, 411, 408, 212, 397, 161, 11])).
% 0.47/0.56 tff(419,plain,
% 0.47/0.56 (multiply(sk_c3, sk_c7) = multiply(sk_c3, sk_c6)),
% 0.47/0.56 inference(monotonicity,[status(thm)],[418])).
% 0.47/0.56 tff(420,plain,
% 0.47/0.56 (multiply(sk_c3, sk_c7) = sk_c6),
% 0.47/0.56 inference(transitivity,[status(thm)],[419, 401, 417, 415, 411, 408, 212, 397, 161, 11])).
% 0.47/0.56 tff(421,plain,
% 0.47/0.56 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(422,plain,
% 0.47/0.56 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(423,plain,
% 0.47/0.56 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6))))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[422])).
% 0.47/0.56 tff(424,plain,
% 0.47/0.56 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.47/0.56 inference(transitivity,[status(thm)],[423, 421])).
% 0.47/0.56 tff(425,plain,
% 0.47/0.56 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(426,plain,
% 0.47/0.56 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6))),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.47/0.56 tff(427,plain,
% 0.47/0.56 ((~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c7) = sk_c6))),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[426, 237, 314, 393, 401, 388, 152, 141])).
% 0.47/0.56 tff(428,plain,
% 0.47/0.56 ($false),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[427, 420, 416])).
% 0.47/0.56 tff(429,plain,(inverse(sk_c2) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.47/0.56 tff(430,plain,
% 0.47/0.56 (sk_c6 = inverse(sk_c2)),
% 0.47/0.56 inference(symmetry,[status(thm)],[429])).
% 0.47/0.56 tff(431,plain,
% 0.47/0.56 (multiply(sk_c6, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.47/0.56 inference(monotonicity,[status(thm)],[430])).
% 0.47/0.56 tff(432,plain,
% 0.47/0.56 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c6, sk_c2)),
% 0.47/0.56 inference(symmetry,[status(thm)],[431])).
% 0.47/0.56 tff(433,plain,
% 0.47/0.56 (identity = multiply(sk_c6, sk_c2)),
% 0.47/0.56 inference(transitivity,[status(thm)],[111, 432])).
% 0.47/0.56 tff(434,plain,
% 0.47/0.56 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c2), sk_c6)),
% 0.47/0.56 inference(monotonicity,[status(thm)],[433])).
% 0.47/0.56 tff(435,plain,
% 0.47/0.56 (multiply(identity, sk_c6) = sk_c7),
% 0.47/0.56 inference(transitivity,[status(thm)],[434, 109, 383, 314, 238, 366, 75, 360, 9])).
% 0.47/0.56 tff(436,plain,
% 0.47/0.56 (multiply(multiply(identity, sk_c6), sk_c5) = multiply(sk_c7, sk_c7)),
% 0.47/0.56 inference(monotonicity,[status(thm)],[435, 367])).
% 0.47/0.56 tff(437,plain,
% 0.47/0.56 (multiply(sk_c7, sk_c7) = multiply(multiply(identity, sk_c6), sk_c5)),
% 0.47/0.56 inference(symmetry,[status(thm)],[436])).
% 0.47/0.56 tff(438,plain,
% 0.47/0.56 (sk_c7 = sk_c5),
% 0.47/0.56 inference(transitivity,[status(thm)],[57, 359, 39, 371, 237])).
% 0.47/0.56 tff(439,plain,
% 0.47/0.56 (sk_c5 = multiply(sk_c2, sk_c6)),
% 0.47/0.56 inference(symmetry,[status(thm)],[381])).
% 0.47/0.56 tff(440,plain,
% 0.47/0.56 (sk_c7 = multiply(sk_c2, sk_c6)),
% 0.47/0.56 inference(transitivity,[status(thm)],[57, 359, 39, 371, 237, 439])).
% 0.47/0.56 tff(441,plain,
% 0.47/0.56 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c2, sk_c6), sk_c5)),
% 0.47/0.56 inference(monotonicity,[status(thm)],[440, 438])).
% 0.47/0.56 tff(442,plain,
% 0.47/0.56 (multiply(multiply(sk_c2, sk_c6), sk_c5) = multiply(sk_c7, sk_c7)),
% 0.47/0.56 inference(symmetry,[status(thm)],[441])).
% 0.47/0.56 tff(443,plain,
% 0.47/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c6), sk_c5) = multiply(sk_c2, multiply(sk_c6, sk_c5)))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(444,plain,
% 0.47/0.56 (multiply(multiply(sk_c2, sk_c6), sk_c5) = multiply(sk_c2, multiply(sk_c6, sk_c5))),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[443, 37])).
% 0.47/0.56 tff(445,plain,
% 0.47/0.56 (multiply(sk_c2, multiply(sk_c6, sk_c5)) = multiply(multiply(sk_c2, sk_c6), sk_c5)),
% 0.47/0.56 inference(symmetry,[status(thm)],[444])).
% 0.47/0.56 tff(446,plain,
% 0.47/0.56 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(sk_c6, sk_c5))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[372])).
% 0.47/0.56 tff(447,plain,
% 0.47/0.56 (multiply(sk_c2, sk_c7) = sk_c7),
% 0.47/0.56 inference(transitivity,[status(thm)],[446, 445, 442, 437, 377, 375, 360, 9])).
% 0.47/0.56 tff(448,plain,
% 0.47/0.56 ((multiply(sk_c2, sk_c7) = sk_c6) <=> (sk_c7 = inverse(sk_c4))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[447, 153])).
% 0.47/0.56 tff(449,plain,
% 0.47/0.57 ((multiply(sk_c2, sk_c7) = sk_c6) <=> (inverse(sk_c4) = sk_c7)),
% 0.47/0.57 inference(transitivity,[status(thm)],[448, 349])).
% 0.47/0.57 tff(450,plain,
% 0.47/0.57 ((inverse(sk_c4) = sk_c7) <=> (multiply(sk_c2, sk_c7) = sk_c6)),
% 0.47/0.57 inference(symmetry,[status(thm)],[449])).
% 0.47/0.57 tff(451,plain,
% 0.47/0.57 ((~(inverse(sk_c4) = sk_c7)) <=> (~(multiply(sk_c2, sk_c7) = sk_c6))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[450])).
% 0.47/0.57 tff(452,plain,
% 0.47/0.57 (inverse(sk_c2) = inverse(sk_c4)),
% 0.47/0.57 inference(transitivity,[status(thm)],[429, 153])).
% 0.47/0.57 tff(453,plain,
% 0.47/0.57 ((inverse(sk_c2) = sk_c7) <=> (inverse(sk_c4) = sk_c7)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[452])).
% 0.47/0.57 tff(454,plain,
% 0.47/0.57 ((~(inverse(sk_c2) = sk_c7)) <=> (~(inverse(sk_c4) = sk_c7))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[453])).
% 0.47/0.57 tff(455,plain,
% 0.47/0.57 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(456,plain,
% 0.47/0.57 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(457,plain,
% 0.47/0.57 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7))))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[456])).
% 0.47/0.57 tff(458,plain,
% 0.47/0.57 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)))),
% 0.47/0.57 inference(transitivity,[status(thm)],[457, 455])).
% 0.47/0.57 tff(459,plain,
% 0.47/0.57 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(460,plain,
% 0.47/0.57 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.47/0.57 tff(461,plain,
% 0.47/0.57 ((~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[460, 237, 314, 364, 354, 381, 429, 141])).
% 0.47/0.57 tff(462,plain,
% 0.47/0.57 (~(inverse(sk_c2) = sk_c7)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[461, 382])).
% 0.47/0.57 tff(463,plain,
% 0.47/0.57 (~(inverse(sk_c4) = sk_c7)),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[462, 454])).
% 0.47/0.57 tff(464,plain,
% 0.47/0.57 (~(multiply(sk_c2, sk_c7) = sk_c6)),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[463, 451])).
% 0.47/0.57 tff(465,plain,
% 0.47/0.57 (multiply(identity, multiply(sk_c6, sk_c5)) = multiply(multiply(identity, sk_c6), sk_c5)),
% 0.47/0.57 inference(symmetry,[status(thm)],[377])).
% 0.47/0.57 tff(466,plain,
% 0.47/0.57 (sk_c7 = multiply(sk_c7, sk_c7)),
% 0.47/0.57 inference(transitivity,[status(thm)],[57, 359, 374, 465, 436])).
% 0.47/0.57 tff(467,plain,
% 0.47/0.57 (multiply(sk_c1, sk_c7) = multiply(sk_c1, multiply(sk_c7, sk_c7))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[466])).
% 0.47/0.57 tff(468,plain,
% 0.47/0.57 (multiply(sk_c1, multiply(sk_c7, sk_c7)) = multiply(sk_c1, sk_c7)),
% 0.47/0.57 inference(symmetry,[status(thm)],[467])).
% 0.47/0.57 tff(469,plain,
% 0.47/0.57 (multiply(multiply(sk_c1, sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[364])).
% 0.47/0.57 tff(470,plain,
% 0.47/0.57 (multiply(sk_c6, sk_c7) = multiply(multiply(sk_c1, sk_c7), sk_c7)),
% 0.47/0.57 inference(symmetry,[status(thm)],[469])).
% 0.47/0.57 tff(471,plain,
% 0.47/0.57 (multiply(sk_c2, sk_c7) = sk_c6),
% 0.47/0.57 inference(transitivity,[status(thm)],[446, 445, 442, 437, 377, 375, 39, 371, 237, 370, 470, 309, 468, 364])).
% 0.47/0.57 tff(472,plain,
% 0.47/0.57 ($false),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[471, 464])).
% 0.47/0.57 tff(473,plain,(multiply(sk_c3, sk_c6) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.47/0.57 tff(474,plain,
% 0.47/0.57 (sk_c7 = multiply(sk_c3, sk_c6)),
% 0.47/0.57 inference(symmetry,[status(thm)],[473])).
% 0.47/0.57 tff(475,plain,
% 0.47/0.57 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c4, sk_c6))),
% 0.47/0.57 inference(symmetry,[status(thm)],[336])).
% 0.47/0.57 tff(476,plain,
% 0.47/0.57 (sk_c5 = sk_c6),
% 0.47/0.57 inference(transitivity,[status(thm)],[370, 475, 403, 161, 11])).
% 0.47/0.57 tff(477,plain,
% 0.47/0.57 (multiply(sk_c4, sk_c5) = multiply(sk_c4, sk_c6)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[476])).
% 0.47/0.57 tff(478,plain,
% 0.47/0.57 (multiply(sk_c4, sk_c5) = sk_c7),
% 0.47/0.57 inference(transitivity,[status(thm)],[477, 335])).
% 0.47/0.57 tff(479,plain,
% 0.47/0.57 (multiply(multiply(sk_c4, sk_c5), sk_c7) = multiply(sk_c7, multiply(sk_c3, sk_c6))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[478, 474])).
% 0.47/0.57 tff(480,plain,
% 0.47/0.57 (multiply(sk_c5, sk_c7) = multiply(sk_c6, sk_c7)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[476])).
% 0.47/0.57 tff(481,plain,
% 0.47/0.57 (multiply(sk_c6, sk_c7) = multiply(sk_c5, sk_c7)),
% 0.47/0.57 inference(symmetry,[status(thm)],[480])).
% 0.47/0.57 tff(482,plain,
% 0.47/0.57 (sk_c6 = multiply(sk_c5, sk_c7)),
% 0.47/0.57 inference(transitivity,[status(thm)],[114, 160, 338, 336, 481])).
% 0.47/0.57 tff(483,plain,
% 0.47/0.57 (multiply(sk_c4, sk_c6) = multiply(sk_c4, multiply(sk_c5, sk_c7))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[482])).
% 0.47/0.57 tff(484,plain,
% 0.47/0.57 (multiply(sk_c4, sk_c6) = sk_c5),
% 0.47/0.57 inference(transitivity,[status(thm)],[483, 411, 479, 212, 348, 338, 336, 314])).
% 0.47/0.57 tff(485,plain,
% 0.47/0.57 (sk_c7 = multiply(sk_c4, sk_c6)),
% 0.47/0.57 inference(symmetry,[status(thm)],[335])).
% 0.47/0.57 tff(486,plain,
% 0.47/0.57 (sk_c7 = sk_c6),
% 0.47/0.57 inference(transitivity,[status(thm)],[485, 483, 411, 479, 212, 348, 161, 11])).
% 0.47/0.57 tff(487,plain,
% 0.47/0.57 (multiply(sk_c3, sk_c7) = multiply(sk_c3, sk_c6)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[486])).
% 0.47/0.57 tff(488,plain,
% 0.47/0.57 (multiply(sk_c3, sk_c7) = sk_c6),
% 0.47/0.57 inference(transitivity,[status(thm)],[487, 473, 485, 483, 411, 479, 212, 348, 161, 11])).
% 0.47/0.57 tff(489,plain,
% 0.47/0.57 ((~(multiply(sk_c4, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c7) = sk_c6))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[426, 237, 314, 344, 473, 335, 152, 141])).
% 0.47/0.57 tff(490,plain,
% 0.47/0.57 ($false),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[489, 488, 484])).
% 0.47/0.57 tff(491,plain,(multiply(sk_c2, sk_c6) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.47/0.57 tff(492,plain,
% 0.47/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), sk_c6) = multiply(sk_c1, multiply(sk_c7, sk_c6)))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(493,plain,
% 0.47/0.57 (multiply(multiply(sk_c1, sk_c7), sk_c6) = multiply(sk_c1, multiply(sk_c7, sk_c6))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[492, 37])).
% 0.47/0.57 tff(494,plain,
% 0.47/0.57 (sk_c6 = multiply(sk_c1, sk_c7)),
% 0.47/0.57 inference(symmetry,[status(thm)],[180])).
% 0.47/0.57 tff(495,plain,
% 0.47/0.57 (multiply(sk_c6, sk_c6) = multiply(multiply(sk_c1, sk_c7), sk_c6)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[494])).
% 0.47/0.57 tff(496,plain,
% 0.47/0.57 (multiply(sk_c6, multiply(sk_c1, sk_c7)) = multiply(sk_c6, sk_c6)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[180])).
% 0.47/0.57 tff(497,plain,
% 0.47/0.57 (multiply(sk_c6, multiply(sk_c1, sk_c7)) = sk_c6),
% 0.47/0.57 inference(transitivity,[status(thm)],[496, 495, 493, 318, 180])).
% 0.47/0.57 tff(498,plain,
% 0.47/0.57 (multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c2, sk_c6)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[497])).
% 0.47/0.57 tff(499,plain,
% 0.47/0.57 (multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))) = sk_c7),
% 0.47/0.57 inference(transitivity,[status(thm)],[498, 491, 238, 182, 75, 174, 9])).
% 0.47/0.57 tff(500,plain,
% 0.47/0.57 (multiply(multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c5) = multiply(sk_c7, sk_c7)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[499, 315])).
% 0.47/0.57 tff(501,plain,
% 0.47/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c5) = multiply(sk_c2, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5)))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(502,plain,
% 0.47/0.57 (multiply(multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c5) = multiply(sk_c2, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[501, 37])).
% 0.47/0.57 tff(503,plain,
% 0.47/0.57 (multiply(sk_c2, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5)) = multiply(multiply(sk_c2, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c5)),
% 0.47/0.57 inference(symmetry,[status(thm)],[502])).
% 0.47/0.57 tff(504,plain,
% 0.47/0.57 (multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5) = multiply(sk_c6, sk_c7)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[497, 315])).
% 0.47/0.57 tff(505,plain,
% 0.47/0.57 (multiply(sk_c6, sk_c7) = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5)),
% 0.47/0.57 inference(symmetry,[status(thm)],[504])).
% 0.47/0.57 tff(506,plain,
% 0.47/0.57 (sk_c7 = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5)),
% 0.47/0.57 inference(transitivity,[status(thm)],[57, 173, 39, 181, 237, 370, 505])).
% 0.47/0.57 tff(507,plain,
% 0.47/0.57 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c5))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[506])).
% 0.47/0.57 tff(508,plain,
% 0.47/0.57 (multiply(sk_c2, sk_c7) = multiply(sk_c5, sk_c5)),
% 0.47/0.57 inference(transitivity,[status(thm)],[507, 503, 500, 330])).
% 0.47/0.57 tff(509,plain,
% 0.47/0.57 (multiply(sk_c1, multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c1, sk_c6)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[497])).
% 0.47/0.57 tff(510,plain,
% 0.47/0.57 (multiply(multiply(sk_c1, multiply(sk_c6, multiply(sk_c1, sk_c7))), multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c1, sk_c6), multiply(sk_c5, sk_c5))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[509, 508])).
% 0.47/0.57 tff(511,plain,
% 0.47/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, multiply(sk_c6, multiply(sk_c1, sk_c7))), multiply(sk_c2, sk_c7)) = multiply(sk_c1, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7))))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(512,plain,
% 0.47/0.57 (multiply(multiply(sk_c1, multiply(sk_c6, multiply(sk_c1, sk_c7))), multiply(sk_c2, sk_c7)) = multiply(sk_c1, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7)))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[511, 37])).
% 0.47/0.57 tff(513,plain,
% 0.47/0.57 (multiply(sk_c1, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7))) = multiply(multiply(sk_c1, multiply(sk_c6, multiply(sk_c1, sk_c7))), multiply(sk_c2, sk_c7))),
% 0.47/0.57 inference(symmetry,[status(thm)],[512])).
% 0.47/0.57 tff(514,plain,
% 0.47/0.57 (multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7)) = multiply(sk_c6, multiply(sk_c2, sk_c7))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[497])).
% 0.47/0.57 tff(515,plain,
% 0.47/0.57 (multiply(sk_c6, multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7))),
% 0.47/0.57 inference(symmetry,[status(thm)],[514])).
% 0.47/0.57 tff(516,plain,
% 0.47/0.57 (multiply(sk_c6, sk_c2) = multiply(sk_c7, sk_c1)),
% 0.47/0.57 inference(transitivity,[status(thm)],[431, 62, 54, 171])).
% 0.47/0.57 tff(517,plain,
% 0.47/0.57 (multiply(multiply(sk_c6, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[516])).
% 0.47/0.57 tff(518,plain,
% 0.47/0.57 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c6, sk_c2), sk_c7)),
% 0.47/0.57 inference(symmetry,[status(thm)],[517])).
% 0.47/0.57 tff(519,plain,
% 0.47/0.57 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7))),
% 0.47/0.57 inference(transitivity,[status(thm)],[182, 75, 518, 72, 515])).
% 0.47/0.57 tff(520,plain,
% 0.47/0.57 (multiply(sk_c1, multiply(sk_c7, sk_c6)) = multiply(sk_c1, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(sk_c2, sk_c7)))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[519])).
% 0.47/0.57 tff(521,plain,
% 0.47/0.57 (inverse(sk_c4) = sk_c7),
% 0.47/0.57 inference(transitivity,[status(thm)],[152, 494, 317, 520, 513, 510, 328, 325, 314, 238, 182, 75, 174, 9])).
% 0.47/0.57 tff(522,plain,
% 0.47/0.57 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.47/0.57 inference(transitivity,[status(thm)],[491, 238, 182, 75, 174, 9])).
% 0.47/0.57 tff(523,plain,
% 0.47/0.57 ((~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c7))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[460, 237, 314, 180, 168, 491, 429, 141])).
% 0.47/0.57 tff(524,plain,
% 0.47/0.57 (~(inverse(sk_c2) = sk_c7)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[523, 522])).
% 0.47/0.57 tff(525,plain,
% 0.47/0.57 (~(inverse(sk_c4) = sk_c7)),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[524, 454])).
% 0.47/0.57 tff(526,plain,
% 0.47/0.57 ($false),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[525, 521])).
% 0.47/0.57 tff(527,plain,(inverse(sk_c3) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.47/0.57 tff(528,plain,
% 0.47/0.57 (sk_c7 = inverse(sk_c3)),
% 0.47/0.57 inference(symmetry,[status(thm)],[527])).
% 0.47/0.57 tff(529,plain,
% 0.47/0.57 (multiply(sk_c3, sk_c6) = inverse(sk_c3)),
% 0.47/0.57 inference(transitivity,[status(thm)],[473, 528])).
% 0.47/0.57 tff(530,plain,
% 0.47/0.57 (multiply(multiply(sk_c3, sk_c6), sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[529])).
% 0.47/0.57 tff(531,plain,
% 0.47/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c6), sk_c3) = multiply(sk_c3, multiply(sk_c6, sk_c3)))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(532,plain,
% 0.47/0.57 (multiply(multiply(sk_c3, sk_c6), sk_c3) = multiply(sk_c3, multiply(sk_c6, sk_c3))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[531, 37])).
% 0.47/0.57 tff(533,plain,
% 0.47/0.57 (multiply(sk_c3, multiply(sk_c6, sk_c3)) = multiply(multiply(sk_c3, sk_c6), sk_c3)),
% 0.47/0.57 inference(symmetry,[status(thm)],[532])).
% 0.47/0.57 tff(534,plain,
% 0.47/0.57 (multiply(sk_c3, multiply(sk_c6, sk_c3)) = multiply(sk_c6, sk_c4)),
% 0.47/0.57 inference(transitivity,[status(thm)],[533, 530, 163, 158, 155])).
% 0.47/0.57 tff(535,plain,
% 0.47/0.57 (multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6) = multiply(multiply(sk_c6, sk_c4), sk_c6)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[534])).
% 0.47/0.57 tff(536,plain,
% 0.47/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6)))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(537,plain,
% 0.47/0.57 (multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[536, 37])).
% 0.47/0.57 tff(538,plain,
% 0.47/0.57 (multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6)) = multiply(multiply(sk_c3, multiply(sk_c6, sk_c3)), sk_c6)),
% 0.47/0.57 inference(symmetry,[status(thm)],[537])).
% 0.47/0.57 tff(539,plain,
% 0.47/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c3), sk_c6) = multiply(sk_c6, multiply(sk_c3, sk_c6)))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(540,plain,
% 0.47/0.57 (multiply(multiply(sk_c6, sk_c3), sk_c6) = multiply(sk_c6, multiply(sk_c3, sk_c6))),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[539, 37])).
% 0.47/0.57 tff(541,plain,
% 0.47/0.57 (multiply(sk_c6, multiply(sk_c3, sk_c6)) = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.47/0.57 inference(symmetry,[status(thm)],[540])).
% 0.47/0.57 tff(542,plain,
% 0.47/0.57 (multiply(sk_c6, multiply(sk_c3, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[473])).
% 0.47/0.57 tff(543,plain,
% 0.47/0.57 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c3, sk_c6))),
% 0.47/0.57 inference(symmetry,[status(thm)],[542])).
% 0.47/0.57 tff(544,assumption,(multiply(sk_c4, sk_c6) = sk_c7), introduced(assumption)).
% 0.47/0.57 tff(545,plain,
% 0.47/0.57 (multiply(sk_c6, multiply(sk_c4, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.47/0.57 inference(monotonicity,[status(thm)],[544])).
% 0.47/0.57 tff(546,plain,
% 0.47/0.57 (sk_c6 = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.47/0.57 inference(transitivity,[status(thm)],[114, 160, 338, 545, 543, 541])).
% 0.47/0.57 tff(547,plain,
% 0.47/0.57 (multiply(sk_c3, sk_c6) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[546])).
% 0.47/0.58 tff(548,plain,
% 0.47/0.58 (sk_c7 = multiply(multiply(sk_c6, sk_c3), sk_c6)),
% 0.47/0.58 inference(transitivity,[status(thm)],[474, 547, 538, 535, 338, 545, 543, 541])).
% 0.47/0.58 tff(549,plain,
% 0.47/0.58 (multiply(sk_c3, sk_c7) = multiply(sk_c3, multiply(multiply(sk_c6, sk_c3), sk_c6))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[548])).
% 0.47/0.58 tff(550,plain,
% 0.47/0.58 (multiply(sk_c3, sk_c7) = sk_c6),
% 0.47/0.58 inference(transitivity,[status(thm)],[549, 538, 535, 161, 11])).
% 0.47/0.58 tff(551,plain,
% 0.47/0.58 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(552,plain,
% 0.47/0.58 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(553,plain,
% 0.47/0.58 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[552])).
% 0.47/0.58 tff(554,plain,
% 0.47/0.58 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6)))),
% 0.47/0.58 inference(transitivity,[status(thm)],[553, 551])).
% 0.47/0.58 tff(555,plain,
% 0.47/0.58 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c4) = sk_c6)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)))),
% 0.47/0.58 inference(quant_inst,[status(thm)],[])).
% 0.47/0.58 tff(556,plain,
% 0.47/0.58 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c6))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.47/0.58 tff(557,plain,
% 0.47/0.58 ((~(multiply(sk_c4, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6))),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[556, 237, 314, 527, 473, 152, 491, 429, 141])).
% 0.47/0.58 tff(558,plain,
% 0.47/0.58 (~(multiply(sk_c3, sk_c7) = sk_c6)),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[557, 544])).
% 0.47/0.58 tff(559,plain,
% 0.47/0.58 ($false),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[558, 550])).
% 0.47/0.58 tff(560,plain,(~(multiply(sk_c4, sk_c6) = sk_c7)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.58 tff(561,plain,
% 0.47/0.58 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c6) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c6) = sk_c7))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(562,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_14')).
% 0.47/0.58 tff(563,plain,
% 0.47/0.58 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c6) = sk_c7)),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.47/0.58 tff(564,plain,
% 0.47/0.58 (inverse(sk_c1) = sk_c7),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[563, 560])).
% 0.47/0.58 tff(565,plain,
% 0.47/0.58 (sk_c7 = inverse(sk_c1)),
% 0.47/0.58 inference(symmetry,[status(thm)],[564])).
% 0.47/0.58 tff(566,plain,
% 0.47/0.58 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.47/0.58 inference(monotonicity,[status(thm)],[565])).
% 0.47/0.58 tff(567,plain,
% 0.47/0.58 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.47/0.58 inference(symmetry,[status(thm)],[566])).
% 0.47/0.58 tff(568,plain,
% 0.47/0.58 (identity = multiply(sk_c7, sk_c1)),
% 0.47/0.58 inference(transitivity,[status(thm)],[54, 567])).
% 0.47/0.58 tff(569,plain,
% 0.47/0.58 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.47/0.58 inference(monotonicity,[status(thm)],[568])).
% 0.47/0.58 tff(570,plain,
% 0.47/0.58 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.47/0.58 inference(symmetry,[status(thm)],[569])).
% 0.47/0.58 tff(571,plain,
% 0.47/0.58 (((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(572,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_9')).
% 0.47/0.58 tff(573,plain,
% 0.47/0.58 ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c6) = sk_c7)),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[572, 571])).
% 0.47/0.58 tff(574,plain,
% 0.47/0.58 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[573, 560])).
% 0.47/0.58 tff(575,plain,
% 0.47/0.58 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.47/0.58 inference(monotonicity,[status(thm)],[574])).
% 0.47/0.58 tff(576,plain,
% 0.47/0.58 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.47/0.58 inference(symmetry,[status(thm)],[575])).
% 0.47/0.58 tff(577,plain,
% 0.47/0.58 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.47/0.58 inference(transitivity,[status(thm)],[491, 238, 576, 75, 570, 9])).
% 0.47/0.58 tff(578,plain,
% 0.47/0.58 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(579,plain,
% 0.47/0.58 (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(580,plain,
% 0.47/0.58 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[579])).
% 0.47/0.58 tff(581,plain,
% 0.47/0.58 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)))),
% 0.47/0.58 inference(transitivity,[status(thm)],[580, 578])).
% 0.47/0.58 tff(582,plain,
% 0.47/0.58 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)))),
% 0.47/0.58 inference(quant_inst,[status(thm)],[])).
% 0.47/0.58 tff(583,plain,
% 0.47/0.58 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(X1, sk_c6) = sk_c7)) | (~(inverse(X1) = sk_c7)) | (~(inverse(X4) = sk_c6)) | (~(multiply(X4, sk_c6) = sk_c5)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))) | (~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c5)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c3, sk_c6) = sk_c7)) | (~(inverse(sk_c3) = sk_c7))),
% 0.47/0.59 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.47/0.59 tff(584,plain,
% 0.47/0.59 (~(multiply(sk_c2, sk_c6) = sk_c7)),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[583, 237, 314, 527, 473, 574, 564, 491, 429, 141])).
% 0.47/0.59 tff(585,plain,
% 0.47/0.59 ($false),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[584, 577])).
% 0.47/0.59 % SZS output end Proof
%------------------------------------------------------------------------------