TSTP Solution File: GRP304-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP304-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 22:27:05 EDT 2022
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP304-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 16:13:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(sk_c7_type, type, (
% 0.20/0.46 sk_c7: $i)).
% 0.20/0.46 tff(multiply_type, type, (
% 0.20/0.46 multiply: ( $i * $i ) > $i)).
% 0.20/0.46 tff(sk_c6_type, type, (
% 0.20/0.46 sk_c6: $i)).
% 0.20/0.46 tff(sk_c1_type, type, (
% 0.20/0.46 sk_c1: $i)).
% 0.20/0.46 tff(identity_type, type, (
% 0.20/0.46 identity: $i)).
% 0.20/0.46 tff(sk_c2_type, type, (
% 0.20/0.46 sk_c2: $i)).
% 0.20/0.46 tff(inverse_type, type, (
% 0.20/0.46 inverse: $i > $i)).
% 0.20/0.46 tff(sk_c5_type, type, (
% 0.20/0.46 sk_c5: $i)).
% 0.20/0.46 tff(sk_c3_type, type, (
% 0.20/0.46 sk_c3: $i)).
% 0.20/0.46 tff(sk_c4_type, type, (
% 0.20/0.46 sk_c4: $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(4,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.46 tff(6,plain,(
% 0.20/0.46 ![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.46 inference(skolemize,[status(sab)],[5])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (multiply(identity, sk_c7) = sk_c7),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.46 tff(10,assumption,(~(inverse(sk_c7) = multiply(sk_c7, sk_c6))), introduced(assumption)).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c7) = sk_c6)) <=> ((inverse(sk_c7) = multiply(sk_c7, sk_c6)) | (multiply(sk_c2, sk_c7) = sk_c6))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c7) = sk_c6)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c7) = sk_c6))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(13,axiom,((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c7) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_7')).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c2, sk_c7) = sk_c6)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 ((inverse(sk_c7) = multiply(sk_c7, sk_c6)) | (multiply(sk_c2, sk_c7) = sk_c6)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (multiply(sk_c2, sk_c7) = sk_c6),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[15, 10])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (multiply(sk_c7, multiply(sk_c2, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(21,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')).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.46 tff(23,plain,(
% 0.20/0.46 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[22])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(sk_c7, multiply(sk_c2, sk_c7)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(sk_c7, multiply(sk_c2, sk_c7))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = sk_c5)) <=> ((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = multiply(sk_c7, sk_c6)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = sk_c5)) <=> ((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = sk_c5))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(29,plain,
% 0.20/0.46 (((inverse(sk_c7) = sk_c5) | (inverse(sk_c2) = sk_c7)) <=> ((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = sk_c5))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(30,axiom,((inverse(sk_c7) = sk_c5) | (inverse(sk_c2) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_8')).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 ((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 ((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.20/0.46 tff(33,plain,
% 0.20/0.46 ((inverse(sk_c2) = sk_c7) | (inverse(sk_c7) = multiply(sk_c7, sk_c6))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (inverse(sk_c2) = sk_c7),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[33, 10])).
% 0.20/0.46 tff(35,plain,
% 0.20/0.46 (sk_c7 = inverse(sk_c2)),
% 0.20/0.46 inference(symmetry,[status(thm)],[34])).
% 0.20/0.46 tff(36,plain,
% 0.20/0.46 (multiply(sk_c7, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c7, sk_c2)),
% 0.20/0.46 inference(symmetry,[status(thm)],[36])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(41,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.46 tff(43,plain,(
% 0.20/0.46 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.46 inference(skolemize,[status(sab)],[42])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.20/0.46 inference(symmetry,[status(thm)],[46])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c3), sk_c3) = identity)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 (multiply(inverse(sk_c3), sk_c3) = identity),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[48, 44])).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5)) <=> ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = multiply(sk_c7, sk_c6)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5)) <=> ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (((inverse(sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(53,axiom,((inverse(sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_11')).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = sk_c5)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 ((inverse(sk_c3) = sk_c7) | (inverse(sk_c7) = multiply(sk_c7, sk_c6))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[55, 50])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (inverse(sk_c3) = sk_c7),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[56, 10])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (sk_c7 = inverse(sk_c3)),
% 0.20/0.47 inference(symmetry,[status(thm)],[57])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[58])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (multiply(sk_c7, sk_c3) = multiply(sk_c7, sk_c2)),
% 0.20/0.47 inference(transitivity,[status(thm)],[59, 49, 47, 37])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(sk_c7, multiply(sk_c3, sk_c7)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(sk_c7, multiply(sk_c3, sk_c7))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[62, 24])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (multiply(sk_c7, multiply(sk_c3, sk_c7)) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.20/0.47 inference(symmetry,[status(thm)],[63])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((inverse(sk_c7) = multiply(sk_c7, sk_c6)) | (multiply(sk_c3, sk_c7) = sk_c4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(67,axiom,((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_10')).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 ((inverse(sk_c7) = multiply(sk_c7, sk_c6)) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (multiply(sk_c3, sk_c7) = sk_c4),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[69, 10])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (sk_c4 = multiply(sk_c3, sk_c7)),
% 0.20/0.47 inference(symmetry,[status(thm)],[70])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (multiply(sk_c7, sk_c4) = multiply(sk_c7, multiply(sk_c3, sk_c7))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.47 tff(73,assumption,(~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))), introduced(assumption)).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (((multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) <=> (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)) <=> ((multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)) | (inverse(sk_c3) = sk_c7))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 (((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 (((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)) <=> ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(79,axiom,((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_6')).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[80, 78])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (inverse(sk_c3) = sk_c7)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[83, 78])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (inverse(sk_c3) = sk_c7),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[85, 73])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 (sk_c7 = inverse(sk_c3)),
% 0.20/0.47 inference(symmetry,[status(thm)],[86])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[87])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c7, sk_c3)),
% 0.20/0.47 inference(symmetry,[status(thm)],[88])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (identity = multiply(inverse(sk_c3), sk_c3)),
% 0.20/0.47 inference(symmetry,[status(thm)],[49])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (identity = multiply(sk_c7, sk_c3)),
% 0.20/0.47 inference(transitivity,[status(thm)],[90, 89])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(identity, sk_c7)),
% 0.20/0.47 inference(symmetry,[status(thm)],[92])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 (((multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((multiply(sk_c3, sk_c7) = sk_c4) | (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)) | (multiply(sk_c3, sk_c7) = sk_c4))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((multiply(sk_c3, sk_c7) = sk_c4) | (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[95, 94])).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(98,axiom,((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_5')).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[99, 97])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[100, 97])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[102, 97])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 ((multiply(sk_c3, sk_c7) = sk_c4) | (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 (multiply(sk_c3, sk_c7) = sk_c4),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[104, 73])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 (multiply(sk_c7, multiply(sk_c3, sk_c7)) = multiply(sk_c7, sk_c4)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (multiply(sk_c7, sk_c4) = multiply(sk_c7, multiply(sk_c3, sk_c7))),
% 0.20/0.47 inference(symmetry,[status(thm)],[106])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)) <=> ((multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)) | (multiply(sk_c7, sk_c4) = sk_c6))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)) <=> ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(110,axiom,((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_4')).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 ((multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)) | (multiply(sk_c7, sk_c4) = sk_c6)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[111, 108])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (multiply(sk_c7, sk_c4) = sk_c6),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[112, 73])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (sk_c6 = multiply(sk_c7, sk_c4)),
% 0.20/0.47 inference(symmetry,[status(thm)],[113])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (sk_c6 = sk_c7),
% 0.20/0.47 inference(transitivity,[status(thm)],[114, 107, 64, 93, 9])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (sk_c7 = multiply(identity, sk_c7)),
% 0.20/0.47 inference(symmetry,[status(thm)],[9])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (sk_c7 = sk_c6),
% 0.20/0.47 inference(transitivity,[status(thm)],[116, 92, 63, 106, 113])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (multiply(sk_c7, sk_c6) = multiply(sk_c6, sk_c7)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[117, 115])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 (multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)),
% 0.20/0.47 inference(symmetry,[status(thm)],[118])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[73, 119])).
% 0.20/0.47 tff(121,plain,(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(122,assumption,(~(multiply(sk_c7, sk_c4) = sk_c6)), introduced(assumption)).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c4) = sk_c6)) <=> ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c4) = sk_c6))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(124,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_14')).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c7, sk_c4) = sk_c6)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (multiply(sk_c1, sk_c6) = sk_c7),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[126])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(sk_c6, multiply(sk_c1, sk_c6)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(sk_c6, multiply(sk_c1, sk_c6))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[128, 24])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 (((inverse(sk_c1) = sk_c6) | (multiply(sk_c7, sk_c4) = sk_c6)) <=> ((inverse(sk_c1) = sk_c6) | (multiply(sk_c7, sk_c4) = sk_c6))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(131,axiom,((inverse(sk_c1) = sk_c6) | (multiply(sk_c7, sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_19')).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 ((inverse(sk_c1) = sk_c6) | (multiply(sk_c7, sk_c4) = sk_c6)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 (inverse(sk_c1) = sk_c6),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[132, 122])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 (sk_c6 = inverse(sk_c1)),
% 0.20/0.47 inference(symmetry,[status(thm)],[133])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 (multiply(sk_c6, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c6, sk_c1)),
% 0.20/0.47 inference(symmetry,[status(thm)],[135])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[137, 44])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.20/0.47 inference(symmetry,[status(thm)],[138])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 (identity = multiply(sk_c6, sk_c1)),
% 0.20/0.47 inference(transitivity,[status(thm)],[139, 136])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[140])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c6) = sk_c6)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (multiply(identity, sk_c6) = sk_c6),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[142, 7])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (sk_c6 = multiply(identity, sk_c6)),
% 0.20/0.47 inference(symmetry,[status(thm)],[143])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (inverse(sk_c1) = multiply(sk_c7, sk_c6)),
% 0.20/0.47 inference(transitivity,[status(thm)],[133, 144, 141, 129, 127, 121])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 ((inverse(sk_c1) = sk_c7) <=> (multiply(sk_c7, sk_c6) = sk_c7)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[145])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 ((~(inverse(sk_c1) = sk_c7)) <=> (~(multiply(sk_c7, sk_c6) = sk_c7))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(identity, sk_c6)),
% 0.20/0.47 inference(symmetry,[status(thm)],[141])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.20/0.47 inference(symmetry,[status(thm)],[129])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c1, sk_c6))),
% 0.20/0.47 inference(symmetry,[status(thm)],[127])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (multiply(sk_c7, sk_c6) = multiply(sk_c6, sk_c7)),
% 0.20/0.47 inference(symmetry,[status(thm)],[121])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (multiply(multiply(sk_c1, sk_c6), sk_c6) = multiply(sk_c7, sk_c6)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[126])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c6), sk_c6) = multiply(sk_c1, multiply(sk_c6, sk_c6)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 (multiply(multiply(sk_c1, sk_c6), sk_c6) = multiply(sk_c1, multiply(sk_c6, sk_c6))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[153, 24])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 (multiply(sk_c1, multiply(sk_c6, sk_c6)) = multiply(multiply(sk_c1, sk_c6), sk_c6)),
% 0.20/0.47 inference(symmetry,[status(thm)],[154])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (sk_c6 = multiply(sk_c7, sk_c6)),
% 0.20/0.47 inference(transitivity,[status(thm)],[144, 141, 129, 127, 121])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (multiply(sk_c6, sk_c6) = multiply(multiply(sk_c7, sk_c6), multiply(sk_c7, sk_c6))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[156, 156])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (multiply(multiply(sk_c7, sk_c6), multiply(sk_c7, sk_c6)) = multiply(sk_c6, sk_c6)),
% 0.20/0.47 inference(symmetry,[status(thm)],[157])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c6), sk_c7), sk_c6) = multiply(multiply(sk_c7, sk_c6), multiply(sk_c7, sk_c6)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (multiply(multiply(multiply(sk_c7, sk_c6), sk_c7), sk_c6) = multiply(multiply(sk_c7, sk_c6), multiply(sk_c7, sk_c6))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[159, 24])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c7), sk_c7) = identity)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 (multiply(inverse(sk_c7), sk_c7) = identity),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[161, 44])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)) <=> ((inverse(sk_c7) = multiply(sk_c7, sk_c6)) | (multiply(sk_c7, sk_c4) = sk_c6))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 (((inverse(sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)) <=> ((inverse(sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(165,axiom,((inverse(sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_9')).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 ((inverse(sk_c7) = sk_c5) | (multiply(sk_c7, sk_c4) = sk_c6)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 ((inverse(sk_c7) = multiply(sk_c7, sk_c6)) | (multiply(sk_c7, sk_c4) = sk_c6)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[166, 163])).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 (inverse(sk_c7) = multiply(sk_c7, sk_c6)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[167, 122])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (multiply(sk_c7, sk_c6) = inverse(sk_c7)),
% 0.20/0.48 inference(symmetry,[status(thm)],[168])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[169])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(sk_c6, sk_c1)),
% 0.20/0.48 inference(transitivity,[status(thm)],[170, 162, 139, 136])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 (multiply(multiply(multiply(sk_c7, sk_c6), sk_c7), sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(multiply(multiply(sk_c7, sk_c6), sk_c7), sk_c6)),
% 0.20/0.48 inference(symmetry,[status(thm)],[172])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (sk_c6 = multiply(sk_c6, sk_c6)),
% 0.20/0.48 inference(transitivity,[status(thm)],[144, 141, 173, 160, 158])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 (multiply(sk_c1, sk_c6) = multiply(sk_c1, multiply(sk_c6, sk_c6))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[174])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 (sk_c7 = multiply(sk_c1, sk_c6)),
% 0.20/0.48 inference(symmetry,[status(thm)],[126])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 (sk_c7 = sk_c6),
% 0.20/0.48 inference(transitivity,[status(thm)],[176, 175, 155, 152, 151, 150, 149, 148, 143])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 (multiply(sk_c1, sk_c7) = multiply(sk_c1, sk_c6)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[177])).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.20/0.48 inference(transitivity,[status(thm)],[178, 175, 155, 152, 151, 150, 149, 148, 143])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 (multiply(sk_c7, sk_c6) = sk_c6),
% 0.20/0.48 inference(transitivity,[status(thm)],[151, 150, 149, 148, 143])).
% 0.20/0.48 tff(181,plain,
% 0.20/0.48 (^[X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6)))) <=> ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6)))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[181])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((~(multiply(sk_c6, sk_c7) = sk_c5)) <=> (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6)))), rewrite((~(inverse(sk_c7) = sk_c5)) <=> (~(inverse(sk_c7) = multiply(sk_c7, sk_c6)))), (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), rewrite(((~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))), (((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[183])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(multiply(sk_c7, sk_c6) = sk_c5), ((multiply(sk_c7, sk_c6) = sk_c5) <=> $true)), ((~(multiply(sk_c7, sk_c6) = sk_c5)) <=> (~$true))), rewrite((~$true) <=> $false), ((~(multiply(sk_c7, sk_c6) = sk_c5)) <=> $false)), (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ($false | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), rewrite(($false | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[186])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (^[X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(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)))), ((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)))), ((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5))))), (((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7)))), (((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7))))), ((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(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(sk_c7) = sk_c5)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(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(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), ((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(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(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), (((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(X1, sk_c7) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(X1, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), (((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), ((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X1) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), ((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), (((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), (((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(X4, sk_c7) = X3))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(multiply(X4, sk_c7) = X3))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))))), (((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X4) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X4) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))), (((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(189,plain,
% 0.20/0.50 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = 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(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[188])).
% 0.20/0.50 tff(190,axiom,(![X4: $i, X3: $i, X2: $i, X1: $i] : ((((((((((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5))) | (~(inverse(sk_c7) = sk_c5))) | (~(multiply(X2, sk_c6) = sk_c7))) | (~(inverse(X2) = sk_c6))) | (~(multiply(X1, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c7))) | (~(multiply(sk_c7, X3) = sk_c6))) | (~(multiply(X4, sk_c7) = X3))) | (~(inverse(X4) = sk_c7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_22')).
% 0.20/0.50 tff(191,plain,
% 0.20/0.50 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c7, sk_c6) = sk_c5)) | (~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.50 tff(192,plain,
% 0.20/0.50 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.20/0.50 tff(193,plain,
% 0.20/0.50 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(multiply(sk_c6, sk_c7) = sk_c5)) | (~(inverse(sk_c7) = sk_c5)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.20/0.50 tff(194,plain,
% 0.20/0.50 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[193, 184])).
% 0.20/0.50 tff(195,plain,(
% 0.20/0.50 ![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[194])).
% 0.20/0.50 tff(196,plain,
% 0.20/0.50 (![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[195, 182])).
% 0.20/0.50 tff(197,plain,
% 0.20/0.50 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 (((~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6)))) <=> ((~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[198])).
% 0.20/0.51 tff(200,plain,
% 0.20/0.51 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[199, 197])).
% 0.20/0.51 tff(201,plain,
% 0.20/0.51 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(202,plain,
% 0.20/0.51 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.51 tff(203,plain,
% 0.20/0.51 ((~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[202, 121, 168, 126, 133, 196])).
% 0.20/0.51 tff(204,plain,
% 0.20/0.51 (~(inverse(sk_c1) = sk_c7)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[203, 180, 179])).
% 0.20/0.51 tff(205,plain,
% 0.20/0.51 (~(multiply(sk_c7, sk_c6) = sk_c7)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[204, 147])).
% 0.20/0.51 tff(206,plain,
% 0.20/0.51 (multiply(sk_c1, multiply(sk_c6, sk_c6)) = multiply(sk_c1, sk_c6)),
% 0.20/0.51 inference(symmetry,[status(thm)],[175])).
% 0.20/0.51 tff(207,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c1, sk_c6), sk_c6)),
% 0.20/0.51 inference(symmetry,[status(thm)],[152])).
% 0.20/0.51 tff(208,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c6) = sk_c7),
% 0.20/0.51 inference(transitivity,[status(thm)],[207, 154, 206, 126])).
% 0.20/0.51 tff(209,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[208, 205])).
% 0.20/0.51 tff(210,plain,(multiply(sk_c7, sk_c4) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(211,plain,
% 0.20/0.51 (sk_c6 = multiply(sk_c7, sk_c4)),
% 0.20/0.51 inference(symmetry,[status(thm)],[210])).
% 0.20/0.51 tff(212,assumption,(~(inverse(sk_c1) = sk_c6)), introduced(assumption)).
% 0.20/0.51 tff(213,plain,
% 0.20/0.51 (((inverse(sk_c1) = sk_c6) | (multiply(sk_c2, sk_c7) = sk_c6)) <=> ((inverse(sk_c1) = sk_c6) | (multiply(sk_c2, sk_c7) = sk_c6))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(214,axiom,((inverse(sk_c1) = sk_c6) | (multiply(sk_c2, sk_c7) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_17')).
% 0.20/0.51 tff(215,plain,
% 0.20/0.51 ((inverse(sk_c1) = sk_c6) | (multiply(sk_c2, sk_c7) = sk_c6)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.20/0.51 tff(216,plain,
% 0.20/0.51 (multiply(sk_c2, sk_c7) = sk_c6),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[215, 212])).
% 0.20/0.51 tff(217,plain,
% 0.20/0.51 (sk_c6 = multiply(sk_c2, sk_c7)),
% 0.20/0.51 inference(symmetry,[status(thm)],[216])).
% 0.20/0.51 tff(218,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c2, sk_c7))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[217])).
% 0.20/0.51 tff(219,plain,
% 0.20/0.51 (multiply(sk_c7, multiply(sk_c2, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.20/0.51 inference(symmetry,[status(thm)],[218])).
% 0.20/0.51 tff(220,plain,
% 0.20/0.51 (((inverse(sk_c1) = sk_c6) | (inverse(sk_c2) = sk_c7)) <=> ((inverse(sk_c1) = sk_c6) | (inverse(sk_c2) = sk_c7))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(221,axiom,((inverse(sk_c1) = sk_c6) | (inverse(sk_c2) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_18')).
% 0.20/0.51 tff(222,plain,
% 0.20/0.51 ((inverse(sk_c1) = sk_c6) | (inverse(sk_c2) = sk_c7)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.20/0.51 tff(223,plain,
% 0.20/0.51 (inverse(sk_c2) = sk_c7),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[222, 212])).
% 0.20/0.51 tff(224,plain,
% 0.20/0.51 (sk_c7 = inverse(sk_c2)),
% 0.20/0.51 inference(symmetry,[status(thm)],[223])).
% 0.20/0.51 tff(225,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[224])).
% 0.20/0.51 tff(226,plain,
% 0.20/0.51 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c7, sk_c2)),
% 0.20/0.51 inference(symmetry,[status(thm)],[225])).
% 0.20/0.51 tff(227,plain,
% 0.20/0.51 (identity = multiply(sk_c7, sk_c2)),
% 0.20/0.51 inference(transitivity,[status(thm)],[47, 226])).
% 0.20/0.51 tff(228,plain,
% 0.20/0.51 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[227])).
% 0.20/0.51 tff(229,plain,
% 0.20/0.51 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c2) = sk_c2)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(230,plain,
% 0.20/0.51 (multiply(identity, sk_c2) = sk_c2),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[229, 7])).
% 0.20/0.51 tff(231,plain,
% 0.20/0.51 (((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c7))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(232,axiom,((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_21')).
% 0.20/0.51 tff(233,plain,
% 0.20/0.51 ((inverse(sk_c1) = sk_c6) | (inverse(sk_c3) = sk_c7)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.51 tff(234,plain,
% 0.20/0.51 (inverse(sk_c3) = sk_c7),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[233, 212])).
% 0.20/0.51 tff(235,plain,
% 0.20/0.51 (sk_c7 = inverse(sk_c3)),
% 0.20/0.51 inference(symmetry,[status(thm)],[234])).
% 0.20/0.51 tff(236,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[235])).
% 0.20/0.51 tff(237,plain,
% 0.20/0.51 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c7, sk_c3)),
% 0.20/0.51 inference(symmetry,[status(thm)],[236])).
% 0.20/0.51 tff(238,plain,
% 0.20/0.51 (identity = multiply(sk_c7, sk_c3)),
% 0.20/0.51 inference(transitivity,[status(thm)],[90, 237])).
% 0.20/0.51 tff(239,plain,
% 0.20/0.51 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(identity, sk_c7)),
% 0.20/0.51 inference(symmetry,[status(thm)],[228])).
% 0.20/0.51 tff(240,plain,
% 0.20/0.51 (multiply(sk_c7, multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.20/0.51 inference(symmetry,[status(thm)],[26])).
% 0.20/0.51 tff(241,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c6) = sk_c7),
% 0.20/0.51 inference(transitivity,[status(thm)],[218, 240, 239, 9])).
% 0.20/0.51 tff(242,plain,
% 0.20/0.51 (multiply(multiply(sk_c7, sk_c6), identity) = multiply(sk_c7, multiply(sk_c7, sk_c3))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[241, 238])).
% 0.20/0.51 tff(243,plain,
% 0.20/0.51 (multiply(sk_c7, multiply(sk_c7, sk_c3)) = multiply(multiply(sk_c7, sk_c6), identity)),
% 0.20/0.51 inference(symmetry,[status(thm)],[242])).
% 0.20/0.51 tff(244,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c7), sk_c3) = multiply(sk_c7, multiply(sk_c7, sk_c3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(245,plain,
% 0.20/0.51 (multiply(multiply(sk_c7, sk_c7), sk_c3) = multiply(sk_c7, multiply(sk_c7, sk_c3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[244, 24])).
% 0.20/0.51 tff(246,plain,
% 0.20/0.51 (multiply(multiply(sk_c7, sk_c4), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[210])).
% 0.20/0.51 tff(247,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c4), sk_c7) = multiply(sk_c7, multiply(sk_c4, sk_c7)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(248,plain,
% 0.20/0.51 (multiply(multiply(sk_c7, sk_c4), sk_c7) = multiply(sk_c7, multiply(sk_c4, sk_c7))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[247, 24])).
% 0.20/0.51 tff(249,plain,
% 0.20/0.51 (multiply(sk_c7, multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c7, sk_c4), sk_c7)),
% 0.20/0.51 inference(symmetry,[status(thm)],[248])).
% 0.20/0.51 tff(250,plain,
% 0.20/0.51 (((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c7) = sk_c4))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(251,axiom,((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c7) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_20')).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 ((inverse(sk_c1) = sk_c6) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 (multiply(sk_c3, sk_c7) = sk_c4),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[252, 212])).
% 0.20/0.51 tff(254,plain,
% 0.20/0.51 (sk_c4 = multiply(sk_c3, sk_c7)),
% 0.20/0.51 inference(symmetry,[status(thm)],[253])).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 (multiply(sk_c4, sk_c7) = multiply(multiply(sk_c3, sk_c7), sk_c7)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[254])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 (multiply(multiply(sk_c3, sk_c7), sk_c7) = multiply(sk_c4, sk_c7)),
% 0.20/0.51 inference(symmetry,[status(thm)],[255])).
% 0.20/0.51 tff(257,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c7), sk_c7) = multiply(sk_c3, multiply(sk_c7, sk_c7)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(258,plain,
% 0.20/0.51 (multiply(multiply(sk_c3, sk_c7), sk_c7) = multiply(sk_c3, multiply(sk_c7, sk_c7))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[257, 24])).
% 0.20/0.51 tff(259,plain,
% 0.20/0.51 (multiply(sk_c3, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c3, sk_c7), sk_c7)),
% 0.20/0.51 inference(symmetry,[status(thm)],[258])).
% 0.20/0.51 tff(260,plain,
% 0.20/0.51 (multiply(sk_c3, multiply(sk_c7, sk_c7)) = multiply(sk_c4, sk_c7)),
% 0.20/0.51 inference(transitivity,[status(thm)],[259, 256])).
% 0.20/0.51 tff(261,plain,
% 0.20/0.51 (multiply(sk_c7, multiply(sk_c3, multiply(sk_c7, sk_c7))) = multiply(sk_c7, multiply(sk_c4, sk_c7))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[260])).
% 0.20/0.51 tff(262,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7)) = multiply(sk_c7, multiply(sk_c3, multiply(sk_c7, sk_c7))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(263,plain,
% 0.20/0.51 (multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7)) = multiply(sk_c7, multiply(sk_c3, multiply(sk_c7, sk_c7)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[262, 24])).
% 0.20/0.51 tff(264,plain,
% 0.20/0.51 (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[238])).
% 0.20/0.51 tff(265,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c7), sk_c7) = multiply(identity, multiply(sk_c7, sk_c7)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(266,plain,
% 0.20/0.51 (multiply(multiply(identity, sk_c7), sk_c7) = multiply(identity, multiply(sk_c7, sk_c7))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[265, 24])).
% 0.20/0.52 tff(267,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c7) = multiply(multiply(identity, sk_c7), sk_c7)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.52 tff(268,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c7) = inverse(sk_c3)),
% 0.20/0.52 inference(transitivity,[status(thm)],[267, 266, 264, 263, 261, 249, 246, 121, 218, 240, 239, 9, 235])).
% 0.20/0.52 tff(269,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c7), sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[268])).
% 0.20/0.52 tff(270,plain,
% 0.20/0.52 (multiply(inverse(sk_c3), sk_c3) = multiply(multiply(sk_c7, sk_c7), sk_c3)),
% 0.20/0.52 inference(symmetry,[status(thm)],[269])).
% 0.20/0.52 tff(271,plain,
% 0.20/0.52 (identity = multiply(multiply(sk_c7, sk_c6), identity)),
% 0.20/0.52 inference(transitivity,[status(thm)],[90, 270, 245, 243])).
% 0.20/0.52 tff(272,plain,
% 0.20/0.52 (multiply(identity, sk_c2) = multiply(multiply(multiply(sk_c7, sk_c6), identity), sk_c2)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[271])).
% 0.20/0.52 tff(273,plain,
% 0.20/0.52 (multiply(multiply(multiply(sk_c7, sk_c6), identity), sk_c2) = multiply(identity, sk_c2)),
% 0.20/0.52 inference(symmetry,[status(thm)],[272])).
% 0.20/0.52 tff(274,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c6), identity), sk_c2) = multiply(multiply(sk_c7, sk_c6), multiply(identity, sk_c2)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(275,plain,
% 0.20/0.52 (multiply(multiply(multiply(sk_c7, sk_c6), identity), sk_c2) = multiply(multiply(sk_c7, sk_c6), multiply(identity, sk_c2))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[274, 24])).
% 0.20/0.52 tff(276,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c6), multiply(identity, sk_c2)) = multiply(multiply(multiply(sk_c7, sk_c6), identity), sk_c2)),
% 0.20/0.52 inference(symmetry,[status(thm)],[275])).
% 0.20/0.52 tff(277,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c6) = inverse(sk_c2)),
% 0.20/0.52 inference(transitivity,[status(thm)],[218, 240, 239, 9, 224])).
% 0.20/0.52 tff(278,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c6), multiply(identity, sk_c2)) = multiply(inverse(sk_c2), sk_c2)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[277, 230])).
% 0.20/0.52 tff(279,plain,
% 0.20/0.52 (multiply(inverse(sk_c2), sk_c2) = multiply(multiply(sk_c7, sk_c6), multiply(identity, sk_c2))),
% 0.20/0.52 inference(symmetry,[status(thm)],[278])).
% 0.20/0.52 tff(280,plain,
% 0.20/0.52 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c6)) = identity)),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(281,plain,
% 0.20/0.52 (multiply(inverse(multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c6)) = identity),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[280, 44])).
% 0.20/0.52 tff(282,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c4) = multiply(sk_c7, multiply(sk_c3, sk_c7))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[254])).
% 0.20/0.52 tff(283,plain,
% 0.20/0.52 (multiply(sk_c7, multiply(sk_c3, sk_c7)) = multiply(sk_c7, sk_c4)),
% 0.20/0.52 inference(symmetry,[status(thm)],[282])).
% 0.20/0.52 tff(284,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c3) = multiply(sk_c7, sk_c2)),
% 0.20/0.52 inference(transitivity,[status(thm)],[236, 49, 47, 226])).
% 0.20/0.52 tff(285,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[284])).
% 0.20/0.52 tff(286,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.20/0.52 inference(symmetry,[status(thm)],[285])).
% 0.20/0.52 tff(287,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c6) = sk_c6),
% 0.20/0.52 inference(transitivity,[status(thm)],[218, 240, 286, 63, 283, 210])).
% 0.20/0.52 tff(288,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c6), multiply(sk_c7, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[287, 241])).
% 0.20/0.52 tff(289,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c6), multiply(sk_c7, sk_c6)) = multiply(sk_c7, sk_c6)),
% 0.20/0.52 inference(transitivity,[status(thm)],[288, 121])).
% 0.20/0.52 tff(290,plain,
% 0.20/0.52 (inverse(multiply(sk_c7, sk_c6)) = inverse(sk_c7)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[241])).
% 0.20/0.52 tff(291,plain,
% 0.20/0.52 (inverse(sk_c7) = inverse(multiply(sk_c7, sk_c6))),
% 0.20/0.52 inference(symmetry,[status(thm)],[290])).
% 0.20/0.52 tff(292,plain,
% 0.20/0.52 (multiply(inverse(sk_c7), multiply(multiply(sk_c7, sk_c6), multiply(sk_c7, sk_c6))) = multiply(inverse(multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c6))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[291, 289])).
% 0.20/0.52 tff(293,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c7), multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c6)) = multiply(inverse(sk_c7), multiply(multiply(sk_c7, sk_c6), multiply(sk_c7, sk_c6))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(294,plain,
% 0.20/0.52 (multiply(multiply(inverse(sk_c7), multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c6)) = multiply(inverse(sk_c7), multiply(multiply(sk_c7, sk_c6), multiply(sk_c7, sk_c6)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[293, 24])).
% 0.20/0.52 tff(295,plain,
% 0.20/0.52 (sk_c7 = multiply(sk_c7, sk_c6)),
% 0.20/0.52 inference(transitivity,[status(thm)],[116, 228, 26, 219])).
% 0.20/0.52 tff(296,plain,
% 0.20/0.52 (multiply(inverse(sk_c7), multiply(sk_c7, sk_c6)) = multiply(inverse(multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c6))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[291])).
% 0.20/0.52 tff(297,plain,
% 0.20/0.52 (multiply(inverse(multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c6)) = multiply(inverse(sk_c7), multiply(sk_c7, sk_c6))),
% 0.20/0.52 inference(symmetry,[status(thm)],[296])).
% 0.20/0.52 tff(298,plain,
% 0.20/0.52 (identity = multiply(inverse(multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c6))),
% 0.20/0.52 inference(symmetry,[status(thm)],[281])).
% 0.20/0.52 tff(299,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c2) = multiply(inverse(sk_c7), multiply(sk_c7, sk_c6))),
% 0.20/0.52 inference(transitivity,[status(thm)],[225, 46, 298, 297])).
% 0.20/0.52 tff(300,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(multiply(inverse(sk_c7), multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c6))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[299, 295])).
% 0.20/0.52 tff(301,plain,
% 0.20/0.52 (sk_c7 = sk_c2),
% 0.20/0.52 inference(transitivity,[status(thm)],[116, 228, 300, 294, 292, 281, 47, 279, 276, 273, 230])).
% 0.20/0.52 tff(302,plain,
% 0.20/0.52 (inverse(sk_c7) = inverse(sk_c2)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[301])).
% 0.20/0.52 tff(303,plain,
% 0.20/0.52 (inverse(sk_c7) = multiply(sk_c7, sk_c6)),
% 0.20/0.52 inference(transitivity,[status(thm)],[302, 223, 116, 228, 26, 219])).
% 0.20/0.52 tff(304,plain,
% 0.20/0.52 (sk_c6 = sk_c7),
% 0.20/0.52 inference(transitivity,[status(thm)],[211, 282, 64, 285, 239, 9])).
% 0.20/0.52 tff(305,plain,
% 0.20/0.52 (multiply(sk_c2, sk_c6) = multiply(sk_c2, sk_c7)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[304])).
% 0.20/0.52 tff(306,plain,
% 0.20/0.52 (multiply(sk_c2, sk_c6) = sk_c7),
% 0.20/0.52 inference(transitivity,[status(thm)],[305, 216, 211, 282, 64, 285, 239, 9])).
% 0.20/0.52 tff(307,plain,
% 0.20/0.52 (inverse(sk_c2) = sk_c6),
% 0.20/0.52 inference(transitivity,[status(thm)],[223, 116, 228, 286, 63, 283, 210])).
% 0.20/0.52 tff(308,plain,
% 0.20/0.52 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c6)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c6)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(309,plain,
% 0.20/0.52 (((~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6)))) <=> ((~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c6)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(310,plain,
% 0.20/0.53 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c6))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[309])).
% 0.20/0.53 tff(311,plain,
% 0.20/0.53 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c6)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[310, 308])).
% 0.20/0.53 tff(312,plain,
% 0.20/0.53 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(313,plain,
% 0.20/0.53 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c2) = sk_c7)) | (~(multiply(sk_c2, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c6))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.20/0.53 tff(314,plain,
% 0.20/0.53 ((~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c2) = sk_c6)) | (~(multiply(sk_c2, sk_c6) = sk_c7)) | (~(multiply(sk_c7, sk_c6) = sk_c6))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[313, 216, 121, 223, 196])).
% 0.20/0.53 tff(315,plain,
% 0.20/0.53 (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[314, 307, 306, 287])).
% 0.20/0.53 tff(316,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[315, 303])).
% 0.20/0.53 tff(317,plain,(inverse(sk_c1) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(318,plain,
% 0.20/0.53 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c1) = sk_c1)),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(319,plain,
% 0.20/0.53 (multiply(identity, sk_c1) = sk_c1),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[318, 7])).
% 0.20/0.53 tff(320,plain,
% 0.20/0.53 (sk_c6 = inverse(sk_c1)),
% 0.20/0.53 inference(symmetry,[status(thm)],[317])).
% 0.20/0.53 tff(321,plain,
% 0.20/0.53 (multiply(sk_c7, multiply(sk_c3, sk_c7)) = multiply(sk_c7, sk_c4)),
% 0.20/0.53 inference(symmetry,[status(thm)],[72])).
% 0.20/0.53 tff(322,plain,
% 0.20/0.53 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[61])).
% 0.20/0.53 tff(323,plain,
% 0.20/0.53 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c7, sk_c2)),
% 0.20/0.53 inference(transitivity,[status(thm)],[162, 47, 37])).
% 0.20/0.53 tff(324,plain,
% 0.20/0.53 (multiply(multiply(inverse(sk_c7), sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[323])).
% 0.20/0.53 tff(325,plain,
% 0.20/0.53 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c7), sk_c7), sk_c7) = multiply(inverse(sk_c7), multiply(sk_c7, sk_c7)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(326,plain,
% 0.20/0.53 (multiply(multiply(inverse(sk_c7), sk_c7), sk_c7) = multiply(inverse(sk_c7), multiply(sk_c7, sk_c7))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[325, 24])).
% 0.20/0.53 tff(327,plain,
% 0.20/0.53 (multiply(inverse(sk_c7), multiply(sk_c7, sk_c7)) = multiply(multiply(inverse(sk_c7), sk_c7), sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[326])).
% 0.20/0.53 tff(328,plain,
% 0.20/0.53 (multiply(multiply(identity, sk_c7), sk_c7) = multiply(sk_c7, sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[267])).
% 0.20/0.53 tff(329,plain,
% 0.20/0.53 (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(multiply(identity, sk_c7), sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[266])).
% 0.20/0.53 tff(330,plain,
% 0.20/0.53 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c7, sk_c3)),
% 0.20/0.53 inference(symmetry,[status(thm)],[59])).
% 0.20/0.53 tff(331,plain,
% 0.20/0.53 (identity = multiply(sk_c7, sk_c3)),
% 0.20/0.53 inference(transitivity,[status(thm)],[90, 330])).
% 0.20/0.53 tff(332,plain,
% 0.20/0.53 (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[331])).
% 0.20/0.53 tff(333,plain,
% 0.20/0.53 (multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7)) = multiply(identity, multiply(sk_c7, sk_c7))),
% 0.20/0.53 inference(symmetry,[status(thm)],[332])).
% 0.20/0.53 tff(334,plain,
% 0.20/0.53 (multiply(sk_c7, multiply(sk_c3, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c7, sk_c3), multiply(sk_c7, sk_c7))),
% 0.20/0.53 inference(symmetry,[status(thm)],[263])).
% 0.20/0.53 tff(335,plain,
% 0.20/0.53 (multiply(sk_c4, sk_c7) = multiply(multiply(sk_c3, sk_c7), sk_c7)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.53 tff(336,plain,
% 0.20/0.53 (multiply(multiply(sk_c3, sk_c7), sk_c7) = multiply(sk_c4, sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[335])).
% 0.20/0.53 tff(337,plain,
% 0.20/0.53 (multiply(sk_c3, multiply(sk_c7, sk_c7)) = multiply(sk_c4, sk_c7)),
% 0.20/0.53 inference(transitivity,[status(thm)],[259, 336])).
% 0.20/0.53 tff(338,plain,
% 0.20/0.53 (multiply(sk_c7, multiply(sk_c3, multiply(sk_c7, sk_c7))) = multiply(sk_c7, multiply(sk_c4, sk_c7))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[337])).
% 0.20/0.53 tff(339,plain,
% 0.20/0.53 (multiply(sk_c7, multiply(sk_c4, sk_c7)) = multiply(sk_c7, multiply(sk_c3, multiply(sk_c7, sk_c7)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[338])).
% 0.20/0.53 tff(340,plain,
% 0.20/0.53 (multiply(sk_c6, sk_c7) = multiply(multiply(sk_c7, sk_c4), sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[246])).
% 0.20/0.53 tff(341,plain,
% 0.20/0.53 (identity = multiply(sk_c7, sk_c2)),
% 0.20/0.53 inference(transitivity,[status(thm)],[47, 37])).
% 0.20/0.53 tff(342,plain,
% 0.20/0.53 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[341])).
% 0.20/0.53 tff(343,plain,
% 0.20/0.53 (sk_c7 = multiply(sk_c7, sk_c7)),
% 0.20/0.53 inference(transitivity,[status(thm)],[116, 342, 26, 17, 151, 340, 248, 339, 334, 333, 329, 328])).
% 0.20/0.53 tff(344,plain,
% 0.20/0.53 (multiply(inverse(sk_c7), sk_c7) = multiply(inverse(sk_c7), multiply(sk_c7, sk_c7))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[343])).
% 0.20/0.53 tff(345,plain,
% 0.20/0.53 (identity = multiply(inverse(sk_c7), sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[162])).
% 0.20/0.53 tff(346,plain,
% 0.20/0.53 (identity = inverse(sk_c1)),
% 0.20/0.53 inference(transitivity,[status(thm)],[345, 344, 327, 324, 322, 63, 321, 210, 320])).
% 0.20/0.53 tff(347,plain,
% 0.20/0.53 (multiply(identity, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[346])).
% 0.20/0.53 tff(348,plain,
% 0.20/0.53 (multiply(inverse(sk_c1), sk_c1) = multiply(identity, sk_c1)),
% 0.20/0.53 inference(symmetry,[status(thm)],[347])).
% 0.20/0.53 tff(349,plain,
% 0.20/0.53 (multiply(inverse(sk_c7), multiply(sk_c7, sk_c7)) = multiply(inverse(sk_c7), sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[344])).
% 0.20/0.53 tff(350,plain,
% 0.20/0.53 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(multiply(inverse(sk_c7), sk_c7), sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[324])).
% 0.20/0.53 tff(351,plain,
% 0.20/0.53 (sk_c7 = sk_c1),
% 0.20/0.53 inference(transitivity,[status(thm)],[116, 342, 350, 326, 349, 162, 139, 348, 319])).
% 0.20/0.53 tff(352,plain,
% 0.20/0.53 (inverse(sk_c7) = inverse(sk_c1)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[351])).
% 0.20/0.53 tff(353,plain,
% 0.20/0.53 (inverse(sk_c7) = multiply(sk_c7, sk_c6)),
% 0.20/0.53 inference(transitivity,[status(thm)],[352, 317, 211, 72, 64, 61, 26, 17])).
% 0.20/0.53 tff(354,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[10, 353])).
% 0.20/0.53 tff(355,plain,(inverse(sk_c7) = multiply(sk_c7, sk_c6)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(356,plain,
% 0.20/0.53 ((inverse(sk_c7) = sk_c7) <=> (multiply(sk_c7, sk_c6) = sk_c7)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[355])).
% 0.20/0.53 tff(357,plain,
% 0.20/0.53 ((multiply(sk_c7, sk_c6) = sk_c7) <=> (inverse(sk_c7) = sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[356])).
% 0.20/0.53 tff(358,plain,
% 0.20/0.53 ((sk_c7 = multiply(sk_c7, sk_c6)) <=> (multiply(sk_c7, sk_c6) = sk_c7)),
% 0.20/0.53 inference(commutativity,[status(thm)],[])).
% 0.20/0.53 tff(359,assumption,(multiply(sk_c1, sk_c6) = sk_c7), introduced(assumption)).
% 0.20/0.53 tff(360,plain,
% 0.20/0.53 (multiply(sk_c6, multiply(sk_c1, sk_c6)) = multiply(sk_c6, sk_c7)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[359])).
% 0.20/0.53 tff(361,plain,
% 0.20/0.53 (multiply(sk_c6, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[320])).
% 0.20/0.53 tff(362,plain,
% 0.20/0.53 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c6, sk_c1)),
% 0.20/0.53 inference(symmetry,[status(thm)],[361])).
% 0.20/0.53 tff(363,plain,
% 0.20/0.53 (identity = multiply(sk_c6, sk_c1)),
% 0.20/0.53 inference(transitivity,[status(thm)],[139, 362])).
% 0.20/0.53 tff(364,plain,
% 0.20/0.53 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c1), sk_c6)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[363])).
% 0.20/0.53 tff(365,plain,
% 0.20/0.53 (sk_c6 = multiply(sk_c6, sk_c7)),
% 0.20/0.53 inference(transitivity,[status(thm)],[144, 364, 129, 360])).
% 0.20/0.53 tff(366,plain,
% 0.20/0.53 (multiply(sk_c1, sk_c6) = multiply(sk_c1, multiply(sk_c6, sk_c7))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[365])).
% 0.20/0.53 tff(367,plain,
% 0.20/0.53 (multiply(sk_c1, multiply(sk_c6, sk_c7)) = multiply(sk_c1, sk_c6)),
% 0.20/0.53 inference(symmetry,[status(thm)],[366])).
% 0.20/0.53 tff(368,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(369,plain,
% 0.20/0.53 (multiply(multiply(sk_c1, sk_c6), sk_c7) = multiply(sk_c1, multiply(sk_c6, sk_c7))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[368, 24])).
% 0.20/0.53 tff(370,plain,
% 0.20/0.53 (multiply(multiply(sk_c1, sk_c6), sk_c7) = multiply(sk_c7, sk_c7)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[359])).
% 0.20/0.53 tff(371,plain,
% 0.20/0.53 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c1, sk_c6), sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[370])).
% 0.20/0.53 tff(372,plain,
% 0.20/0.53 (multiply(sk_c7, sk_c7) = sk_c7),
% 0.20/0.53 inference(transitivity,[status(thm)],[371, 369, 367, 359])).
% 0.20/0.53 tff(373,plain,
% 0.20/0.53 ((multiply(sk_c7, sk_c7) = multiply(sk_c7, sk_c6)) <=> (sk_c7 = multiply(sk_c7, sk_c6))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[372])).
% 0.20/0.53 tff(374,plain,
% 0.20/0.53 ((multiply(sk_c7, sk_c7) = multiply(sk_c7, sk_c6)) <=> (multiply(sk_c7, sk_c6) = sk_c7)),
% 0.20/0.53 inference(transitivity,[status(thm)],[373, 358])).
% 0.20/0.53 tff(375,plain,
% 0.20/0.53 (sk_c6 = multiply(sk_c7, sk_c6)),
% 0.20/0.53 inference(transitivity,[status(thm)],[144, 364, 129, 360, 121])).
% 0.20/0.53 tff(376,plain,
% 0.20/0.53 (sk_c7 = multiply(sk_c1, sk_c6)),
% 0.20/0.53 inference(symmetry,[status(thm)],[359])).
% 0.20/0.53 tff(377,plain,
% 0.20/0.53 (multiply(sk_c7, sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c6))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[376])).
% 0.20/0.53 tff(378,plain,
% 0.20/0.53 (multiply(sk_c7, multiply(sk_c1, sk_c6)) = multiply(sk_c7, sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[377])).
% 0.20/0.53 tff(379,plain,
% 0.20/0.53 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c1), sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c6)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(380,plain,
% 0.20/0.53 (multiply(multiply(sk_c7, sk_c1), sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c6))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[379, 24])).
% 0.20/0.54 tff(381,plain,
% 0.20/0.54 (multiply(multiply(sk_c7, sk_c1), sk_c6) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c7, sk_c6))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[375])).
% 0.20/0.54 tff(382,plain,
% 0.20/0.54 (multiply(multiply(sk_c7, sk_c1), multiply(sk_c7, sk_c6)) = multiply(multiply(sk_c7, sk_c1), sk_c6)),
% 0.20/0.54 inference(symmetry,[status(thm)],[381])).
% 0.20/0.54 tff(383,plain,
% 0.20/0.54 (multiply(multiply(sk_c7, sk_c1), multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c7, sk_c6))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[121])).
% 0.20/0.54 tff(384,plain,
% 0.20/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c1), sk_c6), sk_c7) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c6, sk_c7)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(385,plain,
% 0.20/0.54 (multiply(multiply(multiply(sk_c7, sk_c1), sk_c6), sk_c7) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c6, sk_c7))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[384, 24])).
% 0.20/0.54 tff(386,plain,
% 0.20/0.54 (multiply(sk_c7, multiply(sk_c1, sk_c6)) = multiply(multiply(sk_c7, sk_c1), sk_c6)),
% 0.20/0.54 inference(symmetry,[status(thm)],[380])).
% 0.20/0.54 tff(387,plain,
% 0.20/0.54 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c6)),
% 0.20/0.54 inference(transitivity,[status(thm)],[377, 386])).
% 0.20/0.54 tff(388,plain,
% 0.20/0.54 (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(multiply(multiply(sk_c7, sk_c1), sk_c6), sk_c7)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[387])).
% 0.20/0.54 tff(389,plain,
% 0.20/0.54 ((~![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)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(390,plain,
% 0.20/0.54 (multiply(multiply(sk_c7, sk_c7), sk_c7) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[389, 24])).
% 0.20/0.54 tff(391,plain,
% 0.20/0.54 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c7, sk_c7), sk_c7)),
% 0.20/0.54 inference(symmetry,[status(thm)],[390])).
% 0.20/0.54 tff(392,plain,
% 0.20/0.54 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(sk_c7, sk_c7)),
% 0.20/0.54 inference(transitivity,[status(thm)],[391, 388, 385, 383, 382, 380, 378])).
% 0.20/0.54 tff(393,plain,
% 0.20/0.54 ((multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6) <=> (multiply(sk_c7, sk_c7) = multiply(sk_c7, sk_c6))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[392, 375])).
% 0.20/0.54 tff(394,plain,
% 0.20/0.54 ((multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6) <=> (inverse(sk_c7) = sk_c7)),
% 0.20/0.54 inference(transitivity,[status(thm)],[393, 374, 357])).
% 0.20/0.54 tff(395,plain,
% 0.20/0.54 (multiply(multiply(sk_c6, sk_c1), sk_c6) = multiply(identity, sk_c6)),
% 0.20/0.54 inference(symmetry,[status(thm)],[364])).
% 0.20/0.54 tff(396,plain,
% 0.20/0.54 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c1, sk_c6))),
% 0.20/0.54 inference(symmetry,[status(thm)],[360])).
% 0.20/0.54 tff(397,plain,
% 0.20/0.54 (multiply(sk_c7, sk_c6) = inverse(sk_c7)),
% 0.20/0.54 inference(symmetry,[status(thm)],[355])).
% 0.20/0.54 tff(398,plain,
% 0.20/0.54 (sk_c6 = inverse(sk_c7)),
% 0.20/0.54 inference(transitivity,[status(thm)],[144, 364, 129, 360, 121, 397])).
% 0.20/0.54 tff(399,plain,
% 0.20/0.54 (multiply(sk_c6, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[398])).
% 0.20/0.54 tff(400,plain,
% 0.20/0.54 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.20/0.54 inference(symmetry,[status(thm)],[399])).
% 0.20/0.54 tff(401,plain,
% 0.20/0.54 (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[397])).
% 0.20/0.54 tff(402,plain,
% 0.20/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(sk_c7, multiply(sk_c6, sk_c7)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(403,plain,
% 0.20/0.54 (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(sk_c7, multiply(sk_c6, sk_c7))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[402, 24])).
% 0.20/0.54 tff(404,plain,
% 0.20/0.54 (multiply(sk_c7, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c7, sk_c6), sk_c7)),
% 0.20/0.54 inference(symmetry,[status(thm)],[403])).
% 0.20/0.54 tff(405,plain,
% 0.20/0.54 (multiply(sk_c7, multiply(sk_c7, sk_c6)) = multiply(sk_c7, multiply(sk_c6, sk_c7))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.54 tff(406,plain,
% 0.20/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c7), sk_c6) = multiply(sk_c7, multiply(sk_c7, sk_c6)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(407,plain,
% 0.20/0.54 (multiply(multiply(sk_c7, sk_c7), sk_c6) = multiply(sk_c7, multiply(sk_c7, sk_c6))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[406, 24])).
% 0.20/0.54 tff(408,plain,
% 0.20/0.54 (multiply(sk_c6, sk_c1) = sk_c6),
% 0.20/0.54 inference(transitivity,[status(thm)],[361, 138, 345, 400, 396, 149, 395, 143])).
% 0.20/0.54 tff(409,plain,
% 0.20/0.54 (multiply(multiply(sk_c1, sk_c6), multiply(sk_c7, sk_c7)) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[359])).
% 0.20/0.54 tff(410,plain,
% 0.20/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c6), multiply(sk_c7, sk_c7)) = multiply(sk_c1, multiply(sk_c6, multiply(sk_c7, sk_c7))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(411,plain,
% 0.20/0.54 (multiply(multiply(sk_c1, sk_c6), multiply(sk_c7, sk_c7)) = multiply(sk_c1, multiply(sk_c6, multiply(sk_c7, sk_c7)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[410, 24])).
% 0.20/0.54 tff(412,plain,
% 0.20/0.54 (multiply(sk_c1, multiply(sk_c6, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c1, sk_c6), multiply(sk_c7, sk_c7))),
% 0.20/0.54 inference(symmetry,[status(thm)],[411])).
% 0.20/0.54 tff(413,plain,
% 0.20/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(sk_c6, multiply(sk_c7, sk_c7)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(414,plain,
% 0.20/0.54 (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[413, 24])).
% 0.20/0.54 tff(415,plain,
% 0.20/0.54 (multiply(sk_c6, sk_c7) = inverse(sk_c7)),
% 0.20/0.54 inference(transitivity,[status(thm)],[121, 397])).
% 0.20/0.54 tff(416,plain,
% 0.20/0.54 (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[415])).
% 0.20/0.54 tff(417,plain,
% 0.20/0.54 (multiply(inverse(sk_c7), sk_c7) = multiply(multiply(sk_c6, sk_c7), sk_c7)),
% 0.20/0.54 inference(symmetry,[status(thm)],[416])).
% 0.20/0.54 tff(418,plain,
% 0.20/0.54 (multiply(sk_c6, sk_c1) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.20/0.54 inference(transitivity,[status(thm)],[361, 138, 345, 417, 414])).
% 0.20/0.54 tff(419,plain,
% 0.20/0.54 (multiply(sk_c1, multiply(sk_c6, sk_c1)) = multiply(sk_c1, multiply(sk_c6, multiply(sk_c7, sk_c7)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[418])).
% 0.20/0.54 tff(420,plain,
% 0.20/0.54 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c6), sk_c1) = multiply(sk_c1, multiply(sk_c6, sk_c1)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(421,plain,
% 0.20/0.54 (multiply(multiply(sk_c1, sk_c6), sk_c1) = multiply(sk_c1, multiply(sk_c6, sk_c1))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[420, 24])).
% 0.20/0.54 tff(422,plain,
% 0.20/0.54 (multiply(sk_c7, sk_c1) = multiply(multiply(sk_c1, sk_c6), sk_c1)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[376])).
% 0.20/0.54 tff(423,plain,
% 0.20/0.54 (multiply(sk_c7, sk_c1) = multiply(sk_c7, sk_c7)),
% 0.20/0.54 inference(transitivity,[status(thm)],[422, 421, 419, 412, 409, 391, 388, 385, 383, 382, 380, 378])).
% 0.20/0.54 tff(424,plain,
% 0.20/0.54 (multiply(multiply(sk_c7, sk_c1), multiply(sk_c6, sk_c1)) = multiply(multiply(sk_c7, sk_c7), sk_c6)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[423, 408])).
% 0.20/0.54 tff(425,plain,
% 0.20/0.54 (multiply(sk_c7, sk_c6) = multiply(sk_c6, sk_c1)),
% 0.20/0.54 inference(transitivity,[status(thm)],[151, 399, 162, 139, 362])).
% 0.20/0.54 tff(426,plain,
% 0.20/0.54 (multiply(multiply(sk_c7, sk_c1), multiply(sk_c7, sk_c6)) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c6, sk_c1))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[425])).
% 0.20/0.54 tff(427,plain,
% 0.20/0.54 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6),
% 0.20/0.54 inference(transitivity,[status(thm)],[391, 388, 385, 383, 426, 424, 407, 405, 404, 401, 400, 396, 149, 395, 143])).
% 0.20/0.54 tff(428,plain,
% 0.20/0.54 (inverse(sk_c7) = sk_c7),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[427, 394])).
% 0.20/0.54 tff(429,plain,
% 0.20/0.54 (multiply(sk_c7, sk_c6) = sk_c6),
% 0.20/0.54 inference(transitivity,[status(thm)],[151, 396, 149, 395, 143])).
% 0.20/0.54 tff(430,plain,
% 0.20/0.54 ((multiply(sk_c7, sk_c7) = sk_c6) <=> (multiply(sk_c7, sk_c7) = multiply(sk_c7, sk_c6))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[375])).
% 0.20/0.54 tff(431,plain,
% 0.20/0.54 ((multiply(sk_c7, sk_c7) = multiply(sk_c7, sk_c6)) <=> (multiply(sk_c7, sk_c7) = sk_c6)),
% 0.20/0.54 inference(symmetry,[status(thm)],[430])).
% 0.20/0.54 tff(432,plain,
% 0.20/0.54 ((multiply(sk_c7, multiply(sk_c7, sk_c7)) = sk_c6) <=> (multiply(sk_c7, sk_c7) = sk_c6)),
% 0.20/0.54 inference(transitivity,[status(thm)],[393, 431])).
% 0.20/0.54 tff(433,plain,
% 0.20/0.54 (multiply(sk_c7, sk_c7) = sk_c6),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[427, 432])).
% 0.20/0.54 tff(434,plain,
% 0.20/0.54 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(435,plain,
% 0.20/0.54 (((~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6)))) <=> ((~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(436,plain,
% 0.20/0.55 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[435])).
% 0.20/0.55 tff(437,plain,
% 0.20/0.55 (((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) <=> ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[436, 434])).
% 0.20/0.55 tff(438,plain,
% 0.20/0.55 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | ((~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(439,plain,
% 0.20/0.55 ((~![X4: $i, X3: $i, X2: $i, X1: $i] : ((~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = X3)) | (~(multiply(sk_c7, X3) = sk_c6)) | (~(inverse(X1) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c6)) | (~(inverse(X2) = sk_c6)) | (~(multiply(X2, sk_c6) = sk_c7)) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))))) | (~(multiply(sk_c6, sk_c7) = multiply(sk_c7, sk_c6))) | (~(inverse(sk_c7) = multiply(sk_c7, sk_c6))) | (~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)) | (~(inverse(sk_c1) = sk_c6)) | (~(multiply(sk_c1, sk_c6) = sk_c7))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.20/0.55 tff(440,plain,
% 0.20/0.55 ((~(multiply(sk_c7, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c6)) | (~(inverse(sk_c7) = sk_c7)) | (~(multiply(sk_c1, sk_c6) = sk_c7))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[439, 121, 355, 317, 196])).
% 0.20/0.55 tff(441,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[440, 433, 429, 359, 428])).
% 0.20/0.55 tff(442,plain,(~(multiply(sk_c1, sk_c6) = sk_c7)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(443,plain,
% 0.20/0.55 (((inverse(sk_c2) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)) <=> ((inverse(sk_c2) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(444,plain,
% 0.20/0.55 (((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c2) = sk_c7)) <=> ((inverse(sk_c2) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(445,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c2) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_13')).
% 0.20/0.55 tff(446,plain,
% 0.20/0.55 ((inverse(sk_c2) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.20/0.55 tff(447,plain,
% 0.20/0.55 ((inverse(sk_c2) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[446, 443])).
% 0.20/0.55 tff(448,plain,
% 0.20/0.55 (inverse(sk_c2) = sk_c7),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[447, 442])).
% 0.20/0.55 tff(449,plain,
% 0.20/0.55 (sk_c7 = inverse(sk_c2)),
% 0.20/0.55 inference(symmetry,[status(thm)],[448])).
% 0.20/0.55 tff(450,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[449])).
% 0.20/0.55 tff(451,plain,
% 0.20/0.55 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c7, sk_c2)),
% 0.20/0.55 inference(symmetry,[status(thm)],[450])).
% 0.20/0.55 tff(452,plain,
% 0.20/0.55 (identity = multiply(sk_c7, sk_c2)),
% 0.20/0.55 inference(transitivity,[status(thm)],[47, 451])).
% 0.20/0.55 tff(453,plain,
% 0.20/0.55 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[452])).
% 0.20/0.55 tff(454,plain,
% 0.20/0.55 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(identity, sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[453])).
% 0.20/0.55 tff(455,plain,
% 0.20/0.55 (((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c2, sk_c7) = sk_c6)) <=> ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c2, sk_c7) = sk_c6))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(456,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c2, sk_c7) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_12')).
% 0.20/0.55 tff(457,plain,
% 0.20/0.55 ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c2, sk_c7) = sk_c6)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.20/0.55 tff(458,plain,
% 0.20/0.55 (multiply(sk_c2, sk_c7) = sk_c6),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[457, 442])).
% 0.20/0.55 tff(459,plain,
% 0.20/0.55 (multiply(sk_c7, multiply(sk_c2, sk_c7)) = multiply(sk_c7, sk_c6)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[458])).
% 0.20/0.55 tff(460,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c2, sk_c7))),
% 0.20/0.55 inference(symmetry,[status(thm)],[459])).
% 0.20/0.55 tff(461,plain,
% 0.20/0.55 (((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(462,plain,
% 0.20/0.55 (((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c7)) <=> ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(463,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (inverse(sk_c3) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_16')).
% 0.20/0.55 tff(464,plain,
% 0.20/0.55 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.20/0.55 tff(465,plain,
% 0.20/0.55 ((inverse(sk_c3) = sk_c7) | (multiply(sk_c1, sk_c6) = sk_c7)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[464, 461])).
% 0.20/0.55 tff(466,plain,
% 0.20/0.55 (inverse(sk_c3) = sk_c7),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[465, 442])).
% 0.20/0.55 tff(467,plain,
% 0.20/0.55 (sk_c7 = inverse(sk_c3)),
% 0.20/0.55 inference(symmetry,[status(thm)],[466])).
% 0.20/0.55 tff(468,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[467])).
% 0.20/0.55 tff(469,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c3) = multiply(sk_c7, sk_c2)),
% 0.20/0.55 inference(transitivity,[status(thm)],[468, 49, 47, 451])).
% 0.20/0.55 tff(470,plain,
% 0.20/0.55 (multiply(multiply(sk_c7, sk_c3), sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[469])).
% 0.20/0.55 tff(471,plain,
% 0.20/0.55 (((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c7) = sk_c4)) <=> ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c7) = sk_c4))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(472,axiom,((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c7) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_15')).
% 0.20/0.55 tff(473,plain,
% 0.20/0.55 ((multiply(sk_c1, sk_c6) = sk_c7) | (multiply(sk_c3, sk_c7) = sk_c4)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.20/0.55 tff(474,plain,
% 0.20/0.55 (multiply(sk_c3, sk_c7) = sk_c4),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[473, 442])).
% 0.20/0.55 tff(475,plain,
% 0.20/0.55 (sk_c4 = multiply(sk_c3, sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[474])).
% 0.20/0.55 tff(476,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c4) = multiply(sk_c7, multiply(sk_c3, sk_c7))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[475])).
% 0.20/0.55 tff(477,plain,
% 0.20/0.55 (sk_c6 = inverse(sk_c7)),
% 0.20/0.55 inference(transitivity,[status(thm)],[211, 476, 64, 470, 26, 459, 397])).
% 0.20/0.55 tff(478,plain,
% 0.20/0.55 (multiply(sk_c6, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[477])).
% 0.20/0.55 tff(479,plain,
% 0.20/0.55 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[478])).
% 0.20/0.55 tff(480,plain,
% 0.20/0.55 (multiply(sk_c6, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c6, sk_c7), sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[414])).
% 0.20/0.55 tff(481,plain,
% 0.20/0.55 (multiply(sk_c7, multiply(sk_c3, sk_c7)) = multiply(sk_c7, sk_c4)),
% 0.20/0.55 inference(symmetry,[status(thm)],[476])).
% 0.20/0.55 tff(482,plain,
% 0.20/0.55 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c3), sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[470])).
% 0.20/0.55 tff(483,plain,
% 0.20/0.55 (identity = sk_c6),
% 0.20/0.55 inference(transitivity,[status(thm)],[345, 479, 121, 460, 240, 482, 63, 481, 210])).
% 0.20/0.55 tff(484,plain,
% 0.20/0.55 (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[483])).
% 0.20/0.55 tff(485,plain,
% 0.20/0.55 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(sk_c7, sk_c7))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(486,plain,
% 0.20/0.55 (multiply(identity, multiply(sk_c7, sk_c7)) = multiply(sk_c7, sk_c7)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[485, 7])).
% 0.20/0.55 tff(487,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c7) = multiply(identity, multiply(sk_c7, sk_c7))),
% 0.20/0.55 inference(symmetry,[status(thm)],[486])).
% 0.20/0.55 tff(488,plain,
% 0.20/0.55 (sk_c6 = sk_c7),
% 0.20/0.55 inference(transitivity,[status(thm)],[211, 476, 64, 470, 454, 9])).
% 0.20/0.55 tff(489,plain,
% 0.20/0.55 (identity = inverse(sk_c1)),
% 0.20/0.55 inference(transitivity,[status(thm)],[345, 479, 121, 460, 240, 482, 63, 481, 210, 320])).
% 0.20/0.55 tff(490,plain,
% 0.20/0.55 (multiply(identity, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[489])).
% 0.20/0.55 tff(491,plain,
% 0.20/0.55 (sk_c1 = multiply(identity, sk_c1)),
% 0.20/0.55 inference(symmetry,[status(thm)],[319])).
% 0.20/0.56 tff(492,plain,
% 0.20/0.56 (sk_c1 = sk_c7),
% 0.20/0.56 inference(transitivity,[status(thm)],[491, 490, 138, 345, 479, 121, 460, 240, 454, 9])).
% 0.20/0.56 tff(493,plain,
% 0.20/0.56 (multiply(sk_c1, sk_c6) = multiply(sk_c7, sk_c7)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[492, 488])).
% 0.20/0.56 tff(494,plain,
% 0.20/0.56 (multiply(sk_c1, sk_c6) = sk_c7),
% 0.20/0.56 inference(transitivity,[status(thm)],[493, 487, 484, 480, 416, 479, 121, 460, 240, 454, 9])).
% 0.20/0.56 tff(495,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[442, 494])).
% 0.20/0.56 % SZS output end Proof
%------------------------------------------------------------------------------