TSTP Solution File: GRP033-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP033-3 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 22:25:34 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP033-3 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 14:16:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(product_type, type, (
% 0.20/0.41 product: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(j_type, type, (
% 0.20/0.41 j: $i > $i)).
% 0.20/0.41 tff(identity_type, type, (
% 0.20/0.41 identity: $i)).
% 0.20/0.41 tff(subgroup_member_type, type, (
% 0.20/0.41 subgroup_member: $i > $o)).
% 0.20/0.41 tff(a_type, type, (
% 0.20/0.41 a: $i)).
% 0.20/0.41 tff(inverse_type, type, (
% 0.20/0.41 inverse: $i > $i)).
% 0.20/0.41 tff(1,assumption,(~product(j(identity), identity, j(identity))), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[X: $i] : refl(product(X, identity, X) <=> product(X, identity, X))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(5,axiom,(![X: $i] : product(X, identity, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','right_identity')).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![X: $i] : product(X, identity, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.41 tff(7,plain,(
% 0.20/0.41 ![X: $i] : product(X, identity, X)),
% 0.20/0.41 inference(skolemize,[status(sab)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![X: $i] : product(X, identity, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 ((~![X: $i] : product(X, identity, X)) | product(j(identity), identity, j(identity))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.41 tff(11,plain,(product(j(identity), identity, j(identity))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (^[A: $i] : refl(((~subgroup_member(A)) | subgroup_member(j(A))) <=> ((~subgroup_member(A)) | subgroup_member(j(A))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A))) <=> ![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A))) <=> ![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(15,axiom,(![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subgr2_clause1')).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.41 tff(17,plain,(
% 0.20/0.41 ![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[16])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (subgroup_member(a) <=> subgroup_member(a)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(20,axiom,(subgroup_member(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_is_in_subgroup')).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (subgroup_member(a)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(a)) | subgroup_member(j(a)))) <=> ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(a)) | subgroup_member(j(a)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(a)) | subgroup_member(j(a)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(a)) | subgroup_member(j(a))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (subgroup_member(j(a))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[24, 21, 18])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(j(a))) | subgroup_member(j(j(a))))) <=> ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(j(a))) | subgroup_member(j(j(a))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(j(a))) | subgroup_member(j(j(a))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(j(a))) | subgroup_member(j(j(a)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (subgroup_member(j(j(a)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[28, 18, 25])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (^[X: $i] : refl(product(X, inverse(X), identity) <=> product(X, inverse(X), identity))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(33,axiom,(![X: $i] : product(X, inverse(X), identity)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','right_inverse')).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![X: $i] : product(X, inverse(X), identity)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.41 tff(35,plain,(
% 0.20/0.41 ![X: $i] : product(X, inverse(X), identity)),
% 0.20/0.41 inference(skolemize,[status(sab)],[34])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (![X: $i] : product(X, inverse(X), identity)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ((~![X: $i] : product(X, inverse(X), identity)) | product(j(j(a)), inverse(j(j(a))), identity)),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (product(j(j(a)), inverse(j(j(a))), identity)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (^[B: $i, A: $i, C: $i] : refl((subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A))) <=> (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A))) <=> ![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A))) <=> ![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((((~subgroup_member(A)) | (~subgroup_member(B))) | (~product(A, inverse(B), C))) <=> ((~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))), (((((~subgroup_member(A)) | (~subgroup_member(B))) | (~product(A, inverse(B), C))) | subgroup_member(C)) <=> (((~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A))) | subgroup_member(C)))), rewrite((((~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A))) | subgroup_member(C)) <=> (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))), (((((~subgroup_member(A)) | (~subgroup_member(B))) | (~product(A, inverse(B), C))) | subgroup_member(C)) <=> (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : ((((~subgroup_member(A)) | (~subgroup_member(B))) | (~product(A, inverse(B), C))) | subgroup_member(C)) <=> ![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.41 tff(44,axiom,(![B: $i, A: $i, C: $i] : ((((~subgroup_member(A)) | (~subgroup_member(B))) | (~product(A, inverse(B), C))) | subgroup_member(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','closure_of_product_and_inverse')).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.41 tff(47,plain,(
% 0.20/0.41 ![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[46])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | ((~subgroup_member(j(j(a)))) | subgroup_member(identity) | (~product(j(j(a)), inverse(j(j(a))), identity)))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (~subgroup_member(j(j(a)))) | subgroup_member(identity) | (~product(j(j(a)), inverse(j(j(a))), identity)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((subgroup_member(identity) | (~product(j(j(a)), inverse(j(j(a))), identity)) | (~subgroup_member(j(j(a)))) | (~subgroup_member(j(j(a))))) <=> ((~subgroup_member(j(j(a)))) | subgroup_member(identity) | (~product(j(j(a)), inverse(j(j(a))), identity)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(identity) | (~product(j(j(a)), inverse(j(j(a))), identity)) | (~subgroup_member(j(j(a)))) | (~subgroup_member(j(j(a)))))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | ((~subgroup_member(j(j(a)))) | subgroup_member(identity) | (~product(j(j(a)), inverse(j(j(a))), identity))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(identity) | (~product(j(j(a)), inverse(j(j(a))), identity)) | (~subgroup_member(j(j(a)))) | (~subgroup_member(j(j(a)))))) <=> ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (~subgroup_member(j(j(a)))) | subgroup_member(identity) | (~product(j(j(a)), inverse(j(j(a))), identity)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[51, 49])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (subgroup_member(identity) | (~product(j(j(a)), inverse(j(j(a))), identity)) | (~subgroup_member(j(j(a)))) | (~subgroup_member(j(j(a)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 ((~![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))) | (~subgroup_member(j(j(a)))) | subgroup_member(identity) | (~product(j(j(a)), inverse(j(j(a))), identity))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (subgroup_member(identity)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[54, 48, 38, 29])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (^[A: $i] : refl(((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A)))) <=> ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A)))) <=> ![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A)))) <=> ![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (^[A: $i] : rewrite((((~product(j(A), A, j(A))) | (~product(A, j(A), j(A)))) | (~subgroup_member(A))) <=> ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (![A: $i] : (((~product(j(A), A, j(A))) | (~product(A, j(A), j(A)))) | (~subgroup_member(A))) <=> ![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.41 tff(61,axiom,(![A: $i] : (((~product(j(A), A, j(A))) | (~product(A, j(A), j(A)))) | (~subgroup_member(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_subgr2')).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.41 tff(64,plain,(
% 0.20/0.41 ![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[63])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (((~![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))) | ((~subgroup_member(identity)) | (~product(identity, j(identity), j(identity))) | (~product(j(identity), identity, j(identity))))) <=> ((~![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))) | (~subgroup_member(identity)) | (~product(identity, j(identity), j(identity))) | (~product(j(identity), identity, j(identity))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 ((~![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))) | ((~subgroup_member(identity)) | (~product(identity, j(identity), j(identity))) | (~product(j(identity), identity, j(identity))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 ((~![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))) | (~subgroup_member(identity)) | (~product(identity, j(identity), j(identity))) | (~product(j(identity), identity, j(identity)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~product(identity, j(identity), j(identity))) | (~product(j(identity), identity, j(identity)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[68, 65, 55])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (~product(identity, j(identity), j(identity))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[69, 11])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (^[X: $i] : refl(product(identity, X, X) <=> product(identity, X, X))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(74,axiom,(![X: $i] : product(identity, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','left_identity')).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (![X: $i] : product(identity, X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.41 tff(76,plain,(
% 0.20/0.41 ![X: $i] : product(identity, X, X)),
% 0.20/0.41 inference(skolemize,[status(sab)],[75])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (![X: $i] : product(identity, X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 ((~![X: $i] : product(identity, X, X)) | product(identity, j(identity), j(identity))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[78, 77, 70])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------