%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP033-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:54 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP033-4 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 15:32:18 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(subgroup_member_type, type, (
% 0.21/0.38 subgroup_member: $i > $o)).
% 0.21/0.38 tff(j_type, type, (
% 0.21/0.38 j: $i > $i)).
% 0.21/0.38 tff(a_type, type, (
% 0.21/0.38 a: $i)).
% 0.21/0.38 tff(identity_type, type, (
% 0.21/0.38 identity: $i)).
% 0.21/0.38 tff(product_type, type, (
% 0.21/0.38 product: ( $i * $i * $i ) > $o)).
% 0.21/0.38 tff(inverse_type, type, (
% 0.21/0.38 inverse: $i > $i)).
% 0.21/0.38 tff(1,assumption,(~product(identity, j(identity), j(identity))), introduced(assumption)).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (^[X: $i] : refl(product(identity, X, X) <=> product(identity, X, X))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 0.21/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(5,axiom,(![X: $i] : product(identity, X, X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax','left_identity')).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (![X: $i] : product(identity, X, X)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.38 tff(7,plain,(
% 0.21/0.38 ![X: $i] : product(identity, X, X)),
% 0.21/0.38 inference(skolemize,[status(sab)],[6])).
% 0.21/0.38 tff(8,plain,
% 0.21/0.38 (![X: $i] : product(identity, X, X)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 ((~![X: $i] : product(identity, X, X)) | product(identity, j(identity), j(identity))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.38 tff(11,plain,(product(identity, j(identity), j(identity))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(12,assumption,(~product(j(identity), identity, j(identity))), introduced(assumption)).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 (^[X: $i] : refl(product(X, identity, X) <=> product(X, identity, X))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.21/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(16,axiom,(![X: $i] : product(X, identity, X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax','right_identity')).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (![X: $i] : product(X, identity, X)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.38 tff(18,plain,(
% 0.21/0.38 ![X: $i] : product(X, identity, X)),
% 0.21/0.38 inference(skolemize,[status(sab)],[17])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 (![X: $i] : product(X, identity, X)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 ((~![X: $i] : product(X, identity, X)) | product(j(identity), identity, j(identity))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.21/0.38 tff(22,plain,(product(j(identity), identity, j(identity))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 (^[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)))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 (![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))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 (![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))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 (^[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)))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(27,plain,
% 0.21/0.38 (![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))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.38 tff(28,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')).
% 0.21/0.38 tff(29,plain,
% 0.21/0.38 (![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.38 tff(30,plain,
% 0.21/0.38 (![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.38 tff(31,plain,(
% 0.21/0.38 ![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))),
% 0.21/0.38 inference(skolemize,[status(sab)],[30])).
% 0.21/0.38 tff(32,plain,
% 0.21/0.38 (![A: $i] : ((~subgroup_member(A)) | (~product(A, j(A), j(A))) | (~product(j(A), A, j(A))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.21/0.38 tff(33,plain,
% 0.21/0.38 (((~![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))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 ((~![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))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(35,plain,
% 0.21/0.38 ((~![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)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.38 tff(36,plain,
% 0.21/0.38 (~subgroup_member(identity)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[35, 32, 22, 11])).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 (^[X: $i] : refl(product(X, inverse(X), identity) <=> product(X, inverse(X), identity))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(38,plain,
% 0.21/0.38 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 0.21/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.38 tff(39,plain,
% 0.21/0.38 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(40,axiom,(![X: $i] : product(X, inverse(X), identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax','right_inverse')).
% 0.21/0.38 tff(41,plain,
% 0.21/0.38 (![X: $i] : product(X, inverse(X), identity)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.38 tff(42,plain,(
% 0.21/0.38 ![X: $i] : product(X, inverse(X), identity)),
% 0.21/0.38 inference(skolemize,[status(sab)],[41])).
% 0.21/0.38 tff(43,plain,
% 0.21/0.38 (![X: $i] : product(X, inverse(X), identity)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.21/0.38 tff(44,plain,
% 0.21/0.38 ((~![X: $i] : product(X, inverse(X), identity)) | product(j(j(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(45,plain,
% 0.21/0.38 (product(j(j(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.21/0.38 tff(46,plain,
% 0.21/0.38 (^[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))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(47,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.38 tff(48,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (^[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)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.39 tff(51,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/Axioms/GRP003-2.ax','closure_of_product_and_inverse')).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.21/0.39 tff(54,plain,(
% 0.21/0.39 ![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[53])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 (![B: $i, A: $i, C: $i] : (subgroup_member(C) | (~product(A, inverse(B), C)) | (~subgroup_member(B)) | (~subgroup_member(A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 (((~![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(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)) | (~subgroup_member(j(j(j(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(identity) | (~product(j(j(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)) | (~subgroup_member(j(j(j(j(j(a))))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 ((subgroup_member(identity) | (~product(j(j(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)) | (~subgroup_member(j(j(j(j(j(a))))))) | (~subgroup_member(j(j(j(j(j(a)))))))) <=> (subgroup_member(identity) | (~product(j(j(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)) | (~subgroup_member(j(j(j(j(j(a))))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 (((~![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(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)) | (~subgroup_member(j(j(j(j(j(a))))))) | (~subgroup_member(j(j(j(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(identity) | (~product(j(j(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)) | (~subgroup_member(j(j(j(j(j(a)))))))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[57])).
% 0.21/0.39 tff(59,plain,
% 0.21/0.39 (((~![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(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)) | (~subgroup_member(j(j(j(j(j(a))))))) | (~subgroup_member(j(j(j(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(identity) | (~product(j(j(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)) | (~subgroup_member(j(j(j(j(j(a))))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[58, 56])).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 ((~![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(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)) | (~subgroup_member(j(j(j(j(j(a))))))) | (~subgroup_member(j(j(j(j(j(a))))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 ((~![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(j(j(j(a))))), inverse(j(j(j(j(j(a)))))), identity)) | (~subgroup_member(j(j(j(j(j(a)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.39 tff(62,plain,
% 0.21/0.39 (subgroup_member(identity) | (~subgroup_member(j(j(j(j(j(a)))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[61, 55, 45])).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 (~subgroup_member(j(j(j(j(j(a))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[62, 36])).
% 0.21/0.39 tff(64,assumption,(subgroup_member(j(j(a)))), introduced(assumption)).
% 0.21/0.39 tff(65,plain,
% 0.21/0.39 (^[A: $i] : refl(((~subgroup_member(A)) | subgroup_member(j(A))) <=> ((~subgroup_member(A)) | subgroup_member(j(A))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(66,plain,
% 0.21/0.39 (![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A))) <=> ![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.39 tff(67,plain,
% 0.21/0.39 (![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A))) <=> ![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(68,axiom,(![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subgr2_clause1')).
% 0.21/0.39 tff(69,plain,
% 0.21/0.39 (![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.39 tff(70,plain,(
% 0.21/0.39 ![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[69])).
% 0.21/0.39 tff(71,plain,
% 0.21/0.39 (![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.21/0.39 tff(72,plain,
% 0.21/0.39 (((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(j(j(a)))) | subgroup_member(j(j(j(a)))))) <=> ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(j(j(a)))) | subgroup_member(j(j(j(a)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(73,plain,
% 0.21/0.39 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(j(j(a)))) | subgroup_member(j(j(j(a)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(74,plain,
% 0.21/0.39 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(j(j(a)))) | subgroup_member(j(j(j(a))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.39 tff(75,plain,
% 0.21/0.39 ((~subgroup_member(j(j(a)))) | subgroup_member(j(j(j(a))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.21/0.39 tff(76,plain,
% 0.21/0.39 (subgroup_member(j(j(j(a))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[75, 64])).
% 0.21/0.39 tff(77,plain,
% 0.21/0.39 (((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(j(j(j(a))))) | subgroup_member(j(j(j(j(a))))))) <=> ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(j(j(j(a))))) | subgroup_member(j(j(j(j(a))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(78,plain,
% 0.21/0.39 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(j(j(j(a))))) | subgroup_member(j(j(j(j(a))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(79,plain,
% 0.21/0.39 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(j(j(j(a))))) | subgroup_member(j(j(j(j(a)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.39 tff(80,plain,
% 0.21/0.39 ((~subgroup_member(j(j(j(a))))) | subgroup_member(j(j(j(j(a)))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[79, 71])).
% 0.21/0.39 tff(81,plain,
% 0.21/0.39 (subgroup_member(j(j(j(j(a)))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[80, 76])).
% 0.21/0.39 tff(82,plain,
% 0.21/0.39 (((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(j(j(j(j(a)))))) | subgroup_member(j(j(j(j(j(a)))))))) <=> ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(j(j(j(j(a)))))) | subgroup_member(j(j(j(j(j(a)))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(83,plain,
% 0.21/0.39 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(j(j(j(j(a)))))) | subgroup_member(j(j(j(j(j(a)))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(84,plain,
% 0.21/0.39 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(j(j(j(j(a)))))) | subgroup_member(j(j(j(j(j(a))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.39 tff(85,plain,
% 0.21/0.39 ((~subgroup_member(j(j(j(j(a)))))) | subgroup_member(j(j(j(j(j(a))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[84, 71])).
% 0.21/0.39 tff(86,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[85, 81, 63])).
% 0.21/0.39 tff(87,plain,(~subgroup_member(j(j(a)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(88,plain,
% 0.21/0.39 (subgroup_member(a) <=> subgroup_member(a)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(89,axiom,(subgroup_member(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_is_in_subgroup')).
% 0.21/0.39 tff(90,plain,
% 0.21/0.39 (subgroup_member(a)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.39 tff(91,plain,
% 0.21/0.39 (((~![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(92,plain,
% 0.21/0.39 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(a)) | subgroup_member(j(a)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(93,plain,
% 0.21/0.39 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(a)) | subgroup_member(j(a))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.39 tff(94,plain,
% 0.21/0.39 (subgroup_member(j(a))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[93, 90, 71])).
% 0.21/0.39 tff(95,plain,
% 0.21/0.39 (((~![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))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(96,plain,
% 0.21/0.39 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | ((~subgroup_member(j(a))) | subgroup_member(j(j(a))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(97,plain,
% 0.21/0.39 ((~![A: $i] : ((~subgroup_member(A)) | subgroup_member(j(A)))) | (~subgroup_member(j(a))) | subgroup_member(j(j(a)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.39 tff(98,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[97, 71, 94, 87])).
% 0.21/0.39 % SZS output end Proof
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------