%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU294+3 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:27:31 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU294+3 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 : Fri Jun 20 06:39:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(element_type, type, (
% 0.19/0.39 element: ( $i * $i ) > $o)).
% 0.19/0.39 tff(powerset_type, type, (
% 0.19/0.39 powerset: $i > $i)).
% 0.19/0.39 tff(tptp_fun_B_26_type, type, (
% 0.19/0.39 tptp_fun_B_26: $i)).
% 0.19/0.39 tff(tptp_fun_A_27_type, type, (
% 0.19/0.39 tptp_fun_A_27: $i)).
% 0.19/0.39 tff(subset_type, type, (
% 0.19/0.39 subset: ( $i * $i ) > $o)).
% 0.19/0.39 tff(finite_type, type, (
% 0.19/0.39 finite: $i > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(A!27, powerset(B!26)) <=> subset(A!27, B!26))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (element(A!27, powerset(B!26)) <=> subset(A!27, B!26)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))) <=> (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((subset(A, B) & finite(B)) => finite(A))) <=> (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(12,axiom,(~![A: $i, B: $i] : ((subset(A, B) & finite(B)) => finite(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t13_finset_1')).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.39 tff(17,plain,(
% 0.19/0.39 ~(finite(A!27) | (~(subset(A!27, B!26) & finite(B!26))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[16])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (subset(A!27, B!26) & finite(B!26)),
% 0.19/0.39 inference(or_elim,[status(thm)],[17])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (subset(A!27, B!26)),
% 0.19/0.39 inference(and_elim,[status(thm)],[18])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ((~(element(A!27, powerset(B!26)) <=> subset(A!27, B!26))) | element(A!27, powerset(B!26)) | (~subset(A!27, B!26))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~(element(A!27, powerset(B!26)) <=> subset(A!27, B!26))) | element(A!27, powerset(B!26))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (element(A!27, powerset(B!26))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[21, 9])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (finite(B!26)),
% 0.19/0.39 inference(and_elim,[status(thm)],[18])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (^[A: $i] : refl(((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[A: $i] : rewrite(((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[27, 25])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(A)) => finite(B)) <=> (finite(B) | (~element(B, powerset(A)))))), (![B: $i] : (element(B, powerset(A)) => finite(B)) <=> ![B: $i] : (finite(B) | (~element(B, powerset(A)))))), ((finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> (finite(A) => ![B: $i] : (finite(B) | (~element(B, powerset(A))))))), rewrite((finite(A) => ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))), ((finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![A: $i] : (finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.39 tff(32,axiom,(![A: $i] : (finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc2_finset_1')).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.39 tff(35,plain,(
% 0.19/0.39 ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[34])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | ((~finite(B!26)) | ![B: $i] : (finite(B) | (~element(B, powerset(B!26)))))) <=> ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | (~finite(B!26)) | ![B: $i] : (finite(B) | (~element(B, powerset(B!26)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | ((~finite(B!26)) | ![B: $i] : (finite(B) | (~element(B, powerset(B!26)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | (~finite(B!26)) | ![B: $i] : (finite(B) | (~element(B, powerset(B!26))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (![B: $i] : (finite(B) | (~element(B, powerset(B!26))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 36, 23])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~finite(A!27)),
% 0.19/0.39 inference(or_elim,[status(thm)],[17])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~![B: $i] : (finite(B) | (~element(B, powerset(B!26))))) | (finite(A!27) | (~element(A!27, powerset(B!26))))) <=> ((~![B: $i] : (finite(B) | (~element(B, powerset(B!26))))) | finite(A!27) | (~element(A!27, powerset(B!26))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.40 ((~![B: $i] : (finite(B) | (~element(B, powerset(B!26))))) | (finite(A!27) | (~element(A!27, powerset(B!26))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 ((~![B: $i] : (finite(B) | (~element(B, powerset(B!26))))) | finite(A!27) | (~element(A!27, powerset(B!26)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[44, 41, 40, 22])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------