%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET933+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:26:42 AM UTC 2025
% Result : Theorem 0.24s 0.41s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SET933+1 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.15 % Command : run_E %s %d THM
% 0.16/0.37 % Computer : n012.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri Jun 20 05:50:25 EDT 2025
% 0.16/0.37 % CPUTime :
% 0.24/0.41 % SZS status Theorem
% 0.24/0.41 % SZS output start Proof
% 0.24/0.41 tff(subset_type, type, (
% 0.24/0.41 subset: ( $i * $i ) > $o)).
% 0.24/0.41 tff(tptp_fun_A_3_type, type, (
% 0.24/0.41 tptp_fun_A_3: $i)).
% 0.24/0.41 tff(in_type, type, (
% 0.24/0.41 in: ( $i * $i ) > $o)).
% 0.24/0.41 tff(powerset_type, type, (
% 0.24/0.41 powerset: $i > $i)).
% 0.24/0.41 tff(singleton_type, type, (
% 0.24/0.41 singleton: $i > $i)).
% 0.24/0.41 tff(tptp_fun_C_0_type, type, (
% 0.24/0.41 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.24/0.41 tff(1,plain,
% 0.24/0.41 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(2,plain,
% 0.24/0.41 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.24/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.24/0.41 tff(3,plain,
% 0.24/0.41 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(4,plain,
% 0.24/0.41 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.24/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.24/0.41 tff(5,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 0.24/0.41 tff(6,plain,
% 0.24/0.41 (![A: $i] : subset(A, A)),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.24/0.41 tff(7,plain,
% 0.24/0.41 (![A: $i] : subset(A, A)),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.24/0.41 tff(8,plain,(
% 0.24/0.41 ![A: $i] : subset(A, A)),
% 0.24/0.41 inference(skolemize,[status(sab)],[7])).
% 0.24/0.41 tff(9,plain,
% 0.24/0.41 (![A: $i] : subset(A, A)),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.24/0.41 tff(10,plain,
% 0.24/0.41 ((~![A: $i] : subset(A, A)) | subset(A!3, A!3)),
% 0.24/0.41 inference(quant_inst,[status(thm)],[])).
% 0.24/0.41 tff(11,plain,
% 0.24/0.41 (subset(A!3, A!3)),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.24/0.41 tff(12,plain,
% 0.24/0.41 (^[A: $i, B: $i] : refl((subset(singleton(A), B) <=> in(A, B)) <=> (subset(singleton(A), B) <=> in(A, B)))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(13,plain,
% 0.24/0.41 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.24/0.41 tff(14,plain,
% 0.24/0.41 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(15,axiom,(![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 0.24/0.41 tff(16,plain,
% 0.24/0.41 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.24/0.41 tff(17,plain,(
% 0.24/0.41 ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.24/0.41 inference(skolemize,[status(sab)],[16])).
% 0.24/0.41 tff(18,plain,
% 0.24/0.41 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.24/0.41 tff(19,plain,
% 0.24/0.41 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) | (subset(singleton(A!3), powerset(A!3)) <=> in(A!3, powerset(A!3)))),
% 0.24/0.41 inference(quant_inst,[status(thm)],[])).
% 0.24/0.41 tff(20,plain,
% 0.24/0.41 (subset(singleton(A!3), powerset(A!3)) <=> in(A!3, powerset(A!3))),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.24/0.41 tff(21,plain,
% 0.24/0.41 ((~![A: $i] : subset(singleton(A), powerset(A))) <=> (~![A: $i] : subset(singleton(A), powerset(A)))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(22,axiom,(~![A: $i] : subset(singleton(A), powerset(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t80_zfmisc_1')).
% 0.24/0.41 tff(23,plain,
% 0.24/0.41 (~![A: $i] : subset(singleton(A), powerset(A))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.24/0.41 tff(24,plain,
% 0.24/0.41 (~![A: $i] : subset(singleton(A), powerset(A))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.24/0.41 tff(25,plain,
% 0.24/0.41 (~![A: $i] : subset(singleton(A), powerset(A))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.24/0.41 tff(26,plain,
% 0.24/0.41 (~![A: $i] : subset(singleton(A), powerset(A))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.24/0.41 tff(27,plain,(
% 0.24/0.41 ~subset(singleton(A!3), powerset(A!3))),
% 0.24/0.41 inference(skolemize,[status(sab)],[26])).
% 0.24/0.41 tff(28,plain,
% 0.24/0.41 ((~(subset(singleton(A!3), powerset(A!3)) <=> in(A!3, powerset(A!3)))) | subset(singleton(A!3), powerset(A!3)) | (~in(A!3, powerset(A!3)))),
% 0.24/0.41 inference(tautology,[status(thm)],[])).
% 0.24/0.41 tff(29,plain,
% 0.24/0.41 ((~(subset(singleton(A!3), powerset(A!3)) <=> in(A!3, powerset(A!3)))) | (~in(A!3, powerset(A!3)))),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.24/0.41 tff(30,plain,
% 0.24/0.41 (~in(A!3, powerset(A!3))),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[29, 20])).
% 0.24/0.41 tff(31,plain,
% 0.24/0.41 ((~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3))) | in(A!3, powerset(A!3)) | (~subset(A!3, A!3))),
% 0.24/0.41 inference(tautology,[status(thm)],[])).
% 0.24/0.41 tff(32,plain,
% 0.24/0.41 (~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3))),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[31, 30, 11])).
% 0.24/0.41 tff(33,plain,
% 0.24/0.41 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(34,plain,
% 0.24/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[33])).
% 0.24/0.41 tff(35,plain,
% 0.24/0.41 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.24/0.41 inference(pull_quant,[status(thm)],[])).
% 0.24/0.41 tff(36,plain,
% 0.24/0.41 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) <=> ![C: $i] : ((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))), ((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) <=> (~![C: $i] : ((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))))), pull_quant((~![C: $i] : ((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) <=> ?[C: $i] : (~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A))))), ((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) <=> ?[C: $i] : (~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))))), (((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> (?[C: $i] : (~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))), pull_quant((?[C: $i] : (~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> ?[C: $i] : ((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))), (((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> ?[C: $i] : ((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))), ((~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> (~?[C: $i] : ((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))))), pull_quant((~?[C: $i] : ((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> ![C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))), ((~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> ![C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(37,plain,
% 0.24/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.24/0.42 tff(38,plain,
% 0.24/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.24/0.42 inference(transitivity,[status(thm)],[37, 35])).
% 0.24/0.42 tff(39,plain,
% 0.24/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.24/0.42 inference(transitivity,[status(thm)],[38, 34])).
% 0.24/0.42 tff(40,plain,
% 0.24/0.42 (^[A: $i, B: $i] : rewrite((~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(41,plain,
% 0.24/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[40])).
% 0.24/0.42 tff(42,plain,
% 0.24/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.24/0.42 inference(transitivity,[status(thm)],[41, 39])).
% 0.24/0.42 tff(43,plain,
% 0.24/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) <=> ((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))), (((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))) <=> ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))), rewrite(((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))) <=> ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))), (((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))) <=> ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))), ((((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))) <=> (((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))))), rewrite((((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))) <=> (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))), ((((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))) <=> (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(44,plain,
% 0.24/0.42 (![A: $i, B: $i] : (((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))) <=> ![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[43])).
% 0.24/0.42 tff(45,plain,
% 0.24/0.42 (![A: $i, B: $i] : ((B = powerset(A)) <=> ![C: $i] : (in(C, B) <=> subset(C, A))) <=> ![A: $i, B: $i] : ((B = powerset(A)) <=> ![C: $i] : (in(C, B) <=> subset(C, A)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(46,axiom,(![A: $i, B: $i] : ((B = powerset(A)) <=> ![C: $i] : (in(C, B) <=> subset(C, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_zfmisc_1')).
% 0.24/0.42 tff(47,plain,
% 0.24/0.42 (![A: $i, B: $i] : ((B = powerset(A)) <=> ![C: $i] : (in(C, B) <=> subset(C, A)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.24/0.42 tff(48,plain,(
% 0.24/0.42 ![A: $i, B: $i] : (((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))),
% 0.24/0.42 inference(skolemize,[status(sab)],[47])).
% 0.24/0.42 tff(49,plain,
% 0.24/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.24/0.42 tff(50,plain,
% 0.24/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.24/0.42 tff(51,plain,
% 0.24/0.42 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(52,plain,
% 0.24/0.42 ((~(~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))) <=> (in(A!3, powerset(A!3)) <=> subset(A!3, A!3))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(53,plain,
% 0.24/0.42 (((~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3))) | $false) <=> (~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(54,plain,
% 0.24/0.42 ((~$true) <=> $false),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(55,plain,
% 0.24/0.42 (($true | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3)))) <=> $true),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(56,plain,
% 0.24/0.42 ((~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3))) <=> (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(57,plain,
% 0.24/0.42 ((powerset(A!3) = powerset(A!3)) <=> $true),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(58,plain,
% 0.24/0.42 (((powerset(A!3) = powerset(A!3)) | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3)))) <=> ($true | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3))))),
% 0.24/0.42 inference(monotonicity,[status(thm)],[57, 56])).
% 0.24/0.42 tff(59,plain,
% 0.24/0.42 (((powerset(A!3) = powerset(A!3)) | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3)))) <=> $true),
% 0.24/0.42 inference(transitivity,[status(thm)],[58, 55])).
% 0.24/0.42 tff(60,plain,
% 0.24/0.42 ((~((powerset(A!3) = powerset(A!3)) | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3))))) <=> (~$true)),
% 0.24/0.42 inference(monotonicity,[status(thm)],[59])).
% 0.24/0.42 tff(61,plain,
% 0.24/0.42 ((~((powerset(A!3) = powerset(A!3)) | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3))))) <=> $false),
% 0.24/0.42 inference(transitivity,[status(thm)],[60, 54])).
% 0.24/0.42 tff(62,plain,
% 0.24/0.42 ((~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3))) <=> (~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(63,plain,
% 0.24/0.42 (($false | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3))) <=> (in(A!3, powerset(A!3)) <=> subset(A!3, A!3))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(64,plain,
% 0.24/0.42 ((~(powerset(A!3) = powerset(A!3))) <=> (~$true)),
% 0.24/0.42 inference(monotonicity,[status(thm)],[57])).
% 0.24/0.42 tff(65,plain,
% 0.24/0.42 ((~(powerset(A!3) = powerset(A!3))) <=> $false),
% 0.24/0.42 inference(transitivity,[status(thm)],[64, 54])).
% 0.24/0.42 tff(66,plain,
% 0.24/0.42 (((~(powerset(A!3) = powerset(A!3))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3))) <=> ($false | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))),
% 0.24/0.42 inference(monotonicity,[status(thm)],[65])).
% 0.24/0.42 tff(67,plain,
% 0.24/0.42 (((~(powerset(A!3) = powerset(A!3))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3))) <=> (in(A!3, powerset(A!3)) <=> subset(A!3, A!3))),
% 0.24/0.42 inference(transitivity,[status(thm)],[66, 63])).
% 0.24/0.42 tff(68,plain,
% 0.24/0.42 ((~((~(powerset(A!3) = powerset(A!3))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))) <=> (~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))),
% 0.24/0.42 inference(monotonicity,[status(thm)],[67])).
% 0.24/0.42 tff(69,plain,
% 0.24/0.42 ((~((~(powerset(A!3) = powerset(A!3))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))) <=> (~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))),
% 0.24/0.42 inference(transitivity,[status(thm)],[68, 62])).
% 0.24/0.42 tff(70,plain,
% 0.24/0.42 (((~((~(powerset(A!3) = powerset(A!3))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))) | (~((powerset(A!3) = powerset(A!3)) | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3)))))) <=> ((~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3))) | $false)),
% 0.24/0.42 inference(monotonicity,[status(thm)],[69, 61])).
% 0.24/0.42 tff(71,plain,
% 0.24/0.42 (((~((~(powerset(A!3) = powerset(A!3))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))) | (~((powerset(A!3) = powerset(A!3)) | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3)))))) <=> (~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))),
% 0.24/0.42 inference(transitivity,[status(thm)],[70, 53])).
% 0.24/0.42 tff(72,plain,
% 0.24/0.42 ((~((~((~(powerset(A!3) = powerset(A!3))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))) | (~((powerset(A!3) = powerset(A!3)) | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3))))))) <=> (~(~(in(A!3, powerset(A!3)) <=> subset(A!3, A!3))))),
% 0.24/0.42 inference(monotonicity,[status(thm)],[71])).
% 0.24/0.42 tff(73,plain,
% 0.24/0.42 ((~((~((~(powerset(A!3) = powerset(A!3))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))) | (~((powerset(A!3) = powerset(A!3)) | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3))))))) <=> (in(A!3, powerset(A!3)) <=> subset(A!3, A!3))),
% 0.24/0.42 inference(transitivity,[status(thm)],[72, 52])).
% 0.24/0.42 tff(74,plain,
% 0.24/0.42 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))) | (~((~((~(powerset(A!3) = powerset(A!3))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))) | (~((powerset(A!3) = powerset(A!3)) | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))),
% 0.24/0.42 inference(monotonicity,[status(thm)],[73])).
% 0.24/0.42 tff(75,plain,
% 0.24/0.42 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))) | (~((~((~(powerset(A!3) = powerset(A!3))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))) | (~((powerset(A!3) = powerset(A!3)) | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))),
% 0.24/0.42 inference(transitivity,[status(thm)],[74, 51])).
% 0.24/0.42 tff(76,plain,
% 0.24/0.42 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))) | (~((~((~(powerset(A!3) = powerset(A!3))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3)))) | (~((powerset(A!3) = powerset(A!3)) | (~(in(tptp_fun_C_0(powerset(A!3), A!3), powerset(A!3)) <=> subset(tptp_fun_C_0(powerset(A!3), A!3), A!3)))))))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(77,plain,
% 0.24/0.42 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))) | (in(A!3, powerset(A!3)) <=> subset(A!3, A!3))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.24/0.42 tff(78,plain,
% 0.24/0.42 ($false),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[77, 50, 32])).
% 0.24/0.42 % SZS output end Proof
% 0.24/0.43 % E exiting
%------------------------------------------------------------------------------