%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET889+1 : TPTP v9.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:26:36 AM UTC 2025
% Result : Theorem 3.25s 3.49s
% Output : Proof 3.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET889+1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:51:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.25/3.49 % SZS status Theorem
% 3.25/3.49 % SZS output start Proof
% 3.25/3.49 tff(in_type, type, (
% 3.25/3.49 in: ( $i * $i ) > $o)).
% 3.25/3.49 tff(unordered_pair_type, type, (
% 3.25/3.49 unordered_pair: ( $i * $i ) > $i)).
% 3.25/3.49 tff(empty_set_type, type, (
% 3.25/3.49 empty_set: $i)).
% 3.25/3.49 tff(singleton_type, type, (
% 3.25/3.49 singleton: $i > $i)).
% 3.25/3.49 tff(tptp_fun_A_5_type, type, (
% 3.25/3.49 tptp_fun_A_5: $i)).
% 3.25/3.49 tff(tptp_fun_C_0_type, type, (
% 3.25/3.49 tptp_fun_C_0: ( $i * $i ) > $i)).
% 3.25/3.49 tff(subset_type, type, (
% 3.25/3.49 subset: ( $i * $i ) > $o)).
% 3.25/3.49 tff(powerset_type, type, (
% 3.25/3.49 powerset: $i > $i)).
% 3.25/3.49 tff(tptp_fun_D_1_type, type, (
% 3.25/3.49 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 3.25/3.49 tff(1,assumption,(~subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))), introduced(assumption)).
% 3.25/3.49 tff(2,assumption,((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))))), introduced(assumption)).
% 3.25/3.49 tff(3,plain,
% 3.25/3.49 (^[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))))))))),
% 3.25/3.49 inference(bind,[status(th)],[])).
% 3.25/3.49 tff(4,plain,
% 3.25/3.49 (![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)))))))),
% 3.25/3.49 inference(quant_intro,[status(thm)],[3])).
% 3.25/3.49 tff(5,plain,
% 3.25/3.49 (![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)))))))),
% 3.25/3.49 inference(pull_quant,[status(thm)],[])).
% 3.25/3.49 tff(6,plain,
% 3.25/3.49 (^[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)))))))))),
% 3.25/3.50 inference(bind,[status(th)],[])).
% 3.25/3.50 tff(7,plain,
% 3.25/3.50 (![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)))))))),
% 3.25/3.50 inference(quant_intro,[status(thm)],[6])).
% 3.25/3.50 tff(8,plain,
% 3.25/3.50 (![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)))))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[7, 5])).
% 3.25/3.50 tff(9,plain,
% 3.25/3.50 (![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)))))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[8, 4])).
% 3.25/3.50 tff(10,plain,
% 3.25/3.50 (^[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))))))))),
% 3.25/3.50 inference(bind,[status(th)],[])).
% 3.25/3.50 tff(11,plain,
% 3.25/3.50 (![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)))))))),
% 3.25/3.50 inference(quant_intro,[status(thm)],[10])).
% 3.25/3.50 tff(12,plain,
% 3.25/3.50 (![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)))))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[11, 9])).
% 3.25/3.50 tff(13,plain,
% 3.25/3.50 (^[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)))))))))),
% 3.25/3.50 inference(bind,[status(th)],[])).
% 3.25/3.50 tff(14,plain,
% 3.25/3.50 (![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)))))))),
% 3.25/3.50 inference(quant_intro,[status(thm)],[13])).
% 3.25/3.50 tff(15,plain,
% 3.25/3.50 (![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)))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(16,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')).
% 3.25/3.50 tff(17,plain,
% 3.25/3.50 (![A: $i, B: $i] : ((B = powerset(A)) <=> ![C: $i] : (in(C, B) <=> subset(C, A)))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[16, 15])).
% 3.25/3.50 tff(18,plain,(
% 3.25/3.50 ![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)))))),
% 3.25/3.50 inference(skolemize,[status(sab)],[17])).
% 3.25/3.50 tff(19,plain,
% 3.25/3.50 (![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)))))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.25/3.50 tff(20,plain,
% 3.25/3.50 (![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)))))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[19, 12])).
% 3.25/3.50 tff(21,plain,
% 3.25/3.50 (((~![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)))))))) | (~((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))))))) <=> ((~![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)))))))) | (~((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))))))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(22,plain,
% 3.25/3.50 ((~((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))) | (~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))))))) <=> (~((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(23,plain,
% 3.25/3.50 (((~![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)))))))) | (~((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))) | (~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))))))))) <=> ((~![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)))))))) | (~((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))))))))),
% 3.25/3.50 inference(monotonicity,[status(thm)],[22])).
% 3.25/3.50 tff(24,plain,
% 3.25/3.50 (((~![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)))))))) | (~((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))) | (~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))))))))) <=> ((~![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)))))))) | (~((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))))))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[23, 21])).
% 3.25/3.50 tff(25,plain,
% 3.25/3.50 ((~![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)))))))) | (~((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))) | (~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))))))))),
% 3.25/3.50 inference(quant_inst,[status(thm)],[])).
% 3.25/3.50 tff(26,plain,
% 3.25/3.50 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))) | (~((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[25, 24])).
% 3.25/3.50 tff(27,plain,
% 3.25/3.50 ($false),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[26, 20, 2])).
% 3.25/3.50 tff(28,plain,(~((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.50 tff(29,plain,
% 3.25/3.50 (((~((~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))) | (in(empty_set, unordered_pair(singleton(A!5), empty_set)) <=> subset(empty_set, singleton(A!5))))) | (~((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))))) | ((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))))),
% 3.25/3.50 inference(tautology,[status(thm)],[])).
% 3.25/3.50 tff(30,plain,
% 3.25/3.50 ((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[29, 28])).
% 3.25/3.50 tff(31,plain,
% 3.25/3.50 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 3.25/3.50 inference(bind,[status(th)],[])).
% 3.25/3.50 tff(32,plain,
% 3.25/3.50 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 3.25/3.50 inference(quant_intro,[status(thm)],[31])).
% 3.25/3.50 tff(33,plain,
% 3.25/3.50 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(34,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 3.25/3.50 tff(35,plain,
% 3.25/3.50 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[34, 33])).
% 3.25/3.50 tff(36,plain,(
% 3.25/3.50 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 3.25/3.50 inference(skolemize,[status(sab)],[35])).
% 3.25/3.50 tff(37,plain,
% 3.25/3.50 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[36, 32])).
% 3.25/3.50 tff(38,plain,
% 3.25/3.50 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(empty_set, singleton(A!5)) = unordered_pair(singleton(A!5), empty_set))),
% 3.25/3.50 inference(quant_inst,[status(thm)],[])).
% 3.25/3.50 tff(39,plain,
% 3.25/3.50 (unordered_pair(empty_set, singleton(A!5)) = unordered_pair(singleton(A!5), empty_set)),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[38, 37])).
% 3.25/3.50 tff(40,plain,
% 3.25/3.50 (unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5))),
% 3.25/3.50 inference(symmetry,[status(thm)],[39])).
% 3.25/3.50 tff(41,assumption,(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))), introduced(assumption)).
% 3.25/3.50 tff(42,plain,
% 3.25/3.50 (powerset(singleton(A!5)) = unordered_pair(singleton(A!5), empty_set)),
% 3.25/3.50 inference(symmetry,[status(thm)],[41])).
% 3.25/3.50 tff(43,plain,
% 3.25/3.50 (powerset(singleton(A!5)) = unordered_pair(empty_set, singleton(A!5))),
% 3.25/3.50 inference(transitivity,[status(thm)],[42, 40])).
% 3.25/3.50 tff(44,plain,
% 3.25/3.50 ((~![A: $i] : (powerset(singleton(A)) = unordered_pair(empty_set, singleton(A)))) <=> (~![A: $i] : (powerset(singleton(A)) = unordered_pair(empty_set, singleton(A))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(45,axiom,(~![A: $i] : (powerset(singleton(A)) = unordered_pair(empty_set, singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_zfmisc_1')).
% 3.25/3.50 tff(46,plain,
% 3.25/3.50 (~![A: $i] : (powerset(singleton(A)) = unordered_pair(empty_set, singleton(A)))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[45, 44])).
% 3.25/3.50 tff(47,plain,
% 3.25/3.50 (~![A: $i] : (powerset(singleton(A)) = unordered_pair(empty_set, singleton(A)))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[46, 44])).
% 3.25/3.50 tff(48,plain,
% 3.25/3.50 (~![A: $i] : (powerset(singleton(A)) = unordered_pair(empty_set, singleton(A)))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[47, 44])).
% 3.25/3.50 tff(49,plain,
% 3.25/3.50 (~![A: $i] : (powerset(singleton(A)) = unordered_pair(empty_set, singleton(A)))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[48, 44])).
% 3.25/3.50 tff(50,plain,(
% 3.25/3.50 ~(powerset(singleton(A!5)) = unordered_pair(empty_set, singleton(A!5)))),
% 3.25/3.50 inference(skolemize,[status(sab)],[49])).
% 3.25/3.50 tff(51,plain,
% 3.25/3.50 ($false),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[50, 43])).
% 3.25/3.50 tff(52,plain,(~(unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.50 tff(53,plain,
% 3.25/3.50 ((~((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))))) | (~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5)))),
% 3.25/3.50 inference(tautology,[status(thm)],[])).
% 3.25/3.50 tff(54,plain,
% 3.25/3.50 ((~((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))) | (unordered_pair(singleton(A!5), empty_set) = powerset(singleton(A!5))))) | (~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[53, 52])).
% 3.25/3.50 tff(55,plain,
% 3.25/3.50 (~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[54, 30])).
% 3.25/3.50 tff(56,plain,
% 3.25/3.50 ((in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))) | in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) | subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))),
% 3.25/3.50 inference(tautology,[status(thm)],[])).
% 3.25/3.50 tff(57,plain,
% 3.25/3.50 (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) | subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[56, 55])).
% 3.25/3.50 tff(58,plain,
% 3.25/3.50 (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[57, 1])).
% 3.25/3.50 tff(59,assumption,(~(subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))), introduced(assumption)).
% 3.25/3.50 tff(60,plain,
% 3.25/3.50 (^[A: $i, B: $i] : refl((subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))))),
% 3.25/3.50 inference(bind,[status(th)],[])).
% 3.25/3.50 tff(61,plain,
% 3.25/3.50 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 3.25/3.50 inference(quant_intro,[status(thm)],[60])).
% 3.25/3.50 tff(62,plain,
% 3.25/3.50 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(63,axiom,(![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l4_zfmisc_1')).
% 3.25/3.50 tff(64,plain,
% 3.25/3.50 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[63, 62])).
% 3.25/3.50 tff(65,plain,(
% 3.25/3.50 ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 3.25/3.50 inference(skolemize,[status(sab)],[64])).
% 3.25/3.50 tff(66,plain,
% 3.25/3.50 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[65, 61])).
% 3.25/3.50 tff(67,plain,
% 3.25/3.50 ((~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))) | (subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))),
% 3.25/3.50 inference(quant_inst,[status(thm)],[])).
% 3.25/3.50 tff(68,plain,
% 3.25/3.50 ($false),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[67, 66, 59])).
% 3.25/3.50 tff(69,plain,(subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.50 tff(70,plain,
% 3.25/3.50 ((~(subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))) | subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)) | (~((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))),
% 3.25/3.50 inference(tautology,[status(thm)],[])).
% 3.25/3.50 tff(71,plain,
% 3.25/3.50 (subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)) | (~((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[70, 69])).
% 3.25/3.50 tff(72,plain,
% 3.25/3.50 (~((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))),
% 3.25/3.50 inference(unit_resolution,[status(thm)],[71, 1])).
% 3.25/3.50 tff(73,assumption,((~((~(unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5)))) | (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))))) | (~((unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5))) | (~(in(tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set) = empty_set) | (tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set) = singleton(A!5)))))))), introduced(assumption)).
% 3.25/3.50 tff(74,plain,
% 3.25/3.50 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))))),
% 3.25/3.50 inference(bind,[status(th)],[])).
% 3.25/3.50 tff(75,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))),
% 3.25/3.50 inference(quant_intro,[status(thm)],[74])).
% 3.25/3.50 tff(76,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))),
% 3.25/3.50 inference(pull_quant,[status(thm)],[])).
% 3.25/3.50 tff(77,plain,
% 3.25/3.50 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))))),
% 3.25/3.50 inference(bind,[status(th)],[])).
% 3.25/3.50 tff(78,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))),
% 3.25/3.50 inference(quant_intro,[status(thm)],[77])).
% 3.25/3.50 tff(79,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[78, 76])).
% 3.25/3.50 tff(80,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[79, 75])).
% 3.25/3.50 tff(81,plain,
% 3.25/3.50 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))))),
% 3.25/3.50 inference(bind,[status(th)],[])).
% 3.25/3.50 tff(82,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))),
% 3.25/3.50 inference(quant_intro,[status(thm)],[81])).
% 3.25/3.50 tff(83,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))),
% 3.25/3.50 inference(transitivity,[status(thm)],[82, 80])).
% 3.25/3.50 tff(84,plain,
% 3.25/3.50 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))) <=> (in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))), ((~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))), rewrite((~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))), ((~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))))),
% 3.25/3.50 inference(bind,[status(th)],[])).
% 3.25/3.50 tff(85,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))),
% 3.25/3.50 inference(quant_intro,[status(thm)],[84])).
% 3.25/3.50 tff(86,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))),
% 3.25/3.50 inference(rewrite,[status(thm)],[])).
% 3.25/3.50 tff(87,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tarski')).
% 3.25/3.50 tff(88,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[87, 86])).
% 3.25/3.50 tff(89,plain,(
% 3.25/3.50 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))),
% 3.25/3.50 inference(skolemize,[status(sab)],[88])).
% 3.25/3.50 tff(90,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[89, 85])).
% 3.25/3.50 tff(91,plain,
% 3.25/3.50 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))),
% 3.25/3.50 inference(modus_ponens,[status(thm)],[90, 83])).
% 3.25/3.50 tff(92,plain,
% 3.25/3.50 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = A) | (D = B))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = A) | (tptp_fun_D_1(C, B, A) = B))))))))) | (~((~((~(unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5)))) | (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))))) | (~((unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5))) | (~(in(tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set) = empty_set) | (tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set) = singleton(A!5)))))))))),
% 3.25/3.51 inference(quant_inst,[status(thm)],[])).
% 3.25/3.51 tff(93,plain,
% 3.25/3.51 ($false),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[92, 91, 73])).
% 3.25/3.51 tff(94,plain,(~((~((~(unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5)))) | (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))))) | (~((unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5))) | (~(in(tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set) = empty_set) | (tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set) = singleton(A!5))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.51 tff(95,plain,
% 3.25/3.51 (((~((~(unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5)))) | (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))))) | (~((unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5))) | (~(in(tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set) = empty_set) | (tptp_fun_D_1(unordered_pair(singleton(A!5), empty_set), singleton(A!5), empty_set) = singleton(A!5)))))))) | ((~(unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5)))) | (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))))),
% 3.25/3.51 inference(tautology,[status(thm)],[])).
% 3.25/3.51 tff(96,plain,
% 3.25/3.51 ((~(unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5)))) | (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[95, 94])).
% 3.25/3.51 tff(97,plain,
% 3.25/3.51 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5)))),
% 3.25/3.51 inference(quant_inst,[status(thm)],[])).
% 3.25/3.51 tff(98,plain,
% 3.25/3.51 (unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[97, 37])).
% 3.25/3.51 tff(99,plain,
% 3.25/3.51 ((~((~(unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5)))) | (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))))) | (~(unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5)))) | (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))),
% 3.25/3.51 inference(tautology,[status(thm)],[])).
% 3.25/3.51 tff(100,plain,
% 3.25/3.51 ((~((~(unordered_pair(singleton(A!5), empty_set) = unordered_pair(empty_set, singleton(A!5)))) | (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))))) | (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[99, 98])).
% 3.25/3.51 tff(101,plain,
% 3.25/3.51 (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[100, 96])).
% 3.25/3.51 tff(102,plain,
% 3.25/3.51 ((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))) | (~in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set))) | ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))),
% 3.25/3.51 inference(tautology,[status(thm)],[])).
% 3.25/3.51 tff(103,plain,
% 3.25/3.51 ((~in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set))) | ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[102, 101])).
% 3.25/3.51 tff(104,plain,
% 3.25/3.51 ($false),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[103, 72, 58])).
% 3.25/3.51 tff(105,plain,(subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.51 tff(106,plain,
% 3.25/3.51 ((in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))) | (~in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set))) | (~subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))),
% 3.25/3.51 inference(tautology,[status(thm)],[])).
% 3.25/3.51 tff(107,plain,
% 3.25/3.51 ((~in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set))) | (~subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)))),
% 3.25/3.51 inference(unit_resolution,[status(thm)],[106, 55])).
% 3.36/3.51 tff(108,plain,
% 3.36/3.51 (~in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set))),
% 3.36/3.51 inference(unit_resolution,[status(thm)],[107, 105])).
% 3.36/3.51 tff(109,plain,
% 3.36/3.51 ((~(subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))) | (~subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))) | ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))),
% 3.36/3.51 inference(tautology,[status(thm)],[])).
% 3.36/3.51 tff(110,plain,
% 3.36/3.51 ((~subset(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), singleton(A!5))) | ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5)))),
% 3.36/3.51 inference(unit_resolution,[status(thm)],[109, 69])).
% 3.36/3.51 tff(111,plain,
% 3.36/3.51 ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))),
% 3.36/3.51 inference(unit_resolution,[status(thm)],[110, 105])).
% 3.36/3.51 tff(112,plain,
% 3.36/3.51 ((~(in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) <=> ((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))) | in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) | (~((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))),
% 3.36/3.51 inference(tautology,[status(thm)],[])).
% 3.36/3.51 tff(113,plain,
% 3.36/3.51 (in(tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)), unordered_pair(singleton(A!5), empty_set)) | (~((tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = empty_set) | (tptp_fun_C_0(unordered_pair(singleton(A!5), empty_set), singleton(A!5)) = singleton(A!5))))),
% 3.36/3.51 inference(unit_resolution,[status(thm)],[112, 101])).
% 3.36/3.51 tff(114,plain,
% 3.36/3.51 ($false),
% 3.36/3.51 inference(unit_resolution,[status(thm)],[113, 111, 108])).
% 3.36/3.51 % SZS output end Proof
% 3.36/3.51 % E exiting
%------------------------------------------------------------------------------