%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET875+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:26:35 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET875+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 05:50:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(in_type, type, (
% 0.18/0.37 in: ( $i * $i ) > $o)).
% 0.18/0.37 tff(singleton_type, type, (
% 0.18/0.37 singleton: $i > $i)).
% 0.18/0.37 tff(tptp_fun_B_3_type, type, (
% 0.18/0.37 tptp_fun_B_3: $i)).
% 0.18/0.37 tff(disjoint_type, type, (
% 0.18/0.37 disjoint: ( $i * $i ) > $o)).
% 0.18/0.37 tff(tptp_fun_C_0_type, type, (
% 0.18/0.37 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 ((~![B: $i] : (~disjoint(singleton(B), singleton(B)))) <=> (~![B: $i] : (~disjoint(singleton(B), singleton(B))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 ((~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B)))) <=> (~![B: $i] : (~disjoint(singleton(B), singleton(B))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(3,axiom,(~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t16_zfmisc_1')).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (~![B: $i] : (~disjoint(singleton(B), singleton(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (~![B: $i] : (~disjoint(singleton(B), singleton(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (~![B: $i] : (~disjoint(singleton(B), singleton(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (~![B: $i] : (~disjoint(singleton(B), singleton(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.18/0.37 tff(8,plain,(
% 0.18/0.37 disjoint(singleton(B!3), singleton(B!3))),
% 0.18/0.37 inference(skolemize,[status(sab)],[7])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (^[A: $i, B: $i] : refl(((~in(A, B)) | (~disjoint(singleton(A), B))) <=> ((~in(A, B)) | (~disjoint(singleton(A), B))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (^[A: $i, B: $i] : trans(monotonicity(rewrite((disjoint(singleton(A), B) & in(A, B)) <=> (~((~in(A, B)) | (~disjoint(singleton(A), B))))), ((~(disjoint(singleton(A), B) & in(A, B))) <=> (~(~((~in(A, B)) | (~disjoint(singleton(A), B))))))), rewrite((~(~((~in(A, B)) | (~disjoint(singleton(A), B))))) <=> ((~in(A, B)) | (~disjoint(singleton(A), B)))), ((~(disjoint(singleton(A), B) & in(A, B))) <=> ((~in(A, B)) | (~disjoint(singleton(A), B)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B))) <=> ![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(14,axiom,(![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l25_zfmisc_1')).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.18/0.37 tff(16,plain,(
% 0.18/0.37 ![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[15])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | ((~in(B!3, singleton(B!3))) | (~disjoint(singleton(B!3), singleton(B!3))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | (~in(B!3, singleton(B!3))) | (~disjoint(singleton(B!3), singleton(B!3))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | ((~in(B!3, singleton(B!3))) | (~disjoint(singleton(B!3), singleton(B!3))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | (~in(B!3, singleton(B!3))) | (~disjoint(singleton(B!3), singleton(B!3)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (~in(B!3, singleton(B!3))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[21, 18, 8])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.37 inference(pull_quant,[status(thm)],[])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[27, 25])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[28, 24])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[31, 29])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite(((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(36,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.18/0.37 tff(38,plain,(
% 0.18/0.37 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[37])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.18/0.37 tff(40,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(B!3, singleton(B!3))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(B!3, singleton(B!3)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(42,plain,
% 0.18/0.37 ((~(~in(B!3, singleton(B!3)))) <=> in(B!3, singleton(B!3))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(43,plain,
% 0.18/0.37 (((~in(B!3, singleton(B!3))) | $false) <=> (~in(B!3, singleton(B!3)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(44,plain,
% 0.18/0.37 ((~$true) <=> $false),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 (($true | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> $true),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 ((~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 ((singleton(B!3) = singleton(B!3)) <=> $true),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 (((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[47, 46])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 (((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> $true),
% 0.18/0.37 inference(transitivity,[status(thm)],[48, 45])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 ((~((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))) <=> (~$true)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[49])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 ((~((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))) <=> $false),
% 0.18/0.38 inference(transitivity,[status(thm)],[50, 44])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 ((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) <=> (~in(B!3, singleton(B!3)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 (((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))) <=> ((~in(B!3, singleton(B!3))) | $false)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[52, 51])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 (((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))) <=> (~in(B!3, singleton(B!3)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[53, 43])).
% 0.18/0.38 tff(55,plain,
% 0.18/0.38 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))))) <=> (~(~in(B!3, singleton(B!3))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[54])).
% 0.18/0.38 tff(56,plain,
% 0.18/0.38 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))))) <=> in(B!3, singleton(B!3))),
% 0.18/0.38 inference(transitivity,[status(thm)],[55, 42])).
% 0.18/0.38 tff(57,plain,
% 0.18/0.38 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(B!3, singleton(B!3)))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[56])).
% 0.18/0.38 tff(58,plain,
% 0.18/0.38 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(B!3, singleton(B!3)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[57, 41])).
% 0.18/0.38 tff(59,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(60,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(B!3, singleton(B!3))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.38 tff(61,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[60, 40, 22])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------