%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU148+3 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:02 AM UTC 2025
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SEU148+3 : TPTP v9.0.0. Released v3.2.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 06:07:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(tptp_fun_B_3_type, type, (
% 0.19/0.44 tptp_fun_B_3: $i)).
% 0.19/0.44 tff(tptp_fun_A_4_type, type, (
% 0.19/0.44 tptp_fun_A_4: $i)).
% 0.19/0.44 tff(in_type, type, (
% 0.19/0.44 in: ( $i * $i ) > $o)).
% 0.19/0.44 tff(singleton_type, type, (
% 0.19/0.44 singleton: $i > $i)).
% 0.19/0.44 tff(tptp_fun_C_0_type, type, (
% 0.19/0.44 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.19/0.44 tff(empty_set_type, type, (
% 0.19/0.44 empty_set: $i)).
% 0.19/0.44 tff(subset_type, type, (
% 0.19/0.44 subset: ( $i * $i ) > $o)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 (^[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))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(pull_quant,[status(thm)],[])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 (^[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)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[5, 3])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[6, 2])).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 (^[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))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[9, 7])).
% 0.19/0.44 tff(11,plain,
% 0.19/0.44 (^[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)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(12,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(14,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.44 tff(16,plain,(
% 0.19/0.44 ![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)))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[15])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (((~![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(A!4))) | in(A!4, singleton(B!3)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4)))))))) <=> ((~![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(A!4))) | in(A!4, singleton(B!3)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 ((~((~((~(singleton(B!3) = singleton(A!4))) | (in(A!4, singleton(B!3)) <=> (A!4 = A!4)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4))))))) <=> (~((~((~(singleton(B!3) = singleton(A!4))) | in(A!4, singleton(B!3)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4)))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (((~![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(A!4))) | (in(A!4, singleton(B!3)) <=> (A!4 = A!4)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4)))))))) <=> ((~![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(A!4))) | in(A!4, singleton(B!3)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (((~![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(A!4))) | (in(A!4, singleton(B!3)) <=> (A!4 = A!4)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4)))))))) <=> ((~![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(A!4))) | in(A!4, singleton(B!3)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[21, 19])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 ((~![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(A!4))) | (in(A!4, singleton(B!3)) <=> (A!4 = A!4)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 ((~![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(A!4))) | in(A!4, singleton(B!3)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (~((~((~(singleton(B!3) = singleton(A!4))) | in(A!4, singleton(B!3)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[24, 18])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (((~((~(singleton(B!3) = singleton(A!4))) | in(A!4, singleton(B!3)))) | (~((singleton(B!3) = singleton(A!4)) | (~(in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4)))))) | ((~(singleton(B!3) = singleton(A!4))) | in(A!4, singleton(B!3)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 ((~(singleton(B!3) = singleton(A!4))) | in(A!4, singleton(B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(31,axiom,(![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l4_zfmisc_1')).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.45 tff(33,plain,(
% 0.19/0.45 ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[32])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))) | (subset(singleton(A!4), singleton(B!3)) <=> ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (subset(singleton(A!4), singleton(B!3)) <=> ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))) <=> (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : (subset(singleton(A), singleton(B)) => (A = B))) <=> (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(39,axiom,(~![A: $i, B: $i] : (subset(singleton(A), singleton(B)) => (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t6_zfmisc_1')).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[42, 37])).
% 0.19/0.45 tff(44,plain,(
% 0.19/0.45 ~((~subset(singleton(A!4), singleton(B!3))) | (A!4 = B!3))),
% 0.19/0.45 inference(skolemize,[status(sab)],[43])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (subset(singleton(A!4), singleton(B!3))),
% 0.19/0.45 inference(or_elim,[status(thm)],[44])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 ((~(subset(singleton(A!4), singleton(B!3)) <=> ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3))))) | (~subset(singleton(A!4), singleton(B!3))) | ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 ((~(subset(singleton(A!4), singleton(B!3)) <=> ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3))))) | ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[47, 36])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (^[A: $i] : refl((~(singleton(A) = empty_set)) <=> (~(singleton(A) = empty_set)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(52,axiom,(![A: $i] : (~(singleton(A) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1_zfmisc_1')).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 (![A: $i] : (~(singleton(A) = empty_set))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.45 tff(54,plain,(
% 0.19/0.45 ![A: $i] : (~(singleton(A) = empty_set))),
% 0.19/0.45 inference(skolemize,[status(sab)],[53])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (![A: $i] : (~(singleton(A) = empty_set))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 ((~![A: $i] : (~(singleton(A) = empty_set))) | (~(singleton(A!4) = empty_set))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (~(singleton(A!4) = empty_set)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 ((~((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3)))) | (singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 ((~((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3)))) | (singleton(A!4) = singleton(B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 (singleton(A!4) = singleton(B!3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[59, 48])).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 (singleton(B!3) = singleton(A!4)),
% 0.19/0.45 inference(symmetry,[status(thm)],[60])).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 ((~((~(singleton(B!3) = singleton(A!4))) | in(A!4, singleton(B!3)))) | (~(singleton(B!3) = singleton(A!4))) | in(A!4, singleton(B!3))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 ((~((~(singleton(B!3) = singleton(A!4))) | in(A!4, singleton(B!3)))) | in(A!4, singleton(B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 (in(A!4, singleton(B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[63, 27])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 (~(A!4 = B!3)),
% 0.19/0.45 inference(or_elim,[status(thm)],[44])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 ((~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))) | (~in(A!4, singleton(B!3))) | (A!4 = B!3)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 (~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[66, 65, 64])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 (((~![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(A!4, singleton(B!3)) <=> (A!4 = 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(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 ((~(~(in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 (((~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))) | $false) <=> (~(in(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 ((~$true) <=> $false),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (($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),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 ((~(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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 ((singleton(B!3) = singleton(B!3)) <=> $true),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> ($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))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[74, 73])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 (((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)))) <=> $true),
% 0.19/0.45 inference(transitivity,[status(thm)],[75, 72])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 ((~((singleton(B!3) = singleton(B!3)) | (~(in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3)) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))) <=> (~$true)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[76])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 ((~((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))))) <=> $false),
% 0.19/0.45 inference(transitivity,[status(thm)],[77, 71])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 ((~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> (~(in(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 (($false | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 ((~(singleton(B!3) = singleton(B!3))) <=> (~$true)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[74])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 ((~(singleton(B!3) = singleton(B!3))) <=> $false),
% 0.19/0.45 inference(transitivity,[status(thm)],[81, 71])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> ($false | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.19/0.45 inference(transitivity,[status(thm)],[83, 80])).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 ((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) <=> (~(in(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[84])).
% 0.19/0.45 tff(86,plain,
% 0.19/0.45 ((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) <=> (~(in(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[85, 79])).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 (((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = 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(A!4, singleton(B!3)) <=> (A!4 = B!3))) | $false)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[86, 78])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = 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(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[87, 70])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = 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(A!4, singleton(B!3)) <=> (A!4 = B!3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.45 tff(90,plain,
% 0.19/0.45 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = 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(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.19/0.45 inference(transitivity,[status(thm)],[89, 69])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 (((~![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(A!4, singleton(B!3)) <=> (A!4 = 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(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 (((~![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(A!4, singleton(B!3)) <=> (A!4 = 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(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[91, 68])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 ((~![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(A!4, singleton(B!3)) <=> (A!4 = 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)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[94, 18, 67])).
% 0.19/0.45 % SZS output end Proof
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------