%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU144+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:27:01 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU144+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.11 % 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 06:07:05 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(in_type, type, (
% 0.11/0.36 in: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_B_2_type, type, (
% 0.11/0.36 tptp_fun_B_2: $i)).
% 0.11/0.36 tff(tptp_fun_C_1_type, type, (
% 0.11/0.36 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.11/0.36 tff(singleton_type, type, (
% 0.11/0.36 singleton: $i > $i)).
% 0.11/0.36 tff(tptp_fun_A_3_type, type, (
% 0.11/0.36 tptp_fun_A_3: $i)).
% 0.11/0.36 tff(tptp_fun_C_0_type, type, (
% 0.11/0.36 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.11/0.36 tff(subset_type, type, (
% 0.11/0.36 subset: ( $i * $i ) > $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (^[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))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(pull_quant,[status(thm)],[])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (^[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)))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[5, 3])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[6, 2])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (^[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))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[8])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[9, 7])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (^[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)))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (![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)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 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')).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.11/0.37 tff(16,plain,(
% 0.11/0.37 ![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)))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[15])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![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)))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![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)))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (((~![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(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!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(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((~(~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) <=> (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (((~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) | $false) <=> (~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 ((~$true) <=> $false),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (($true | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))) <=> $true),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 ((~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))) <=> (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 ((singleton(A!3) = singleton(A!3)) <=> $true),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[25, 24])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))) <=> $true),
% 0.11/0.37 inference(transitivity,[status(thm)],[26, 23])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 ((~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))) <=> (~$true)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[27])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 ((~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))) <=> $false),
% 0.11/0.37 inference(transitivity,[status(thm)],[28, 22])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ((~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) <=> (~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (($false | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) <=> (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 ((~(singleton(A!3) = singleton(A!3))) <=> (~$true)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[25])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 ((~(singleton(A!3) = singleton(A!3))) <=> $false),
% 0.11/0.37 inference(transitivity,[status(thm)],[32, 22])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) <=> ($false | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[33])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) <=> (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.11/0.37 inference(transitivity,[status(thm)],[34, 31])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 ((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) <=> (~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[35])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 ((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) <=> (~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[36, 30])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))))) <=> ((~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) | $false)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[37, 29])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))))) <=> (~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[38, 21])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 ((~((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))))) <=> (~(~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[39])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 ((~((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))))) <=> (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.11/0.37 inference(transitivity,[status(thm)],[40, 20])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (((~![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)))))))) | (~((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!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(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[41])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (((~![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)))))))) | (~((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!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(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[42, 19])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 ((~![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)))))))) | (~((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 ((~![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(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.11/0.37 tff(46,plain,
% 0.11/0.37 (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[45, 18])).
% 0.11/0.37 tff(47,assumption,(~in(A!3, singleton(A!3))), introduced(assumption)).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (((~![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(A!3, singleton(A!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!3, singleton(A!3)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 ((~(~in(A!3, singleton(A!3)))) <=> in(A!3, singleton(A!3))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (((~in(A!3, singleton(A!3))) | $false) <=> (~in(A!3, singleton(A!3)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 ((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) <=> (~in(A!3, singleton(A!3)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))))) <=> ((~in(A!3, singleton(A!3))) | $false)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[51, 29])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))))) <=> (~in(A!3, singleton(A!3)))),
% 0.11/0.38 inference(transitivity,[status(thm)],[52, 50])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 ((~((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))))) <=> (~(~in(A!3, singleton(A!3))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[53])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 ((~((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))))) <=> in(A!3, singleton(A!3))),
% 0.11/0.38 inference(transitivity,[status(thm)],[54, 49])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (((~![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(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!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!3, singleton(A!3)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[55])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (((~![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(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!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!3, singleton(A!3)))),
% 0.11/0.38 inference(transitivity,[status(thm)],[56, 48])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 ((~![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(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3)) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(A!3, singleton(A!3))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[59, 18, 47])).
% 0.11/0.38 tff(61,plain,(in(A!3, singleton(A!3))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(62,assumption,(~in(A!3, B!2)), introduced(assumption)).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 ((~(subset(singleton(A!3), B!2) <=> in(A!3, B!2))) <=> (~(subset(singleton(A!3), B!2) <=> in(A!3, B!2)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) <=> (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(65,axiom,(~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[66, 64])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.11/0.38 tff(70,plain,(
% 0.11/0.38 ~(subset(singleton(A!3), B!2) <=> in(A!3, B!2))),
% 0.11/0.38 inference(skolemize,[status(sab)],[69])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 (~(subset(singleton(A!3), B!2) <=> in(A!3, B!2))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 ((subset(singleton(A!3), B!2) <=> in(A!3, B!2)) | subset(singleton(A!3), B!2) | in(A!3, B!2)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 (subset(singleton(A!3), B!2) | in(A!3, B!2)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 (subset(singleton(A!3), B!2)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[73, 62])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[75])).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[77])).
% 0.11/0.38 tff(79,plain,
% 0.11/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[78, 76])).
% 0.11/0.38 tff(80,plain,
% 0.11/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(81,plain,
% 0.11/0.38 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[80])).
% 0.11/0.38 tff(82,plain,
% 0.11/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(83,plain,
% 0.11/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(84,plain,
% 0.11/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[83])).
% 0.11/0.38 tff(85,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.11/0.38 tff(86,plain,
% 0.11/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.11/0.38 tff(87,plain,
% 0.11/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.11/0.38 tff(88,plain,(
% 0.11/0.38 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[87])).
% 0.11/0.38 tff(89,plain,
% 0.11/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.11/0.38 tff(90,plain,
% 0.11/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.11/0.38 tff(91,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))) | (~((~((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))) | (~(subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(92,plain,
% 0.11/0.38 (~((~((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))) | (~(subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.11/0.38 tff(93,plain,
% 0.11/0.38 (((~((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))) | (~(subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))))) | ((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(94,plain,
% 0.11/0.38 ((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.11/0.38 tff(95,plain,
% 0.11/0.38 ((~((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))) | (~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(96,plain,
% 0.11/0.38 ((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.11/0.38 tff(97,plain,
% 0.11/0.38 (![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[96, 74])).
% 0.11/0.38 tff(98,plain,
% 0.11/0.38 (((~![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))) | ((~in(A!3, singleton(A!3))) | in(A!3, B!2))) <=> ((~![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))) | (~in(A!3, singleton(A!3))) | in(A!3, B!2))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(99,plain,
% 0.11/0.38 ((~![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))) | ((~in(A!3, singleton(A!3))) | in(A!3, B!2))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(100,plain,
% 0.11/0.38 ((~![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))) | (~in(A!3, singleton(A!3))) | in(A!3, B!2)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.11/0.38 tff(101,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[100, 62, 97, 61])).
% 0.11/0.38 tff(102,plain,(in(A!3, B!2)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(103,plain,
% 0.11/0.38 ((subset(singleton(A!3), B!2) <=> in(A!3, B!2)) | (~subset(singleton(A!3), B!2)) | (~in(A!3, B!2))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(104,plain,
% 0.11/0.38 ((~subset(singleton(A!3), B!2)) | (~in(A!3, B!2))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[103, 71])).
% 0.11/0.38 tff(105,plain,
% 0.11/0.38 (~subset(singleton(A!3), B!2)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[104, 102])).
% 0.11/0.38 tff(106,plain,
% 0.11/0.38 (((~((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))) | (~(subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))))) | (subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(107,plain,
% 0.11/0.38 (subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[106, 92])).
% 0.11/0.38 tff(108,plain,
% 0.11/0.38 ((~(subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2))))) | subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(109,plain,
% 0.11/0.38 (subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.11/0.38 tff(110,plain,
% 0.11/0.38 (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[109, 105])).
% 0.11/0.38 tff(111,plain,
% 0.11/0.38 (((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)) | in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(112,plain,
% 0.11/0.38 (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.11/0.38 tff(113,plain,
% 0.11/0.38 ((~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) | (~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(114,plain,
% 0.11/0.38 ((~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) | (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.11/0.39 tff(115,plain,
% 0.11/0.39 (tptp_fun_C_1(B!2, singleton(A!3)) = A!3),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[114, 46])).
% 0.11/0.39 tff(116,plain,
% 0.11/0.39 (in(tptp_fun_C_1(B!2, singleton(A!3)), B!2) <=> in(A!3, B!2)),
% 0.11/0.39 inference(monotonicity,[status(thm)],[115])).
% 0.11/0.39 tff(117,plain,
% 0.11/0.39 (in(A!3, B!2) <=> in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)),
% 0.11/0.39 inference(symmetry,[status(thm)],[116])).
% 0.11/0.39 tff(118,plain,
% 0.11/0.39 (in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[102, 117])).
% 0.11/0.39 tff(119,plain,
% 0.11/0.39 (((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)) | (~in(tptp_fun_C_1(B!2, singleton(A!3)), B!2))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(120,plain,
% 0.11/0.39 (~in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[119, 110])).
% 0.11/0.39 tff(121,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[120, 118])).
% 0.11/0.39 % SZS output end Proof
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------