%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET890+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:26:37 AM UTC 2025
% Result : Theorem 0.23s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET890+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 05:51:16 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.23/0.42 % SZS status Theorem
% 0.23/0.42 % SZS output start Proof
% 0.23/0.42 tff(in_type, type, (
% 0.23/0.42 in: ( $i * $i ) > $o)).
% 0.23/0.42 tff(tptp_fun_D_4_type, type, (
% 0.23/0.42 tptp_fun_D_4: ( $i * $i ) > $i)).
% 0.23/0.42 tff(singleton_type, type, (
% 0.23/0.42 singleton: $i > $i)).
% 0.23/0.42 tff(tptp_fun_A_7_type, type, (
% 0.23/0.42 tptp_fun_A_7: $i)).
% 0.23/0.42 tff(tptp_fun_C_3_type, type, (
% 0.23/0.42 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_C_0_type, type, (
% 0.23/0.42 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.23/0.42 tff(union_type, type, (
% 0.23/0.42 union: $i > $i)).
% 0.23/0.42 tff(tptp_fun_D_2_type, type, (
% 0.23/0.42 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.23/0.42 tff(subset_type, type, (
% 0.23/0.42 subset: ( $i * $i ) > $o)).
% 0.23/0.42 tff(1,plain,
% 0.23/0.42 (^[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))))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(2,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.42 tff(3,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(pull_quant,[status(thm)],[])).
% 0.23/0.42 tff(4,plain,
% 0.23/0.42 (^[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)))))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(5,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.23/0.42 tff(6,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(transitivity,[status(thm)],[5, 3])).
% 0.23/0.42 tff(7,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(transitivity,[status(thm)],[6, 2])).
% 0.23/0.42 tff(8,plain,
% 0.23/0.42 (^[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))))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(9,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[8])).
% 0.23/0.42 tff(10,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(transitivity,[status(thm)],[9, 7])).
% 0.23/0.42 tff(11,plain,
% 0.23/0.42 (^[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)))))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(12,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[11])).
% 0.23/0.42 tff(13,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 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')).
% 0.23/0.42 tff(15,plain,
% 0.23/0.42 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.23/0.42 tff(16,plain,(
% 0.23/0.42 ![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)))))),
% 0.23/0.42 inference(skolemize,[status(sab)],[15])).
% 0.23/0.42 tff(17,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.23/0.42 tff(18,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.23/0.42 tff(19,plain,
% 0.23/0.42 (((~![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_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))) <=> ((~![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_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(20,plain,
% 0.23/0.42 ((~(~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))) <=> (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(21,plain,
% 0.23/0.42 (((~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))) | $false) <=> (~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(22,plain,
% 0.23/0.42 ((~$true) <=> $false),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(23,plain,
% 0.23/0.42 (($true | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> $true),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(24,plain,
% 0.23/0.42 ((~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(25,plain,
% 0.23/0.42 ((singleton(A!7) = singleton(A!7)) <=> $true),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(26,plain,
% 0.23/0.42 (((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[25, 24])).
% 0.23/0.42 tff(27,plain,
% 0.23/0.42 (((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> $true),
% 0.23/0.42 inference(transitivity,[status(thm)],[26, 23])).
% 0.23/0.42 tff(28,plain,
% 0.23/0.42 ((~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> (~$true)),
% 0.23/0.42 inference(monotonicity,[status(thm)],[27])).
% 0.23/0.42 tff(29,plain,
% 0.23/0.42 ((~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> $false),
% 0.23/0.42 inference(transitivity,[status(thm)],[28, 22])).
% 0.23/0.42 tff(30,plain,
% 0.23/0.42 ((~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))) <=> (~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(31,plain,
% 0.23/0.42 (($false | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))) <=> (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(32,plain,
% 0.23/0.42 ((~(singleton(A!7) = singleton(A!7))) <=> (~$true)),
% 0.23/0.42 inference(monotonicity,[status(thm)],[25])).
% 0.23/0.42 tff(33,plain,
% 0.23/0.42 ((~(singleton(A!7) = singleton(A!7))) <=> $false),
% 0.23/0.42 inference(transitivity,[status(thm)],[32, 22])).
% 0.23/0.42 tff(34,plain,
% 0.23/0.42 (((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))) <=> ($false | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[33])).
% 0.23/0.42 tff(35,plain,
% 0.23/0.42 (((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))) <=> (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))),
% 0.23/0.42 inference(transitivity,[status(thm)],[34, 31])).
% 0.23/0.42 tff(36,plain,
% 0.23/0.42 ((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))) <=> (~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[35])).
% 0.23/0.42 tff(37,plain,
% 0.23/0.42 ((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))) <=> (~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))),
% 0.23/0.42 inference(transitivity,[status(thm)],[36, 30])).
% 0.23/0.42 tff(38,plain,
% 0.23/0.42 (((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> ((~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))) | $false)),
% 0.23/0.42 inference(monotonicity,[status(thm)],[37, 29])).
% 0.23/0.42 tff(39,plain,
% 0.23/0.42 (((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> (~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))),
% 0.23/0.42 inference(transitivity,[status(thm)],[38, 21])).
% 0.23/0.42 tff(40,plain,
% 0.23/0.42 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> (~(~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[39])).
% 0.23/0.43 tff(41,plain,
% 0.23/0.43 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))),
% 0.23/0.43 inference(transitivity,[status(thm)],[40, 20])).
% 0.23/0.43 tff(42,plain,
% 0.23/0.43 (((~![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!7) = singleton(A!7))) | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![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_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[41])).
% 0.23/0.43 tff(43,plain,
% 0.23/0.43 (((~![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!7) = singleton(A!7))) | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![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_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))),
% 0.23/0.43 inference(transitivity,[status(thm)],[42, 19])).
% 0.23/0.43 tff(44,plain,
% 0.23/0.43 ((~![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!7) = singleton(A!7))) | (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(45,plain,
% 0.23/0.43 ((~![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_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.23/0.43 tff(46,plain,
% 0.23/0.43 (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[45, 18])).
% 0.23/0.43 tff(47,plain,
% 0.23/0.43 (^[A: $i, B: $i, D_8: $i, C: $i, D: $i] : rewrite((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8)))))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(48,plain,
% 0.23/0.43 (![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.23/0.43 tff(49,plain,
% 0.23/0.43 (^[A: $i, B: $i, D_8: $i, C: $i, D: $i] : refl((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(50,plain,
% 0.23/0.43 (![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8)))))))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[49])).
% 0.23/0.43 tff(51,plain,
% 0.23/0.43 (![A: $i, B: $i] : ![D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8)))))))))))),
% 0.23/0.43 inference(pull_quant,[status(thm)],[])).
% 0.23/0.43 tff(52,plain,
% 0.23/0.43 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))) <=> ![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))), ((~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))) <=> (~![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))))), pull_quant((~![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))) <=> ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))), ((~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))) <=> ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), pull_quant(((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> (~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant((~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i] : ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant(![C: $i] : ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) <=> ((~(B = union(A))) | ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), pull_quant(((~(B = union(A))) | ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))) <=> ![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) <=> ![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), ((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) <=> (~![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))))), pull_quant((~![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) <=> ?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), ((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) <=> ?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))) <=> ![D: $i] : ((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))), ((~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))) <=> (~![D: $i] : ((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))), pull_quant((~![D: $i] : ((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))), ((~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))), (((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))) <=> ((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))), pull_quant(((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))), (((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))), ((~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))) <=> (~?[D: $i] : ((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))), pull_quant((~?[D: $i] : ((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))), ((~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))) <=> ((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))), pull_quant(((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))) <=> (~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))), pull_quant((~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))) <=> (?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))))), pull_quant((?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))) <=> ?[D_8: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))) <=> ?[D_8: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))) <=> (~?[D_8: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))))), pull_quant((~?[D_8: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) <=> ![D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))) <=> ![D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8)))))))))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(53,plain,
% 0.23/0.44 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))) <=> ![A: $i, B: $i] : ![D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8)))))))))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[52])).
% 0.23/0.44 tff(54,plain,
% 0.23/0.44 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8)))))))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[53, 51])).
% 0.23/0.44 tff(55,plain,
% 0.23/0.44 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8)))))))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[54, 50])).
% 0.23/0.44 tff(56,plain,
% 0.23/0.44 (^[A: $i, B: $i] : rewrite((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(57,plain,
% 0.23/0.44 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[56])).
% 0.23/0.44 tff(58,plain,
% 0.23/0.44 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8)))))))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[57, 55])).
% 0.23/0.44 tff(59,plain,
% 0.23/0.44 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_2(C, A)) & in(tptp_fun_D_2(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) <=> ((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) & in(tptp_fun_D_4(B, A), A)) <=> (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A))))), ((in(tptp_fun_C_3(B, A), B) | (in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) & in(tptp_fun_D_4(B, A), A))) <=> (in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A))))))), rewrite((in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A))))) <=> (in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))), ((in(tptp_fun_C_3(B, A), B) | (in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) & in(tptp_fun_D_4(B, A), A))) <=> (in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A))))))), rewrite(((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_3(B, A), D) & in(D, A)))) <=> ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))), (((in(tptp_fun_C_3(B, A), B) | (in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) & in(tptp_fun_D_4(B, A), A))) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_3(B, A), D) & in(D, A))))) <=> ((in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A))))) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))), rewrite(((in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A))))) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))) <=> (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))), (((in(tptp_fun_C_3(B, A), B) | (in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) & in(tptp_fun_D_4(B, A), A))) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_3(B, A), D) & in(D, A))))) <=> (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_3(B, A), B) | (in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) & in(tptp_fun_D_4(B, A), A))) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_3(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))), rewrite(((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_3(B, A), B) | (in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) & in(tptp_fun_D_4(B, A), A))) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_3(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_2(C, A)) & in(tptp_fun_D_2(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_3(B, A), B) | (in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) & in(tptp_fun_D_4(B, A), A))) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_3(B, A), D) & in(D, A))))))) <=> (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))))), rewrite((((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_2(C, A)) & in(tptp_fun_D_2(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_3(B, A), B) | (in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) & in(tptp_fun_D_4(B, A), A))) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_3(B, A), D) & in(D, A))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(60,plain,
% 0.23/0.44 (![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_2(C, A)) & in(tptp_fun_D_2(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_3(B, A), B) | (in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) & in(tptp_fun_D_4(B, A), A))) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_3(B, A), D) & in(D, A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[59])).
% 0.23/0.44 tff(61,plain,
% 0.23/0.44 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A)))) <=> ![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(62,axiom,(![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_tarski')).
% 0.23/0.44 tff(63,plain,
% 0.23/0.44 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.23/0.44 tff(64,plain,(
% 0.23/0.44 ![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_2(C, A)) & in(tptp_fun_D_2(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_3(B, A), B) | (in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) & in(tptp_fun_D_4(B, A), A))) & ((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_3(B, A), D) & in(D, A)))))))),
% 0.23/0.44 inference(skolemize,[status(sab)],[63])).
% 0.23/0.44 tff(65,plain,
% 0.23/0.44 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_3(B, A), D)))))))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.23/0.44 tff(66,plain,
% 0.23/0.44 (![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8)))))))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.23/0.44 tff(67,plain,
% 0.23/0.44 (![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[66, 48])).
% 0.23/0.45 tff(68,plain,
% 0.23/0.45 (((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) | (~((~((~in(singleton(A!7), A!7)) | (~(A!7 = union(singleton(A!7)))) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))))))))))) <=> ((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) | (~((~((~in(singleton(A!7), A!7)) | (~(A!7 = union(singleton(A!7)))) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)))))))))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(69,plain,
% 0.23/0.45 ((~((~((~(A!7 = union(singleton(A!7)))) | (~((~((~in(singleton(A!7), A!7)) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((~in(singleton(A!7), A!7)) | in(singleton(A!7), A!7) | (~in(A!7, singleton(A!7))))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)) | (~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)))))))))) <=> (~((~((~in(singleton(A!7), A!7)) | (~(A!7 = union(singleton(A!7)))) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))))))))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(70,plain,
% 0.23/0.45 (((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) | (~((~((~(A!7 = union(singleton(A!7)))) | (~((~((~in(singleton(A!7), A!7)) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((~in(singleton(A!7), A!7)) | in(singleton(A!7), A!7) | (~in(A!7, singleton(A!7))))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)) | (~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))))))))))) <=> ((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) | (~((~((~in(singleton(A!7), A!7)) | (~(A!7 = union(singleton(A!7)))) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)))))))))))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[69])).
% 0.23/0.45 tff(71,plain,
% 0.23/0.45 (((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) | (~((~((~(A!7 = union(singleton(A!7)))) | (~((~((~in(singleton(A!7), A!7)) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((~in(singleton(A!7), A!7)) | in(singleton(A!7), A!7) | (~in(A!7, singleton(A!7))))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)) | (~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))))))))))) <=> ((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) | (~((~((~in(singleton(A!7), A!7)) | (~(A!7 = union(singleton(A!7)))) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)))))))))))),
% 0.23/0.45 inference(transitivity,[status(thm)],[70, 68])).
% 0.23/0.45 tff(72,plain,
% 0.23/0.45 ((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) | (~((~((~(A!7 = union(singleton(A!7)))) | (~((~((~in(singleton(A!7), A!7)) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((~in(singleton(A!7), A!7)) | in(singleton(A!7), A!7) | (~in(A!7, singleton(A!7))))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)) | (~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))))))))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(73,plain,
% 0.23/0.45 ((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_2(C, A))) | (~in(tptp_fun_D_2(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_3(B, A), B) | (~((~in(tptp_fun_C_3(B, A), tptp_fun_D_4(B, A))) | (~in(tptp_fun_D_4(B, A), A)))))) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_3(B, A), D_8))))))))))) | (~((~((~in(singleton(A!7), A!7)) | (~(A!7 = union(singleton(A!7)))) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))))))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.23/0.45 tff(74,plain,
% 0.23/0.45 (~((~((~in(singleton(A!7), A!7)) | (~(A!7 = union(singleton(A!7)))) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)))))))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[73, 67])).
% 0.23/0.45 tff(75,plain,
% 0.23/0.45 (((~((~in(singleton(A!7), A!7)) | (~(A!7 = union(singleton(A!7)))) | (~((~in(singleton(A!7), tptp_fun_D_2(singleton(A!7), singleton(A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), singleton(A!7)), singleton(A!7))))))) | (~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))))))))) | ((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)))))))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(76,plain,
% 0.23/0.45 ((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.23/0.45 tff(77,plain,
% 0.23/0.45 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(78,plain,
% 0.23/0.46 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[77])).
% 0.23/0.46 tff(79,plain,
% 0.23/0.46 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(80,plain,
% 0.23/0.46 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[79])).
% 0.23/0.46 tff(81,plain,
% 0.23/0.46 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(82,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.23/0.46 tff(83,plain,
% 0.23/0.46 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.23/0.46 tff(84,plain,(
% 0.23/0.46 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.23/0.46 inference(skolemize,[status(sab)],[83])).
% 0.23/0.46 tff(85,plain,
% 0.23/0.46 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.23/0.46 tff(86,plain,
% 0.23/0.46 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.23/0.46 tff(87,plain,
% 0.23/0.46 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (A!7 = union(singleton(A!7)))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(88,plain,
% 0.23/0.46 (~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (A!7 = union(singleton(A!7))))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.23/0.46 tff(89,plain,
% 0.23/0.46 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7)))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(90,plain,
% 0.23/0.46 ((~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7))) <=> (~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(91,plain,
% 0.23/0.46 ((((~subset(union(singleton(A!7)), A!7)) | (~subset(A!7, union(singleton(A!7))))) <=> (union(singleton(A!7)) = A!7)) <=> (((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(92,plain,
% 0.23/0.46 ((~(((~subset(union(singleton(A!7)), A!7)) | (~subset(A!7, union(singleton(A!7))))) <=> (union(singleton(A!7)) = A!7))) <=> (~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7)))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[91])).
% 0.23/0.46 tff(93,plain,
% 0.23/0.46 ((~(((~subset(union(singleton(A!7)), A!7)) | (~subset(A!7, union(singleton(A!7))))) <=> (union(singleton(A!7)) = A!7))) <=> (~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[92, 90])).
% 0.23/0.46 tff(94,plain,
% 0.23/0.46 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(union(singleton(A!7)), A!7)) | (~subset(A!7, union(singleton(A!7))))) <=> (union(singleton(A!7)) = A!7)))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[93])).
% 0.23/0.46 tff(95,plain,
% 0.23/0.46 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(union(singleton(A!7)), A!7)) | (~subset(A!7, union(singleton(A!7))))) <=> (union(singleton(A!7)) = A!7)))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[94, 89])).
% 0.23/0.46 tff(96,plain,
% 0.23/0.46 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(union(singleton(A!7)), A!7)) | (~subset(A!7, union(singleton(A!7))))) <=> (union(singleton(A!7)) = A!7)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(97,plain,
% 0.23/0.46 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.23/0.46 tff(98,plain,
% 0.23/0.46 (~(((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[97, 86])).
% 0.23/0.46 tff(99,plain,
% 0.23/0.46 ((~![A: $i] : (union(singleton(A)) = A)) <=> (~![A: $i] : (union(singleton(A)) = A))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(100,axiom,(~![A: $i] : (union(singleton(A)) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t31_zfmisc_1')).
% 0.23/0.46 tff(101,plain,
% 0.23/0.46 (~![A: $i] : (union(singleton(A)) = A)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.23/0.46 tff(102,plain,
% 0.23/0.46 (~![A: $i] : (union(singleton(A)) = A)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[101, 99])).
% 0.23/0.46 tff(103,plain,
% 0.23/0.46 (~![A: $i] : (union(singleton(A)) = A)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.23/0.46 tff(104,plain,
% 0.23/0.46 (~![A: $i] : (union(singleton(A)) = A)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.23/0.46 tff(105,plain,(
% 0.23/0.46 ~(union(singleton(A!7)) = A!7)),
% 0.23/0.46 inference(skolemize,[status(sab)],[104])).
% 0.23/0.46 tff(106,plain,
% 0.23/0.46 ((((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7)) | ((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) | (union(singleton(A!7)) = A!7)),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(107,plain,
% 0.23/0.46 ((((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (union(singleton(A!7)) = A!7)) | ((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.23/0.46 tff(108,plain,
% 0.23/0.46 ((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[107, 98])).
% 0.23/0.46 tff(109,plain,
% 0.23/0.46 ((((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7))) <=> (A!7 = union(singleton(A!7)))) | (~((~subset(A!7, union(singleton(A!7)))) | (~subset(union(singleton(A!7)), A!7)))) | (~(A!7 = union(singleton(A!7))))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(110,plain,
% 0.23/0.46 (~(A!7 = union(singleton(A!7)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[109, 108, 88])).
% 0.23/0.46 tff(111,plain,
% 0.23/0.46 ((~((A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)))))))) | (A!7 = union(singleton(A!7))) | (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))))))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(112,plain,
% 0.23/0.46 (~((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)))))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[111, 110, 76])).
% 0.23/0.46 tff(113,plain,
% 0.23/0.46 (((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))))) | (in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(114,plain,
% 0.23/0.46 (in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)))))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.23/0.46 tff(115,plain,
% 0.23/0.46 (((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | (~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))))) | ((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(116,plain,
% 0.23/0.46 ((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[115, 112])).
% 0.23/0.46 tff(117,plain,
% 0.23/0.46 (((~![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!7, singleton(A!7))) <=> ((~![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!7, singleton(A!7)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(118,plain,
% 0.23/0.46 ((~(~in(A!7, singleton(A!7)))) <=> in(A!7, singleton(A!7))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(119,plain,
% 0.23/0.46 (((~in(A!7, singleton(A!7))) | $false) <=> (~in(A!7, singleton(A!7)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(120,plain,
% 0.23/0.46 ((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) <=> (~in(A!7, singleton(A!7)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(121,plain,
% 0.23/0.46 (((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> ((~in(A!7, singleton(A!7))) | $false)),
% 0.23/0.46 inference(monotonicity,[status(thm)],[120, 29])).
% 0.23/0.46 tff(122,plain,
% 0.23/0.46 (((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> (~in(A!7, singleton(A!7)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[121, 119])).
% 0.23/0.46 tff(123,plain,
% 0.23/0.46 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> (~(~in(A!7, singleton(A!7))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[122])).
% 0.23/0.47 tff(124,plain,
% 0.23/0.47 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> in(A!7, singleton(A!7))),
% 0.23/0.47 inference(transitivity,[status(thm)],[123, 118])).
% 0.23/0.47 tff(125,plain,
% 0.23/0.47 (((~![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!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![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!7, singleton(A!7)))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[124])).
% 0.23/0.47 tff(126,plain,
% 0.23/0.47 (((~![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!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![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!7, singleton(A!7)))),
% 0.23/0.47 inference(transitivity,[status(thm)],[125, 117])).
% 0.23/0.47 tff(127,plain,
% 0.23/0.47 ((~![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!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(128,plain,
% 0.23/0.47 ((~![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!7, singleton(A!7))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.23/0.47 tff(129,plain,
% 0.23/0.47 (in(A!7, singleton(A!7))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[128, 18])).
% 0.23/0.47 tff(130,plain,
% 0.23/0.47 ((~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)))) | (~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(131,plain,
% 0.23/0.47 ((~((~in(A!7, singleton(A!7))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)))) | (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.23/0.47 tff(132,plain,
% 0.23/0.47 (~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[131, 116])).
% 0.23/0.47 tff(133,plain,
% 0.23/0.47 ((~(in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))))) | in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) | (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)))))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(134,plain,
% 0.23/0.47 (~((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[133, 132, 114])).
% 0.23/0.47 tff(135,plain,
% 0.23/0.47 (((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)))) | in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(136,plain,
% 0.23/0.47 (in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.23/0.47 tff(137,plain,
% 0.23/0.47 ((~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7))) | (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(138,plain,
% 0.23/0.47 ((~(in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_4(A!7, singleton(A!7)) = A!7))) | (tptp_fun_D_4(A!7, singleton(A!7)) = A!7)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.23/0.47 tff(139,plain,
% 0.23/0.47 (tptp_fun_D_4(A!7, singleton(A!7)) = A!7),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[138, 46])).
% 0.23/0.47 tff(140,plain,
% 0.23/0.47 (in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7))) <=> in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)),
% 0.23/0.47 inference(monotonicity,[status(thm)],[139])).
% 0.23/0.47 tff(141,plain,
% 0.23/0.47 (in(tptp_fun_C_3(A!7, singleton(A!7)), A!7) <=> in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))),
% 0.23/0.47 inference(symmetry,[status(thm)],[140])).
% 0.23/0.47 tff(142,plain,
% 0.23/0.47 ((~in(tptp_fun_C_3(A!7, singleton(A!7)), A!7)) <=> (~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[141])).
% 0.23/0.47 tff(143,plain,
% 0.23/0.47 (~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[132, 142])).
% 0.23/0.47 tff(144,plain,
% 0.23/0.47 (((~in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))) | (~in(tptp_fun_D_4(A!7, singleton(A!7)), singleton(A!7)))) | in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(145,plain,
% 0.23/0.47 (in(tptp_fun_C_3(A!7, singleton(A!7)), tptp_fun_D_4(A!7, singleton(A!7)))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[144, 134])).
% 0.23/0.47 tff(146,plain,
% 0.23/0.47 ($false),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[145, 143])).
% 0.23/0.47 % SZS output end Proof
% 0.23/0.47 % E exiting
%------------------------------------------------------------------------------