%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU154+2 : TPTP v9.0.0. Released v3.3.0.
% 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 05:27:03 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 : SEU154+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 06:09:46 EDT 2025
% 0.14/0.36 % 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_B_8_type, type, (
% 0.23/0.42 tptp_fun_B_8: $i)).
% 0.23/0.42 tff(tptp_fun_C_13_type, type, (
% 0.23/0.42 tptp_fun_C_13: ( $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_9_type, type, (
% 0.23/0.42 tptp_fun_A_9: $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(disjoint_type, type, (
% 0.23/0.42 disjoint: ( $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_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(20,plain,
% 0.23/0.42 ((~(~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))) <=> (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(21,plain,
% 0.23/0.42 (((~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))) | $false) <=> (~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(22,plain,
% 0.23/0.42 ((~$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!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9)))) <=> $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!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9))) <=> (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(25,plain,
% 0.23/0.42 ((singleton(A!9) = singleton(A!9)) <=> $true),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(26,plain,
% 0.23/0.42 (((singleton(A!9) = singleton(A!9)) | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9))))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[25, 24])).
% 0.23/0.42 tff(27,plain,
% 0.23/0.42 (((singleton(A!9) = singleton(A!9)) | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9)))) <=> $true),
% 0.23/0.42 inference(transitivity,[status(thm)],[26, 23])).
% 0.23/0.42 tff(28,plain,
% 0.23/0.42 ((~((singleton(A!9) = singleton(A!9)) | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9))))) <=> (~$true)),
% 0.23/0.42 inference(monotonicity,[status(thm)],[27])).
% 0.23/0.42 tff(29,plain,
% 0.23/0.42 ((~((singleton(A!9) = singleton(A!9)) | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9))))) <=> $false),
% 0.23/0.42 inference(transitivity,[status(thm)],[28, 22])).
% 0.23/0.42 tff(30,plain,
% 0.23/0.42 ((~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))) <=> (~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(31,plain,
% 0.23/0.43 (($false | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))) <=> (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(32,plain,
% 0.23/0.43 ((~(singleton(A!9) = singleton(A!9))) <=> (~$true)),
% 0.23/0.43 inference(monotonicity,[status(thm)],[25])).
% 0.23/0.43 tff(33,plain,
% 0.23/0.43 ((~(singleton(A!9) = singleton(A!9))) <=> $false),
% 0.23/0.43 inference(transitivity,[status(thm)],[32, 22])).
% 0.23/0.43 tff(34,plain,
% 0.23/0.43 (((~(singleton(A!9) = singleton(A!9))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))) <=> ($false | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[33])).
% 0.23/0.43 tff(35,plain,
% 0.23/0.43 (((~(singleton(A!9) = singleton(A!9))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))) <=> (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))),
% 0.23/0.43 inference(transitivity,[status(thm)],[34, 31])).
% 0.23/0.43 tff(36,plain,
% 0.23/0.43 ((~((~(singleton(A!9) = singleton(A!9))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))) <=> (~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[35])).
% 0.23/0.43 tff(37,plain,
% 0.23/0.43 ((~((~(singleton(A!9) = singleton(A!9))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))) <=> (~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))),
% 0.23/0.43 inference(transitivity,[status(thm)],[36, 30])).
% 0.23/0.43 tff(38,plain,
% 0.23/0.43 (((~((~(singleton(A!9) = singleton(A!9))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))) | (~((singleton(A!9) = singleton(A!9)) | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9)))))) <=> ((~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))) | $false)),
% 0.23/0.43 inference(monotonicity,[status(thm)],[37, 29])).
% 0.23/0.43 tff(39,plain,
% 0.23/0.43 (((~((~(singleton(A!9) = singleton(A!9))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))) | (~((singleton(A!9) = singleton(A!9)) | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9)))))) <=> (~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))),
% 0.23/0.43 inference(transitivity,[status(thm)],[38, 21])).
% 0.23/0.43 tff(40,plain,
% 0.23/0.43 ((~((~((~(singleton(A!9) = singleton(A!9))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))) | (~((singleton(A!9) = singleton(A!9)) | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9))))))) <=> (~(~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[39])).
% 0.23/0.43 tff(41,plain,
% 0.23/0.43 ((~((~((~(singleton(A!9) = singleton(A!9))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))) | (~((singleton(A!9) = singleton(A!9)) | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9))))))) <=> (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))),
% 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!9) = singleton(A!9))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))) | (~((singleton(A!9) = singleton(A!9)) | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))),
% 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!9) = singleton(A!9))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))) | (~((singleton(A!9) = singleton(A!9)) | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))),
% 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!9) = singleton(A!9))) | (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)))) | (~((singleton(A!9) = singleton(A!9)) | (~(in(tptp_fun_C_0(singleton(A!9), A!9), singleton(A!9)) <=> (tptp_fun_C_0(singleton(A!9), A!9) = A!9)))))))),
% 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_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))),
% 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_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)),
% 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] : refl((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(48,plain,
% 0.23/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 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] : rewrite((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(50,plain,
% 0.23/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 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] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[50, 48])).
% 0.23/0.43 tff(52,plain,
% 0.23/0.43 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_13(B, A), A) & in(tptp_fun_C_13(B, A), B)) <=> (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B))))), ((disjoint(A, B) | (in(tptp_fun_C_13(B, A), A) & in(tptp_fun_C_13(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B))))))), rewrite((disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B))))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))), ((disjoint(A, B) | (in(tptp_fun_C_13(B, A), A) & in(tptp_fun_C_13(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B))))))), trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(C, A) & in(C, B)) <=> (~((~in(C, B)) | (~in(C, A))))), ((~(in(C, A) & in(C, B))) <=> (~(~((~in(C, B)) | (~in(C, A))))))), rewrite((~(~((~in(C, B)) | (~in(C, A))))) <=> ((~in(C, B)) | (~in(C, A)))), ((~(in(C, A) & in(C, B))) <=> ((~in(C, B)) | (~in(C, A)))))), (![C: $i] : (~(in(C, A) & in(C, B))) <=> ![C: $i] : ((~in(C, B)) | (~in(C, A))))), ((![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))) <=> (![C: $i] : ((~in(C, B)) | (~in(C, A))) | (~disjoint(A, B))))), rewrite((![C: $i] : ((~in(C, B)) | (~in(C, A))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))), ((![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))), (((disjoint(A, B) | (in(tptp_fun_C_13(B, A), A) & in(tptp_fun_C_13(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))), rewrite(((disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))), (((disjoint(A, B) | (in(tptp_fun_C_13(B, A), A) & in(tptp_fun_C_13(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(53,plain,
% 0.23/0.43 (![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_13(B, A), A) & in(tptp_fun_C_13(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[52])).
% 0.23/0.43 tff(54,plain,
% 0.23/0.43 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B)))) <=> ![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(55,axiom,(![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_xboole_0')).
% 0.23/0.43 tff(56,plain,
% 0.23/0.43 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.23/0.43 tff(57,plain,(
% 0.23/0.43 ![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_13(B, A), A) & in(tptp_fun_C_13(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))))),
% 0.23/0.43 inference(skolemize,[status(sab)],[56])).
% 0.23/0.43 tff(58,plain,
% 0.23/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.23/0.43 tff(59,plain,
% 0.23/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.23/0.43 tff(60,plain,
% 0.23/0.43 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9)))))) | (~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9)))))) | (~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))))))))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(61,plain,
% 0.23/0.43 ((~((~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)))))) | (~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9)))))))) <=> (~((~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9)))))) | (~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)))))))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(62,plain,
% 0.23/0.43 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)))))) | (~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9)))))) | (~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))))))))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[61])).
% 0.23/0.44 tff(63,plain,
% 0.23/0.44 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)))))) | (~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9)))))) | (~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))))))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[62, 60])).
% 0.23/0.44 tff(64,plain,
% 0.23/0.44 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)))))) | (~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9))))))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(65,plain,
% 0.23/0.44 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_13(B, A), A)) | (~in(tptp_fun_C_13(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9)))))) | (~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)))))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.23/0.44 tff(66,plain,
% 0.23/0.44 (~((~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9)))))) | (~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))))))))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[65, 59])).
% 0.23/0.44 tff(67,plain,
% 0.23/0.44 (((~((~disjoint(singleton(A!9), B!8)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, singleton(A!9)))))) | (~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)))))))) | (disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))))))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(68,plain,
% 0.23/0.44 (disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)))))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.23/0.44 tff(69,plain,
% 0.23/0.44 ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) <=> (~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(70,plain,
% 0.23/0.44 ((~![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B))) <=> (~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(71,axiom,(~![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l28_zfmisc_1')).
% 0.23/0.44 tff(72,plain,
% 0.23/0.44 (~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.23/0.44 tff(73,plain,
% 0.23/0.44 (~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[72, 69])).
% 0.23/0.44 tff(74,plain,
% 0.23/0.44 (~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.23/0.44 tff(75,plain,
% 0.23/0.44 (~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[74, 69])).
% 0.23/0.44 tff(76,plain,(
% 0.23/0.44 ~(in(A!9, B!8) | disjoint(singleton(A!9), B!8))),
% 0.23/0.44 inference(skolemize,[status(sab)],[75])).
% 0.23/0.44 tff(77,plain,
% 0.23/0.44 (~disjoint(singleton(A!9), B!8)),
% 0.23/0.44 inference(or_elim,[status(thm)],[76])).
% 0.23/0.44 tff(78,plain,
% 0.23/0.44 ((~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))))))) | disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)))))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(79,plain,
% 0.23/0.44 ((~(disjoint(singleton(A!9), B!8) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))))))) | (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)))))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.23/0.44 tff(80,plain,
% 0.23/0.44 (~((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[79, 68])).
% 0.23/0.44 tff(81,plain,
% 0.23/0.44 (((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)))) | in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(82,plain,
% 0.23/0.44 (in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.23/0.44 tff(83,plain,
% 0.23/0.44 ((~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9))) | (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(84,plain,
% 0.23/0.44 ((~(in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)) <=> (tptp_fun_C_13(B!8, singleton(A!9)) = A!9))) | (tptp_fun_C_13(B!8, singleton(A!9)) = A!9)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.23/0.44 tff(85,plain,
% 0.23/0.44 (tptp_fun_C_13(B!8, singleton(A!9)) = A!9),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[84, 46])).
% 0.23/0.44 tff(86,plain,
% 0.23/0.44 (in(tptp_fun_C_13(B!8, singleton(A!9)), B!8) <=> in(A!9, B!8)),
% 0.23/0.44 inference(monotonicity,[status(thm)],[85])).
% 0.23/0.44 tff(87,plain,
% 0.23/0.44 (in(A!9, B!8) <=> in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)),
% 0.23/0.44 inference(symmetry,[status(thm)],[86])).
% 0.23/0.44 tff(88,plain,
% 0.23/0.44 ((~in(A!9, B!8)) <=> (~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[87])).
% 0.23/0.44 tff(89,plain,
% 0.23/0.44 (~in(A!9, B!8)),
% 0.23/0.44 inference(or_elim,[status(thm)],[76])).
% 0.23/0.44 tff(90,plain,
% 0.23/0.44 (~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.23/0.44 tff(91,plain,
% 0.23/0.44 (((~in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)) | (~in(tptp_fun_C_13(B!8, singleton(A!9)), singleton(A!9)))) | in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(92,plain,
% 0.23/0.44 (in(tptp_fun_C_13(B!8, singleton(A!9)), B!8)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[91, 80])).
% 0.23/0.44 tff(93,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[92, 90])).
% 0.23/0.44 % SZS output end Proof
% 0.23/0.44 % E exiting
%------------------------------------------------------------------------------