%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM385+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:20:52 AM UTC 2025
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM385+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 01:03:11 EDT 2025
% 0.20/0.35 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(tptp_fun_B_13_type, type, (
% 0.20/0.42 tptp_fun_B_13: $i)).
% 0.20/0.42 tff(tptp_fun_A_14_type, type, (
% 0.20/0.42 tptp_fun_A_14: $i)).
% 0.20/0.42 tff(in_type, type, (
% 0.20/0.42 in: ( $i * $i ) > $o)).
% 0.20/0.42 tff(singleton_type, type, (
% 0.20/0.42 singleton: $i > $i)).
% 0.20/0.42 tff(tptp_fun_C_0_type, type, (
% 0.20/0.42 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.20/0.42 tff(succ_type, type, (
% 0.20/0.42 succ: $i > $i)).
% 0.20/0.42 tff(set_union2_type, type, (
% 0.20/0.42 set_union2: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_D_1_type, type, (
% 0.20/0.42 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(1,assumption,(~(in(B!13, singleton(A!14)) <=> (B!13 = A!14))), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[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))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(pull_quant,[status(thm)],[])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (^[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)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[7, 3])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (^[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))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[10, 8])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (^[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)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(15,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.42 tff(17,plain,(
% 0.20/0.42 ![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)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[16])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (((~![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(B!13, singleton(A!14)) <=> (B!13 = A!14))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 ((~(~(in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) <=> (in(B!13, singleton(A!14)) <=> (B!13 = A!14))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (((~(in(B!13, singleton(A!14)) <=> (B!13 = A!14))) | $false) <=> (~(in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((~$true) <=> $false),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (($true | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))) <=> $true),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 ((~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))) <=> (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 ((singleton(A!14) = singleton(A!14)) <=> $true),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (((singleton(A!14) = singleton(A!14)) | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[26, 25])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (((singleton(A!14) = singleton(A!14)) | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))) <=> $true),
% 0.20/0.42 inference(transitivity,[status(thm)],[27, 24])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 ((~((singleton(A!14) = singleton(A!14)) | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))))) <=> (~$true)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 ((~((singleton(A!14) = singleton(A!14)) | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))))) <=> $false),
% 0.20/0.42 inference(transitivity,[status(thm)],[29, 23])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 ((~(in(B!13, singleton(A!14)) <=> (B!13 = A!14))) <=> (~(in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (($false | (in(B!13, singleton(A!14)) <=> (B!13 = A!14))) <=> (in(B!13, singleton(A!14)) <=> (B!13 = A!14))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~(singleton(A!14) = singleton(A!14))) <=> (~$true)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 ((~(singleton(A!14) = singleton(A!14))) <=> $false),
% 0.20/0.42 inference(transitivity,[status(thm)],[33, 23])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14))) <=> ($false | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14))) <=> (in(B!13, singleton(A!14)) <=> (B!13 = A!14))),
% 0.20/0.42 inference(transitivity,[status(thm)],[35, 32])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 ((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) <=> (~(in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 ((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) <=> (~(in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[37, 31])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))))) <=> ((~(in(B!13, singleton(A!14)) <=> (B!13 = A!14))) | $false)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[38, 30])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))))) <=> (~(in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[39, 22])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 ((~((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))))))) <=> (~(~(in(B!13, singleton(A!14)) <=> (B!13 = A!14))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ((~((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))))))) <=> (in(B!13, singleton(A!14)) <=> (B!13 = A!14))),
% 0.20/0.42 inference(transitivity,[status(thm)],[41, 21])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (((~![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)))))))) | (~((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (((~![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!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[43, 20])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 ((~![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!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | (~(in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14)) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[46, 19, 1])).
% 0.20/0.43 tff(48,plain,(in(B!13, singleton(A!14)) <=> (B!13 = A!14)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 ((B!13 = A!14) <=> (A!14 = B!13)),
% 0.20/0.43 inference(commutativity,[status(thm)],[])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 ((A!14 = B!13) <=> (B!13 = A!14)),
% 0.20/0.43 inference(symmetry,[status(thm)],[49])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 ((~(A!14 = B!13)) <=> (~(B!13 = A!14))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))) <=> (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : ((succ(A) = succ(B)) => (A = B))) <=> (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(54,axiom,(~![A: $i, B: $i] : ((succ(A) = succ(B)) => (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_ordinal1')).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[57, 52])).
% 0.20/0.43 tff(59,plain,(
% 0.20/0.43 ~((~(succ(A!14) = succ(B!13))) | (A!14 = B!13))),
% 0.20/0.43 inference(skolemize,[status(sab)],[58])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (~(A!14 = B!13)),
% 0.20/0.43 inference(or_elim,[status(thm)],[59])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (~(B!13 = A!14)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[60, 51])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 ((~(in(B!13, singleton(A!14)) <=> (B!13 = A!14))) | (~in(B!13, singleton(A!14))) | (B!13 = A!14)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 ((~(in(B!13, singleton(A!14)) <=> (B!13 = A!14))) | (~in(B!13, singleton(A!14)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (~in(B!13, singleton(A!14))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[63, 48])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.43 inference(pull_quant,[status(thm)],[])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[70, 66])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[73, 71])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))) <=> (in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))), ((~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))), rewrite((~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))), ((~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(78,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.43 tff(80,plain,(
% 0.21/0.43 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[79])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))) | (~((succ(B!13) = set_union2(A!14, singleton(A!14))) | (~(in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), succ(B!13)) <=> (in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), A!14) | in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), singleton(A!14)))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (~((~((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))) | (~((succ(B!13) = set_union2(A!14, singleton(A!14))) | (~(in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), succ(B!13)) <=> (in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), A!14) | in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), singleton(A!14))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (((~((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))) | (~((succ(B!13) = set_union2(A!14, singleton(A!14))) | (~(in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), succ(B!13)) <=> (in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), A!14) | in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), singleton(A!14)))))))) | ((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 ((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (^[A: $i] : refl((succ(A) = set_union2(A, singleton(A))) <=> (succ(A) = set_union2(A, singleton(A))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[87])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(90,axiom,(![A: $i] : (succ(A) = set_union2(A, singleton(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_ordinal1')).
% 0.21/0.43 tff(91,plain,
% 0.21/0.44 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.44 tff(92,plain,(
% 0.21/0.44 ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[91])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.44 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 ((~![A: $i] : (succ(A) = set_union2(A, singleton(A)))) | (succ(A!14) = set_union2(A!14, singleton(A!14)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(95,plain,
% 0.21/0.44 (succ(A!14) = set_union2(A!14, singleton(A!14))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (succ(A!14) = succ(B!13)),
% 0.21/0.44 inference(or_elim,[status(thm)],[59])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (succ(B!13) = succ(A!14)),
% 0.21/0.44 inference(symmetry,[status(thm)],[96])).
% 0.21/0.44 tff(98,plain,
% 0.21/0.44 (succ(B!13) = set_union2(A!14, singleton(A!14))),
% 0.21/0.44 inference(transitivity,[status(thm)],[97, 95])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 ((~((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))) | (~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 ((~((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[100, 86])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 (^[A: $i] : refl(in(A, succ(A)) <=> in(A, succ(A)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (![A: $i] : in(A, succ(A)) <=> ![A: $i] : in(A, succ(A))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (![A: $i] : in(A, succ(A)) <=> ![A: $i] : in(A, succ(A))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(105,axiom,(![A: $i] : in(A, succ(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t10_ordinal1')).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (![A: $i] : in(A, succ(A))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.44 tff(107,plain,(
% 0.21/0.44 ![A: $i] : in(A, succ(A))),
% 0.21/0.44 inference(skolemize,[status(sab)],[106])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (![A: $i] : in(A, succ(A))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 ((~![A: $i] : in(A, succ(A))) | in(B!13, succ(B!13))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (in(B!13, succ(B!13))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 ((~(in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14))))) | (~in(B!13, succ(B!13))) | (in(B!13, A!14) | in(B!13, singleton(A!14)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 ((~(in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14))))) | (in(B!13, A!14) | in(B!13, singleton(A!14)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (in(B!13, A!14) | in(B!13, singleton(A!14))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[112, 101])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 ((~(in(B!13, A!14) | in(B!13, singleton(A!14)))) | in(B!13, A!14) | in(B!13, singleton(A!14))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (in(B!13, A!14) | in(B!13, singleton(A!14))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (in(B!13, A!14)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[115, 64])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (^[A: $i, B: $i] : refl(((~in(B, A)) | (~in(A, B))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (^[A: $i, B: $i] : rewrite((in(A, B) => (~in(B, A))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (![A: $i, B: $i] : (in(A, B) => (~in(B, A))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.44 tff(122,axiom,(![A: $i, B: $i] : (in(A, B) => (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','antisymmetry_r2_hidden')).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.21/0.44 tff(125,plain,(
% 0.21/0.44 ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[124])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!14, B!13)) | (~in(B!13, A!14)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!14, B!13)) | (~in(B!13, A!14)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (((~in(B!13, A!14)) | (~in(A!14, B!13))) <=> ((~in(A!14, B!13)) | (~in(B!13, A!14)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(B!13, A!14)) | (~in(A!14, B!13)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!14, B!13)) | (~in(B!13, A!14))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[128])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(B!13, A!14)) | (~in(A!14, B!13)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!14, B!13)) | (~in(B!13, A!14)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[129, 127])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(B!13, A!14)) | (~in(A!14, B!13)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!14, B!13)) | (~in(B!13, A!14))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (~in(A!14, B!13)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[132, 126, 116])).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))) | (~((succ(B!13) = set_union2(B!13, singleton(B!13))) | (~(in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), succ(B!13)) <=> (in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), B!13) | in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), singleton(B!13)))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (~((~((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))) | (~((succ(B!13) = set_union2(B!13, singleton(B!13))) | (~(in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), succ(B!13)) <=> (in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), B!13) | in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), singleton(B!13))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[134, 82])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (((~((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))) | (~((succ(B!13) = set_union2(B!13, singleton(B!13))) | (~(in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), succ(B!13)) <=> (in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), B!13) | in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), singleton(B!13)))))))) | ((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 ((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 ((~![A: $i] : (succ(A) = set_union2(A, singleton(A)))) | (succ(B!13) = set_union2(B!13, singleton(B!13)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (succ(B!13) = set_union2(B!13, singleton(B!13))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[138, 93])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 ((~((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))) | (~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 ((~((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[141, 137])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 (in(A!14, succ(B!13)) <=> in(A!14, succ(A!14))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 (in(A!14, succ(A!14)) <=> in(A!14, succ(B!13))),
% 0.21/0.44 inference(symmetry,[status(thm)],[143])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 ((~![A: $i] : in(A, succ(A))) | in(A!14, succ(A!14))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 (in(A!14, succ(A!14))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[145, 108])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 (in(A!14, succ(B!13))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[146, 144])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 ((~(in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13))))) | (~in(A!14, succ(B!13))) | (in(A!14, B!13) | in(A!14, singleton(B!13)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(149,plain,
% 0.21/0.44 (in(A!14, B!13) | in(A!14, singleton(B!13))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[148, 147, 142])).
% 0.21/0.44 tff(150,plain,
% 0.21/0.44 ((~(in(A!14, B!13) | in(A!14, singleton(B!13)))) | in(A!14, B!13) | in(A!14, singleton(B!13))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(151,plain,
% 0.21/0.44 (in(A!14, B!13) | in(A!14, singleton(B!13))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.21/0.44 tff(152,plain,
% 0.21/0.44 (in(A!14, singleton(B!13))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[151, 133])).
% 0.21/0.44 tff(153,plain,
% 0.21/0.44 ((~(in(A!14, singleton(B!13)) <=> (A!14 = B!13))) | (~in(A!14, singleton(B!13))) | (A!14 = B!13)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(154,plain,
% 0.21/0.44 (~(in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[153, 60, 152])).
% 0.21/0.44 tff(155,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13))) <=> ((~![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!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(156,plain,
% 0.21/0.44 ((~(~(in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) <=> (in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(157,plain,
% 0.21/0.44 (((~(in(A!14, singleton(B!13)) <=> (A!14 = B!13))) | $false) <=> (~(in(A!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(158,plain,
% 0.21/0.44 (($true | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))) <=> $true),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(159,plain,
% 0.21/0.44 ((~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))) <=> (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(160,plain,
% 0.21/0.45 ((singleton(B!13) = singleton(B!13)) <=> $true),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(161,plain,
% 0.21/0.45 (((singleton(B!13) = singleton(B!13)) | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[160, 159])).
% 0.21/0.45 tff(162,plain,
% 0.21/0.45 (((singleton(B!13) = singleton(B!13)) | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))) <=> $true),
% 0.21/0.45 inference(transitivity,[status(thm)],[161, 158])).
% 0.21/0.45 tff(163,plain,
% 0.21/0.45 ((~((singleton(B!13) = singleton(B!13)) | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))))) <=> (~$true)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[162])).
% 0.21/0.45 tff(164,plain,
% 0.21/0.45 ((~((singleton(B!13) = singleton(B!13)) | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))))) <=> $false),
% 0.21/0.45 inference(transitivity,[status(thm)],[163, 23])).
% 0.21/0.45 tff(165,plain,
% 0.21/0.45 ((~(in(A!14, singleton(B!13)) <=> (A!14 = B!13))) <=> (~(in(A!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(166,plain,
% 0.21/0.45 (($false | (in(A!14, singleton(B!13)) <=> (A!14 = B!13))) <=> (in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(167,plain,
% 0.21/0.45 ((~(singleton(B!13) = singleton(B!13))) <=> (~$true)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[160])).
% 0.21/0.45 tff(168,plain,
% 0.21/0.45 ((~(singleton(B!13) = singleton(B!13))) <=> $false),
% 0.21/0.45 inference(transitivity,[status(thm)],[167, 23])).
% 0.21/0.45 tff(169,plain,
% 0.21/0.45 (((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13))) <=> ($false | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[168])).
% 0.21/0.45 tff(170,plain,
% 0.21/0.45 (((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13))) <=> (in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.21/0.45 inference(transitivity,[status(thm)],[169, 166])).
% 0.21/0.45 tff(171,plain,
% 0.21/0.45 ((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) <=> (~(in(A!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[170])).
% 0.21/0.45 tff(172,plain,
% 0.21/0.45 ((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) <=> (~(in(A!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[171, 165])).
% 0.21/0.45 tff(173,plain,
% 0.21/0.45 (((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))))) <=> ((~(in(A!14, singleton(B!13)) <=> (A!14 = B!13))) | $false)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[172, 164])).
% 0.21/0.45 tff(174,plain,
% 0.21/0.45 (((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))))) <=> (~(in(A!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[173, 157])).
% 0.21/0.45 tff(175,plain,
% 0.21/0.45 ((~((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))))))) <=> (~(~(in(A!14, singleton(B!13)) <=> (A!14 = B!13))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[174])).
% 0.21/0.45 tff(176,plain,
% 0.21/0.45 ((~((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))))))) <=> (in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.21/0.45 inference(transitivity,[status(thm)],[175, 156])).
% 0.21/0.45 tff(177,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))))))) <=> ((~![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!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[176])).
% 0.21/0.45 tff(178,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))))))) <=> ((~![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!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[177, 155])).
% 0.21/0.45 tff(179,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | (~(in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13)) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(180,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.21/0.45 tff(181,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[180, 19, 154])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------