%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU144+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:01 AM UTC 2025
% Result : Theorem 2.25s 2.45s
% Output : Proof 2.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : SEU144+2 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 06:07:20 EDT 2025
% 0.12/0.32 % CPUTime :
% 2.25/2.45 % SZS status Theorem
% 2.25/2.45 % SZS output start Proof
% 2.25/2.45 tff(in_type, type, (
% 2.25/2.45 in: ( $i * $i ) > $o)).
% 2.25/2.45 tff(tptp_fun_B_7_type, type, (
% 2.25/2.45 tptp_fun_B_7: $i)).
% 2.25/2.45 tff(tptp_fun_C_4_type, type, (
% 2.25/2.45 tptp_fun_C_4: ( $i * $i ) > $i)).
% 2.25/2.45 tff(singleton_type, type, (
% 2.25/2.45 singleton: $i > $i)).
% 2.25/2.45 tff(tptp_fun_A_8_type, type, (
% 2.25/2.45 tptp_fun_A_8: $i)).
% 2.25/2.45 tff(tptp_fun_C_0_type, type, (
% 2.25/2.45 tptp_fun_C_0: ( $i * $i ) > $i)).
% 2.25/2.45 tff(subset_type, type, (
% 2.25/2.45 subset: ( $i * $i ) > $o)).
% 2.25/2.45 tff(set_difference_type, type, (
% 2.25/2.45 set_difference: ( $i * $i ) > $i)).
% 2.25/2.45 tff(tptp_fun_C_12_type, type, (
% 2.25/2.45 tptp_fun_C_12: ( $i * $i ) > $i)).
% 2.25/2.45 tff(disjoint_type, type, (
% 2.25/2.45 disjoint: ( $i * $i ) > $o)).
% 2.25/2.45 tff(empty_set_type, type, (
% 2.25/2.45 empty_set: $i)).
% 2.25/2.45 tff(set_union2_type, type, (
% 2.25/2.45 set_union2: ( $i * $i ) > $i)).
% 2.25/2.45 tff(tptp_fun_D_3_type, type, (
% 2.25/2.45 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 2.25/2.45 tff(1,plain,
% 2.25/2.45 (^[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))))))))),
% 2.25/2.45 inference(bind,[status(th)],[])).
% 2.25/2.45 tff(2,plain,
% 2.25/2.45 (![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))))))) <=> ![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)))))))),
% 2.25/2.45 inference(quant_intro,[status(thm)],[1])).
% 2.25/2.45 tff(3,plain,
% 2.25/2.45 (![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))))))) <=> ![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)))))))),
% 2.25/2.45 inference(pull_quant,[status(thm)],[])).
% 2.25/2.45 tff(4,plain,
% 2.25/2.45 (^[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)))))))))),
% 2.25/2.45 inference(bind,[status(th)],[])).
% 2.25/2.45 tff(5,plain,
% 2.25/2.45 (![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)))))))),
% 2.25/2.45 inference(quant_intro,[status(thm)],[4])).
% 2.25/2.45 tff(6,plain,
% 2.25/2.45 (![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)))))))),
% 2.25/2.45 inference(transitivity,[status(thm)],[5, 3])).
% 2.25/2.45 tff(7,plain,
% 2.25/2.45 (![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)))))))),
% 2.25/2.45 inference(transitivity,[status(thm)],[6, 2])).
% 2.25/2.45 tff(8,plain,
% 2.25/2.45 (^[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))))))))),
% 2.25/2.45 inference(bind,[status(th)],[])).
% 2.25/2.45 tff(9,plain,
% 2.25/2.45 (![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)))))))),
% 2.25/2.45 inference(quant_intro,[status(thm)],[8])).
% 2.25/2.45 tff(10,plain,
% 2.25/2.45 (![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)))))))),
% 2.25/2.45 inference(transitivity,[status(thm)],[9, 7])).
% 2.25/2.45 tff(11,plain,
% 2.25/2.45 (^[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)))))))))),
% 2.25/2.45 inference(bind,[status(th)],[])).
% 2.25/2.45 tff(12,plain,
% 2.25/2.45 (![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)))))))),
% 2.25/2.45 inference(quant_intro,[status(thm)],[11])).
% 2.25/2.45 tff(13,plain,
% 2.25/2.45 (![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)))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 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')).
% 2.25/2.45 tff(15,plain,
% 2.25/2.45 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[14, 13])).
% 2.25/2.45 tff(16,plain,(
% 2.25/2.45 ![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)))))),
% 2.25/2.45 inference(skolemize,[status(sab)],[15])).
% 2.25/2.45 tff(17,plain,
% 2.25/2.45 (![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)))))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[16, 12])).
% 2.25/2.46 tff(18,plain,
% 2.25/2.46 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[17, 10])).
% 2.25/2.46 tff(19,plain,
% 2.25/2.46 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) <=> ((~![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_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(20,plain,
% 2.25/2.46 ((~(~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) <=> (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(21,plain,
% 2.25/2.46 (((~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) | $false) <=> (~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(22,plain,
% 2.25/2.46 ((~$true) <=> $false),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(23,plain,
% 2.25/2.46 (($true | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))) <=> $true),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(24,plain,
% 2.25/2.46 ((~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))) <=> (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(25,plain,
% 2.25/2.46 ((singleton(A!8) = singleton(A!8)) <=> $true),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(26,plain,
% 2.25/2.46 (((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[25, 24])).
% 2.25/2.46 tff(27,plain,
% 2.25/2.46 (((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))) <=> $true),
% 2.25/2.46 inference(transitivity,[status(thm)],[26, 23])).
% 2.25/2.46 tff(28,plain,
% 2.25/2.46 ((~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))) <=> (~$true)),
% 2.25/2.46 inference(monotonicity,[status(thm)],[27])).
% 2.25/2.46 tff(29,plain,
% 2.25/2.46 ((~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))) <=> $false),
% 2.25/2.46 inference(transitivity,[status(thm)],[28, 22])).
% 2.25/2.46 tff(30,plain,
% 2.25/2.46 ((~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) <=> (~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(31,plain,
% 2.25/2.46 (($false | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) <=> (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(32,plain,
% 2.25/2.46 ((~(singleton(A!8) = singleton(A!8))) <=> (~$true)),
% 2.25/2.46 inference(monotonicity,[status(thm)],[25])).
% 2.25/2.46 tff(33,plain,
% 2.25/2.46 ((~(singleton(A!8) = singleton(A!8))) <=> $false),
% 2.25/2.46 inference(transitivity,[status(thm)],[32, 22])).
% 2.25/2.46 tff(34,plain,
% 2.25/2.46 (((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) <=> ($false | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[33])).
% 2.25/2.46 tff(35,plain,
% 2.25/2.46 (((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) <=> (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 2.25/2.46 inference(transitivity,[status(thm)],[34, 31])).
% 2.25/2.46 tff(36,plain,
% 2.25/2.46 ((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) <=> (~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[35])).
% 2.25/2.46 tff(37,plain,
% 2.25/2.46 ((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) <=> (~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(transitivity,[status(thm)],[36, 30])).
% 2.25/2.46 tff(38,plain,
% 2.25/2.46 (((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))) <=> ((~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) | $false)),
% 2.25/2.46 inference(monotonicity,[status(thm)],[37, 29])).
% 2.25/2.46 tff(39,plain,
% 2.25/2.46 (((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))) <=> (~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(transitivity,[status(thm)],[38, 21])).
% 2.25/2.46 tff(40,plain,
% 2.25/2.46 ((~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))))) <=> (~(~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[39])).
% 2.25/2.46 tff(41,plain,
% 2.25/2.46 ((~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))))) <=> (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 2.25/2.46 inference(transitivity,[status(thm)],[40, 20])).
% 2.25/2.46 tff(42,plain,
% 2.25/2.46 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))))) <=> ((~![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_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[41])).
% 2.25/2.46 tff(43,plain,
% 2.25/2.46 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))))) <=> ((~![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_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(transitivity,[status(thm)],[42, 19])).
% 2.25/2.46 tff(44,plain,
% 2.25/2.46 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(45,plain,
% 2.25/2.46 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[44, 43])).
% 2.25/2.46 tff(46,plain,
% 2.25/2.46 (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[45, 18])).
% 2.25/2.46 tff(47,assumption,(~in(A!8, B!7)), introduced(assumption)).
% 2.25/2.46 tff(48,plain,
% 2.25/2.46 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) <=> ((~![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_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(49,plain,
% 2.25/2.46 ((~(~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) <=> (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(50,plain,
% 2.25/2.46 (((~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) | $false) <=> (~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(51,plain,
% 2.25/2.46 ((~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) <=> (~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(52,plain,
% 2.25/2.46 (($false | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) <=> (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(53,plain,
% 2.25/2.46 (((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) <=> ($false | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[33])).
% 2.25/2.46 tff(54,plain,
% 2.25/2.46 (((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) <=> (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 2.25/2.46 inference(transitivity,[status(thm)],[53, 52])).
% 2.25/2.46 tff(55,plain,
% 2.25/2.46 ((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) <=> (~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[54])).
% 2.25/2.46 tff(56,plain,
% 2.25/2.46 ((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) <=> (~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(transitivity,[status(thm)],[55, 51])).
% 2.25/2.46 tff(57,plain,
% 2.25/2.46 (((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))) <=> ((~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) | $false)),
% 2.25/2.46 inference(monotonicity,[status(thm)],[56, 29])).
% 2.25/2.46 tff(58,plain,
% 2.25/2.46 (((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))) <=> (~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(transitivity,[status(thm)],[57, 50])).
% 2.25/2.46 tff(59,plain,
% 2.25/2.46 ((~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))))) <=> (~(~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[58])).
% 2.25/2.46 tff(60,plain,
% 2.25/2.46 ((~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))))) <=> (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 2.25/2.46 inference(transitivity,[status(thm)],[59, 49])).
% 2.25/2.46 tff(61,plain,
% 2.25/2.46 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))))) <=> ((~![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_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[60])).
% 2.25/2.46 tff(62,plain,
% 2.25/2.46 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))))) <=> ((~![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_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 2.25/2.46 inference(transitivity,[status(thm)],[61, 48])).
% 2.25/2.46 tff(63,plain,
% 2.25/2.46 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | (~(in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8)) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(64,plain,
% 2.25/2.46 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[63, 62])).
% 2.25/2.46 tff(65,plain,
% 2.25/2.46 (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[64, 18])).
% 2.25/2.46 tff(66,plain,
% 2.25/2.46 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))))),
% 2.25/2.46 inference(bind,[status(th)],[])).
% 2.25/2.46 tff(67,plain,
% 2.25/2.46 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(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_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.25/2.46 inference(quant_intro,[status(thm)],[66])).
% 2.25/2.46 tff(68,plain,
% 2.25/2.46 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))))),
% 2.25/2.46 inference(bind,[status(th)],[])).
% 2.25/2.46 tff(69,plain,
% 2.25/2.46 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(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_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.25/2.46 inference(quant_intro,[status(thm)],[68])).
% 2.25/2.46 tff(70,plain,
% 2.25/2.46 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(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_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.25/2.46 inference(transitivity,[status(thm)],[69, 67])).
% 2.25/2.46 tff(71,plain,
% 2.25/2.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B)) <=> (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B))))), ((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B))))))), rewrite((disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B))))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))), ((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(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_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))), rewrite(((disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))), (((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))))),
% 2.25/2.46 inference(bind,[status(th)],[])).
% 2.25/2.46 tff(72,plain,
% 2.25/2.46 (![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(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_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.25/2.46 inference(quant_intro,[status(thm)],[71])).
% 2.25/2.46 tff(73,plain,
% 2.25/2.46 (![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))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(74,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')).
% 2.25/2.46 tff(75,plain,
% 2.25/2.46 (![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))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[74, 73])).
% 2.25/2.46 tff(76,plain,(
% 2.25/2.46 ![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))))),
% 2.25/2.46 inference(skolemize,[status(sab)],[75])).
% 2.25/2.46 tff(77,plain,
% 2.25/2.46 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[76, 72])).
% 2.25/2.46 tff(78,plain,
% 2.25/2.46 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[77, 70])).
% 2.25/2.46 tff(79,plain,
% 2.25/2.46 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8))))))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(80,plain,
% 2.25/2.46 ((~((~(disjoint(singleton(A!8), singleton(A!8)) | (~((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) | (~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))))))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : ((~in(C, singleton(A!8))) | (~in(C, singleton(A!8)))))))) <=> (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8)))))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(81,plain,
% 2.25/2.46 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | (~((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) | (~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))))))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : ((~in(C, singleton(A!8))) | (~in(C, singleton(A!8))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8))))))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[80])).
% 2.25/2.46 tff(82,plain,
% 2.25/2.46 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | (~((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) | (~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))))))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : ((~in(C, singleton(A!8))) | (~in(C, singleton(A!8))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8))))))))),
% 2.25/2.46 inference(transitivity,[status(thm)],[81, 79])).
% 2.25/2.46 tff(83,plain,
% 2.25/2.46 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | (~((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) | (~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))))))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : ((~in(C, singleton(A!8))) | (~in(C, singleton(A!8))))))))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(84,plain,
% 2.25/2.46 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8)))))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[83, 82])).
% 2.25/2.46 tff(85,plain,
% 2.25/2.46 (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8))))))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[84, 78])).
% 2.25/2.46 tff(86,plain,
% 2.25/2.46 (((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8)))))) | (disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))),
% 2.25/2.46 inference(tautology,[status(thm)],[])).
% 2.25/2.46 tff(87,plain,
% 2.25/2.46 (disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[86, 85])).
% 2.25/2.46 tff(88,plain,
% 2.25/2.46 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_difference(A, B) = A)) <=> (disjoint(A, B) <=> (set_difference(A, B) = A)))),
% 2.25/2.46 inference(bind,[status(th)],[])).
% 2.25/2.46 tff(89,plain,
% 2.25/2.46 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 2.25/2.46 inference(quant_intro,[status(thm)],[88])).
% 2.25/2.46 tff(90,plain,
% 2.25/2.46 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(91,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t83_xboole_1')).
% 2.25/2.46 tff(92,plain,
% 2.25/2.46 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[91, 90])).
% 2.25/2.46 tff(93,plain,(
% 2.25/2.46 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 2.25/2.46 inference(skolemize,[status(sab)],[92])).
% 2.25/2.46 tff(94,plain,
% 2.25/2.46 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[93, 89])).
% 2.25/2.46 tff(95,plain,
% 2.25/2.46 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))) | (disjoint(singleton(A!8), singleton(A!8)) <=> (set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8)))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(96,plain,
% 2.25/2.46 (disjoint(singleton(A!8), singleton(A!8)) <=> (set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[95, 94])).
% 2.25/2.46 tff(97,plain,
% 2.25/2.46 ((empty_set = singleton(A!8)) <=> (singleton(A!8) = empty_set)),
% 2.25/2.46 inference(commutativity,[status(thm)],[])).
% 2.25/2.46 tff(98,plain,
% 2.25/2.46 (^[A: $i, B: $i] : refl(((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ((set_difference(A, B) = empty_set) <=> subset(A, B)))),
% 2.25/2.46 inference(bind,[status(th)],[])).
% 2.25/2.46 tff(99,plain,
% 2.25/2.46 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 2.25/2.46 inference(quant_intro,[status(thm)],[98])).
% 2.25/2.46 tff(100,plain,
% 2.25/2.46 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(101,axiom,(![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l32_xboole_1')).
% 2.25/2.46 tff(102,plain,
% 2.25/2.46 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 2.25/2.46 tff(103,plain,(
% 2.25/2.46 ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 2.25/2.46 inference(skolemize,[status(sab)],[102])).
% 2.25/2.46 tff(104,plain,
% 2.25/2.46 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[103, 99])).
% 2.25/2.46 tff(105,plain,
% 2.25/2.46 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) | ((set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set) <=> subset(set_difference(singleton(A!8), B!7), singleton(A!8)))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(106,plain,
% 2.25/2.46 ((set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set) <=> subset(set_difference(singleton(A!8), B!7), singleton(A!8))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[105, 104])).
% 2.25/2.46 tff(107,plain,
% 2.25/2.46 (^[A: $i, B: $i] : refl(subset(set_difference(A, B), A) <=> subset(set_difference(A, B), A))),
% 2.25/2.46 inference(bind,[status(th)],[])).
% 2.25/2.46 tff(108,plain,
% 2.25/2.46 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 2.25/2.46 inference(quant_intro,[status(thm)],[107])).
% 2.25/2.46 tff(109,plain,
% 2.25/2.46 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(110,axiom,(![A: $i, B: $i] : subset(set_difference(A, B), A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t36_xboole_1')).
% 2.25/2.46 tff(111,plain,
% 2.25/2.46 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[110, 109])).
% 2.25/2.46 tff(112,plain,(
% 2.25/2.46 ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 2.25/2.46 inference(skolemize,[status(sab)],[111])).
% 2.25/2.46 tff(113,plain,
% 2.25/2.46 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[112, 108])).
% 2.25/2.47 tff(114,plain,
% 2.25/2.47 ((~![A: $i, B: $i] : subset(set_difference(A, B), A)) | subset(set_difference(singleton(A!8), B!7), singleton(A!8))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(115,plain,
% 2.25/2.47 (subset(set_difference(singleton(A!8), B!7), singleton(A!8))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[114, 113])).
% 2.25/2.47 tff(116,plain,
% 2.25/2.47 ((~((set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set) <=> subset(set_difference(singleton(A!8), B!7), singleton(A!8)))) | (set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set) | (~subset(set_difference(singleton(A!8), B!7), singleton(A!8)))),
% 2.25/2.47 inference(tautology,[status(thm)],[])).
% 2.25/2.47 tff(117,plain,
% 2.25/2.47 ((~((set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set) <=> subset(set_difference(singleton(A!8), B!7), singleton(A!8)))) | (set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[116, 115])).
% 2.25/2.47 tff(118,plain,
% 2.25/2.47 (set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[117, 106])).
% 2.25/2.47 tff(119,plain,
% 2.25/2.47 (^[A: $i, B: $i] : refl((set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> (set_difference(set_union2(A, B), B) = set_difference(A, B)))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(120,plain,
% 2.25/2.47 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[119])).
% 2.25/2.47 tff(121,plain,
% 2.25/2.47 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(122,axiom,(![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t40_xboole_1')).
% 2.25/2.47 tff(123,plain,
% 2.25/2.47 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[122, 121])).
% 2.25/2.47 tff(124,plain,(
% 2.25/2.47 ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 2.25/2.47 inference(skolemize,[status(sab)],[123])).
% 2.25/2.47 tff(125,plain,
% 2.25/2.47 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[124, 120])).
% 2.25/2.47 tff(126,plain,
% 2.25/2.47 ((~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))) | (set_difference(set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)), singleton(A!8)) = set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(127,plain,
% 2.25/2.47 (set_difference(set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)), singleton(A!8)) = set_difference(set_difference(singleton(A!8), B!7), singleton(A!8))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[126, 125])).
% 2.25/2.47 tff(128,plain,
% 2.25/2.47 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(129,plain,
% 2.25/2.47 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[128])).
% 2.25/2.47 tff(130,plain,
% 2.25/2.47 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(131,plain,
% 2.25/2.47 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(132,plain,
% 2.25/2.47 (![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[131])).
% 2.25/2.47 tff(133,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_xboole_1')).
% 2.25/2.47 tff(134,plain,
% 2.25/2.47 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[133, 132])).
% 2.25/2.47 tff(135,plain,
% 2.25/2.47 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[134, 130])).
% 2.25/2.47 tff(136,plain,(
% 2.25/2.47 ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.25/2.47 inference(skolemize,[status(sab)],[135])).
% 2.25/2.47 tff(137,plain,
% 2.25/2.47 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[136, 129])).
% 2.25/2.47 tff(138,plain,
% 2.25/2.47 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_difference(singleton(A!8), B!7), singleton(A!8))) | (set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)) = singleton(A!8)))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_difference(singleton(A!8), B!7), singleton(A!8))) | (set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)) = singleton(A!8)))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(139,plain,
% 2.25/2.47 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_difference(singleton(A!8), B!7), singleton(A!8))) | (set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)) = singleton(A!8)))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(140,plain,
% 2.25/2.47 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_difference(singleton(A!8), B!7), singleton(A!8))) | (set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)) = singleton(A!8))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[139, 138])).
% 2.25/2.47 tff(141,plain,
% 2.25/2.47 (set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)) = singleton(A!8)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[140, 137, 115])).
% 2.25/2.47 tff(142,plain,
% 2.25/2.47 (singleton(A!8) = set_union2(set_difference(singleton(A!8), B!7), singleton(A!8))),
% 2.25/2.47 inference(symmetry,[status(thm)],[141])).
% 2.25/2.47 tff(143,plain,
% 2.25/2.47 (set_difference(singleton(A!8), singleton(A!8)) = set_difference(set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)), singleton(A!8))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[142])).
% 2.25/2.47 tff(144,plain,
% 2.25/2.47 (set_difference(singleton(A!8), singleton(A!8)) = empty_set),
% 2.25/2.47 inference(transitivity,[status(thm)],[143, 127, 118])).
% 2.25/2.47 tff(145,plain,
% 2.25/2.47 ((set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8)) <=> (empty_set = singleton(A!8))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[144])).
% 2.25/2.47 tff(146,plain,
% 2.25/2.47 ((set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8)) <=> (singleton(A!8) = empty_set)),
% 2.25/2.47 inference(transitivity,[status(thm)],[145, 97])).
% 2.25/2.47 tff(147,plain,
% 2.25/2.47 ((singleton(A!8) = empty_set) <=> (set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8))),
% 2.25/2.47 inference(symmetry,[status(thm)],[146])).
% 2.25/2.47 tff(148,plain,
% 2.25/2.47 ((~(singleton(A!8) = empty_set)) <=> (~(set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8)))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[147])).
% 2.25/2.47 tff(149,plain,
% 2.25/2.47 (^[A: $i] : refl((~(singleton(A) = empty_set)) <=> (~(singleton(A) = empty_set)))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(150,plain,
% 2.25/2.47 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[149])).
% 2.25/2.47 tff(151,plain,
% 2.25/2.47 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(152,axiom,(![A: $i] : (~(singleton(A) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1_zfmisc_1')).
% 2.25/2.47 tff(153,plain,
% 2.25/2.47 (![A: $i] : (~(singleton(A) = empty_set))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[152, 151])).
% 2.25/2.47 tff(154,plain,(
% 2.25/2.47 ![A: $i] : (~(singleton(A) = empty_set))),
% 2.25/2.47 inference(skolemize,[status(sab)],[153])).
% 2.25/2.47 tff(155,plain,
% 2.25/2.47 (![A: $i] : (~(singleton(A) = empty_set))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[154, 150])).
% 2.25/2.47 tff(156,plain,
% 2.25/2.47 ((~![A: $i] : (~(singleton(A) = empty_set))) | (~(singleton(A!8) = empty_set))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(157,plain,
% 2.25/2.47 (~(singleton(A!8) = empty_set)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[156, 155])).
% 2.25/2.47 tff(158,plain,
% 2.25/2.47 (~(set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[157, 148])).
% 2.25/2.47 tff(159,plain,
% 2.25/2.47 ((~(disjoint(singleton(A!8), singleton(A!8)) <=> (set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8)))) | (~disjoint(singleton(A!8), singleton(A!8))) | (set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8))),
% 2.25/2.47 inference(tautology,[status(thm)],[])).
% 2.25/2.47 tff(160,plain,
% 2.25/2.47 (~disjoint(singleton(A!8), singleton(A!8))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[159, 158, 96])).
% 2.25/2.47 tff(161,plain,
% 2.25/2.47 ((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))),
% 2.25/2.47 inference(tautology,[status(thm)],[])).
% 2.25/2.47 tff(162,plain,
% 2.25/2.47 (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[161, 160, 87])).
% 2.25/2.47 tff(163,plain,
% 2.25/2.47 ((~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) | (~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) | (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)),
% 2.25/2.47 inference(tautology,[status(thm)],[])).
% 2.25/2.47 tff(164,plain,
% 2.25/2.47 ((~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) | (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[163, 162])).
% 2.25/2.47 tff(165,plain,
% 2.25/2.47 (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[164, 65])).
% 2.25/2.47 tff(166,plain,
% 2.25/2.47 (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> in(A!8, singleton(A!8))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[165])).
% 2.25/2.47 tff(167,plain,
% 2.25/2.47 (in(A!8, singleton(A!8))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[162, 166])).
% 2.25/2.47 tff(168,plain,
% 2.25/2.47 ((in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))) | (~in(A!8, singleton(A!8)))),
% 2.25/2.47 inference(tautology,[status(thm)],[])).
% 2.25/2.47 tff(169,plain,
% 2.25/2.47 (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[168, 167])).
% 2.25/2.47 tff(170,plain,
% 2.25/2.47 ((~(in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))) | in(A!8, B!7) | (~(in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))),
% 2.25/2.47 inference(tautology,[status(thm)],[])).
% 2.25/2.47 tff(171,plain,
% 2.25/2.47 ((~(in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))) | in(A!8, B!7)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[170, 169])).
% 2.25/2.47 tff(172,plain,
% 2.25/2.47 (~(in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[171, 47])).
% 2.25/2.47 tff(173,plain,
% 2.25/2.47 ((~(subset(singleton(A!8), B!7) <=> in(A!8, B!7))) <=> (~(subset(singleton(A!8), B!7) <=> in(A!8, B!7)))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(174,plain,
% 2.25/2.47 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) <=> (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(175,axiom,(~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 2.25/2.47 tff(176,plain,
% 2.25/2.47 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[175, 174])).
% 2.25/2.47 tff(177,plain,
% 2.25/2.47 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[176, 174])).
% 2.25/2.47 tff(178,plain,
% 2.25/2.47 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[177, 174])).
% 2.25/2.47 tff(179,plain,
% 2.25/2.47 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[178, 174])).
% 2.25/2.47 tff(180,plain,(
% 2.25/2.47 ~(subset(singleton(A!8), B!7) <=> in(A!8, B!7))),
% 2.25/2.47 inference(skolemize,[status(sab)],[179])).
% 2.25/2.47 tff(181,plain,
% 2.25/2.47 (~(subset(singleton(A!8), B!7) <=> in(A!8, B!7))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[180, 173])).
% 2.25/2.47 tff(182,plain,
% 2.25/2.47 ((subset(singleton(A!8), B!7) <=> in(A!8, B!7)) | subset(singleton(A!8), B!7) | in(A!8, B!7)),
% 2.25/2.47 inference(tautology,[status(thm)],[])).
% 2.25/2.47 tff(183,plain,
% 2.25/2.47 (subset(singleton(A!8), B!7) | in(A!8, B!7)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[182, 181])).
% 2.25/2.47 tff(184,plain,
% 2.25/2.47 (subset(singleton(A!8), B!7)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[183, 47])).
% 2.25/2.47 tff(185,plain,
% 2.25/2.47 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(186,plain,
% 2.25/2.47 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[185])).
% 2.25/2.47 tff(187,plain,
% 2.25/2.47 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(188,plain,
% 2.25/2.47 (^[A: $i, B: $i] : rewrite((subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(189,plain,
% 2.25/2.47 (![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[188])).
% 2.25/2.47 tff(190,axiom,(![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t45_xboole_1')).
% 2.25/2.47 tff(191,plain,
% 2.25/2.47 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[190, 189])).
% 2.25/2.47 tff(192,plain,
% 2.25/2.47 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[191, 187])).
% 2.25/2.47 tff(193,plain,(
% 2.25/2.47 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 2.25/2.47 inference(skolemize,[status(sab)],[192])).
% 2.25/2.47 tff(194,plain,
% 2.25/2.47 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[193, 186])).
% 2.25/2.47 tff(195,plain,
% 2.25/2.47 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(singleton(A!8), B!7)) | (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(singleton(A!8), B!7)) | (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(196,plain,
% 2.25/2.47 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(singleton(A!8), B!7)) | (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(197,plain,
% 2.25/2.47 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(singleton(A!8), B!7)) | (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[196, 195])).
% 2.25/2.47 tff(198,plain,
% 2.25/2.47 ((~subset(singleton(A!8), B!7)) | (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[197, 194])).
% 2.25/2.47 tff(199,plain,
% 2.25/2.47 (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[198, 184])).
% 2.25/2.47 tff(200,plain,
% 2.25/2.47 (^[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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(201,plain,
% 2.25/2.47 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[200])).
% 2.25/2.47 tff(202,plain,
% 2.25/2.47 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 2.25/2.47 inference(pull_quant,[status(thm)],[])).
% 2.25/2.47 tff(203,plain,
% 2.25/2.47 (^[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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(204,plain,
% 2.25/2.47 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[203])).
% 2.25/2.47 tff(205,plain,
% 2.25/2.47 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 2.25/2.47 inference(transitivity,[status(thm)],[204, 202])).
% 2.25/2.47 tff(206,plain,
% 2.25/2.47 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 2.25/2.47 inference(transitivity,[status(thm)],[205, 201])).
% 2.25/2.47 tff(207,plain,
% 2.25/2.47 (^[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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(208,plain,
% 2.25/2.47 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[207])).
% 2.25/2.47 tff(209,plain,
% 2.25/2.47 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 2.25/2.47 inference(transitivity,[status(thm)],[208, 206])).
% 2.25/2.47 tff(210,plain,
% 2.25/2.47 (^[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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))) <=> (in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))), ((~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))) <=> (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))), rewrite((~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))) <=> (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))), ((~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))) <=> (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(211,plain,
% 2.25/2.47 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[210])).
% 2.25/2.47 tff(212,plain,
% 2.25/2.47 (![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))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(213,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')).
% 2.25/2.47 tff(214,plain,
% 2.25/2.47 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[213, 212])).
% 2.25/2.47 tff(215,plain,(
% 2.25/2.47 ![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))),
% 2.25/2.47 inference(skolemize,[status(sab)],[214])).
% 2.25/2.47 tff(216,plain,
% 2.25/2.47 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[215, 211])).
% 2.25/2.47 tff(217,plain,
% 2.25/2.47 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[216, 209])).
% 2.25/2.47 tff(218,plain,
% 2.25/2.47 ((~![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))) | (~((~((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8))))))) | (~((B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))) | (~(in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), B!7) <=> (in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), singleton(A!8)) | in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), set_difference(B!7, singleton(A!8))))))))))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(219,plain,
% 2.25/2.47 (~((~((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8))))))) | (~((B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))) | (~(in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), B!7) <=> (in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), singleton(A!8)) | in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), set_difference(B!7, singleton(A!8)))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[218, 217])).
% 2.25/2.47 tff(220,plain,
% 2.25/2.47 (((~((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8))))))) | (~((B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))) | (~(in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), B!7) <=> (in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), singleton(A!8)) | in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), set_difference(B!7, singleton(A!8))))))))) | ((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8))))))),
% 2.25/2.47 inference(tautology,[status(thm)],[])).
% 2.25/2.47 tff(221,plain,
% 2.25/2.47 ((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[220, 219])).
% 2.25/2.47 tff(222,plain,
% 2.25/2.47 ((~((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8))))))) | (~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))),
% 2.25/2.47 inference(tautology,[status(thm)],[])).
% 2.25/2.47 tff(223,plain,
% 2.25/2.47 ((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[222, 221])).
% 2.25/2.47 tff(224,plain,
% 2.25/2.47 ($false),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[223, 199, 172])).
% 2.25/2.47 tff(225,plain,(in(A!8, B!7)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.47 tff(226,plain,
% 2.25/2.47 ((subset(singleton(A!8), B!7) <=> in(A!8, B!7)) | (~subset(singleton(A!8), B!7)) | (~in(A!8, B!7))),
% 2.25/2.47 inference(tautology,[status(thm)],[])).
% 2.25/2.47 tff(227,plain,
% 2.25/2.47 ((~subset(singleton(A!8), B!7)) | (~in(A!8, B!7))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[226, 181])).
% 2.25/2.47 tff(228,plain,
% 2.25/2.47 (~subset(singleton(A!8), B!7)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[227, 225])).
% 2.25/2.47 tff(229,plain,
% 2.25/2.47 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(230,plain,
% 2.25/2.47 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[229])).
% 2.25/2.47 tff(231,plain,
% 2.25/2.47 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(232,plain,
% 2.25/2.47 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[231])).
% 2.25/2.47 tff(233,plain,
% 2.25/2.47 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 2.25/2.47 inference(transitivity,[status(thm)],[232, 230])).
% 2.25/2.47 tff(234,plain,
% 2.25/2.47 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))))),
% 2.25/2.48 inference(bind,[status(th)],[])).
% 2.25/2.48 tff(235,plain,
% 2.25/2.48 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 2.25/2.48 inference(quant_intro,[status(thm)],[234])).
% 2.25/2.48 tff(236,plain,
% 2.25/2.48 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(237,plain,
% 2.25/2.48 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 2.25/2.48 inference(bind,[status(th)],[])).
% 2.25/2.48 tff(238,plain,
% 2.25/2.48 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.25/2.48 inference(quant_intro,[status(thm)],[237])).
% 2.25/2.48 tff(239,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 2.25/2.48 tff(240,plain,
% 2.25/2.48 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[239, 238])).
% 2.25/2.48 tff(241,plain,
% 2.25/2.48 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[240, 236])).
% 2.25/2.48 tff(242,plain,(
% 2.25/2.48 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))),
% 2.25/2.48 inference(skolemize,[status(sab)],[241])).
% 2.25/2.48 tff(243,plain,
% 2.25/2.48 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[242, 235])).
% 2.25/2.48 tff(244,plain,
% 2.25/2.48 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[243, 233])).
% 2.25/2.48 tff(245,plain,
% 2.25/2.48 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))) | (~((~((~subset(singleton(A!8), B!7)) | ![C: $i] : ((~in(C, singleton(A!8))) | in(C, B!7)))) | (~(subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)))))))),
% 2.25/2.48 inference(quant_inst,[status(thm)],[])).
% 2.25/2.48 tff(246,plain,
% 2.25/2.48 (~((~((~subset(singleton(A!8), B!7)) | ![C: $i] : ((~in(C, singleton(A!8))) | in(C, B!7)))) | (~(subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7))))))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[245, 244])).
% 2.25/2.48 tff(247,plain,
% 2.25/2.48 (((~((~subset(singleton(A!8), B!7)) | ![C: $i] : ((~in(C, singleton(A!8))) | in(C, B!7)))) | (~(subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)))))) | (subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7))))),
% 2.25/2.48 inference(tautology,[status(thm)],[])).
% 2.25/2.48 tff(248,plain,
% 2.25/2.48 (subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[247, 246])).
% 2.25/2.48 tff(249,plain,
% 2.25/2.48 ((~(subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7))))) | subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)))),
% 2.25/2.49 inference(tautology,[status(thm)],[])).
% 2.25/2.49 tff(250,plain,
% 2.25/2.49 (subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[249, 248])).
% 2.25/2.49 tff(251,plain,
% 2.25/2.49 (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[250, 228])).
% 2.25/2.49 tff(252,plain,
% 2.25/2.49 (((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)) | in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))),
% 2.25/2.49 inference(tautology,[status(thm)],[])).
% 2.25/2.49 tff(253,plain,
% 2.25/2.49 (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[252, 251])).
% 2.25/2.49 tff(254,plain,
% 2.25/2.49 ((~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) | (~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)),
% 2.25/2.49 inference(tautology,[status(thm)],[])).
% 2.25/2.49 tff(255,plain,
% 2.25/2.49 ((~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) | (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[254, 253])).
% 2.25/2.49 tff(256,plain,
% 2.25/2.49 (tptp_fun_C_4(B!7, singleton(A!8)) = A!8),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[255, 46])).
% 2.25/2.49 tff(257,plain,
% 2.25/2.49 (in(tptp_fun_C_4(B!7, singleton(A!8)), B!7) <=> in(A!8, B!7)),
% 2.25/2.49 inference(monotonicity,[status(thm)],[256])).
% 2.25/2.49 tff(258,plain,
% 2.25/2.49 (in(A!8, B!7) <=> in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)),
% 2.25/2.49 inference(symmetry,[status(thm)],[257])).
% 2.25/2.49 tff(259,plain,
% 2.25/2.49 (in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)),
% 2.25/2.49 inference(modus_ponens,[status(thm)],[225, 258])).
% 2.25/2.49 tff(260,plain,
% 2.25/2.49 (((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)) | (~in(tptp_fun_C_4(B!7, singleton(A!8)), B!7))),
% 2.25/2.49 inference(tautology,[status(thm)],[])).
% 2.25/2.49 tff(261,plain,
% 2.25/2.49 (~in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[260, 251])).
% 2.25/2.49 tff(262,plain,
% 2.25/2.49 ($false),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[261, 259])).
% 2.25/2.49 % SZS output end Proof
% 2.35/2.49 % E exiting
%------------------------------------------------------------------------------