%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU145+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 1.07s 1.27s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU145+2 : TPTP v9.0.0. Released v3.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 06:07:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.07/1.27 % SZS status Theorem
% 1.07/1.27 % SZS output start Proof
% 1.07/1.27 tff(in_type, type, (
% 1.07/1.27 in: ( $i * $i ) > $o)).
% 1.07/1.27 tff(tptp_fun_A_9_type, type, (
% 1.07/1.27 tptp_fun_A_9: $i)).
% 1.07/1.27 tff(tptp_fun_C_4_type, type, (
% 1.07/1.27 tptp_fun_C_4: ( $i * $i ) > $i)).
% 1.07/1.27 tff(set_difference_type, type, (
% 1.07/1.27 set_difference: ( $i * $i ) > $i)).
% 1.07/1.27 tff(singleton_type, type, (
% 1.07/1.27 singleton: $i > $i)).
% 1.07/1.27 tff(tptp_fun_C_7_type, type, (
% 1.07/1.27 tptp_fun_C_7: $i)).
% 1.07/1.27 tff(tptp_fun_B_8_type, type, (
% 1.07/1.27 tptp_fun_B_8: $i)).
% 1.07/1.27 tff(tptp_fun_C_0_type, type, (
% 1.07/1.27 tptp_fun_C_0: ( $i * $i ) > $i)).
% 1.07/1.27 tff(set_union2_type, type, (
% 1.07/1.27 set_union2: ( $i * $i ) > $i)).
% 1.07/1.27 tff(tptp_fun_D_6_type, type, (
% 1.07/1.27 tptp_fun_D_6: ( $i * $i * $i ) > $i)).
% 1.07/1.27 tff(subset_type, type, (
% 1.07/1.27 subset: ( $i * $i ) > $o)).
% 1.07/1.27 tff(1,plain,
% 1.07/1.27 (^[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))))))))),
% 1.07/1.27 inference(bind,[status(th)],[])).
% 1.07/1.27 tff(2,plain,
% 1.07/1.27 (![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)))))))),
% 1.07/1.27 inference(quant_intro,[status(thm)],[1])).
% 1.07/1.27 tff(3,plain,
% 1.07/1.27 (![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)))))))),
% 1.07/1.27 inference(pull_quant,[status(thm)],[])).
% 1.07/1.27 tff(4,plain,
% 1.07/1.27 (^[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)))))))))),
% 1.07/1.27 inference(bind,[status(th)],[])).
% 1.07/1.27 tff(5,plain,
% 1.07/1.27 (![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)))))))),
% 1.07/1.27 inference(quant_intro,[status(thm)],[4])).
% 1.07/1.27 tff(6,plain,
% 1.07/1.27 (![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)))))))),
% 1.07/1.27 inference(transitivity,[status(thm)],[5, 3])).
% 1.07/1.27 tff(7,plain,
% 1.07/1.27 (![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)))))))),
% 1.07/1.27 inference(transitivity,[status(thm)],[6, 2])).
% 1.07/1.27 tff(8,plain,
% 1.07/1.27 (^[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))))))))),
% 1.07/1.27 inference(bind,[status(th)],[])).
% 1.07/1.27 tff(9,plain,
% 1.07/1.27 (![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)))))))),
% 1.07/1.27 inference(quant_intro,[status(thm)],[8])).
% 1.07/1.27 tff(10,plain,
% 1.07/1.27 (![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)))))))),
% 1.07/1.27 inference(transitivity,[status(thm)],[9, 7])).
% 1.07/1.27 tff(11,plain,
% 1.07/1.27 (^[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)))))))))),
% 1.07/1.27 inference(bind,[status(th)],[])).
% 1.07/1.27 tff(12,plain,
% 1.07/1.27 (![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)))))))),
% 1.07/1.27 inference(quant_intro,[status(thm)],[11])).
% 1.07/1.27 tff(13,plain,
% 1.07/1.27 (![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)))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 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')).
% 1.07/1.27 tff(15,plain,
% 1.07/1.27 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.07/1.27 tff(16,plain,(
% 1.07/1.27 ![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)))))),
% 1.07/1.27 inference(skolemize,[status(sab)],[15])).
% 1.07/1.27 tff(17,plain,
% 1.07/1.27 (![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)))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.07/1.27 tff(18,plain,
% 1.07/1.27 (![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)))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[17, 10])).
% 1.07/1.27 tff(19,plain,
% 1.07/1.27 (((~![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(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(20,plain,
% 1.07/1.27 ((~(~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))) <=> (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(21,plain,
% 1.07/1.27 (((~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))) | $false) <=> (~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(22,plain,
% 1.07/1.27 ((~$true) <=> $false),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(23,plain,
% 1.07/1.27 (($true | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7)))) <=> $true),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(24,plain,
% 1.07/1.27 ((~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7))) <=> (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7)))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(25,plain,
% 1.07/1.28 ((singleton(C!7) = singleton(C!7)) <=> $true),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(26,plain,
% 1.07/1.28 (((singleton(C!7) = singleton(C!7)) | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7))))),
% 1.07/1.28 inference(monotonicity,[status(thm)],[25, 24])).
% 1.07/1.28 tff(27,plain,
% 1.07/1.28 (((singleton(C!7) = singleton(C!7)) | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7)))) <=> $true),
% 1.07/1.28 inference(transitivity,[status(thm)],[26, 23])).
% 1.07/1.28 tff(28,plain,
% 1.07/1.28 ((~((singleton(C!7) = singleton(C!7)) | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7))))) <=> (~$true)),
% 1.07/1.28 inference(monotonicity,[status(thm)],[27])).
% 1.07/1.28 tff(29,plain,
% 1.07/1.28 ((~((singleton(C!7) = singleton(C!7)) | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7))))) <=> $false),
% 1.07/1.28 inference(transitivity,[status(thm)],[28, 22])).
% 1.07/1.28 tff(30,plain,
% 1.07/1.28 ((~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))) <=> (~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(31,plain,
% 1.07/1.28 (($false | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))) <=> (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(32,plain,
% 1.07/1.28 ((~(singleton(C!7) = singleton(C!7))) <=> (~$true)),
% 1.07/1.28 inference(monotonicity,[status(thm)],[25])).
% 1.07/1.28 tff(33,plain,
% 1.07/1.28 ((~(singleton(C!7) = singleton(C!7))) <=> $false),
% 1.07/1.28 inference(transitivity,[status(thm)],[32, 22])).
% 1.07/1.28 tff(34,plain,
% 1.07/1.28 (((~(singleton(C!7) = singleton(C!7))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))) <=> ($false | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))),
% 1.07/1.28 inference(monotonicity,[status(thm)],[33])).
% 1.07/1.28 tff(35,plain,
% 1.07/1.28 (((~(singleton(C!7) = singleton(C!7))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))) <=> (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))),
% 1.07/1.28 inference(transitivity,[status(thm)],[34, 31])).
% 1.07/1.28 tff(36,plain,
% 1.07/1.28 ((~((~(singleton(C!7) = singleton(C!7))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))) <=> (~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))),
% 1.07/1.28 inference(monotonicity,[status(thm)],[35])).
% 1.07/1.28 tff(37,plain,
% 1.07/1.28 ((~((~(singleton(C!7) = singleton(C!7))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))) <=> (~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))),
% 1.07/1.28 inference(transitivity,[status(thm)],[36, 30])).
% 1.07/1.28 tff(38,plain,
% 1.07/1.28 (((~((~(singleton(C!7) = singleton(C!7))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))) | (~((singleton(C!7) = singleton(C!7)) | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7)))))) <=> ((~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))) | $false)),
% 1.07/1.28 inference(monotonicity,[status(thm)],[37, 29])).
% 1.07/1.28 tff(39,plain,
% 1.07/1.28 (((~((~(singleton(C!7) = singleton(C!7))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))) | (~((singleton(C!7) = singleton(C!7)) | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7)))))) <=> (~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))),
% 1.07/1.28 inference(transitivity,[status(thm)],[38, 21])).
% 1.07/1.28 tff(40,plain,
% 1.07/1.28 ((~((~((~(singleton(C!7) = singleton(C!7))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))) | (~((singleton(C!7) = singleton(C!7)) | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7))))))) <=> (~(~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))))),
% 1.07/1.28 inference(monotonicity,[status(thm)],[39])).
% 1.07/1.28 tff(41,plain,
% 1.07/1.28 ((~((~((~(singleton(C!7) = singleton(C!7))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))) | (~((singleton(C!7) = singleton(C!7)) | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7))))))) <=> (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))),
% 1.07/1.28 inference(transitivity,[status(thm)],[40, 20])).
% 1.07/1.28 tff(42,plain,
% 1.07/1.28 (((~![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(C!7) = singleton(C!7))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))) | (~((singleton(C!7) = singleton(C!7)) | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))),
% 1.07/1.28 inference(monotonicity,[status(thm)],[41])).
% 1.07/1.28 tff(43,plain,
% 1.07/1.28 (((~![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(C!7) = singleton(C!7))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))) | (~((singleton(C!7) = singleton(C!7)) | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))),
% 1.07/1.28 inference(transitivity,[status(thm)],[42, 19])).
% 1.07/1.28 tff(44,plain,
% 1.07/1.28 ((~![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(C!7) = singleton(C!7))) | (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)))) | (~((singleton(C!7) = singleton(C!7)) | (~(in(tptp_fun_C_0(singleton(C!7), C!7), singleton(C!7)) <=> (tptp_fun_C_0(singleton(C!7), C!7) = C!7)))))))),
% 1.07/1.28 inference(quant_inst,[status(thm)],[])).
% 1.07/1.28 tff(45,plain,
% 1.07/1.28 ((~![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(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.07/1.28 tff(46,plain,
% 1.07/1.28 (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)),
% 1.07/1.28 inference(unit_resolution,[status(thm)],[45, 18])).
% 1.07/1.28 tff(47,plain,
% 1.07/1.28 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))))),
% 1.07/1.28 inference(bind,[status(th)],[])).
% 1.07/1.28 tff(48,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))),
% 1.07/1.28 inference(quant_intro,[status(thm)],[47])).
% 1.07/1.28 tff(49,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))),
% 1.07/1.28 inference(pull_quant,[status(thm)],[])).
% 1.07/1.28 tff(50,plain,
% 1.07/1.28 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))))),
% 1.07/1.28 inference(bind,[status(th)],[])).
% 1.07/1.28 tff(51,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))),
% 1.07/1.28 inference(quant_intro,[status(thm)],[50])).
% 1.07/1.28 tff(52,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))),
% 1.07/1.28 inference(transitivity,[status(thm)],[51, 49])).
% 1.07/1.28 tff(53,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))),
% 1.07/1.28 inference(transitivity,[status(thm)],[52, 48])).
% 1.07/1.28 tff(54,plain,
% 1.07/1.28 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))))),
% 1.07/1.28 inference(bind,[status(th)],[])).
% 1.07/1.28 tff(55,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))),
% 1.07/1.28 inference(quant_intro,[status(thm)],[54])).
% 1.07/1.28 tff(56,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))),
% 1.07/1.28 inference(transitivity,[status(thm)],[55, 53])).
% 1.07/1.28 tff(57,plain,
% 1.07/1.28 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), rewrite(((C = set_difference(A, B)) | (~(in(tptp_fun_D_6(C, B, A), C) <=> (in(tptp_fun_D_6(C, B, A), A) & (~in(tptp_fun_D_6(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_6(C, B, A), C) <=> (in(tptp_fun_D_6(C, B, A), A) & (~in(tptp_fun_D_6(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C)))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_6(C, B, A), C) <=> (in(tptp_fun_D_6(C, B, A), A) & (~in(tptp_fun_D_6(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))))),
% 1.07/1.28 inference(bind,[status(th)],[])).
% 1.07/1.28 tff(58,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_6(C, B, A), C) <=> (in(tptp_fun_D_6(C, B, A), A) & (~in(tptp_fun_D_6(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))),
% 1.07/1.28 inference(quant_intro,[status(thm)],[57])).
% 1.07/1.28 tff(59,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(60,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_xboole_0')).
% 1.07/1.28 tff(61,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.07/1.28 tff(62,plain,(
% 1.07/1.28 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_6(C, B, A), C) <=> (in(tptp_fun_D_6(C, B, A), A) & (~in(tptp_fun_D_6(C, B, A), B)))))))),
% 1.07/1.28 inference(skolemize,[status(sab)],[61])).
% 1.07/1.28 tff(63,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[62, 58])).
% 1.07/1.28 tff(64,plain,
% 1.07/1.28 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[63, 56])).
% 1.07/1.28 tff(65,plain,
% 1.07/1.28 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_6(C, B, A), A)) | in(tptp_fun_D_6(C, B, A), B)) <=> in(tptp_fun_D_6(C, B, A), C))))))) | (~((~((~(set_difference(B!8, singleton(C!7)) = set_difference(set_union2(A!9, set_difference(B!8, A!9)), singleton(C!7)))) | (~(((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))))) | (~((set_difference(B!8, singleton(C!7)) = set_difference(set_union2(A!9, set_difference(B!8, A!9)), singleton(C!7))) | (((~in(tptp_fun_D_6(set_difference(B!8, singleton(C!7)), singleton(C!7), set_union2(A!9, set_difference(B!8, A!9))), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_D_6(set_difference(B!8, singleton(C!7)), singleton(C!7), set_union2(A!9, set_difference(B!8, A!9))), singleton(C!7))) <=> in(tptp_fun_D_6(set_difference(B!8, singleton(C!7)), singleton(C!7), set_union2(A!9, set_difference(B!8, A!9))), set_difference(B!8, singleton(C!7))))))))),
% 1.07/1.28 inference(quant_inst,[status(thm)],[])).
% 1.07/1.28 tff(66,plain,
% 1.07/1.28 (~((~((~(set_difference(B!8, singleton(C!7)) = set_difference(set_union2(A!9, set_difference(B!8, A!9)), singleton(C!7)))) | (~(((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))))) | (~((set_difference(B!8, singleton(C!7)) = set_difference(set_union2(A!9, set_difference(B!8, A!9)), singleton(C!7))) | (((~in(tptp_fun_D_6(set_difference(B!8, singleton(C!7)), singleton(C!7), set_union2(A!9, set_difference(B!8, A!9))), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_D_6(set_difference(B!8, singleton(C!7)), singleton(C!7), set_union2(A!9, set_difference(B!8, A!9))), singleton(C!7))) <=> in(tptp_fun_D_6(set_difference(B!8, singleton(C!7)), singleton(C!7), set_union2(A!9, set_difference(B!8, A!9))), set_difference(B!8, singleton(C!7)))))))),
% 1.07/1.28 inference(unit_resolution,[status(thm)],[65, 64])).
% 1.07/1.28 tff(67,plain,
% 1.07/1.28 (((~((~(set_difference(B!8, singleton(C!7)) = set_difference(set_union2(A!9, set_difference(B!8, A!9)), singleton(C!7)))) | (~(((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))))) | (~((set_difference(B!8, singleton(C!7)) = set_difference(set_union2(A!9, set_difference(B!8, A!9)), singleton(C!7))) | (((~in(tptp_fun_D_6(set_difference(B!8, singleton(C!7)), singleton(C!7), set_union2(A!9, set_difference(B!8, A!9))), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_D_6(set_difference(B!8, singleton(C!7)), singleton(C!7), set_union2(A!9, set_difference(B!8, A!9))), singleton(C!7))) <=> in(tptp_fun_D_6(set_difference(B!8, singleton(C!7)), singleton(C!7), set_union2(A!9, set_difference(B!8, A!9))), set_difference(B!8, singleton(C!7))))))) | ((~(set_difference(B!8, singleton(C!7)) = set_difference(set_union2(A!9, set_difference(B!8, A!9)), singleton(C!7)))) | (~(((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))))),
% 1.07/1.28 inference(tautology,[status(thm)],[])).
% 1.07/1.28 tff(68,plain,
% 1.07/1.28 ((~(set_difference(B!8, singleton(C!7)) = set_difference(set_union2(A!9, set_difference(B!8, A!9)), singleton(C!7)))) | (~(((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))))),
% 1.07/1.28 inference(unit_resolution,[status(thm)],[67, 66])).
% 1.07/1.28 tff(69,plain,
% 1.07/1.28 (^[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)))))),
% 1.07/1.28 inference(bind,[status(th)],[])).
% 1.07/1.28 tff(70,plain,
% 1.07/1.28 (![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))))),
% 1.07/1.28 inference(quant_intro,[status(thm)],[69])).
% 1.07/1.28 tff(71,plain,
% 1.07/1.28 (![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))))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(72,plain,
% 1.07/1.28 (^[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)))))),
% 1.07/1.28 inference(bind,[status(th)],[])).
% 1.07/1.28 tff(73,plain,
% 1.07/1.28 (![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))))),
% 1.07/1.28 inference(quant_intro,[status(thm)],[72])).
% 1.07/1.28 tff(74,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')).
% 1.07/1.28 tff(75,plain,
% 1.07/1.28 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.07/1.28 tff(76,plain,
% 1.07/1.28 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[75, 71])).
% 1.07/1.28 tff(77,plain,(
% 1.07/1.28 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 1.07/1.28 inference(skolemize,[status(sab)],[76])).
% 1.07/1.28 tff(78,plain,
% 1.07/1.28 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[77, 70])).
% 1.07/1.28 tff(79,plain,
% 1.07/1.28 ((~(in(C!7, A!9) | subset(A!9, set_difference(B!8, singleton(C!7))) | (~subset(A!9, B!8)))) <=> (~(in(C!7, A!9) | subset(A!9, set_difference(B!8, singleton(C!7))) | (~subset(A!9, B!8))))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(80,plain,
% 1.07/1.28 ((~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))) <=> (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B))))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(81,plain,
% 1.07/1.28 ((~![A: $i, B: $i, C: $i] : (subset(A, B) => (in(C, A) | subset(A, set_difference(B, singleton(C)))))) <=> (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B))))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(82,axiom,(~![A: $i, B: $i, C: $i] : (subset(A, B) => (in(C, A) | subset(A, set_difference(B, singleton(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l3_zfmisc_1')).
% 1.07/1.28 tff(83,plain,
% 1.07/1.28 (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.07/1.28 tff(84,plain,
% 1.07/1.28 (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[83, 80])).
% 1.07/1.28 tff(85,plain,
% 1.07/1.28 (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[84, 80])).
% 1.07/1.28 tff(86,plain,
% 1.07/1.28 (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[85, 80])).
% 1.07/1.28 tff(87,plain,(
% 1.07/1.28 ~(in(C!7, A!9) | subset(A!9, set_difference(B!8, singleton(C!7))) | (~subset(A!9, B!8)))),
% 1.07/1.28 inference(skolemize,[status(sab)],[86])).
% 1.07/1.28 tff(88,plain,
% 1.07/1.28 (~(in(C!7, A!9) | subset(A!9, set_difference(B!8, singleton(C!7))) | (~subset(A!9, B!8)))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[87, 79])).
% 1.07/1.28 tff(89,plain,
% 1.07/1.28 (subset(A!9, B!8)),
% 1.07/1.28 inference(or_elim,[status(thm)],[88])).
% 1.07/1.28 tff(90,plain,
% 1.07/1.28 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(A!9, B!8)) | (B!8 = set_union2(A!9, set_difference(B!8, A!9))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(A!9, B!8)) | (B!8 = set_union2(A!9, set_difference(B!8, A!9))))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(91,plain,
% 1.07/1.28 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(A!9, B!8)) | (B!8 = set_union2(A!9, set_difference(B!8, A!9))))),
% 1.07/1.28 inference(quant_inst,[status(thm)],[])).
% 1.07/1.28 tff(92,plain,
% 1.07/1.28 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(A!9, B!8)) | (B!8 = set_union2(A!9, set_difference(B!8, A!9)))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.07/1.28 tff(93,plain,
% 1.07/1.28 (B!8 = set_union2(A!9, set_difference(B!8, A!9))),
% 1.07/1.28 inference(unit_resolution,[status(thm)],[92, 89, 78])).
% 1.07/1.28 tff(94,plain,
% 1.07/1.28 (set_difference(B!8, singleton(C!7)) = set_difference(set_union2(A!9, set_difference(B!8, A!9)), singleton(C!7))),
% 1.07/1.28 inference(monotonicity,[status(thm)],[93])).
% 1.07/1.28 tff(95,plain,
% 1.07/1.28 ((~((~(set_difference(B!8, singleton(C!7)) = set_difference(set_union2(A!9, set_difference(B!8, A!9)), singleton(C!7)))) | (~(((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))))) | (~(set_difference(B!8, singleton(C!7)) = set_difference(set_union2(A!9, set_difference(B!8, A!9)), singleton(C!7)))) | (~(((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))))),
% 1.07/1.28 inference(tautology,[status(thm)],[])).
% 1.07/1.28 tff(96,plain,
% 1.07/1.28 (~(((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))),
% 1.07/1.28 inference(unit_resolution,[status(thm)],[95, 94, 68])).
% 1.07/1.28 tff(97,plain,
% 1.07/1.28 (^[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))))))))),
% 1.07/1.28 inference(bind,[status(th)],[])).
% 1.07/1.28 tff(98,plain,
% 1.07/1.28 (![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)))))))),
% 1.07/1.28 inference(quant_intro,[status(thm)],[97])).
% 1.07/1.28 tff(99,plain,
% 1.07/1.28 (^[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))))))))),
% 1.07/1.28 inference(bind,[status(th)],[])).
% 1.07/1.28 tff(100,plain,
% 1.07/1.28 (![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)))))))),
% 1.07/1.28 inference(quant_intro,[status(thm)],[99])).
% 1.07/1.28 tff(101,plain,
% 1.07/1.28 (![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)))))))),
% 1.07/1.28 inference(transitivity,[status(thm)],[100, 98])).
% 1.07/1.28 tff(102,plain,
% 1.07/1.28 (^[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)))))))))),
% 1.07/1.28 inference(bind,[status(th)],[])).
% 1.07/1.28 tff(103,plain,
% 1.07/1.28 (![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)))))))),
% 1.07/1.28 inference(quant_intro,[status(thm)],[102])).
% 1.07/1.28 tff(104,plain,
% 1.07/1.28 (![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)))),
% 1.07/1.28 inference(rewrite,[status(thm)],[])).
% 1.07/1.28 tff(105,plain,
% 1.07/1.28 (^[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))))),
% 1.07/1.28 inference(bind,[status(th)],[])).
% 1.07/1.28 tff(106,plain,
% 1.07/1.28 (![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)))),
% 1.07/1.28 inference(quant_intro,[status(thm)],[105])).
% 1.07/1.28 tff(107,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')).
% 1.07/1.28 tff(108,plain,
% 1.07/1.28 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.07/1.28 tff(109,plain,
% 1.07/1.28 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[108, 104])).
% 1.07/1.28 tff(110,plain,(
% 1.07/1.28 ![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)))))),
% 1.07/1.28 inference(skolemize,[status(sab)],[109])).
% 1.07/1.28 tff(111,plain,
% 1.07/1.28 (![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)))))))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[110, 103])).
% 1.07/1.28 tff(112,plain,
% 1.07/1.28 (![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)))))))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[111, 101])).
% 1.07/1.28 tff(113,plain,
% 1.07/1.28 ((~![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(A!9, set_difference(B!8, singleton(C!7)))) | ![C: $i] : ((~in(C, A!9)) | in(C, set_difference(B!8, singleton(C!7)))))) | (~(subset(A!9, set_difference(B!8, singleton(C!7))) | (~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))))))))),
% 1.07/1.28 inference(quant_inst,[status(thm)],[])).
% 1.07/1.28 tff(114,plain,
% 1.07/1.28 (~((~((~subset(A!9, set_difference(B!8, singleton(C!7)))) | ![C: $i] : ((~in(C, A!9)) | in(C, set_difference(B!8, singleton(C!7)))))) | (~(subset(A!9, set_difference(B!8, singleton(C!7))) | (~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))))))),
% 1.07/1.28 inference(unit_resolution,[status(thm)],[113, 112])).
% 1.07/1.28 tff(115,plain,
% 1.07/1.28 (((~((~subset(A!9, set_difference(B!8, singleton(C!7)))) | ![C: $i] : ((~in(C, A!9)) | in(C, set_difference(B!8, singleton(C!7)))))) | (~(subset(A!9, set_difference(B!8, singleton(C!7))) | (~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))))))) | (subset(A!9, set_difference(B!8, singleton(C!7))) | (~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))))),
% 1.07/1.28 inference(tautology,[status(thm)],[])).
% 1.07/1.28 tff(116,plain,
% 1.07/1.28 (subset(A!9, set_difference(B!8, singleton(C!7))) | (~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))))),
% 1.07/1.28 inference(unit_resolution,[status(thm)],[115, 114])).
% 1.07/1.28 tff(117,plain,
% 1.07/1.28 (~subset(A!9, set_difference(B!8, singleton(C!7)))),
% 1.07/1.28 inference(or_elim,[status(thm)],[88])).
% 1.07/1.28 tff(118,plain,
% 1.07/1.28 ((~(subset(A!9, set_difference(B!8, singleton(C!7))) | (~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))))) | subset(A!9, set_difference(B!8, singleton(C!7))) | (~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))))),
% 1.07/1.29 inference(tautology,[status(thm)],[])).
% 1.07/1.29 tff(119,plain,
% 1.07/1.29 ((~(subset(A!9, set_difference(B!8, singleton(C!7))) | (~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))))) | (~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[118, 117])).
% 1.07/1.29 tff(120,plain,
% 1.07/1.29 (~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[119, 116])).
% 1.07/1.29 tff(121,plain,
% 1.07/1.29 (((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))) | (~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7))))),
% 1.07/1.29 inference(tautology,[status(thm)],[])).
% 1.07/1.29 tff(122,plain,
% 1.07/1.29 (~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[121, 120])).
% 1.07/1.29 tff(123,plain,
% 1.07/1.29 ((((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))) | ((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))),
% 1.07/1.29 inference(tautology,[status(thm)],[])).
% 1.07/1.29 tff(124,plain,
% 1.07/1.29 ((((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))) | ((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[123, 122])).
% 1.07/1.29 tff(125,plain,
% 1.07/1.29 ((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[124, 96])).
% 1.07/1.29 tff(126,plain,
% 1.07/1.29 (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), B!8) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))),
% 1.07/1.29 inference(monotonicity,[status(thm)],[93])).
% 1.07/1.29 tff(127,plain,
% 1.07/1.29 ((~![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(A!9, B!8)) | ![C: $i] : ((~in(C, A!9)) | in(C, B!8)))) | (~(subset(A!9, B!8) | (~((~in(tptp_fun_C_4(B!8, A!9), A!9)) | in(tptp_fun_C_4(B!8, A!9), B!8)))))))),
% 1.07/1.29 inference(quant_inst,[status(thm)],[])).
% 1.07/1.29 tff(128,plain,
% 1.07/1.29 (~((~((~subset(A!9, B!8)) | ![C: $i] : ((~in(C, A!9)) | in(C, B!8)))) | (~(subset(A!9, B!8) | (~((~in(tptp_fun_C_4(B!8, A!9), A!9)) | in(tptp_fun_C_4(B!8, A!9), B!8))))))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[127, 112])).
% 1.07/1.29 tff(129,plain,
% 1.07/1.29 (((~((~subset(A!9, B!8)) | ![C: $i] : ((~in(C, A!9)) | in(C, B!8)))) | (~(subset(A!9, B!8) | (~((~in(tptp_fun_C_4(B!8, A!9), A!9)) | in(tptp_fun_C_4(B!8, A!9), B!8)))))) | ((~subset(A!9, B!8)) | ![C: $i] : ((~in(C, A!9)) | in(C, B!8)))),
% 1.07/1.29 inference(tautology,[status(thm)],[])).
% 1.07/1.29 tff(130,plain,
% 1.07/1.29 ((~subset(A!9, B!8)) | ![C: $i] : ((~in(C, A!9)) | in(C, B!8))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[129, 128])).
% 1.07/1.29 tff(131,plain,
% 1.07/1.29 ((~((~subset(A!9, B!8)) | ![C: $i] : ((~in(C, A!9)) | in(C, B!8)))) | (~subset(A!9, B!8)) | ![C: $i] : ((~in(C, A!9)) | in(C, B!8))),
% 1.07/1.29 inference(tautology,[status(thm)],[])).
% 1.07/1.29 tff(132,plain,
% 1.07/1.29 ((~((~subset(A!9, B!8)) | ![C: $i] : ((~in(C, A!9)) | in(C, B!8)))) | ![C: $i] : ((~in(C, A!9)) | in(C, B!8))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[131, 89])).
% 1.07/1.29 tff(133,plain,
% 1.07/1.29 (![C: $i] : ((~in(C, A!9)) | in(C, B!8))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[132, 130])).
% 1.07/1.29 tff(134,plain,
% 1.07/1.29 (((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_difference(B!8, singleton(C!7)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)),
% 1.07/1.29 inference(tautology,[status(thm)],[])).
% 1.07/1.29 tff(135,plain,
% 1.07/1.29 (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[134, 120])).
% 1.07/1.29 tff(136,plain,
% 1.07/1.29 (((~![C: $i] : ((~in(C, A!9)) | in(C, B!8))) | ((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), B!8))) <=> ((~![C: $i] : ((~in(C, A!9)) | in(C, B!8))) | (~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), B!8))),
% 1.07/1.29 inference(rewrite,[status(thm)],[])).
% 1.07/1.29 tff(137,plain,
% 1.07/1.29 ((~![C: $i] : ((~in(C, A!9)) | in(C, B!8))) | ((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), B!8))),
% 1.07/1.29 inference(quant_inst,[status(thm)],[])).
% 1.07/1.29 tff(138,plain,
% 1.07/1.29 ((~![C: $i] : ((~in(C, A!9)) | in(C, B!8))) | (~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), B!8)),
% 1.07/1.29 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.07/1.29 tff(139,plain,
% 1.07/1.29 (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), B!8)),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[138, 135, 133])).
% 1.07/1.29 tff(140,plain,
% 1.07/1.29 (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))),
% 1.07/1.29 inference(modus_ponens,[status(thm)],[139, 126])).
% 1.07/1.29 tff(141,plain,
% 1.07/1.29 ((~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)))) | (~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))),
% 1.07/1.29 inference(tautology,[status(thm)],[])).
% 1.07/1.29 tff(142,plain,
% 1.07/1.29 ((~((~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), set_union2(A!9, set_difference(B!8, A!9)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)))) | in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[141, 140])).
% 1.07/1.29 tff(143,plain,
% 1.07/1.29 (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[142, 125])).
% 1.07/1.29 tff(144,plain,
% 1.07/1.29 ((~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))) | (~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7))) | (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)),
% 1.07/1.29 inference(tautology,[status(thm)],[])).
% 1.07/1.29 tff(145,plain,
% 1.07/1.29 ((~(in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), singleton(C!7)) <=> (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7))) | (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7)),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[144, 143])).
% 1.07/1.29 tff(146,plain,
% 1.07/1.29 (tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9) = C!7),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[145, 46])).
% 1.07/1.29 tff(147,plain,
% 1.07/1.29 (in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9) <=> in(C!7, A!9)),
% 1.07/1.29 inference(monotonicity,[status(thm)],[146])).
% 1.07/1.29 tff(148,plain,
% 1.07/1.29 (in(C!7, A!9) <=> in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)),
% 1.07/1.29 inference(symmetry,[status(thm)],[147])).
% 1.07/1.29 tff(149,plain,
% 1.07/1.29 ((~in(C!7, A!9)) <=> (~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9))),
% 1.07/1.29 inference(monotonicity,[status(thm)],[148])).
% 1.07/1.29 tff(150,plain,
% 1.07/1.29 (~in(C!7, A!9)),
% 1.07/1.29 inference(or_elim,[status(thm)],[88])).
% 1.07/1.29 tff(151,plain,
% 1.07/1.29 (~in(tptp_fun_C_4(set_difference(B!8, singleton(C!7)), A!9), A!9)),
% 1.07/1.29 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.07/1.29 tff(152,plain,
% 1.07/1.29 ($false),
% 1.07/1.29 inference(unit_resolution,[status(thm)],[135, 151])).
% 1.07/1.29 % SZS output end Proof
% 1.07/1.30 % E exiting
%------------------------------------------------------------------------------