%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET918+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:39 AM UTC 2025
% Result : Theorem 0.59s 0.77s
% Output : Proof 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : SET918+1 : TPTP v9.0.0. Released v3.2.0.
% 0.14/0.15 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n015.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 05:50:56 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.59/0.77 % SZS status Theorem
% 0.59/0.77 % SZS output start Proof
% 0.59/0.77 tff(tptp_fun_A_7_type, type, (
% 0.59/0.77 tptp_fun_A_7: $i)).
% 0.59/0.77 tff(tptp_fun_B_6_type, type, (
% 0.59/0.77 tptp_fun_B_6: $i)).
% 0.59/0.77 tff(in_type, type, (
% 0.59/0.77 in: ( $i * $i ) > $o)).
% 0.59/0.77 tff(singleton_type, type, (
% 0.59/0.77 singleton: $i > $i)).
% 0.59/0.77 tff(tptp_fun_C_0_type, type, (
% 0.59/0.77 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.59/0.77 tff(unordered_pair_type, type, (
% 0.59/0.77 unordered_pair: ( $i * $i ) > $i)).
% 0.59/0.77 tff(tptp_fun_C_5_type, type, (
% 0.59/0.77 tptp_fun_C_5: $i)).
% 0.59/0.77 tff(set_intersection2_type, type, (
% 0.59/0.77 set_intersection2: ( $i * $i ) > $i)).
% 0.59/0.77 tff(tptp_fun_D_2_type, type, (
% 0.59/0.77 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.59/0.77 tff(tptp_fun_D_1_type, type, (
% 0.59/0.77 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.59/0.77 tff(1,assumption,(~(in(B!6, singleton(A!7)) <=> (B!6 = A!7))), introduced(assumption)).
% 0.59/0.77 tff(2,plain,
% 0.59/0.77 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(3,plain,
% 0.59/0.77 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[2])).
% 0.59/0.77 tff(4,plain,
% 0.59/0.77 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.59/0.77 inference(pull_quant,[status(thm)],[])).
% 0.59/0.77 tff(5,plain,
% 0.59/0.77 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(6,plain,
% 0.59/0.78 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[5])).
% 0.59/0.78 tff(7,plain,
% 0.59/0.78 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.59/0.78 inference(transitivity,[status(thm)],[6, 4])).
% 0.59/0.78 tff(8,plain,
% 0.59/0.78 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.59/0.78 inference(transitivity,[status(thm)],[7, 3])).
% 0.59/0.78 tff(9,plain,
% 0.59/0.78 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(10,plain,
% 0.59/0.78 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[9])).
% 0.59/0.78 tff(11,plain,
% 0.59/0.78 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.59/0.78 inference(transitivity,[status(thm)],[10, 8])).
% 0.59/0.78 tff(12,plain,
% 0.59/0.78 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite(((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(13,plain,
% 0.59/0.78 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[12])).
% 0.59/0.78 tff(14,plain,
% 0.59/0.78 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(15,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.59/0.78 tff(16,plain,
% 0.59/0.78 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.59/0.78 tff(17,plain,(
% 0.59/0.78 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.59/0.78 inference(skolemize,[status(sab)],[16])).
% 0.59/0.78 tff(18,plain,
% 0.59/0.78 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.59/0.78 tff(19,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.59/0.78 tff(20,plain,
% 0.59/0.78 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(21,plain,
% 0.59/0.78 ((~(~(in(B!6, singleton(A!7)) <=> (B!6 = A!7)))) <=> (in(B!6, singleton(A!7)) <=> (B!6 = A!7))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(22,plain,
% 0.59/0.78 (((~(in(B!6, singleton(A!7)) <=> (B!6 = A!7))) | $false) <=> (~(in(B!6, singleton(A!7)) <=> (B!6 = A!7)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(23,plain,
% 0.59/0.78 ((~$true) <=> $false),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(24,plain,
% 0.59/0.78 (($true | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> $true),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(25,plain,
% 0.59/0.78 ((~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(26,plain,
% 0.59/0.78 ((singleton(A!7) = singleton(A!7)) <=> $true),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(27,plain,
% 0.59/0.78 (((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[26, 25])).
% 0.59/0.78 tff(28,plain,
% 0.59/0.78 (((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> $true),
% 0.59/0.78 inference(transitivity,[status(thm)],[27, 24])).
% 0.59/0.78 tff(29,plain,
% 0.59/0.78 ((~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> (~$true)),
% 0.59/0.78 inference(monotonicity,[status(thm)],[28])).
% 0.59/0.78 tff(30,plain,
% 0.59/0.78 ((~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> $false),
% 0.59/0.78 inference(transitivity,[status(thm)],[29, 23])).
% 0.59/0.78 tff(31,plain,
% 0.59/0.78 ((~(in(B!6, singleton(A!7)) <=> (B!6 = A!7))) <=> (~(in(B!6, singleton(A!7)) <=> (B!6 = A!7)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(32,plain,
% 0.59/0.78 (($false | (in(B!6, singleton(A!7)) <=> (B!6 = A!7))) <=> (in(B!6, singleton(A!7)) <=> (B!6 = A!7))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(33,plain,
% 0.59/0.78 ((~(singleton(A!7) = singleton(A!7))) <=> (~$true)),
% 0.59/0.78 inference(monotonicity,[status(thm)],[26])).
% 0.59/0.78 tff(34,plain,
% 0.59/0.78 ((~(singleton(A!7) = singleton(A!7))) <=> $false),
% 0.59/0.78 inference(transitivity,[status(thm)],[33, 23])).
% 0.59/0.78 tff(35,plain,
% 0.59/0.78 (((~(singleton(A!7) = singleton(A!7))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7))) <=> ($false | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[34])).
% 0.59/0.78 tff(36,plain,
% 0.59/0.78 (((~(singleton(A!7) = singleton(A!7))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7))) <=> (in(B!6, singleton(A!7)) <=> (B!6 = A!7))),
% 0.59/0.78 inference(transitivity,[status(thm)],[35, 32])).
% 0.59/0.78 tff(37,plain,
% 0.59/0.78 ((~((~(singleton(A!7) = singleton(A!7))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))) <=> (~(in(B!6, singleton(A!7)) <=> (B!6 = A!7)))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[36])).
% 0.59/0.78 tff(38,plain,
% 0.59/0.78 ((~((~(singleton(A!7) = singleton(A!7))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))) <=> (~(in(B!6, singleton(A!7)) <=> (B!6 = A!7)))),
% 0.59/0.78 inference(transitivity,[status(thm)],[37, 31])).
% 0.59/0.78 tff(39,plain,
% 0.59/0.78 (((~((~(singleton(A!7) = singleton(A!7))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> ((~(in(B!6, singleton(A!7)) <=> (B!6 = A!7))) | $false)),
% 0.59/0.78 inference(monotonicity,[status(thm)],[38, 30])).
% 0.59/0.78 tff(40,plain,
% 0.59/0.78 (((~((~(singleton(A!7) = singleton(A!7))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> (~(in(B!6, singleton(A!7)) <=> (B!6 = A!7)))),
% 0.59/0.78 inference(transitivity,[status(thm)],[39, 22])).
% 0.59/0.78 tff(41,plain,
% 0.59/0.78 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> (~(~(in(B!6, singleton(A!7)) <=> (B!6 = A!7))))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[40])).
% 0.59/0.78 tff(42,plain,
% 0.59/0.78 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> (in(B!6, singleton(A!7)) <=> (B!6 = A!7))),
% 0.59/0.78 inference(transitivity,[status(thm)],[41, 21])).
% 0.59/0.78 tff(43,plain,
% 0.59/0.78 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[42])).
% 0.59/0.78 tff(44,plain,
% 0.59/0.78 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))),
% 0.59/0.78 inference(transitivity,[status(thm)],[43, 20])).
% 0.59/0.78 tff(45,plain,
% 0.59/0.78 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))),
% 0.59/0.78 inference(quant_inst,[status(thm)],[])).
% 0.59/0.78 tff(46,plain,
% 0.59/0.78 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(B!6, singleton(A!7)) <=> (B!6 = A!7))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.59/0.78 tff(47,plain,
% 0.59/0.78 ($false),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[46, 19, 1])).
% 0.59/0.78 tff(48,plain,(in(B!6, singleton(A!7)) <=> (B!6 = A!7)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.78 tff(49,assumption,((~((~(singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7)))) | (~(((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7))) | (((~in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), C!5)) | (~in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), singleton(A!7)))))), introduced(assumption)).
% 0.59/0.78 tff(50,plain,
% 0.59/0.78 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(51,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[50])).
% 0.59/0.78 tff(52,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.59/0.78 inference(pull_quant,[status(thm)],[])).
% 0.59/0.78 tff(53,plain,
% 0.59/0.78 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(54,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[53])).
% 0.59/0.78 tff(55,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.59/0.78 inference(transitivity,[status(thm)],[54, 52])).
% 0.59/0.78 tff(56,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.59/0.78 inference(transitivity,[status(thm)],[55, 51])).
% 0.59/0.78 tff(57,plain,
% 0.59/0.78 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(58,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[57])).
% 0.59/0.78 tff(59,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.59/0.78 inference(transitivity,[status(thm)],[58, 56])).
% 0.59/0.78 tff(60,plain,
% 0.59/0.78 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), rewrite(((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(61,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[60])).
% 0.59/0.78 tff(62,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(63,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.59/0.78 tff(64,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.59/0.78 tff(65,plain,(
% 0.59/0.78 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B))))))),
% 0.59/0.78 inference(skolemize,[status(sab)],[64])).
% 0.59/0.78 tff(66,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.59/0.78 tff(67,plain,
% 0.59/0.78 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.59/0.78 tff(68,plain,
% 0.59/0.78 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7)))) | (~(((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7))) | (((~in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), C!5)) | (~in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), singleton(A!7)))))))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(69,plain,
% 0.59/0.79 ($false),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[68, 67, 49])).
% 0.59/0.79 tff(70,plain,(~((~((~(singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7)))) | (~(((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7))) | (((~in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), C!5)) | (~in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), singleton(A!7))))))), inference(lemma,lemma(discharge,[]))).
% 0.59/0.79 tff(71,plain,
% 0.59/0.79 (((~((~(singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7)))) | (~(((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7))) | (((~in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), C!5)) | (~in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), unordered_pair(B!6, A!7), C!5), singleton(A!7)))))) | ((~(singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7)))) | (~(((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7)))))),
% 0.59/0.79 inference(tautology,[status(thm)],[])).
% 0.59/0.79 tff(72,plain,
% 0.59/0.79 ((~(singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7)))) | (~(((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.59/0.79 tff(73,plain,
% 0.59/0.79 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(74,plain,
% 0.59/0.79 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[73])).
% 0.59/0.79 tff(75,plain,
% 0.59/0.79 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(76,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.59/0.79 tff(77,plain,
% 0.59/0.79 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.59/0.79 tff(78,plain,(
% 0.59/0.79 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.59/0.79 inference(skolemize,[status(sab)],[77])).
% 0.59/0.79 tff(79,plain,
% 0.59/0.79 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.59/0.79 tff(80,plain,
% 0.59/0.79 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(81,plain,
% 0.59/0.79 (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.59/0.79 tff(82,plain,
% 0.59/0.79 (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)),
% 0.59/0.79 inference(symmetry,[status(thm)],[81])).
% 0.59/0.79 tff(83,plain,
% 0.59/0.79 (set_intersection2(C!5, unordered_pair(B!6, A!7)) = set_intersection2(C!5, unordered_pair(A!7, B!6))),
% 0.59/0.79 inference(monotonicity,[status(thm)],[82])).
% 0.59/0.79 tff(84,plain,
% 0.59/0.79 (set_intersection2(C!5, unordered_pair(A!7, B!6)) = set_intersection2(C!5, unordered_pair(B!6, A!7))),
% 0.59/0.79 inference(symmetry,[status(thm)],[83])).
% 0.59/0.79 tff(85,plain,
% 0.59/0.79 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(86,plain,
% 0.59/0.79 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[85])).
% 0.59/0.79 tff(87,plain,
% 0.59/0.79 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(88,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.59/0.79 tff(89,plain,
% 0.59/0.79 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.59/0.79 tff(90,plain,(
% 0.59/0.79 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.59/0.79 inference(skolemize,[status(sab)],[89])).
% 0.59/0.79 tff(91,plain,
% 0.59/0.79 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.59/0.79 tff(92,plain,
% 0.59/0.79 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(unordered_pair(A!7, B!6), C!5) = set_intersection2(C!5, unordered_pair(A!7, B!6)))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(93,plain,
% 0.59/0.79 (set_intersection2(unordered_pair(A!7, B!6), C!5) = set_intersection2(C!5, unordered_pair(A!7, B!6))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.59/0.79 tff(94,plain,
% 0.59/0.79 ((~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))) <=> (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B)))))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(95,plain,
% 0.59/0.79 ((~![A: $i, B: $i, C: $i] : (~(((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C)) & (~(A = B))))) <=> (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B)))))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(96,axiom,(~![A: $i, B: $i, C: $i] : (~(((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C)) & (~(A = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t59_zfmisc_1')).
% 0.59/0.79 tff(97,plain,
% 0.59/0.79 (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.59/0.79 tff(98,plain,
% 0.59/0.79 (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[97, 94])).
% 0.59/0.79 tff(99,plain,
% 0.59/0.79 (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.59/0.79 tff(100,plain,
% 0.59/0.79 (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[99, 94])).
% 0.59/0.79 tff(101,plain,(
% 0.59/0.79 (set_intersection2(unordered_pair(A!7, B!6), C!5) = singleton(A!7)) & in(B!6, C!5) & (~(A!7 = B!6))),
% 0.59/0.79 inference(skolemize,[status(sab)],[100])).
% 0.59/0.79 tff(102,plain,
% 0.59/0.79 (set_intersection2(unordered_pair(A!7, B!6), C!5) = singleton(A!7)),
% 0.59/0.79 inference(and_elim,[status(thm)],[101])).
% 0.59/0.79 tff(103,plain,
% 0.59/0.79 (singleton(A!7) = set_intersection2(unordered_pair(A!7, B!6), C!5)),
% 0.59/0.79 inference(symmetry,[status(thm)],[102])).
% 0.59/0.79 tff(104,plain,
% 0.59/0.79 (singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7))),
% 0.59/0.79 inference(transitivity,[status(thm)],[103, 93, 84])).
% 0.59/0.79 tff(105,plain,
% 0.59/0.79 ((~((~(singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7)))) | (~(((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7)))))) | (~(singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7)))) | (~(((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7))))),
% 0.59/0.79 inference(tautology,[status(thm)],[])).
% 0.59/0.79 tff(106,plain,
% 0.59/0.79 ((~((~(singleton(A!7) = set_intersection2(C!5, unordered_pair(B!6, A!7)))) | (~(((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7)))))) | (~(((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7))))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.59/0.79 tff(107,plain,
% 0.59/0.79 (~(((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7)))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[106, 72])).
% 0.59/0.79 tff(108,assumption,((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))), introduced(assumption)).
% 0.59/0.79 tff(109,plain,
% 0.59/0.79 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(110,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[109])).
% 0.59/0.79 tff(111,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.59/0.79 inference(pull_quant,[status(thm)],[])).
% 0.59/0.79 tff(112,plain,
% 0.59/0.79 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(113,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[112])).
% 0.59/0.79 tff(114,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.59/0.79 inference(transitivity,[status(thm)],[113, 111])).
% 0.59/0.79 tff(115,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.59/0.79 inference(transitivity,[status(thm)],[114, 110])).
% 0.59/0.79 tff(116,plain,
% 0.59/0.79 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(117,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[116])).
% 0.59/0.79 tff(118,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.59/0.79 inference(transitivity,[status(thm)],[117, 115])).
% 0.59/0.79 tff(119,plain,
% 0.59/0.79 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(120,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[119])).
% 0.59/0.79 tff(121,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(122,plain,
% 0.59/0.79 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(123,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[122])).
% 0.59/0.79 tff(124,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tarski')).
% 0.59/0.79 tff(125,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.59/0.79 tff(126,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.59/0.79 tff(127,plain,(
% 0.59/0.79 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 0.59/0.79 inference(skolemize,[status(sab)],[126])).
% 0.59/0.79 tff(128,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.59/0.79 tff(129,plain,
% 0.59/0.79 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[128, 118])).
% 0.59/0.79 tff(130,plain,
% 0.59/0.79 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(131,plain,
% 0.59/0.79 ((~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(B!6, unordered_pair(B!6, A!7)) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))) <=> (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(132,plain,
% 0.59/0.79 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(B!6, unordered_pair(B!6, A!7)) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))))),
% 0.59/0.79 inference(monotonicity,[status(thm)],[131])).
% 0.59/0.79 tff(133,plain,
% 0.59/0.79 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(B!6, unordered_pair(B!6, A!7)) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))))),
% 0.59/0.79 inference(transitivity,[status(thm)],[132, 130])).
% 0.59/0.79 tff(134,plain,
% 0.59/0.79 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(B!6, unordered_pair(B!6, A!7)) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(135,plain,
% 0.59/0.80 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.59/0.80 tff(136,plain,
% 0.59/0.80 ($false),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[135, 129, 108])).
% 0.59/0.80 tff(137,plain,(~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))), inference(lemma,lemma(discharge,[]))).
% 0.59/0.80 tff(138,plain,
% 0.59/0.80 (((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))) | ((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))),
% 0.59/0.80 inference(tautology,[status(thm)],[])).
% 0.59/0.80 tff(139,plain,
% 0.59/0.80 ((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.59/0.80 tff(140,plain,
% 0.59/0.80 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(141,plain,
% 0.59/0.80 (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[140, 79])).
% 0.59/0.80 tff(142,plain,
% 0.59/0.80 ((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7))),
% 0.59/0.80 inference(tautology,[status(thm)],[])).
% 0.59/0.80 tff(143,plain,
% 0.59/0.80 ((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | in(B!6, unordered_pair(B!6, A!7))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.59/0.80 tff(144,plain,
% 0.59/0.80 (in(B!6, unordered_pair(B!6, A!7))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[143, 139])).
% 0.59/0.80 tff(145,plain,
% 0.59/0.80 (in(B!6, C!5)),
% 0.59/0.80 inference(and_elim,[status(thm)],[101])).
% 0.59/0.80 tff(146,plain,
% 0.59/0.80 ((~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))) | (~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))),
% 0.59/0.80 inference(tautology,[status(thm)],[])).
% 0.59/0.80 tff(147,plain,
% 0.59/0.80 ((~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))) | (~in(B!6, unordered_pair(B!6, A!7)))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.59/0.80 tff(148,plain,
% 0.59/0.80 (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[147, 144])).
% 0.59/0.80 tff(149,plain,
% 0.59/0.80 ((((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7))) | ((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) | in(B!6, singleton(A!7))),
% 0.59/0.80 inference(tautology,[status(thm)],[])).
% 0.59/0.80 tff(150,plain,
% 0.59/0.80 ((((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))) <=> in(B!6, singleton(A!7))) | in(B!6, singleton(A!7))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.59/0.80 tff(151,plain,
% 0.59/0.80 (in(B!6, singleton(A!7))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[150, 107])).
% 0.59/0.80 tff(152,plain,
% 0.59/0.80 ((B!6 = A!7) <=> (A!7 = B!6)),
% 0.59/0.80 inference(commutativity,[status(thm)],[])).
% 0.59/0.80 tff(153,plain,
% 0.59/0.80 ((A!7 = B!6) <=> (B!6 = A!7)),
% 0.59/0.80 inference(symmetry,[status(thm)],[152])).
% 0.59/0.80 tff(154,plain,
% 0.59/0.80 ((~(A!7 = B!6)) <=> (~(B!6 = A!7))),
% 0.59/0.80 inference(monotonicity,[status(thm)],[153])).
% 0.59/0.80 tff(155,plain,
% 0.59/0.80 (~(A!7 = B!6)),
% 0.59/0.80 inference(and_elim,[status(thm)],[101])).
% 0.59/0.80 tff(156,plain,
% 0.59/0.80 (~(B!6 = A!7)),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.59/0.80 tff(157,plain,
% 0.59/0.80 ((~(in(B!6, singleton(A!7)) <=> (B!6 = A!7))) | (~in(B!6, singleton(A!7))) | (B!6 = A!7)),
% 0.59/0.80 inference(tautology,[status(thm)],[])).
% 0.59/0.80 tff(158,plain,
% 0.59/0.80 (~(in(B!6, singleton(A!7)) <=> (B!6 = A!7))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[157, 156, 151])).
% 0.59/0.80 tff(159,plain,
% 0.59/0.80 ($false),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[158, 48])).
% 0.59/0.80 % SZS output end Proof
% 0.59/0.80 % E exiting
%------------------------------------------------------------------------------