%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET894+1 : TPTP v9.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:26:37 AM UTC 2025
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET894+1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 05:50:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(in_type, type, (
% 0.19/0.42 in: ( $i * $i ) > $o)).
% 0.19/0.42 tff(singleton_type, type, (
% 0.19/0.42 singleton: $i > $i)).
% 0.19/0.42 tff(tptp_fun_B_9_type, type, (
% 0.19/0.42 tptp_fun_B_9: $i)).
% 0.19/0.42 tff(tptp_fun_A_10_type, type, (
% 0.19/0.42 tptp_fun_A_10: $i)).
% 0.19/0.42 tff(tptp_fun_C_0_type, type, (
% 0.19/0.42 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.19/0.42 tff(cartesian_product2_type, type, (
% 0.19/0.42 cartesian_product2: ( $i * $i ) > $i)).
% 0.19/0.42 tff(ordered_pair_type, type, (
% 0.19/0.42 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.42 tff(unordered_pair_type, type, (
% 0.19/0.42 unordered_pair: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_E_2_type, type, (
% 0.19/0.42 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_F_1_type, type, (
% 0.19/0.42 tptp_fun_F_1: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_D_3_type, type, (
% 0.19/0.42 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_F_4_type, type, (
% 0.19/0.42 tptp_fun_F_4: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_E_5_type, type, (
% 0.19/0.42 tptp_fun_E_5: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(1,assumption,(~in(A!10, singleton(A!10))), introduced(assumption)).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.42 inference(pull_quant,[status(thm)],[])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[6, 4])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[7, 3])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[10, 8])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite(((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(15,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.43 tff(17,plain,(
% 0.19/0.43 ![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)))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[16])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(A!10, singleton(A!10))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(A!10, singleton(A!10)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 ((~(~in(A!10, singleton(A!10)))) <=> in(A!10, singleton(A!10))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (((~in(A!10, singleton(A!10))) | $false) <=> (~in(A!10, singleton(A!10)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 ((~$true) <=> $false),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (($true | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))) <=> $true),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 ((~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10))) <=> (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 ((singleton(A!10) = singleton(A!10)) <=> $true),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[26, 25])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))) <=> $true),
% 0.19/0.43 inference(transitivity,[status(thm)],[27, 24])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 ((~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10))))) <=> (~$true)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 ((~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10))))) <=> $false),
% 0.19/0.43 inference(transitivity,[status(thm)],[29, 23])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 ((~((~(singleton(A!10) = singleton(A!10))) | (in(A!10, singleton(A!10)) <=> (A!10 = A!10)))) <=> (~in(A!10, singleton(A!10)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (((~((~(singleton(A!10) = singleton(A!10))) | (in(A!10, singleton(A!10)) <=> (A!10 = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))))) <=> ((~in(A!10, singleton(A!10))) | $false)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[31, 30])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 (((~((~(singleton(A!10) = singleton(A!10))) | (in(A!10, singleton(A!10)) <=> (A!10 = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))))) <=> (~in(A!10, singleton(A!10)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[32, 22])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 ((~((~((~(singleton(A!10) = singleton(A!10))) | (in(A!10, singleton(A!10)) <=> (A!10 = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10))))))) <=> (~(~in(A!10, singleton(A!10))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 ((~((~((~(singleton(A!10) = singleton(A!10))) | (in(A!10, singleton(A!10)) <=> (A!10 = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10))))))) <=> in(A!10, singleton(A!10))),
% 0.19/0.43 inference(transitivity,[status(thm)],[34, 21])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!10) = singleton(A!10))) | (in(A!10, singleton(A!10)) <=> (A!10 = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(A!10, singleton(A!10)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!10) = singleton(A!10))) | (in(A!10, singleton(A!10)) <=> (A!10 = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(A!10, singleton(A!10)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[36, 20])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!10) = singleton(A!10))) | (in(A!10, singleton(A!10)) <=> (A!10 = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(A!10, singleton(A!10))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[39, 19, 1])).
% 0.19/0.43 tff(41,plain,(in(A!10, singleton(A!10))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (^[A: $i, B: $i] : refl((ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(45,axiom,(![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_tarski')).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.43 tff(47,plain,(
% 0.19/0.43 ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[46])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))) | (ordered_pair(A!10, B!9) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 (ordered_pair(A!10, B!9) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)) = ordered_pair(A!10, B!9)),
% 0.19/0.43 inference(symmetry,[status(thm)],[50])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))) <=> ((~![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_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 ((~(~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))) <=> (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(54,plain,
% 0.19/0.44 (((~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))) | $false) <=> (~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 ((~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))) <=> (~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 (($false | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))) <=> (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 ((~(singleton(A!10) = singleton(A!10))) <=> (~$true)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[26])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 ((~(singleton(A!10) = singleton(A!10))) <=> $false),
% 0.19/0.44 inference(transitivity,[status(thm)],[57, 23])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 (((~(singleton(A!10) = singleton(A!10))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))) <=> ($false | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 (((~(singleton(A!10) = singleton(A!10))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))) <=> (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))),
% 0.19/0.44 inference(transitivity,[status(thm)],[59, 56])).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 ((~((~(singleton(A!10) = singleton(A!10))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))) <=> (~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 ((~((~(singleton(A!10) = singleton(A!10))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))) <=> (~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[61, 55])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 (((~((~(singleton(A!10) = singleton(A!10))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))))) <=> ((~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))) | $false)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[62, 30])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 (((~((~(singleton(A!10) = singleton(A!10))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))))) <=> (~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[63, 54])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 ((~((~((~(singleton(A!10) = singleton(A!10))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10))))))) <=> (~(~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[64])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 ((~((~((~(singleton(A!10) = singleton(A!10))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10))))))) <=> (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))),
% 0.19/0.44 inference(transitivity,[status(thm)],[65, 53])).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!10) = singleton(A!10))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))))))) <=> ((~![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_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!10) = singleton(A!10))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))))))) <=> ((~![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_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[67, 52])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!10) = singleton(A!10))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)))) | (~((singleton(A!10) = singleton(A!10)) | (~(in(tptp_fun_C_0(singleton(A!10), A!10), singleton(A!10)) <=> (tptp_fun_C_0(singleton(A!10), A!10) = A!10)))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[70, 19])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : rewrite((~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : refl((~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ![E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 0.19/0.45 inference(pull_quant,[status(thm)],[])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))) <=> ![E: $i, F: $i] : (in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))), ((~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))) <=> (~![E: $i, F: $i] : (in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))), pull_quant((~![E: $i, F: $i] : (in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))) <=> ?[E: $i, F: $i] : (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))), ((~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))) <=> ?[E: $i, F: $i] : (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))), (((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))) <=> ((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | ?[E: $i, F: $i] : (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))), pull_quant(((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | ?[E: $i, F: $i] : (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))) <=> ?[E: $i, F: $i] : ((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))), (((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))) <=> ?[E: $i, F: $i] : ((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))), ((~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> (~?[E: $i, F: $i] : ((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))), pull_quant((~?[E: $i, F: $i] : ((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> ![E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))), ((~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> ![E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))))), (![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> ![D: $i] : ![E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))), pull_quant(![D: $i] : ![E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> ![D: $i, E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))), (![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))) <=> ![D: $i, E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))), (((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))) <=> ((~(C = cartesian_product2(A, B))) | ![D: $i, E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))))), pull_quant(((~(C = cartesian_product2(A, B))) | ![D: $i, E: $i, F: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))) <=> ![D: $i, E: $i, F: $i] : ((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))), (((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))) <=> ![D: $i, E: $i, F: $i] : ((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))))), ((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) <=> (~![D: $i, E: $i, F: $i] : ((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))))), pull_quant((~![D: $i, E: $i, F: $i] : ((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) <=> ?[D: $i, E: $i, F: $i] : (~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))))), ((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) <=> ?[D: $i, E: $i, F: $i] : (~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))) <=> ![E: $i, F: $i] : ((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))), ((~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))) <=> (~![E: $i, F: $i] : ((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))), pull_quant((~![E: $i, F: $i] : ((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))) <=> ?[E: $i, F: $i] : (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))), ((~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))) <=> ?[E: $i, F: $i] : (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))), (((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))) <=> ((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | ?[E: $i, F: $i] : (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))), pull_quant(((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | ?[E: $i, F: $i] : (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))) <=> ?[E: $i, F: $i] : ((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))), (((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))) <=> ?[E: $i, F: $i] : ((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))), ((~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))) <=> (~?[E: $i, F: $i] : ((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))), pull_quant((~?[E: $i, F: $i] : ((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))) <=> ![E: $i, F: $i] : (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))), ((~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))) <=> ![E: $i, F: $i] : (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))), (((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))) <=> ((C = cartesian_product2(A, B)) | ![E: $i, F: $i] : (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))), pull_quant(((C = cartesian_product2(A, B)) | ![E: $i, F: $i] : (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))) <=> ![E: $i, F: $i] : ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))), (((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))) <=> ![E: $i, F: $i] : ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))), ((~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))) <=> (~![E: $i, F: $i] : ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))), pull_quant((~![E: $i, F: $i] : ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))) <=> ?[E: $i, F: $i] : (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))), ((~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))) <=> ?[E: $i, F: $i] : (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))), (((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))) <=> (?[D: $i, E: $i, F: $i] : (~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | ?[E: $i, F: $i] : (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))))), pull_quant((?[D: $i, E: $i, F: $i] : (~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | ?[E: $i, F: $i] : (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))) <=> ?[E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : ((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))), (((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))) <=> ?[E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : ((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11))))))))))))), ((~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))) <=> (~?[E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : ((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))))), pull_quant((~?[E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : ((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) <=> ![E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11))))))))))))), ((~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11))))))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![A: $i, B: $i, C: $i] : ![E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[78, 76])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[79, 75])).
% 0.19/0.46 tff(81,plain,
% 0.19/0.46 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))) <=> (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.46 tff(83,plain,
% 0.19/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))) <=> ![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = cartesian_product2(A, B))) | ![D: $i] : (((~in(D, C)) | (in(tptp_fun_E_2(D, B, A), A) & in(tptp_fun_F_1(D, B, A), B) & (D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A))))) & (in(D, C) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))) <=> ((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_E_5(C, B, A), A) & in(tptp_fun_F_4(C, B, A), B) & (tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))) <=> (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))))), ((in(tptp_fun_D_3(C, B, A), C) | (in(tptp_fun_E_5(C, B, A), A) & in(tptp_fun_F_4(C, B, A), B) & (tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))) <=> (in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))))))), rewrite((in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))))) <=> (in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))), ((in(tptp_fun_D_3(C, B, A), C) | (in(tptp_fun_E_5(C, B, A), A) & in(tptp_fun_F_4(C, B, A), B) & (tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))) <=> (in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))))))), rewrite(((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))) <=> ((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))), (((in(tptp_fun_D_3(C, B, A), C) | (in(tptp_fun_E_5(C, B, A), A) & in(tptp_fun_F_4(C, B, A), B) & (tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))) & ((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))) <=> ((in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))))) & ((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))), rewrite(((in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))))) & ((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))) <=> (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))), (((in(tptp_fun_D_3(C, B, A), C) | (in(tptp_fun_E_5(C, B, A), A) & in(tptp_fun_F_4(C, B, A), B) & (tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))) & ((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))) <=> (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))), (((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_3(C, B, A), C) | (in(tptp_fun_E_5(C, B, A), A) & in(tptp_fun_F_4(C, B, A), B) & (tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))) & ((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))) <=> ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))), rewrite(((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))) <=> ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))), (((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_3(C, B, A), C) | (in(tptp_fun_E_5(C, B, A), A) & in(tptp_fun_F_4(C, B, A), B) & (tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))) & ((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))) <=> ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))), ((((~(C = cartesian_product2(A, B))) | ![D: $i] : (((~in(D, C)) | (in(tptp_fun_E_2(D, B, A), A) & in(tptp_fun_F_1(D, B, A), B) & (D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A))))) & (in(D, C) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))) & ((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_3(C, B, A), C) | (in(tptp_fun_E_5(C, B, A), A) & in(tptp_fun_F_4(C, B, A), B) & (tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))) & ((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))) <=> (((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))) & ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))))), rewrite((((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F))))))))) & ((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))))) <=> (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))))), ((((~(C = cartesian_product2(A, B))) | ![D: $i] : (((~in(D, C)) | (in(tptp_fun_E_2(D, B, A), A) & in(tptp_fun_F_1(D, B, A), B) & (D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A))))) & (in(D, C) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))) & ((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_3(C, B, A), C) | (in(tptp_fun_E_5(C, B, A), A) & in(tptp_fun_F_4(C, B, A), B) & (tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))) & ((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))) <=> (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(85,plain,
% 0.19/0.46 (![A: $i, B: $i, C: $i] : (((~(C = cartesian_product2(A, B))) | ![D: $i] : (((~in(D, C)) | (in(tptp_fun_E_2(D, B, A), A) & in(tptp_fun_F_1(D, B, A), B) & (D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A))))) & (in(D, C) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))) & ((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_3(C, B, A), C) | (in(tptp_fun_E_5(C, B, A), A) & in(tptp_fun_F_4(C, B, A), B) & (tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))) & ((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_3(C, B, A) = ordered_pair(E, F)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 (![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F))))) <=> ![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 (^[A: $i, B: $i, C: $i] : rewrite(((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : ((in(E, A) & in(F, B)) & (D = ordered_pair(E, F))))) <=> ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 (![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : ((in(E, A) & in(F, B)) & (D = ordered_pair(E, F))))) <=> ![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.47 tff(89,axiom,(![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : ((in(E, A) & in(F, B)) & (D = ordered_pair(E, F)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_zfmisc_1')).
% 0.19/0.47 tff(90,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.47 tff(91,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : ((C = cartesian_product2(A, B)) <=> ![D: $i] : (in(D, C) <=> ?[E: $i, F: $i] : (in(E, A) & in(F, B) & (D = ordered_pair(E, F)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.19/0.47 tff(92,plain,(
% 0.19/0.47 ![A: $i, B: $i, C: $i] : (((~(C = cartesian_product2(A, B))) | ![D: $i] : (((~in(D, C)) | (in(tptp_fun_E_2(D, B, A), A) & in(tptp_fun_F_1(D, B, A), B) & (D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A))))) & (in(D, C) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (D = ordered_pair(E, F))))))) & ((C = cartesian_product2(A, B)) | ((in(tptp_fun_D_3(C, B, A), C) | (in(tptp_fun_E_5(C, B, A), A) & in(tptp_fun_F_4(C, B, A), B) & (tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A))))) & ((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : (~(in(E, A) & in(F, B) & (tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[91])).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = cartesian_product2(A, B))) | ![D: $i] : (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ![E: $i, F: $i] : ((~in(E, A)) | (~in(F, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E, F))))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~(in(D, C) | ((~in(E, A)) | (~in(F, B)) | (~(D = ordered_pair(E, F)))))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | ((~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11))))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[94, 73])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 (((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9)))))))) <=> ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 ((~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))))))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = cartesian_product2(singleton(A!10), singleton(B!9))) | (~((~(in(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))) | (~((~in(tptp_fun_E_5(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_4(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)) = ordered_pair(tptp_fun_E_5(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), tptp_fun_F_4(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10))))))))) | (~((~in(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | (~(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)) = ordered_pair(A!10, B!9))))))))))) <=> (~((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9)))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 (((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))))))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = cartesian_product2(singleton(A!10), singleton(B!9))) | (~((~(in(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))) | (~((~in(tptp_fun_E_5(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_4(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)) = ordered_pair(tptp_fun_E_5(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), tptp_fun_F_4(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10))))))))) | (~((~in(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | (~(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)) = ordered_pair(A!10, B!9)))))))))))) <=> ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[97])).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 (((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))))))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = cartesian_product2(singleton(A!10), singleton(B!9))) | (~((~(in(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))) | (~((~in(tptp_fun_E_5(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_4(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)) = ordered_pair(tptp_fun_E_5(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), tptp_fun_F_4(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10))))))))) | (~((~in(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | (~(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)) = ordered_pair(A!10, B!9)))))))))))) <=> ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[98, 96])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))))))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = cartesian_product2(singleton(A!10), singleton(B!9))) | (~((~(in(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))) | (~((~in(tptp_fun_E_5(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_4(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)) = ordered_pair(tptp_fun_E_5(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), tptp_fun_F_4(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10))))))))) | (~((~in(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | (~(tptp_fun_D_3(cartesian_product2(singleton(A!10), singleton(B!9)), singleton(B!9), singleton(A!10)) = ordered_pair(A!10, B!9)))))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i, E_12: $i, F_11: $i, D: $i, E: $i, F: $i] : (~((~((~(C = cartesian_product2(A, B))) | (~((~((~in(D, C)) | (~((~in(tptp_fun_E_2(D, B, A), A)) | (~in(tptp_fun_F_1(D, B, A), B)) | (~(D = ordered_pair(tptp_fun_E_2(D, B, A), tptp_fun_F_1(D, B, A)))))))) | (~((~(D = ordered_pair(E, F))) | in(D, C) | (~in(E, A)) | (~in(F, B)))))))) | (~((C = cartesian_product2(A, B)) | (~((~(in(tptp_fun_D_3(C, B, A), C) | (~((~in(tptp_fun_E_5(C, B, A), A)) | (~in(tptp_fun_F_4(C, B, A), B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(tptp_fun_E_5(C, B, A), tptp_fun_F_4(C, B, A)))))))) | (~((~in(tptp_fun_D_3(C, B, A), C)) | (~in(E_12, A)) | (~in(F_11, B)) | (~(tptp_fun_D_3(C, B, A) = ordered_pair(E_12, F_11)))))))))))) | (~((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 (~((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[101, 95])).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 (((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9)))))) | ((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 ((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.48 tff(105,assumption,(~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))), introduced(assumption)).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 (((~![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)))))))) | (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))))))) <=> ((~![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)))))))) | (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 ((~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | (in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))))))) <=> (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (((~![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)))))))) | (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | (in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))))))) <=> ((~![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)))))))) | (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (((~![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)))))))) | (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | (in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))))))) <=> ((~![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)))))))) | (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[108, 106])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 ((~![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)))))))) | (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | (in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 ((~![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)))))))) | (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 (~((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[111, 19])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 (((~((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))) | in(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)), cartesian_product2(singleton(A!10), singleton(B!9))))) | (~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))))) | ((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 ((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.19/0.49 tff(115,plain,
% 0.19/0.49 (singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = singleton(ordered_pair(A!10, B!9))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.49 tff(116,plain,
% 0.19/0.49 ((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) <=> (cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(ordered_pair(A!10, B!9)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 ((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(ordered_pair(A!10, B!9))) <=> (cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))),
% 0.19/0.49 inference(symmetry,[status(thm)],[116])).
% 0.19/0.49 tff(118,plain,
% 0.19/0.49 ((~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(ordered_pair(A!10, B!9)))) <=> (~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 ((~![A: $i, B: $i] : (cartesian_product2(singleton(A), singleton(B)) = singleton(ordered_pair(A, B)))) <=> (~![A: $i, B: $i] : (cartesian_product2(singleton(A), singleton(B)) = singleton(ordered_pair(A, B))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(120,axiom,(~![A: $i, B: $i] : (cartesian_product2(singleton(A), singleton(B)) = singleton(ordered_pair(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t35_zfmisc_1')).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 (~![A: $i, B: $i] : (cartesian_product2(singleton(A), singleton(B)) = singleton(ordered_pair(A, B)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.49 tff(122,plain,
% 0.19/0.49 (~![A: $i, B: $i] : (cartesian_product2(singleton(A), singleton(B)) = singleton(ordered_pair(A, B)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[121, 119])).
% 0.19/0.49 tff(123,plain,
% 0.19/0.49 (~![A: $i, B: $i] : (cartesian_product2(singleton(A), singleton(B)) = singleton(ordered_pair(A, B)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[122, 119])).
% 0.19/0.49 tff(124,plain,
% 0.19/0.49 (~![A: $i, B: $i] : (cartesian_product2(singleton(A), singleton(B)) = singleton(ordered_pair(A, B)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.19/0.49 tff(125,plain,(
% 0.19/0.49 ~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(ordered_pair(A!10, B!9)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[124])).
% 0.19/0.49 tff(126,plain,
% 0.19/0.49 (~(cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.19/0.49 tff(127,plain,
% 0.19/0.49 ((~((cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))))) | (cartesian_product2(singleton(A!10), singleton(B!9)) = singleton(unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(128,plain,
% 0.19/0.49 (~(in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[127, 126, 114])).
% 0.19/0.49 tff(129,plain,
% 0.19/0.49 ((in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 (in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) | (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.19/0.49 tff(131,plain,
% 0.19/0.49 (in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[130, 105])).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 ((~((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))))) | (~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(133,plain,
% 0.19/0.49 (~((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[132, 131, 104])).
% 0.19/0.49 tff(134,plain,
% 0.19/0.49 (((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)))))) | in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(135,plain,
% 0.19/0.49 (in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.49 tff(136,plain,
% 0.19/0.49 ((~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))) | (~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 ((~(in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10)) <=> (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10))) | (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 (tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = A!10),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[137, 71])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 (ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), B!9) = ordered_pair(A!10, B!9)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[138])).
% 0.19/0.49 tff(140,plain,
% 0.19/0.49 (((~![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_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(141,plain,
% 0.19/0.49 ((~(~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))) <=> (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(142,plain,
% 0.19/0.49 (((~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))) | $false) <=> (~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(143,plain,
% 0.19/0.49 (($true | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))) <=> $true),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(144,plain,
% 0.19/0.49 ((~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9))) <=> (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(145,plain,
% 0.19/0.49 ((singleton(B!9) = singleton(B!9)) <=> $true),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(146,plain,
% 0.19/0.49 (((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[145, 144])).
% 0.19/0.49 tff(147,plain,
% 0.19/0.49 (((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))) <=> $true),
% 0.19/0.49 inference(transitivity,[status(thm)],[146, 143])).
% 0.19/0.49 tff(148,plain,
% 0.19/0.49 ((~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9))))) <=> (~$true)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[147])).
% 0.19/0.49 tff(149,plain,
% 0.19/0.49 ((~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9))))) <=> $false),
% 0.19/0.49 inference(transitivity,[status(thm)],[148, 23])).
% 0.19/0.49 tff(150,plain,
% 0.19/0.49 ((~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))) <=> (~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(151,plain,
% 0.19/0.49 (($false | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))) <=> (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(152,plain,
% 0.19/0.49 ((~(singleton(B!9) = singleton(B!9))) <=> (~$true)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.49 tff(153,plain,
% 0.19/0.49 ((~(singleton(B!9) = singleton(B!9))) <=> $false),
% 0.19/0.49 inference(transitivity,[status(thm)],[152, 23])).
% 0.19/0.49 tff(154,plain,
% 0.19/0.49 (((~(singleton(B!9) = singleton(B!9))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))) <=> ($false | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[153])).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 (((~(singleton(B!9) = singleton(B!9))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))) <=> (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))),
% 0.19/0.49 inference(transitivity,[status(thm)],[154, 151])).
% 0.19/0.50 tff(156,plain,
% 0.19/0.50 ((~((~(singleton(B!9) = singleton(B!9))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))) <=> (~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[155])).
% 0.19/0.50 tff(157,plain,
% 0.19/0.50 ((~((~(singleton(B!9) = singleton(B!9))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))) <=> (~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[156, 150])).
% 0.19/0.50 tff(158,plain,
% 0.19/0.50 (((~((~(singleton(B!9) = singleton(B!9))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))))) <=> ((~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))) | $false)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[157, 149])).
% 0.19/0.50 tff(159,plain,
% 0.19/0.50 (((~((~(singleton(B!9) = singleton(B!9))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))))) <=> (~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[158, 142])).
% 0.19/0.50 tff(160,plain,
% 0.19/0.50 ((~((~((~(singleton(B!9) = singleton(B!9))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9))))))) <=> (~(~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.50 tff(161,plain,
% 0.19/0.50 ((~((~((~(singleton(B!9) = singleton(B!9))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9))))))) <=> (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))),
% 0.19/0.50 inference(transitivity,[status(thm)],[160, 141])).
% 0.19/0.50 tff(162,plain,
% 0.19/0.50 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!9) = singleton(B!9))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[161])).
% 0.19/0.50 tff(163,plain,
% 0.19/0.50 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!9) = singleton(B!9))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[162, 140])).
% 0.19/0.50 tff(164,plain,
% 0.19/0.50 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!9) = singleton(B!9))) | (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(165,plain,
% 0.19/0.50 ((~![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_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.50 tff(166,plain,
% 0.19/0.50 (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[165, 19])).
% 0.19/0.50 tff(167,plain,
% 0.19/0.50 (((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)))))) | in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(168,plain,
% 0.19/0.50 (in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[167, 133])).
% 0.19/0.50 tff(169,plain,
% 0.19/0.50 ((~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(170,plain,
% 0.19/0.50 ((~(in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9)) <=> (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9))) | (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.19/0.50 tff(171,plain,
% 0.19/0.50 (tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)) = B!9),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[170, 166])).
% 0.19/0.50 tff(172,plain,
% 0.19/0.50 (ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), B!9)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[171])).
% 0.19/0.50 tff(173,plain,
% 0.19/0.50 (((~in(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(A!10))) | (~in(tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), singleton(B!9))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)))))) | (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(174,plain,
% 0.19/0.50 (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(tptp_fun_E_2(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)), tptp_fun_F_1(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), singleton(B!9), singleton(A!10)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[173, 133])).
% 0.19/0.50 tff(175,plain,
% 0.19/0.50 (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))),
% 0.19/0.50 inference(transitivity,[status(thm)],[174, 172, 139, 50])).
% 0.19/0.50 tff(176,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[105, 175])).
% 0.19/0.50 tff(177,plain,(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(178,plain,
% 0.19/0.50 (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = ordered_pair(A!10, B!9)),
% 0.19/0.50 inference(transitivity,[status(thm)],[177, 51])).
% 0.19/0.50 tff(179,plain,
% 0.19/0.50 (in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> in(ordered_pair(A!10, B!9), cartesian_product2(singleton(A!10), singleton(B!9)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[178])).
% 0.19/0.50 tff(180,plain,
% 0.19/0.50 ((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) <=> (~in(ordered_pair(A!10, B!9), cartesian_product2(singleton(A!10), singleton(B!9))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[179])).
% 0.19/0.50 tff(181,plain,
% 0.19/0.50 ((in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9))) <=> (tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10)))) | (~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(182,plain,
% 0.19/0.50 ((~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))) | (~(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))) = unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[181, 128])).
% 0.19/0.50 tff(183,plain,
% 0.19/0.50 (~in(tptp_fun_C_0(cartesian_product2(singleton(A!10), singleton(B!9)), unordered_pair(unordered_pair(A!10, B!9), singleton(A!10))), cartesian_product2(singleton(A!10), singleton(B!9)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[182, 177])).
% 0.19/0.50 tff(184,plain,
% 0.19/0.50 (~in(ordered_pair(A!10, B!9), cartesian_product2(singleton(A!10), singleton(B!9)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[183, 180])).
% 0.19/0.50 tff(185,plain,
% 0.19/0.50 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(186,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[185])).
% 0.19/0.50 tff(187,plain,
% 0.19/0.50 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(A, C)) | (~in(B, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(188,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.50 tff(189,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(190,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l55_zfmisc_1')).
% 0.19/0.50 tff(191,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.50 tff(192,plain,(
% 0.19/0.50 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[191])).
% 0.19/0.50 tff(193,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.19/0.50 tff(194,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.19/0.50 tff(195,plain,
% 0.19/0.50 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9)))) <=> in(ordered_pair(A!10, B!9), cartesian_product2(singleton(A!10), singleton(B!9)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(196,plain,
% 0.19/0.50 (~(((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9)))) <=> in(ordered_pair(A!10, B!9), cartesian_product2(singleton(A!10), singleton(B!9))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.19/0.50 tff(197,plain,
% 0.19/0.50 ((((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9)))) <=> in(ordered_pair(A!10, B!9), cartesian_product2(singleton(A!10), singleton(B!9)))) | ((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9)))) | in(ordered_pair(A!10, B!9), cartesian_product2(singleton(A!10), singleton(B!9)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(198,plain,
% 0.19/0.50 (((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9)))) | in(ordered_pair(A!10, B!9), cartesian_product2(singleton(A!10), singleton(B!9)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.19/0.50 tff(199,plain,
% 0.19/0.50 ((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[198, 184])).
% 0.19/0.50 tff(200,plain,
% 0.19/0.50 ((~((~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9))))) | (~in(A!10, singleton(A!10))) | (~in(B!9, singleton(B!9)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(201,plain,
% 0.19/0.50 (~in(B!9, singleton(B!9))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[200, 199, 41])).
% 0.19/0.50 tff(202,plain,
% 0.19/0.50 (((~![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!9, singleton(B!9))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(B!9, singleton(B!9)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(203,plain,
% 0.19/0.51 ((~(~in(B!9, singleton(B!9)))) <=> in(B!9, singleton(B!9))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(204,plain,
% 0.19/0.51 (((~in(B!9, singleton(B!9))) | $false) <=> (~in(B!9, singleton(B!9)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(205,plain,
% 0.19/0.51 ((~((~(singleton(B!9) = singleton(B!9))) | (in(B!9, singleton(B!9)) <=> (B!9 = B!9)))) <=> (~in(B!9, singleton(B!9)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(206,plain,
% 0.19/0.51 (((~((~(singleton(B!9) = singleton(B!9))) | (in(B!9, singleton(B!9)) <=> (B!9 = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))))) <=> ((~in(B!9, singleton(B!9))) | $false)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[205, 149])).
% 0.19/0.51 tff(207,plain,
% 0.19/0.51 (((~((~(singleton(B!9) = singleton(B!9))) | (in(B!9, singleton(B!9)) <=> (B!9 = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))))) <=> (~in(B!9, singleton(B!9)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[206, 204])).
% 0.19/0.51 tff(208,plain,
% 0.19/0.51 ((~((~((~(singleton(B!9) = singleton(B!9))) | (in(B!9, singleton(B!9)) <=> (B!9 = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9))))))) <=> (~(~in(B!9, singleton(B!9))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[207])).
% 0.19/0.51 tff(209,plain,
% 0.19/0.51 ((~((~((~(singleton(B!9) = singleton(B!9))) | (in(B!9, singleton(B!9)) <=> (B!9 = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9))))))) <=> in(B!9, singleton(B!9))),
% 0.19/0.51 inference(transitivity,[status(thm)],[208, 203])).
% 0.19/0.51 tff(210,plain,
% 0.19/0.51 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!9) = singleton(B!9))) | (in(B!9, singleton(B!9)) <=> (B!9 = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(B!9, singleton(B!9)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[209])).
% 0.19/0.51 tff(211,plain,
% 0.19/0.51 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!9) = singleton(B!9))) | (in(B!9, singleton(B!9)) <=> (B!9 = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(B!9, singleton(B!9)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[210, 202])).
% 0.19/0.51 tff(212,plain,
% 0.19/0.51 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!9) = singleton(B!9))) | (in(B!9, singleton(B!9)) <=> (B!9 = B!9)))) | (~((singleton(B!9) = singleton(B!9)) | (~(in(tptp_fun_C_0(singleton(B!9), B!9), singleton(B!9)) <=> (tptp_fun_C_0(singleton(B!9), B!9) = B!9)))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(213,plain,
% 0.19/0.51 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(B!9, singleton(B!9))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.19/0.51 tff(214,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[213, 19, 201])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------