%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET919+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:26:40 AM UTC 2025
% Result : Theorem 4.12s 4.27s
% Output : Proof 4.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET919+1 : TPTP v9.0.0. Released v3.2.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 05:50:54 EDT 2025
% 0.14/0.36 % CPUTime :
% 4.12/4.27 % SZS status Theorem
% 4.12/4.27 % SZS output start Proof
% 4.12/4.27 tff(tptp_fun_A_7_type, type, (
% 4.12/4.27 tptp_fun_A_7: $i)).
% 4.12/4.27 tff(tptp_fun_D_2_type, type, (
% 4.12/4.27 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 4.12/4.27 tff(unordered_pair_type, type, (
% 4.12/4.27 unordered_pair: ( $i * $i ) > $i)).
% 4.12/4.27 tff(tptp_fun_C_5_type, type, (
% 4.12/4.27 tptp_fun_C_5: $i)).
% 4.12/4.27 tff(tptp_fun_B_6_type, type, (
% 4.12/4.27 tptp_fun_B_6: $i)).
% 4.12/4.27 tff(singleton_type, type, (
% 4.12/4.27 singleton: $i > $i)).
% 4.12/4.27 tff(in_type, type, (
% 4.12/4.27 in: ( $i * $i ) > $o)).
% 4.12/4.27 tff(set_intersection2_type, type, (
% 4.12/4.27 set_intersection2: ( $i * $i ) > $i)).
% 4.12/4.27 tff(tptp_fun_C_0_type, type, (
% 4.12/4.27 tptp_fun_C_0: ( $i * $i ) > $i)).
% 4.12/4.27 tff(tptp_fun_D_1_type, type, (
% 4.12/4.27 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 4.12/4.27 tff(1,plain,
% 4.12/4.27 ((C!5 = A!7) <=> (A!7 = C!5)),
% 4.12/4.27 inference(commutativity,[status(thm)],[])).
% 4.12/4.27 tff(2,assumption,(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7), introduced(assumption)).
% 4.12/4.27 tff(3,plain,
% 4.12/4.27 (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6) <=> in(A!7, B!6)),
% 4.12/4.27 inference(monotonicity,[status(thm)],[2])).
% 4.12/4.27 tff(4,plain,
% 4.12/4.27 (in(A!7, B!6) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 4.12/4.27 inference(symmetry,[status(thm)],[3])).
% 4.12/4.27 tff(5,plain,
% 4.12/4.27 ((~((set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)) | (in(C!5, B!6) & (~(A!7 = C!5))) | (~in(A!7, B!6)))) <=> (~((set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)) | (in(C!5, B!6) & (~(A!7 = C!5))) | (~in(A!7, B!6))))),
% 4.12/4.27 inference(rewrite,[status(thm)],[])).
% 4.12/4.27 tff(6,plain,
% 4.12/4.27 ((~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))) <=> (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B))))),
% 4.12/4.27 inference(rewrite,[status(thm)],[])).
% 4.12/4.27 tff(7,plain,
% 4.12/4.27 ((~![A: $i, B: $i, C: $i] : (in(A, B) => ((in(C, B) & (~(A = C))) | (set_intersection2(unordered_pair(A, C), B) = singleton(A))))) <=> (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B))))),
% 4.12/4.27 inference(rewrite,[status(thm)],[])).
% 4.12/4.27 tff(8,axiom,(~![A: $i, B: $i, C: $i] : (in(A, B) => ((in(C, B) & (~(A = C))) | (set_intersection2(unordered_pair(A, C), B) = singleton(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t60_zfmisc_1')).
% 4.12/4.27 tff(9,plain,
% 4.12/4.27 (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))),
% 4.12/4.27 inference(modus_ponens,[status(thm)],[8, 7])).
% 4.12/4.27 tff(10,plain,
% 4.12/4.27 (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))),
% 4.12/4.27 inference(modus_ponens,[status(thm)],[9, 6])).
% 4.12/4.27 tff(11,plain,
% 4.12/4.27 (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))),
% 4.12/4.27 inference(modus_ponens,[status(thm)],[10, 6])).
% 4.12/4.27 tff(12,plain,
% 4.12/4.27 (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))),
% 4.12/4.27 inference(modus_ponens,[status(thm)],[11, 6])).
% 4.12/4.27 tff(13,plain,(
% 4.12/4.27 ~((set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)) | (in(C!5, B!6) & (~(A!7 = C!5))) | (~in(A!7, B!6)))),
% 4.12/4.27 inference(skolemize,[status(sab)],[12])).
% 4.12/4.27 tff(14,plain,
% 4.12/4.27 (~((set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)) | (in(C!5, B!6) & (~(A!7 = C!5))) | (~in(A!7, B!6)))),
% 4.12/4.27 inference(modus_ponens,[status(thm)],[13, 5])).
% 4.12/4.27 tff(15,plain,
% 4.12/4.27 (in(A!7, B!6)),
% 4.12/4.27 inference(or_elim,[status(thm)],[14])).
% 4.12/4.27 tff(16,plain,
% 4.12/4.27 (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 4.12/4.27 inference(modus_ponens,[status(thm)],[15, 4])).
% 4.12/4.27 tff(17,plain,
% 4.12/4.27 (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> in(A!7, singleton(A!7))),
% 4.12/4.27 inference(monotonicity,[status(thm)],[2])).
% 4.12/4.27 tff(18,plain,
% 4.12/4.27 (in(A!7, singleton(A!7)) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))),
% 4.12/4.27 inference(symmetry,[status(thm)],[17])).
% 4.12/4.27 tff(19,assumption,(~in(A!7, singleton(A!7))), introduced(assumption)).
% 4.12/4.27 tff(20,plain,
% 4.12/4.27 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 4.12/4.27 inference(bind,[status(th)],[])).
% 4.12/4.27 tff(21,plain,
% 4.12/4.27 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 4.12/4.27 inference(quant_intro,[status(thm)],[20])).
% 4.12/4.27 tff(22,plain,
% 4.12/4.27 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 4.12/4.27 inference(pull_quant,[status(thm)],[])).
% 4.12/4.27 tff(23,plain,
% 4.12/4.27 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 4.12/4.27 inference(bind,[status(th)],[])).
% 4.12/4.27 tff(24,plain,
% 4.12/4.27 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 4.12/4.27 inference(quant_intro,[status(thm)],[23])).
% 4.12/4.27 tff(25,plain,
% 4.12/4.27 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 4.12/4.27 inference(transitivity,[status(thm)],[24, 22])).
% 4.12/4.27 tff(26,plain,
% 4.12/4.27 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 4.12/4.27 inference(transitivity,[status(thm)],[25, 21])).
% 4.12/4.27 tff(27,plain,
% 4.12/4.27 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 4.12/4.27 inference(bind,[status(th)],[])).
% 4.12/4.27 tff(28,plain,
% 4.12/4.27 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 4.12/4.27 inference(quant_intro,[status(thm)],[27])).
% 4.12/4.27 tff(29,plain,
% 4.12/4.27 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 4.12/4.27 inference(transitivity,[status(thm)],[28, 26])).
% 4.12/4.27 tff(30,plain,
% 4.12/4.27 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite(((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 4.12/4.27 inference(bind,[status(th)],[])).
% 4.12/4.27 tff(31,plain,
% 4.12/4.27 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 4.12/4.27 inference(quant_intro,[status(thm)],[30])).
% 4.12/4.27 tff(32,plain,
% 4.12/4.27 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 4.12/4.27 inference(rewrite,[status(thm)],[])).
% 4.12/4.27 tff(33,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 4.12/4.27 tff(34,plain,
% 4.12/4.27 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 4.12/4.27 inference(modus_ponens,[status(thm)],[33, 32])).
% 4.12/4.27 tff(35,plain,(
% 4.12/4.27 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 4.12/4.27 inference(skolemize,[status(sab)],[34])).
% 4.12/4.27 tff(36,plain,
% 4.12/4.27 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 4.12/4.27 inference(modus_ponens,[status(thm)],[35, 31])).
% 4.12/4.27 tff(37,plain,
% 4.12/4.27 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 4.12/4.27 inference(modus_ponens,[status(thm)],[36, 29])).
% 4.12/4.27 tff(38,plain,
% 4.12/4.27 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(A!7, singleton(A!7))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(A!7, singleton(A!7)))),
% 4.12/4.27 inference(rewrite,[status(thm)],[])).
% 4.12/4.27 tff(39,plain,
% 4.12/4.27 ((~(~in(A!7, singleton(A!7)))) <=> in(A!7, singleton(A!7))),
% 4.12/4.27 inference(rewrite,[status(thm)],[])).
% 4.12/4.27 tff(40,plain,
% 4.12/4.27 (((~in(A!7, singleton(A!7))) | $false) <=> (~in(A!7, singleton(A!7)))),
% 4.12/4.27 inference(rewrite,[status(thm)],[])).
% 4.12/4.27 tff(41,plain,
% 4.12/4.27 ((~$true) <=> $false),
% 4.12/4.27 inference(rewrite,[status(thm)],[])).
% 4.12/4.27 tff(42,plain,
% 4.12/4.27 (($true | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> $true),
% 4.12/4.27 inference(rewrite,[status(thm)],[])).
% 4.12/4.27 tff(43,plain,
% 4.12/4.27 ((~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))),
% 4.12/4.27 inference(rewrite,[status(thm)],[])).
% 4.12/4.27 tff(44,plain,
% 4.12/4.27 ((singleton(A!7) = singleton(A!7)) <=> $true),
% 4.12/4.27 inference(rewrite,[status(thm)],[])).
% 4.12/4.27 tff(45,plain,
% 4.12/4.27 (((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))),
% 4.12/4.27 inference(monotonicity,[status(thm)],[44, 43])).
% 4.12/4.27 tff(46,plain,
% 4.12/4.27 (((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> $true),
% 4.12/4.27 inference(transitivity,[status(thm)],[45, 42])).
% 4.12/4.27 tff(47,plain,
% 4.12/4.27 ((~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> (~$true)),
% 4.12/4.27 inference(monotonicity,[status(thm)],[46])).
% 4.12/4.27 tff(48,plain,
% 4.12/4.27 ((~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> $false),
% 4.12/4.27 inference(transitivity,[status(thm)],[47, 41])).
% 4.12/4.28 tff(49,plain,
% 4.12/4.28 ((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) <=> (~in(A!7, singleton(A!7)))),
% 4.12/4.28 inference(rewrite,[status(thm)],[])).
% 4.12/4.28 tff(50,plain,
% 4.12/4.28 (((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> ((~in(A!7, singleton(A!7))) | $false)),
% 4.12/4.28 inference(monotonicity,[status(thm)],[49, 48])).
% 4.12/4.28 tff(51,plain,
% 4.12/4.28 (((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> (~in(A!7, singleton(A!7)))),
% 4.12/4.28 inference(transitivity,[status(thm)],[50, 40])).
% 4.12/4.28 tff(52,plain,
% 4.12/4.28 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> (~(~in(A!7, singleton(A!7))))),
% 4.12/4.28 inference(monotonicity,[status(thm)],[51])).
% 4.12/4.28 tff(53,plain,
% 4.12/4.28 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> in(A!7, singleton(A!7))),
% 4.12/4.28 inference(transitivity,[status(thm)],[52, 39])).
% 4.12/4.28 tff(54,plain,
% 4.12/4.28 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(A!7, singleton(A!7)))),
% 4.12/4.28 inference(monotonicity,[status(thm)],[53])).
% 4.12/4.28 tff(55,plain,
% 4.12/4.28 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(A!7, singleton(A!7)))),
% 4.12/4.28 inference(transitivity,[status(thm)],[54, 38])).
% 4.12/4.28 tff(56,plain,
% 4.12/4.28 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(A!7, singleton(A!7)) <=> (A!7 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))),
% 4.12/4.28 inference(quant_inst,[status(thm)],[])).
% 4.12/4.28 tff(57,plain,
% 4.12/4.28 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(A!7, singleton(A!7))),
% 4.12/4.28 inference(modus_ponens,[status(thm)],[56, 55])).
% 4.12/4.28 tff(58,plain,
% 4.12/4.28 ($false),
% 4.12/4.28 inference(unit_resolution,[status(thm)],[57, 37, 19])).
% 4.12/4.28 tff(59,plain,(in(A!7, singleton(A!7))), inference(lemma,lemma(discharge,[]))).
% 4.12/4.28 tff(60,plain,
% 4.12/4.28 (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))),
% 4.12/4.28 inference(modus_ponens,[status(thm)],[59, 18])).
% 4.12/4.28 tff(61,assumption,((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, B!6)) | (~in(C!5, unordered_pair(C!5, A!7)))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))))), introduced(assumption)).
% 4.12/4.28 tff(62,plain,
% 4.12/4.28 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 4.12/4.28 inference(bind,[status(th)],[])).
% 4.12/4.28 tff(63,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 4.12/4.28 inference(quant_intro,[status(thm)],[62])).
% 4.12/4.28 tff(64,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 4.12/4.28 inference(pull_quant,[status(thm)],[])).
% 4.12/4.28 tff(65,plain,
% 4.12/4.28 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 4.12/4.28 inference(bind,[status(th)],[])).
% 4.12/4.28 tff(66,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 4.12/4.28 inference(quant_intro,[status(thm)],[65])).
% 4.12/4.28 tff(67,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 4.12/4.28 inference(transitivity,[status(thm)],[66, 64])).
% 4.12/4.28 tff(68,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 4.12/4.28 inference(transitivity,[status(thm)],[67, 63])).
% 4.12/4.28 tff(69,plain,
% 4.12/4.28 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 4.12/4.28 inference(bind,[status(th)],[])).
% 4.12/4.28 tff(70,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 4.12/4.28 inference(quant_intro,[status(thm)],[69])).
% 4.12/4.28 tff(71,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 4.12/4.28 inference(transitivity,[status(thm)],[70, 68])).
% 4.12/4.28 tff(72,plain,
% 4.12/4.28 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), rewrite(((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 4.12/4.28 inference(bind,[status(th)],[])).
% 4.12/4.28 tff(73,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 4.12/4.28 inference(quant_intro,[status(thm)],[72])).
% 4.12/4.28 tff(74,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 4.12/4.28 inference(rewrite,[status(thm)],[])).
% 4.12/4.28 tff(75,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 4.12/4.28 tff(76,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 4.12/4.28 inference(modus_ponens,[status(thm)],[75, 74])).
% 4.12/4.28 tff(77,plain,(
% 4.12/4.28 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B))))))),
% 4.12/4.28 inference(skolemize,[status(sab)],[76])).
% 4.12/4.28 tff(78,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 4.12/4.28 inference(modus_ponens,[status(thm)],[77, 73])).
% 4.12/4.28 tff(79,plain,
% 4.12/4.28 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 4.12/4.28 inference(modus_ponens,[status(thm)],[78, 71])).
% 4.12/4.28 tff(80,plain,
% 4.12/4.28 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, B!6)) | (~in(C!5, unordered_pair(C!5, A!7)))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, B!6)) | (~in(C!5, unordered_pair(C!5, A!7)))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))))))))),
% 4.12/4.28 inference(rewrite,[status(thm)],[])).
% 4.12/4.28 tff(81,plain,
% 4.12/4.28 ((~((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, unordered_pair(C!5, A!7))) | (~in(C!5, B!6))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))))))) <=> (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, B!6)) | (~in(C!5, unordered_pair(C!5, A!7)))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))))))),
% 4.14/4.28 inference(rewrite,[status(thm)],[])).
% 4.14/4.28 tff(82,plain,
% 4.14/4.28 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, unordered_pair(C!5, A!7))) | (~in(C!5, B!6))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, B!6)) | (~in(C!5, unordered_pair(C!5, A!7)))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))))))))),
% 4.14/4.28 inference(monotonicity,[status(thm)],[81])).
% 4.14/4.28 tff(83,plain,
% 4.14/4.28 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, unordered_pair(C!5, A!7))) | (~in(C!5, B!6))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, B!6)) | (~in(C!5, unordered_pair(C!5, A!7)))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))))))))),
% 4.14/4.28 inference(transitivity,[status(thm)],[82, 80])).
% 4.14/4.28 tff(84,plain,
% 4.14/4.28 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, unordered_pair(C!5, A!7))) | (~in(C!5, B!6))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))))))),
% 4.14/4.28 inference(quant_inst,[status(thm)],[])).
% 4.14/4.28 tff(85,plain,
% 4.14/4.28 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, B!6)) | (~in(C!5, unordered_pair(C!5, A!7)))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))))))),
% 4.14/4.28 inference(modus_ponens,[status(thm)],[84, 83])).
% 4.14/4.28 tff(86,plain,
% 4.14/4.28 ($false),
% 4.14/4.28 inference(unit_resolution,[status(thm)],[85, 79, 61])).
% 4.14/4.28 tff(87,plain,(~((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, B!6)) | (~in(C!5, unordered_pair(C!5, A!7)))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.28 tff(88,plain,
% 4.14/4.28 (((~((~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(C!5, B!6)) | (~in(C!5, unordered_pair(C!5, A!7)))) <=> in(C!5, singleton(A!7)))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))))) | ((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))))),
% 4.14/4.28 inference(tautology,[status(thm)],[])).
% 4.14/4.28 tff(89,plain,
% 4.14/4.28 ((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))),
% 4.14/4.28 inference(unit_resolution,[status(thm)],[88, 87])).
% 4.14/4.28 tff(90,assumption,(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)), introduced(assumption)).
% 4.14/4.28 tff(91,plain,
% 4.14/4.28 (set_intersection2(unordered_pair(C!5, A!7), B!6) = singleton(A!7)),
% 4.14/4.28 inference(symmetry,[status(thm)],[90])).
% 4.14/4.28 tff(92,plain,
% 4.14/4.28 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 4.14/4.28 inference(bind,[status(th)],[])).
% 4.14/4.28 tff(93,plain,
% 4.14/4.28 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 4.14/4.28 inference(quant_intro,[status(thm)],[92])).
% 4.14/4.28 tff(94,plain,
% 4.14/4.28 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 4.14/4.28 inference(rewrite,[status(thm)],[])).
% 4.14/4.28 tff(95,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 4.14/4.28 tff(96,plain,
% 4.14/4.28 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 4.14/4.28 inference(modus_ponens,[status(thm)],[95, 94])).
% 4.14/4.28 tff(97,plain,(
% 4.14/4.28 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 4.14/4.28 inference(skolemize,[status(sab)],[96])).
% 4.14/4.28 tff(98,plain,
% 4.14/4.28 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 4.14/4.28 inference(modus_ponens,[status(thm)],[97, 93])).
% 4.14/4.28 tff(99,plain,
% 4.14/4.28 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!7, C!5) = unordered_pair(C!5, A!7))),
% 4.14/4.28 inference(quant_inst,[status(thm)],[])).
% 4.14/4.28 tff(100,plain,
% 4.14/4.28 (unordered_pair(A!7, C!5) = unordered_pair(C!5, A!7)),
% 4.14/4.28 inference(unit_resolution,[status(thm)],[99, 98])).
% 4.14/4.28 tff(101,plain,
% 4.14/4.28 (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)),
% 4.14/4.28 inference(symmetry,[status(thm)],[100])).
% 4.14/4.28 tff(102,plain,
% 4.14/4.28 (set_intersection2(unordered_pair(C!5, A!7), B!6) = set_intersection2(unordered_pair(A!7, C!5), B!6)),
% 4.14/4.28 inference(monotonicity,[status(thm)],[101])).
% 4.14/4.28 tff(103,plain,
% 4.14/4.28 (set_intersection2(unordered_pair(A!7, C!5), B!6) = set_intersection2(unordered_pair(C!5, A!7), B!6)),
% 4.14/4.28 inference(symmetry,[status(thm)],[102])).
% 4.14/4.28 tff(104,plain,
% 4.14/4.28 (set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)),
% 4.14/4.28 inference(transitivity,[status(thm)],[103, 91])).
% 4.14/4.28 tff(105,plain,
% 4.14/4.28 (~(set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7))),
% 4.14/4.28 inference(or_elim,[status(thm)],[14])).
% 4.14/4.28 tff(106,plain,
% 4.14/4.28 ($false),
% 4.14/4.28 inference(unit_resolution,[status(thm)],[105, 104])).
% 4.14/4.28 tff(107,plain,(~(singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.28 tff(108,plain,
% 4.14/4.28 ((~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))))) | (singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))),
% 4.14/4.28 inference(tautology,[status(thm)],[])).
% 4.14/4.28 tff(109,plain,
% 4.14/4.28 ((~((singleton(A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))))) | (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))),
% 4.14/4.28 inference(unit_resolution,[status(thm)],[108, 107])).
% 4.14/4.28 tff(110,plain,
% 4.14/4.28 (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))),
% 4.14/4.28 inference(unit_resolution,[status(thm)],[109, 89])).
% 4.14/4.28 tff(111,plain,
% 4.14/4.28 ((~(((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))) | ((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))),
% 4.14/4.28 inference(tautology,[status(thm)],[])).
% 4.14/4.29 tff(112,plain,
% 4.14/4.29 (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))),
% 4.14/4.29 inference(unit_resolution,[status(thm)],[111, 110])).
% 4.14/4.29 tff(113,plain,
% 4.14/4.29 ((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))),
% 4.14/4.29 inference(unit_resolution,[status(thm)],[112, 60])).
% 4.14/4.29 tff(114,assumption,(~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))), introduced(assumption)).
% 4.14/4.29 tff(115,plain,
% 4.14/4.29 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 4.14/4.29 inference(bind,[status(th)],[])).
% 4.14/4.29 tff(116,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 4.14/4.29 inference(quant_intro,[status(thm)],[115])).
% 4.14/4.29 tff(117,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 4.14/4.29 inference(pull_quant,[status(thm)],[])).
% 4.14/4.29 tff(118,plain,
% 4.14/4.29 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 4.14/4.29 inference(bind,[status(th)],[])).
% 4.14/4.29 tff(119,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 4.14/4.29 inference(quant_intro,[status(thm)],[118])).
% 4.14/4.29 tff(120,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 4.14/4.29 inference(transitivity,[status(thm)],[119, 117])).
% 4.14/4.29 tff(121,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 4.14/4.29 inference(transitivity,[status(thm)],[120, 116])).
% 4.14/4.29 tff(122,plain,
% 4.14/4.29 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 4.14/4.29 inference(bind,[status(th)],[])).
% 4.14/4.29 tff(123,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 4.14/4.29 inference(quant_intro,[status(thm)],[122])).
% 4.14/4.29 tff(124,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 4.14/4.29 inference(transitivity,[status(thm)],[123, 121])).
% 4.14/4.29 tff(125,plain,
% 4.14/4.29 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 4.14/4.29 inference(bind,[status(th)],[])).
% 4.14/4.29 tff(126,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 4.14/4.29 inference(quant_intro,[status(thm)],[125])).
% 4.14/4.29 tff(127,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 4.14/4.29 inference(rewrite,[status(thm)],[])).
% 4.14/4.29 tff(128,plain,
% 4.14/4.29 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 4.14/4.29 inference(bind,[status(th)],[])).
% 4.14/4.29 tff(129,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 4.14/4.29 inference(quant_intro,[status(thm)],[128])).
% 4.14/4.29 tff(130,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_tarski')).
% 4.14/4.29 tff(131,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 4.14/4.29 inference(modus_ponens,[status(thm)],[130, 129])).
% 4.14/4.29 tff(132,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 4.14/4.29 inference(modus_ponens,[status(thm)],[131, 127])).
% 4.14/4.29 tff(133,plain,(
% 4.14/4.29 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 4.14/4.29 inference(skolemize,[status(sab)],[132])).
% 4.14/4.29 tff(134,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 4.14/4.29 inference(modus_ponens,[status(thm)],[133, 126])).
% 4.14/4.29 tff(135,plain,
% 4.14/4.29 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 4.14/4.29 inference(modus_ponens,[status(thm)],[134, 124])).
% 4.14/4.29 tff(136,plain,
% 4.14/4.29 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))),
% 4.14/4.29 inference(rewrite,[status(thm)],[])).
% 4.14/4.29 tff(137,plain,
% 4.14/4.29 ((~(~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) <=> (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))),
% 4.14/4.29 inference(rewrite,[status(thm)],[])).
% 4.14/4.29 tff(138,plain,
% 4.14/4.29 (((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | $false) <=> (~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))),
% 4.14/4.29 inference(rewrite,[status(thm)],[])).
% 4.14/4.29 tff(139,plain,
% 4.14/4.29 (($true | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))) <=> $true),
% 4.14/4.29 inference(rewrite,[status(thm)],[])).
% 4.14/4.29 tff(140,plain,
% 4.14/4.29 ((~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))) <=> (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))),
% 4.14/4.29 inference(rewrite,[status(thm)],[])).
% 4.14/4.29 tff(141,plain,
% 4.14/4.29 ((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) <=> $true),
% 4.14/4.29 inference(rewrite,[status(thm)],[])).
% 4.14/4.29 tff(142,plain,
% 4.14/4.29 (((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))) <=> ($true | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))),
% 4.14/4.29 inference(monotonicity,[status(thm)],[141, 140])).
% 4.14/4.29 tff(143,plain,
% 4.14/4.29 (((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))) <=> $true),
% 4.14/4.29 inference(transitivity,[status(thm)],[142, 139])).
% 4.14/4.29 tff(144,plain,
% 4.14/4.29 ((~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))) <=> (~$true)),
% 4.14/4.29 inference(monotonicity,[status(thm)],[143])).
% 4.14/4.29 tff(145,plain,
% 4.14/4.29 ((~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))) <=> $false),
% 4.14/4.29 inference(transitivity,[status(thm)],[144, 41])).
% 4.14/4.29 tff(146,plain,
% 4.14/4.29 ((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) <=> (~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))),
% 4.14/4.29 inference(rewrite,[status(thm)],[])).
% 4.14/4.29 tff(147,plain,
% 4.14/4.29 (($false | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) <=> (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))),
% 4.14/4.29 inference(rewrite,[status(thm)],[])).
% 4.14/4.29 tff(148,plain,
% 4.14/4.29 ((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) <=> (~$true)),
% 4.14/4.29 inference(monotonicity,[status(thm)],[141])).
% 4.14/4.29 tff(149,plain,
% 4.14/4.29 ((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) <=> $false),
% 4.14/4.29 inference(transitivity,[status(thm)],[148, 41])).
% 4.14/4.29 tff(150,plain,
% 4.14/4.29 (((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) <=> ($false | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))),
% 4.14/4.29 inference(monotonicity,[status(thm)],[149])).
% 4.14/4.29 tff(151,plain,
% 4.14/4.29 (((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) <=> (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))),
% 4.14/4.29 inference(transitivity,[status(thm)],[150, 147])).
% 4.14/4.29 tff(152,plain,
% 4.14/4.29 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) <=> (~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))),
% 4.14/4.29 inference(monotonicity,[status(thm)],[151])).
% 4.14/4.29 tff(153,plain,
% 4.14/4.29 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) <=> (~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))),
% 4.14/4.29 inference(transitivity,[status(thm)],[152, 146])).
% 4.14/4.29 tff(154,plain,
% 4.14/4.29 (((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))))) <=> ((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | $false)),
% 4.14/4.29 inference(monotonicity,[status(thm)],[153, 145])).
% 4.14/4.29 tff(155,plain,
% 4.14/4.29 (((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))))) <=> (~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))),
% 4.14/4.29 inference(transitivity,[status(thm)],[154, 138])).
% 4.14/4.29 tff(156,plain,
% 4.14/4.29 ((~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))))) <=> (~(~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))))),
% 4.14/4.29 inference(monotonicity,[status(thm)],[155])).
% 4.14/4.29 tff(157,plain,
% 4.14/4.29 ((~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))))) <=> (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))),
% 4.14/4.29 inference(transitivity,[status(thm)],[156, 137])).
% 4.14/4.29 tff(158,plain,
% 4.14/4.29 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))),
% 4.14/4.29 inference(monotonicity,[status(thm)],[157])).
% 4.14/4.29 tff(159,plain,
% 4.14/4.29 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))),
% 4.14/4.30 inference(transitivity,[status(thm)],[158, 136])).
% 4.14/4.30 tff(160,plain,
% 4.14/4.30 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))))))),
% 4.14/4.30 inference(quant_inst,[status(thm)],[])).
% 4.14/4.30 tff(161,plain,
% 4.14/4.30 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[160, 159])).
% 4.14/4.30 tff(162,plain,
% 4.14/4.30 ($false),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[161, 135, 114])).
% 4.14/4.30 tff(163,plain,(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.30 tff(164,assumption,(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))), introduced(assumption)).
% 4.14/4.30 tff(165,assumption,(~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))), introduced(assumption)).
% 4.14/4.30 tff(166,plain,
% 4.14/4.30 ((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) | (~((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))),
% 4.14/4.30 inference(tautology,[status(thm)],[])).
% 4.14/4.30 tff(167,plain,
% 4.14/4.30 ((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[166, 165])).
% 4.14/4.30 tff(168,plain,
% 4.14/4.30 (~((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[167, 164])).
% 4.14/4.30 tff(169,plain,
% 4.14/4.30 (((~![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_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(170,plain,
% 4.14/4.30 ((~(~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))) <=> (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(171,plain,
% 4.14/4.30 (((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))) | $false) <=> (~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(172,plain,
% 4.14/4.30 ((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))) <=> (~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(173,plain,
% 4.14/4.30 (($false | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))) <=> (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(174,plain,
% 4.14/4.30 ((~(singleton(A!7) = singleton(A!7))) <=> (~$true)),
% 4.14/4.30 inference(monotonicity,[status(thm)],[44])).
% 4.14/4.30 tff(175,plain,
% 4.14/4.30 ((~(singleton(A!7) = singleton(A!7))) <=> $false),
% 4.14/4.30 inference(transitivity,[status(thm)],[174, 41])).
% 4.14/4.30 tff(176,plain,
% 4.14/4.30 (((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))) <=> ($false | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[175])).
% 4.14/4.30 tff(177,plain,
% 4.14/4.30 (((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))) <=> (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))),
% 4.14/4.30 inference(transitivity,[status(thm)],[176, 173])).
% 4.14/4.30 tff(178,plain,
% 4.14/4.30 ((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))) <=> (~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[177])).
% 4.14/4.30 tff(179,plain,
% 4.14/4.30 ((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))) <=> (~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.30 inference(transitivity,[status(thm)],[178, 172])).
% 4.14/4.30 tff(180,plain,
% 4.14/4.30 (((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> ((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))) | $false)),
% 4.14/4.30 inference(monotonicity,[status(thm)],[179, 48])).
% 4.14/4.30 tff(181,plain,
% 4.14/4.30 (((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> (~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.30 inference(transitivity,[status(thm)],[180, 171])).
% 4.14/4.30 tff(182,plain,
% 4.14/4.30 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> (~(~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[181])).
% 4.14/4.30 tff(183,plain,
% 4.14/4.30 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))),
% 4.14/4.30 inference(transitivity,[status(thm)],[182, 170])).
% 4.14/4.30 tff(184,plain,
% 4.14/4.30 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[183])).
% 4.14/4.30 tff(185,plain,
% 4.14/4.30 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.30 inference(transitivity,[status(thm)],[184, 169])).
% 4.14/4.30 tff(186,plain,
% 4.14/4.30 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))),
% 4.14/4.30 inference(quant_inst,[status(thm)],[])).
% 4.14/4.30 tff(187,plain,
% 4.14/4.30 ((~![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_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[186, 185])).
% 4.14/4.30 tff(188,plain,
% 4.14/4.30 (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[187, 37])).
% 4.14/4.30 tff(189,plain,
% 4.14/4.30 (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) | in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))),
% 4.14/4.30 inference(tautology,[status(thm)],[])).
% 4.14/4.30 tff(190,plain,
% 4.14/4.30 ((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[189, 165])).
% 4.14/4.30 tff(191,plain,
% 4.14/4.30 ((~(((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))) | (~((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))),
% 4.14/4.30 inference(tautology,[status(thm)],[])).
% 4.14/4.30 tff(192,plain,
% 4.14/4.30 ((~((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[191, 110])).
% 4.14/4.30 tff(193,plain,
% 4.14/4.30 (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[192, 190])).
% 4.14/4.30 tff(194,plain,
% 4.14/4.30 ((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)),
% 4.14/4.30 inference(tautology,[status(thm)],[])).
% 4.14/4.30 tff(195,plain,
% 4.14/4.30 ((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[194, 193])).
% 4.14/4.30 tff(196,plain,
% 4.14/4.30 (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[195, 188])).
% 4.14/4.30 tff(197,plain,
% 4.14/4.30 (((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)) | (~(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7))),
% 4.14/4.30 inference(tautology,[status(thm)],[])).
% 4.14/4.30 tff(198,plain,
% 4.14/4.30 ($false),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[197, 196, 168])).
% 4.14/4.30 tff(199,plain,((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.30 tff(200,plain,
% 4.14/4.30 (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[199, 163])).
% 4.14/4.30 tff(201,plain,
% 4.14/4.30 ((~((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))),
% 4.14/4.30 inference(tautology,[status(thm)],[])).
% 4.14/4.30 tff(202,plain,
% 4.14/4.30 ((~((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[201, 200])).
% 4.14/4.30 tff(203,plain,
% 4.14/4.30 ($false),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[202, 113, 16])).
% 4.14/4.30 tff(204,plain,(~(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.30 tff(205,plain,
% 4.14/4.30 ((~(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))),
% 4.14/4.30 inference(tautology,[status(thm)],[])).
% 4.14/4.30 tff(206,plain,
% 4.14/4.30 ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[205, 200, 163])).
% 4.14/4.30 tff(207,plain,
% 4.14/4.30 ((~((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5))) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)),
% 4.14/4.30 inference(tautology,[status(thm)],[])).
% 4.14/4.30 tff(208,plain,
% 4.14/4.30 ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) | (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[207, 206])).
% 4.14/4.30 tff(209,plain,
% 4.14/4.30 (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[208, 204])).
% 4.14/4.30 tff(210,plain,
% 4.14/4.30 ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) <=> (C!5 = A!7)),
% 4.14/4.30 inference(monotonicity,[status(thm)],[209])).
% 4.14/4.30 tff(211,plain,
% 4.14/4.30 ((tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7) <=> (A!7 = C!5)),
% 4.14/4.30 inference(transitivity,[status(thm)],[210, 1])).
% 4.14/4.30 tff(212,plain,
% 4.14/4.30 ((A!7 = C!5) <=> (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7)),
% 4.14/4.30 inference(symmetry,[status(thm)],[211])).
% 4.14/4.30 tff(213,assumption,(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5), introduced(assumption)).
% 4.14/4.30 tff(214,plain,
% 4.14/4.30 (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)) <=> in(C!5, singleton(A!7))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[213])).
% 4.14/4.30 tff(215,plain,
% 4.14/4.30 (in(C!5, singleton(A!7)) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))),
% 4.14/4.30 inference(symmetry,[status(thm)],[214])).
% 4.14/4.30 tff(216,plain,
% 4.14/4.30 ((~in(C!5, singleton(A!7))) <=> (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7)))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[215])).
% 4.14/4.30 tff(217,plain,
% 4.14/4.30 ((A!7 = C!5) <=> (C!5 = A!7)),
% 4.14/4.30 inference(symmetry,[status(thm)],[1])).
% 4.14/4.30 tff(218,assumption,(~in(C!5, B!6)), introduced(assumption)).
% 4.14/4.30 tff(219,assumption,(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)), introduced(assumption)).
% 4.14/4.30 tff(220,plain,
% 4.14/4.30 (set_intersection2(unordered_pair(C!5, A!7), B!6) = unordered_pair(C!5, A!7)),
% 4.14/4.30 inference(symmetry,[status(thm)],[219])).
% 4.14/4.30 tff(221,plain,
% 4.14/4.30 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 4.14/4.30 inference(bind,[status(th)],[])).
% 4.14/4.30 tff(222,plain,
% 4.14/4.30 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 4.14/4.30 inference(quant_intro,[status(thm)],[221])).
% 4.14/4.30 tff(223,plain,
% 4.14/4.30 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(224,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 4.14/4.30 tff(225,plain,
% 4.14/4.30 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[224, 223])).
% 4.14/4.30 tff(226,plain,(
% 4.14/4.30 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 4.14/4.30 inference(skolemize,[status(sab)],[225])).
% 4.14/4.30 tff(227,plain,
% 4.14/4.30 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[226, 222])).
% 4.14/4.30 tff(228,plain,
% 4.14/4.30 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(unordered_pair(A!7, C!5), B!6) = set_intersection2(B!6, unordered_pair(A!7, C!5)))),
% 4.14/4.30 inference(quant_inst,[status(thm)],[])).
% 4.14/4.30 tff(229,plain,
% 4.14/4.30 (set_intersection2(unordered_pair(A!7, C!5), B!6) = set_intersection2(B!6, unordered_pair(A!7, C!5))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[228, 227])).
% 4.14/4.30 tff(230,plain,
% 4.14/4.30 (set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(A!7, C!5), B!6)),
% 4.14/4.30 inference(symmetry,[status(thm)],[229])).
% 4.14/4.30 tff(231,plain,
% 4.14/4.30 (set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(C!5, A!7)),
% 4.14/4.30 inference(transitivity,[status(thm)],[230, 103, 220])).
% 4.14/4.30 tff(232,plain,
% 4.14/4.30 (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[231])).
% 4.14/4.30 tff(233,plain,
% 4.14/4.30 (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))),
% 4.14/4.30 inference(symmetry,[status(thm)],[232])).
% 4.14/4.30 tff(234,plain,
% 4.14/4.30 ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[233])).
% 4.14/4.30 tff(235,plain,
% 4.14/4.30 (unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(A!7, C!5), B!6)),
% 4.14/4.30 inference(transitivity,[status(thm)],[219, 102])).
% 4.14/4.30 tff(236,plain,
% 4.14/4.30 ((unordered_pair(C!5, A!7) = singleton(A!7)) <=> (set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[235])).
% 4.14/4.30 tff(237,plain,
% 4.14/4.30 ((set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)) <=> (unordered_pair(C!5, A!7) = singleton(A!7))),
% 4.14/4.30 inference(symmetry,[status(thm)],[236])).
% 4.14/4.30 tff(238,plain,
% 4.14/4.30 ((~(set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7))) <=> (~(unordered_pair(C!5, A!7) = singleton(A!7)))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[237])).
% 4.14/4.30 tff(239,plain,
% 4.14/4.30 (~(unordered_pair(C!5, A!7) = singleton(A!7))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[105, 238])).
% 4.14/4.30 tff(240,plain,
% 4.14/4.30 ((~![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)))))))) | (~((~((~(unordered_pair(C!5, A!7) = singleton(A!7))) | (in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6) = A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))))))),
% 4.14/4.30 inference(quant_inst,[status(thm)],[])).
% 4.14/4.30 tff(241,plain,
% 4.14/4.30 (~((~((~(unordered_pair(C!5, A!7) = singleton(A!7))) | (in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6) = A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))))))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[240, 37])).
% 4.14/4.30 tff(242,plain,
% 4.14/4.30 (((~((~(unordered_pair(C!5, A!7) = singleton(A!7))) | (in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6) = A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))))) | ((unordered_pair(C!5, A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))))),
% 4.14/4.30 inference(tautology,[status(thm)],[])).
% 4.14/4.30 tff(243,plain,
% 4.14/4.30 ((unordered_pair(C!5, A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[242, 241])).
% 4.14/4.30 tff(244,plain,
% 4.14/4.30 ((~((unordered_pair(C!5, A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))))) | (unordered_pair(C!5, A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))),
% 4.14/4.30 inference(tautology,[status(thm)],[])).
% 4.14/4.30 tff(245,plain,
% 4.14/4.30 ((unordered_pair(C!5, A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[244, 243])).
% 4.14/4.30 tff(246,plain,
% 4.14/4.30 (~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[245, 239])).
% 4.14/4.30 tff(247,assumption,(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7), introduced(assumption)).
% 4.14/4.30 tff(248,plain,
% 4.14/4.30 ((in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) | (~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))),
% 4.14/4.30 inference(tautology,[status(thm)],[])).
% 4.14/4.30 tff(249,plain,
% 4.14/4.30 (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[248, 247, 246])).
% 4.14/4.31 tff(250,plain,
% 4.14/4.31 (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[249, 234])).
% 4.14/4.31 tff(251,plain,
% 4.14/4.31 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7)))))))))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(252,plain,
% 4.14/4.31 ((~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7)))))))) <=> (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7))))))))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(253,plain,
% 4.14/4.31 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7)))))))))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[252])).
% 4.14/4.31 tff(254,plain,
% 4.14/4.31 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7)))))))))),
% 4.14/4.31 inference(transitivity,[status(thm)],[253, 251])).
% 4.14/4.31 tff(255,plain,
% 4.14/4.31 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7))))))))),
% 4.14/4.31 inference(quant_inst,[status(thm)],[])).
% 4.14/4.31 tff(256,plain,
% 4.14/4.31 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7))))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[255, 254])).
% 4.14/4.31 tff(257,plain,
% 4.14/4.31 (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7)))))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[256, 135])).
% 4.14/4.31 tff(258,plain,
% 4.14/4.31 (((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = C!5) | (tptp_fun_D_1(set_intersection2(B!6, unordered_pair(A!7, C!5)), C!5, A!7) = A!7))))))) | ((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))),
% 4.14/4.31 inference(tautology,[status(thm)],[])).
% 4.14/4.31 tff(259,plain,
% 4.14/4.31 ((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[258, 257])).
% 4.14/4.31 tff(260,plain,
% 4.14/4.31 (set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5)),
% 4.14/4.31 inference(transitivity,[status(thm)],[230, 103, 220, 101])).
% 4.14/4.31 tff(261,plain,
% 4.14/4.31 ((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 4.14/4.31 inference(tautology,[status(thm)],[])).
% 4.14/4.31 tff(262,plain,
% 4.14/4.31 ((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[261, 260])).
% 4.14/4.31 tff(263,plain,
% 4.14/4.31 (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[262, 259])).
% 4.14/4.31 tff(264,plain,
% 4.14/4.31 (((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)) | (~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))),
% 4.14/4.31 inference(tautology,[status(thm)],[])).
% 4.14/4.31 tff(265,plain,
% 4.14/4.31 ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[264, 247])).
% 4.14/4.31 tff(266,plain,
% 4.14/4.31 ((~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))) | in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) | (~((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 4.14/4.31 inference(tautology,[status(thm)],[])).
% 4.14/4.31 tff(267,plain,
% 4.14/4.31 (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[266, 265, 263])).
% 4.14/4.31 tff(268,plain,
% 4.14/4.31 ($false),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[267, 250])).
% 4.14/4.31 tff(269,plain,((~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)) | (~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.31 tff(270,plain,
% 4.14/4.31 (~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[269, 219])).
% 4.14/4.31 tff(271,plain,
% 4.14/4.31 ((in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)) | in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)),
% 4.14/4.31 inference(tautology,[status(thm)],[])).
% 4.14/4.31 tff(272,plain,
% 4.14/4.31 (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[271, 270, 246])).
% 4.14/4.31 tff(273,plain,
% 4.14/4.31 (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[272, 233])).
% 4.14/4.31 tff(274,plain,
% 4.14/4.31 ((~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))),
% 4.14/4.31 inference(tautology,[status(thm)],[])).
% 4.14/4.31 tff(275,plain,
% 4.14/4.31 ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[274, 273, 263])).
% 4.14/4.31 tff(276,plain,
% 4.14/4.31 ((~((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)),
% 4.14/4.31 inference(tautology,[status(thm)],[])).
% 4.14/4.31 tff(277,plain,
% 4.14/4.31 (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[276, 275, 270])).
% 4.14/4.31 tff(278,plain,
% 4.14/4.31 (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6) <=> in(C!5, B!6)),
% 4.14/4.31 inference(monotonicity,[status(thm)],[277])).
% 4.14/4.31 tff(279,plain,
% 4.14/4.31 (in(C!5, B!6) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6)),
% 4.14/4.31 inference(symmetry,[status(thm)],[278])).
% 4.14/4.31 tff(280,plain,
% 4.14/4.31 ((~in(C!5, B!6)) <=> (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[279])).
% 4.14/4.31 tff(281,plain,
% 4.14/4.31 (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6)),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[218, 280])).
% 4.14/4.31 tff(282,plain,
% 4.14/4.31 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6))) | (~(((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6))) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6)) | (((~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, set_intersection2(B!6, unordered_pair(A!7, C!5))), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, set_intersection2(B!6, unordered_pair(A!7, C!5))), B!6))) <=> in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, set_intersection2(B!6, unordered_pair(A!7, C!5))), set_intersection2(B!6, unordered_pair(A!7, C!5))))))))),
% 4.14/4.31 inference(quant_inst,[status(thm)],[])).
% 4.14/4.31 tff(283,plain,
% 4.14/4.31 (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6))) | (~(((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6))) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6)) | (((~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, set_intersection2(B!6, unordered_pair(A!7, C!5))), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, set_intersection2(B!6, unordered_pair(A!7, C!5))), B!6))) <=> in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, set_intersection2(B!6, unordered_pair(A!7, C!5))), set_intersection2(B!6, unordered_pair(A!7, C!5)))))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[282, 79])).
% 4.14/4.31 tff(284,plain,
% 4.14/4.31 (((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6))) | (~(((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6))) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6)) | (((~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, set_intersection2(B!6, unordered_pair(A!7, C!5))), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, set_intersection2(B!6, unordered_pair(A!7, C!5))), B!6))) <=> in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, set_intersection2(B!6, unordered_pair(A!7, C!5))), set_intersection2(B!6, unordered_pair(A!7, C!5))))))) | ((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6))) | (~(((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6))) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))))))),
% 4.14/4.31 inference(tautology,[status(thm)],[])).
% 4.14/4.31 tff(285,plain,
% 4.14/4.31 ((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6))) | (~(((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6))) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[284, 283])).
% 4.14/4.31 tff(286,plain,
% 4.14/4.31 (set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6) = set_intersection2(unordered_pair(A!7, C!5), B!6)),
% 4.14/4.31 inference(monotonicity,[status(thm)],[260])).
% 4.14/4.31 tff(287,plain,
% 4.14/4.31 (set_intersection2(unordered_pair(A!7, C!5), B!6) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6)),
% 4.14/4.31 inference(symmetry,[status(thm)],[286])).
% 4.14/4.31 tff(288,plain,
% 4.14/4.31 (set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6)),
% 4.14/4.31 inference(transitivity,[status(thm)],[230, 287])).
% 4.14/4.31 tff(289,plain,
% 4.14/4.31 ((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6))) | (~(((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6))) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))))))) | (~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6))) | (~(((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6))) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))))),
% 4.14/4.32 inference(tautology,[status(thm)],[])).
% 4.14/4.32 tff(290,plain,
% 4.14/4.32 (~(((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6))) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[289, 288, 285])).
% 4.14/4.32 tff(291,plain,
% 4.14/4.32 ((((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6))) <=> in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))))),
% 4.14/4.32 inference(tautology,[status(thm)],[])).
% 4.14/4.32 tff(292,plain,
% 4.14/4.32 (~((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[291, 273, 290])).
% 4.14/4.32 tff(293,plain,
% 4.14/4.32 (((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6))) | in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6)),
% 4.14/4.32 inference(tautology,[status(thm)],[])).
% 4.14/4.32 tff(294,plain,
% 4.14/4.32 (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), B!6)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[293, 292])).
% 4.14/4.32 tff(295,plain,
% 4.14/4.32 ($false),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[294, 281])).
% 4.14/4.32 tff(296,plain,((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | in(C!5, B!6)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.32 tff(297,plain,
% 4.14/4.32 (~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[296, 218])).
% 4.14/4.32 tff(298,plain,
% 4.14/4.32 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | (~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | (~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))))),
% 4.14/4.32 inference(rewrite,[status(thm)],[])).
% 4.14/4.32 tff(299,plain,
% 4.14/4.32 ((~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))))) <=> (~((~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | (~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))))),
% 4.14/4.32 inference(rewrite,[status(thm)],[])).
% 4.14/4.32 tff(300,plain,
% 4.14/4.32 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | (~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[299])).
% 4.14/4.32 tff(301,plain,
% 4.14/4.32 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | (~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))))),
% 4.14/4.32 inference(transitivity,[status(thm)],[300, 298])).
% 4.14/4.32 tff(302,plain,
% 4.14/4.32 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))))))),
% 4.14/4.32 inference(quant_inst,[status(thm)],[])).
% 4.14/4.32 tff(303,plain,
% 4.14/4.32 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | (~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))))),
% 4.14/4.32 inference(modus_ponens,[status(thm)],[302, 301])).
% 4.14/4.32 tff(304,plain,
% 4.14/4.32 (~((~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | (~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[303, 79])).
% 4.14/4.32 tff(305,plain,
% 4.14/4.32 (((~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | (~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))) <=> in(tptp_fun_D_2(B!6, unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))) | ((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))),
% 4.14/4.32 inference(tautology,[status(thm)],[])).
% 4.14/4.32 tff(306,plain,
% 4.14/4.32 ((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[305, 304])).
% 4.14/4.32 tff(307,plain,
% 4.14/4.32 ((~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))) | (unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))),
% 4.14/4.32 inference(tautology,[status(thm)],[])).
% 4.14/4.32 tff(308,plain,
% 4.14/4.32 ((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[307, 306])).
% 4.14/4.32 tff(309,plain,
% 4.14/4.32 (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[308, 297])).
% 4.14/4.32 tff(310,assumption,(((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))), introduced(assumption)).
% 4.14/4.32 tff(311,assumption,(~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))), introduced(assumption)).
% 4.14/4.32 tff(312,plain,
% 4.14/4.32 (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) | in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))),
% 4.14/4.32 inference(tautology,[status(thm)],[])).
% 4.14/4.32 tff(313,plain,
% 4.14/4.32 ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[312, 311])).
% 4.14/4.32 tff(314,plain,
% 4.14/4.32 ((~(((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) | (~((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))) | in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))),
% 4.14/4.32 inference(tautology,[status(thm)],[])).
% 4.14/4.32 tff(315,plain,
% 4.14/4.32 ($false),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[314, 313, 311, 310])).
% 4.14/4.32 tff(316,plain,(in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) | (~(((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.32 tff(317,plain,
% 4.14/4.32 (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[316, 309])).
% 4.14/4.32 tff(318,plain,
% 4.14/4.32 ((~(((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) | ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))),
% 4.14/4.32 inference(tautology,[status(thm)],[])).
% 4.14/4.32 tff(319,plain,
% 4.14/4.32 ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[318, 317, 309])).
% 4.14/4.32 tff(320,plain,
% 4.14/4.32 ((~((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))),
% 4.14/4.32 inference(tautology,[status(thm)],[])).
% 4.14/4.32 tff(321,plain,
% 4.14/4.32 (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[320, 319, 317])).
% 4.14/4.32 tff(322,plain,
% 4.14/4.32 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7))))))))),
% 4.14/4.32 inference(quant_inst,[status(thm)],[])).
% 4.14/4.32 tff(323,plain,
% 4.14/4.32 (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7)))))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[322, 135])).
% 4.14/4.32 tff(324,plain,
% 4.14/4.32 (((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7))))))) | ((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7))))),
% 4.14/4.33 inference(tautology,[status(thm)],[])).
% 4.14/4.33 tff(325,plain,
% 4.14/4.33 ((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[324, 323])).
% 4.14/4.33 tff(326,plain,
% 4.14/4.33 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))),
% 4.14/4.33 inference(quant_inst,[status(thm)],[])).
% 4.14/4.33 tff(327,plain,
% 4.14/4.33 (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[326, 98])).
% 4.14/4.33 tff(328,plain,
% 4.14/4.33 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7))))) | (~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.33 inference(tautology,[status(thm)],[])).
% 4.14/4.33 tff(329,plain,
% 4.14/4.33 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7))))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[328, 327])).
% 4.14/4.33 tff(330,plain,
% 4.14/4.33 (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[329, 325])).
% 4.14/4.33 tff(331,assumption,(~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)), introduced(assumption)).
% 4.14/4.33 tff(332,plain,
% 4.14/4.33 (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) | in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 4.14/4.33 inference(tautology,[status(thm)],[])).
% 4.14/4.33 tff(333,plain,
% 4.14/4.33 ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[332, 331])).
% 4.14/4.33 tff(334,plain,
% 4.14/4.33 (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[314, 333, 310])).
% 4.14/4.33 tff(335,assumption,(~(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)), introduced(assumption)).
% 4.14/4.33 tff(336,assumption,(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7), introduced(assumption)).
% 4.14/4.33 tff(337,plain,
% 4.14/4.33 (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6) <=> in(A!7, B!6)),
% 4.14/4.33 inference(monotonicity,[status(thm)],[336])).
% 4.14/4.33 tff(338,plain,
% 4.14/4.33 (in(A!7, B!6) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 4.14/4.33 inference(symmetry,[status(thm)],[337])).
% 4.14/4.33 tff(339,plain,
% 4.14/4.33 (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[15, 338])).
% 4.14/4.33 tff(340,plain,
% 4.14/4.33 ($false),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[331, 339])).
% 4.14/4.33 tff(341,plain,((~(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)) | in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.33 tff(342,plain,
% 4.14/4.33 (~(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[341, 331])).
% 4.14/4.33 tff(343,plain,
% 4.14/4.33 ((~((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7))) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)),
% 4.14/4.33 inference(tautology,[status(thm)],[])).
% 4.14/4.33 tff(344,plain,
% 4.14/4.33 (~((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[343, 342, 335])).
% 4.14/4.33 tff(345,plain,
% 4.14/4.33 ((~(in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7))),
% 4.14/4.33 inference(tautology,[status(thm)],[])).
% 4.14/4.33 tff(346,plain,
% 4.14/4.33 ($false),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[345, 344, 334, 330])).
% 4.14/4.33 tff(347,plain,(in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (~(((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.33 tff(348,plain,
% 4.14/4.33 (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[347, 321, 309])).
% 4.14/4.33 tff(349,plain,
% 4.14/4.33 ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7) <=> (C!5 = A!7)),
% 4.14/4.33 inference(monotonicity,[status(thm)],[348])).
% 4.14/4.33 tff(350,plain,
% 4.14/4.33 ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7) <=> (A!7 = C!5)),
% 4.14/4.33 inference(transitivity,[status(thm)],[349, 1])).
% 4.14/4.33 tff(351,plain,
% 4.14/4.33 ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7) <=> (C!5 = A!7)),
% 4.14/4.33 inference(transitivity,[status(thm)],[350, 217])).
% 4.14/4.33 tff(352,plain,
% 4.14/4.33 ((~(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)) <=> (~(C!5 = A!7))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[351])).
% 4.14/4.33 tff(353,plain,
% 4.14/4.33 (~(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[341, 321])).
% 4.14/4.33 tff(354,plain,
% 4.14/4.33 (~(C!5 = A!7)),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[353, 352])).
% 4.14/4.33 tff(355,assumption,(~(in(C!5, singleton(A!7)) <=> (C!5 = A!7))), introduced(assumption)).
% 4.14/4.33 tff(356,plain,
% 4.14/4.33 (((~![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(C!5, singleton(A!7)) <=> (C!5 = A!7))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(357,plain,
% 4.14/4.33 ((~(~(in(C!5, singleton(A!7)) <=> (C!5 = A!7)))) <=> (in(C!5, singleton(A!7)) <=> (C!5 = A!7))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(358,plain,
% 4.14/4.33 (((~(in(C!5, singleton(A!7)) <=> (C!5 = A!7))) | $false) <=> (~(in(C!5, singleton(A!7)) <=> (C!5 = A!7)))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(359,plain,
% 4.14/4.33 ((~(in(C!5, singleton(A!7)) <=> (C!5 = A!7))) <=> (~(in(C!5, singleton(A!7)) <=> (C!5 = A!7)))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(360,plain,
% 4.14/4.33 (($false | (in(C!5, singleton(A!7)) <=> (C!5 = A!7))) <=> (in(C!5, singleton(A!7)) <=> (C!5 = A!7))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(361,plain,
% 4.14/4.33 (((~(singleton(A!7) = singleton(A!7))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7))) <=> ($false | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[175])).
% 4.14/4.33 tff(362,plain,
% 4.14/4.33 (((~(singleton(A!7) = singleton(A!7))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7))) <=> (in(C!5, singleton(A!7)) <=> (C!5 = A!7))),
% 4.14/4.33 inference(transitivity,[status(thm)],[361, 360])).
% 4.14/4.33 tff(363,plain,
% 4.14/4.33 ((~((~(singleton(A!7) = singleton(A!7))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))) <=> (~(in(C!5, singleton(A!7)) <=> (C!5 = A!7)))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[362])).
% 4.14/4.33 tff(364,plain,
% 4.14/4.33 ((~((~(singleton(A!7) = singleton(A!7))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))) <=> (~(in(C!5, singleton(A!7)) <=> (C!5 = A!7)))),
% 4.14/4.33 inference(transitivity,[status(thm)],[363, 359])).
% 4.14/4.33 tff(365,plain,
% 4.14/4.33 (((~((~(singleton(A!7) = singleton(A!7))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> ((~(in(C!5, singleton(A!7)) <=> (C!5 = A!7))) | $false)),
% 4.14/4.33 inference(monotonicity,[status(thm)],[364, 48])).
% 4.14/4.33 tff(366,plain,
% 4.14/4.33 (((~((~(singleton(A!7) = singleton(A!7))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> (~(in(C!5, singleton(A!7)) <=> (C!5 = A!7)))),
% 4.14/4.33 inference(transitivity,[status(thm)],[365, 358])).
% 4.14/4.33 tff(367,plain,
% 4.14/4.33 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> (~(~(in(C!5, singleton(A!7)) <=> (C!5 = A!7))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[366])).
% 4.14/4.33 tff(368,plain,
% 4.14/4.33 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> (in(C!5, singleton(A!7)) <=> (C!5 = A!7))),
% 4.14/4.33 inference(transitivity,[status(thm)],[367, 357])).
% 4.14/4.33 tff(369,plain,
% 4.14/4.33 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[368])).
% 4.14/4.33 tff(370,plain,
% 4.14/4.33 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))),
% 4.14/4.33 inference(transitivity,[status(thm)],[369, 356])).
% 4.14/4.33 tff(371,plain,
% 4.14/4.33 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!7) = singleton(A!7))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | (~(in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7)) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))))),
% 4.14/4.33 inference(quant_inst,[status(thm)],[])).
% 4.14/4.33 tff(372,plain,
% 4.14/4.33 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(C!5, singleton(A!7)) <=> (C!5 = A!7))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[371, 370])).
% 4.14/4.33 tff(373,plain,
% 4.14/4.33 ($false),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[372, 37, 355])).
% 4.14/4.33 tff(374,plain,(in(C!5, singleton(A!7)) <=> (C!5 = A!7)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.33 tff(375,plain,
% 4.14/4.33 ((~(in(C!5, singleton(A!7)) <=> (C!5 = A!7))) | (~in(C!5, singleton(A!7))) | (C!5 = A!7)),
% 4.14/4.33 inference(tautology,[status(thm)],[])).
% 4.14/4.33 tff(376,plain,
% 4.14/4.33 ((~in(C!5, singleton(A!7))) | (C!5 = A!7)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[375, 374])).
% 4.14/4.33 tff(377,plain,
% 4.14/4.33 (~in(C!5, singleton(A!7))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[376, 354])).
% 4.14/4.33 tff(378,plain,
% 4.14/4.33 (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[377, 216])).
% 4.14/4.33 tff(379,plain,
% 4.14/4.33 (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6) <=> in(C!5, B!6)),
% 4.14/4.33 inference(monotonicity,[status(thm)],[213])).
% 4.14/4.33 tff(380,plain,
% 4.14/4.33 (in(C!5, B!6) <=> in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 4.14/4.33 inference(symmetry,[status(thm)],[379])).
% 4.14/4.33 tff(381,plain,
% 4.14/4.33 ((~in(C!5, B!6)) <=> (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[380])).
% 4.14/4.33 tff(382,plain,
% 4.14/4.33 (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[218, 381])).
% 4.14/4.33 tff(383,assumption,(in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)), introduced(assumption)).
% 4.14/4.33 tff(384,plain,
% 4.14/4.33 ($false),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[383, 382])).
% 4.14/4.33 tff(385,plain,((~(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | in(C!5, B!6)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.33 tff(386,plain,
% 4.14/4.33 (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[385, 213, 218])).
% 4.14/4.33 tff(387,plain,
% 4.14/4.33 (((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))) | in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 4.14/4.33 inference(tautology,[status(thm)],[])).
% 4.14/4.33 tff(388,plain,
% 4.14/4.33 ((~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), B!6)) | (~in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[387, 386])).
% 4.14/4.33 tff(389,plain,
% 4.14/4.33 (in(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)), singleton(A!7))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[192, 388])).
% 4.14/4.33 tff(390,plain,
% 4.14/4.33 ($false),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[389, 378])).
% 4.14/4.33 tff(391,plain,((~(tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = C!5)) | in(C!5, B!6)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.33 tff(392,plain,
% 4.14/4.33 (in(C!5, B!6)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[391, 209])).
% 4.14/4.33 tff(393,plain,
% 4.14/4.33 ((~(~((~in(C!5, B!6)) | (A!7 = C!5)))) <=> ((~in(C!5, B!6)) | (A!7 = C!5))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(394,plain,
% 4.14/4.33 ((in(C!5, B!6) & (~(A!7 = C!5))) <=> (~((~in(C!5, B!6)) | (A!7 = C!5)))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(395,plain,
% 4.14/4.33 ((~(in(C!5, B!6) & (~(A!7 = C!5)))) <=> (~(~((~in(C!5, B!6)) | (A!7 = C!5))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[394])).
% 4.14/4.33 tff(396,plain,
% 4.14/4.33 ((~(in(C!5, B!6) & (~(A!7 = C!5)))) <=> ((~in(C!5, B!6)) | (A!7 = C!5))),
% 4.14/4.33 inference(transitivity,[status(thm)],[395, 393])).
% 4.14/4.33 tff(397,plain,
% 4.14/4.33 (~(in(C!5, B!6) & (~(A!7 = C!5)))),
% 4.14/4.33 inference(or_elim,[status(thm)],[14])).
% 4.14/4.33 tff(398,plain,
% 4.14/4.33 ((~in(C!5, B!6)) | (A!7 = C!5)),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[397, 396])).
% 4.14/4.33 tff(399,plain,
% 4.14/4.33 (A!7 = C!5),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[398, 392])).
% 4.14/4.33 tff(400,plain,
% 4.14/4.33 (tptp_fun_D_2(singleton(A!7), B!6, unordered_pair(C!5, A!7)) = A!7),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[399, 212])).
% 4.14/4.33 tff(401,plain,
% 4.14/4.33 ($false),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[204, 400])).
% 4.14/4.33 % SZS output end Proof
% 4.14/4.34 % E exiting
%------------------------------------------------------------------------------