%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET920+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET920+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:50:54 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.42 % SZS status Theorem
% 0.22/0.42 % SZS output start Proof
% 0.22/0.42 tff(in_type, type, (
% 0.22/0.42 in: ( $i * $i ) > $o)).
% 0.22/0.42 tff(unordered_pair_type, type, (
% 0.22/0.42 unordered_pair: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_B_5_type, type, (
% 0.22/0.42 tptp_fun_B_5: $i)).
% 0.22/0.42 tff(tptp_fun_A_6_type, type, (
% 0.22/0.42 tptp_fun_A_6: $i)).
% 0.22/0.42 tff(tptp_fun_D_1_type, type, (
% 0.22/0.42 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_C_4_type, type, (
% 0.22/0.42 tptp_fun_C_4: $i)).
% 0.22/0.42 tff(set_intersection2_type, type, (
% 0.22/0.42 set_intersection2: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_D_0_type, type, (
% 0.22/0.42 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.22/0.42 tff(1,plain,
% 0.22/0.42 ((~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(2,plain,
% 0.22/0.42 ((~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B)) => in(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(3,axiom,(~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B)) => in(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t63_zfmisc_1')).
% 0.22/0.42 tff(4,plain,
% 0.22/0.42 (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.22/0.42 tff(5,plain,
% 0.22/0.42 (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.22/0.42 tff(6,plain,
% 0.22/0.42 (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.22/0.42 tff(7,plain,
% 0.22/0.42 (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.22/0.42 tff(8,plain,(
% 0.22/0.42 ~((~(set_intersection2(unordered_pair(A!6, B!5), C!4) = unordered_pair(A!6, B!5))) | in(A!6, C!4))),
% 0.22/0.42 inference(skolemize,[status(sab)],[7])).
% 0.22/0.42 tff(9,plain,
% 0.22/0.42 (~in(A!6, C!4)),
% 0.22/0.42 inference(or_elim,[status(thm)],[8])).
% 0.22/0.42 tff(10,plain,
% 0.22/0.42 (((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))) | in(A!6, C!4)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(11,plain,
% 0.22/0.42 ((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.22/0.42 tff(12,assumption,(~in(A!6, unordered_pair(A!6, B!5))), introduced(assumption)).
% 0.22/0.42 tff(13,plain,
% 0.22/0.42 (^[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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(14,plain,
% 0.22/0.42 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.22/0.42 tff(15,plain,
% 0.22/0.42 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.42 inference(pull_quant,[status(thm)],[])).
% 0.22/0.42 tff(16,plain,
% 0.22/0.42 (^[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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(17,plain,
% 0.22/0.42 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.22/0.42 tff(18,plain,
% 0.22/0.42 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[17, 15])).
% 0.22/0.42 tff(19,plain,
% 0.22/0.42 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[18, 14])).
% 0.22/0.42 tff(20,plain,
% 0.22/0.42 (^[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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(21,plain,
% 0.22/0.42 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.22/0.42 tff(22,plain,
% 0.22/0.42 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[21, 19])).
% 0.22/0.42 tff(23,plain,
% 0.22/0.42 (^[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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))) <=> (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(24,plain,
% 0.22/0.42 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.42 tff(25,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(26,plain,
% 0.22/0.42 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(27,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.42 tff(28,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tarski')).
% 0.22/0.42 tff(29,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.22/0.42 tff(31,plain,(
% 0.22/0.42 ![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[30])).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 (((~![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | in(A!6, unordered_pair(A!6, B!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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | in(A!6, unordered_pair(A!6, B!5)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 ((~(~in(A!6, unordered_pair(A!6, B!5)))) <=> in(A!6, unordered_pair(A!6, B!5))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 (((~in(A!6, unordered_pair(A!6, B!5))) | $false) <=> (~in(A!6, unordered_pair(A!6, B!5)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 ((~$true) <=> $false),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 (($true | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))) <=> $true),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 ((~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))) <=> (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 ((in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))) <=> (in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(41,plain,
% 0.22/0.42 ((~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))) <=> (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[40])).
% 0.22/0.42 tff(42,plain,
% 0.22/0.42 ((~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))) <=> (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[41, 39])).
% 0.22/0.42 tff(43,plain,
% 0.22/0.42 ((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) <=> $true),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 (((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))) <=> ($true | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[43, 42])).
% 0.22/0.43 tff(45,plain,
% 0.22/0.43 (((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))) <=> $true),
% 0.22/0.43 inference(transitivity,[status(thm)],[44, 38])).
% 0.22/0.43 tff(46,plain,
% 0.22/0.43 ((~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))))) <=> (~$true)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[45])).
% 0.22/0.43 tff(47,plain,
% 0.22/0.43 ((~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))))) <=> $false),
% 0.22/0.43 inference(transitivity,[status(thm)],[46, 37])).
% 0.22/0.43 tff(48,plain,
% 0.22/0.43 ((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) <=> (~in(A!6, unordered_pair(A!6, B!5)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(49,plain,
% 0.22/0.43 (((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))))) <=> ((~in(A!6, unordered_pair(A!6, B!5))) | $false)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[48, 47])).
% 0.22/0.43 tff(50,plain,
% 0.22/0.43 (((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))))) <=> (~in(A!6, unordered_pair(A!6, B!5)))),
% 0.22/0.43 inference(transitivity,[status(thm)],[49, 36])).
% 0.22/0.43 tff(51,plain,
% 0.22/0.43 ((~((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))))))) <=> (~(~in(A!6, unordered_pair(A!6, B!5))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[50])).
% 0.22/0.43 tff(52,plain,
% 0.22/0.43 ((~((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))))))) <=> in(A!6, unordered_pair(A!6, B!5))),
% 0.22/0.43 inference(transitivity,[status(thm)],[51, 35])).
% 0.22/0.43 tff(53,plain,
% 0.22/0.43 (((~![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))))))) <=> ((~![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | in(A!6, unordered_pair(A!6, B!5)))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[52])).
% 0.22/0.43 tff(54,plain,
% 0.22/0.43 (((~![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))))))) <=> ((~![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | in(A!6, unordered_pair(A!6, B!5)))),
% 0.22/0.43 inference(transitivity,[status(thm)],[53, 34])).
% 0.22/0.43 tff(55,plain,
% 0.22/0.43 ((~![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5)) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(56,plain,
% 0.22/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | in(A!6, unordered_pair(A!6, B!5))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.22/0.43 tff(57,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[56, 33, 12])).
% 0.22/0.43 tff(58,plain,(in(A!6, unordered_pair(A!6, B!5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(59,plain,
% 0.22/0.43 ((((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))) <=> in(A!6, unordered_pair(A!6, B!5))) | (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5))))) | (~in(A!6, unordered_pair(A!6, B!5)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(60,plain,
% 0.22/0.43 (((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))) <=> in(A!6, unordered_pair(A!6, B!5))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[59, 58, 11])).
% 0.22/0.43 tff(61,plain,
% 0.22/0.43 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(62,plain,
% 0.22/0.43 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[61])).
% 0.22/0.43 tff(63,plain,
% 0.22/0.43 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(64,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.22/0.43 tff(65,plain,
% 0.22/0.43 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.22/0.43 tff(66,plain,(
% 0.22/0.44 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.44 inference(skolemize,[status(sab)],[65])).
% 0.22/0.44 tff(67,plain,
% 0.22/0.44 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.22/0.44 tff(68,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(unordered_pair(A!6, B!5), C!4) = set_intersection2(C!4, unordered_pair(A!6, B!5)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(69,plain,
% 0.22/0.44 (set_intersection2(unordered_pair(A!6, B!5), C!4) = set_intersection2(C!4, unordered_pair(A!6, B!5))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.22/0.44 tff(70,plain,
% 0.22/0.44 (set_intersection2(unordered_pair(A!6, B!5), C!4) = unordered_pair(A!6, B!5)),
% 0.22/0.44 inference(or_elim,[status(thm)],[8])).
% 0.22/0.44 tff(71,plain,
% 0.22/0.44 (unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)),
% 0.22/0.44 inference(symmetry,[status(thm)],[70])).
% 0.22/0.44 tff(72,plain,
% 0.22/0.44 (unordered_pair(A!6, B!5) = set_intersection2(C!4, unordered_pair(A!6, B!5))),
% 0.22/0.44 inference(transitivity,[status(thm)],[71, 69])).
% 0.22/0.44 tff(73,plain,
% 0.22/0.44 ((~((~(unordered_pair(A!6, B!5) = set_intersection2(C!4, unordered_pair(A!6, B!5)))) | (~(((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))) <=> in(A!6, unordered_pair(A!6, B!5)))))) | (~(unordered_pair(A!6, B!5) = set_intersection2(C!4, unordered_pair(A!6, B!5)))) | (~(((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))) <=> in(A!6, unordered_pair(A!6, B!5))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(74,plain,
% 0.22/0.44 (~((~(unordered_pair(A!6, B!5) = set_intersection2(C!4, unordered_pair(A!6, B!5)))) | (~(((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))) <=> in(A!6, unordered_pair(A!6, B!5)))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[73, 72, 60])).
% 0.22/0.44 tff(75,plain,
% 0.22/0.44 (((~((~(unordered_pair(A!6, B!5) = set_intersection2(C!4, unordered_pair(A!6, B!5)))) | (~(((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))) <=> in(A!6, unordered_pair(A!6, B!5)))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(C!4, unordered_pair(A!6, B!5))) | (((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5), C!4), C!4)) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5), C!4), unordered_pair(A!6, B!5)))) <=> in(tptp_fun_D_1(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5), C!4), unordered_pair(A!6, B!5)))))) | ((~(unordered_pair(A!6, B!5) = set_intersection2(C!4, unordered_pair(A!6, B!5)))) | (~(((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))) <=> in(A!6, unordered_pair(A!6, B!5)))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(76,plain,
% 0.22/0.44 ((~((~(unordered_pair(A!6, B!5) = set_intersection2(C!4, unordered_pair(A!6, B!5)))) | (~(((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))) <=> in(A!6, unordered_pair(A!6, B!5)))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(C!4, unordered_pair(A!6, B!5))) | (((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5), C!4), C!4)) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5), C!4), unordered_pair(A!6, B!5)))) <=> in(tptp_fun_D_1(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5), C!4), unordered_pair(A!6, B!5)))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.22/0.44 tff(77,plain,
% 0.22/0.44 (^[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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(78,plain,
% 0.22/0.44 (![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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[77])).
% 0.22/0.44 tff(79,plain,
% 0.22/0.44 (![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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.22/0.44 inference(pull_quant,[status(thm)],[])).
% 0.22/0.44 tff(80,plain,
% 0.22/0.44 (^[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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(81,plain,
% 0.22/0.44 (![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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[80])).
% 0.22/0.44 tff(82,plain,
% 0.22/0.44 (![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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[81, 79])).
% 0.22/0.44 tff(83,plain,
% 0.22/0.44 (![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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[82, 78])).
% 0.22/0.44 tff(84,plain,
% 0.22/0.44 (^[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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(85,plain,
% 0.22/0.44 (![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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[84])).
% 0.22/0.44 tff(86,plain,
% 0.22/0.44 (![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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[85, 83])).
% 0.22/0.44 tff(87,plain,
% 0.22/0.44 (^[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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(88,plain,
% 0.22/0.44 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[87])).
% 0.22/0.44 tff(89,plain,
% 0.22/0.44 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(90,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.22/0.44 tff(91,plain,
% 0.22/0.44 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.22/0.44 tff(92,plain,(
% 0.22/0.44 ![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[91])).
% 0.22/0.44 tff(93,plain,
% 0.22/0.44 (![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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.22/0.44 tff(94,plain,
% 0.22/0.44 (![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_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.22/0.44 tff(95,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(unordered_pair(A!6, B!5) = set_intersection2(C!4, unordered_pair(A!6, B!5)))) | (~(((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))) <=> in(A!6, unordered_pair(A!6, B!5)))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(C!4, unordered_pair(A!6, B!5))) | (((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5), C!4), C!4)) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5), C!4), unordered_pair(A!6, B!5)))) <=> in(tptp_fun_D_1(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5), C!4), unordered_pair(A!6, B!5)))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(96,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[95, 94, 76])).
% 0.22/0.44 % SZS output end Proof
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------