%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU148+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:02 AM UTC 2025
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU148+2 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 06:07:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(in_type, type, (
% 0.11/0.38 in: ( $i * $i ) > $o)).
% 0.11/0.38 tff(set_union2_type, type, (
% 0.11/0.38 set_union2: ( $i * $i ) > $i)).
% 0.11/0.38 tff(set_difference_type, type, (
% 0.11/0.38 set_difference: ( $i * $i ) > $i)).
% 0.11/0.38 tff(singleton_type, type, (
% 0.11/0.38 singleton: $i > $i)).
% 0.11/0.38 tff(tptp_fun_A_14_type, type, (
% 0.11/0.38 tptp_fun_A_14: $i)).
% 0.11/0.38 tff(tptp_fun_B_13_type, type, (
% 0.11/0.38 tptp_fun_B_13: $i)).
% 0.11/0.38 tff(subset_type, type, (
% 0.11/0.38 subset: ( $i * $i ) > $o)).
% 0.11/0.38 tff(unordered_pair_type, type, (
% 0.11/0.38 unordered_pair: ( $i * $i ) > $i)).
% 0.11/0.38 tff(tptp_fun_D_3_type, type, (
% 0.11/0.38 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))) <=> (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : (subset(singleton(A), singleton(B)) => (A = B))) <=> (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(3,axiom,(~![A: $i, B: $i] : (subset(singleton(A), singleton(B)) => (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t6_zfmisc_1')).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.11/0.38 tff(8,plain,(
% 0.11/0.38 ~((~subset(singleton(A!14), singleton(B!13))) | (A!14 = B!13))),
% 0.11/0.38 inference(skolemize,[status(sab)],[7])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (subset(singleton(A!14), singleton(B!13))),
% 0.11/0.38 inference(or_elim,[status(thm)],[8])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.38 tff(15,axiom,(![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_xboole_1')).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.11/0.38 tff(18,plain,(
% 0.11/0.38 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[17])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(singleton(A!14), singleton(B!13))) | (singleton(B!13) = set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(singleton(A!14), singleton(B!13))) | (singleton(B!13) = set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(21,plain,
% 0.11/0.39 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(singleton(A!14), singleton(B!13))) | (singleton(B!13) = set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(22,plain,
% 0.11/0.39 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(singleton(A!14), singleton(B!13))) | (singleton(B!13) = set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.11/0.39 tff(23,plain,
% 0.11/0.39 (singleton(B!13) = set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.11/0.39 tff(24,plain,
% 0.11/0.39 (set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = singleton(B!13)),
% 0.11/0.39 inference(symmetry,[status(thm)],[23])).
% 0.11/0.39 tff(25,plain,
% 0.11/0.39 (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> in(A!14, singleton(B!13))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.11/0.39 tff(26,plain,
% 0.11/0.39 (in(A!14, singleton(B!13)) <=> in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))),
% 0.11/0.39 inference(symmetry,[status(thm)],[25])).
% 0.11/0.39 tff(27,plain,
% 0.11/0.39 (^[A: $i, B: $i] : refl((subset(singleton(A), B) <=> in(A, B)) <=> (subset(singleton(A), B) <=> in(A, B)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(30,axiom,(![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 0.11/0.39 tff(31,plain,
% 0.11/0.39 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.11/0.39 tff(32,plain,(
% 0.11/0.39 ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.11/0.39 inference(skolemize,[status(sab)],[31])).
% 0.11/0.39 tff(33,plain,
% 0.11/0.39 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) | (subset(singleton(A!14), singleton(B!13)) <=> in(A!14, singleton(B!13)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(35,plain,
% 0.11/0.39 (subset(singleton(A!14), singleton(B!13)) <=> in(A!14, singleton(B!13))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.11/0.39 tff(36,plain,
% 0.11/0.39 ((~(subset(singleton(A!14), singleton(B!13)) <=> in(A!14, singleton(B!13)))) | (~subset(singleton(A!14), singleton(B!13))) | in(A!14, singleton(B!13))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 ((~(subset(singleton(A!14), singleton(B!13)) <=> in(A!14, singleton(B!13)))) | in(A!14, singleton(B!13))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[36, 9])).
% 0.11/0.39 tff(38,plain,
% 0.11/0.39 (in(A!14, singleton(B!13))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[37, 35])).
% 0.11/0.39 tff(39,plain,
% 0.11/0.39 (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[38, 26])).
% 0.11/0.39 tff(40,plain,
% 0.11/0.39 (^[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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(41,plain,
% 0.11/0.39 (![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.11/0.39 tff(42,plain,
% 0.11/0.39 (![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.11/0.39 inference(pull_quant,[status(thm)],[])).
% 0.11/0.39 tff(43,plain,
% 0.11/0.39 (^[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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(44,plain,
% 0.11/0.39 (![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.11/0.39 tff(45,plain,
% 0.11/0.39 (![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[44, 42])).
% 0.11/0.39 tff(46,plain,
% 0.11/0.39 (![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[45, 41])).
% 0.11/0.39 tff(47,plain,
% 0.11/0.39 (^[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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(48,plain,
% 0.11/0.39 (![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 (![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[48, 46])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 (^[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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))) <=> (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(51,plain,
% 0.11/0.40 (![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.11/0.40 tff(52,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(53,plain,
% 0.11/0.40 (^[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)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(54,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.11/0.40 tff(55,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')).
% 0.11/0.40 tff(56,plain,
% 0.11/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.11/0.40 tff(57,plain,
% 0.11/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.11/0.40 tff(58,plain,(
% 0.11/0.40 ![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))),
% 0.11/0.40 inference(skolemize,[status(sab)],[57])).
% 0.11/0.40 tff(59,plain,
% 0.11/0.40 (![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.11/0.40 tff(60,plain,
% 0.11/0.40 (![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.11/0.40 tff(61,plain,
% 0.11/0.40 (((~![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))))) <=> ((~![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(62,plain,
% 0.11/0.40 ((~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((A!14 = B!13) | (A!14 = B!13))))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13) | (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))))) <=> (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(63,plain,
% 0.11/0.40 (((~![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((A!14 = B!13) | (A!14 = B!13))))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13) | (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))))))) <=> ((~![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))))))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[62])).
% 0.11/0.40 tff(64,plain,
% 0.11/0.40 (((~![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((A!14 = B!13) | (A!14 = B!13))))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13) | (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))))))) <=> ((~![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[63, 61])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 ((~![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((A!14 = B!13) | (A!14 = B!13))))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13) | (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 ((~![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_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[66, 60])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | (~(in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))) | ((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (^[A: $i] : refl((unordered_pair(A, A) = singleton(A)) <=> (unordered_pair(A, A) = singleton(A)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![A: $i] : (unordered_pair(A, A) = singleton(A)) <=> ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![A: $i] : (unordered_pair(A, A) = singleton(A)) <=> ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(73,axiom,(![A: $i] : (unordered_pair(A, A) = singleton(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t69_enumset1')).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.41 tff(75,plain,(
% 0.19/0.41 ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.41 inference(skolemize,[status(sab)],[74])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 ((~![A: $i] : (unordered_pair(A, A) = singleton(A))) | (unordered_pair(B!13, B!13) = singleton(B!13))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (unordered_pair(B!13, B!13) = singleton(B!13)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (singleton(B!13) = unordered_pair(B!13, B!13)),
% 0.19/0.41 inference(symmetry,[status(thm)],[78])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)),
% 0.19/0.41 inference(transitivity,[status(thm)],[24, 79])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 ((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 ((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[82, 69])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (~(A!14 = B!13)),
% 0.19/0.41 inference(or_elim,[status(thm)],[8])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((~(in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13))) | (~in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) | (A!14 = B!13)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ((~(in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13))) | (~in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (~in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[86, 83])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[87, 39])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------