%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET881+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:36 AM UTC 2025
% Result : Theorem 0.23s 0.40s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET881+1 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.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 05:50:11 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.23/0.40 % SZS status Theorem
% 0.23/0.40 % SZS output start Proof
% 0.23/0.40 tff(in_type, type, (
% 0.23/0.40 in: ( $i * $i ) > $o)).
% 0.23/0.40 tff(unordered_pair_type, type, (
% 0.23/0.40 unordered_pair: ( $i * $i ) > $i)).
% 0.23/0.40 tff(tptp_fun_A_4_type, type, (
% 0.23/0.40 tptp_fun_A_4: $i)).
% 0.23/0.40 tff(tptp_fun_B_3_type, type, (
% 0.23/0.40 tptp_fun_B_3: $i)).
% 0.23/0.40 tff(empty_set_type, type, (
% 0.23/0.40 empty_set: $i)).
% 0.23/0.40 tff(set_difference_type, type, (
% 0.23/0.40 set_difference: ( $i * $i ) > $i)).
% 0.23/0.40 tff(singleton_type, type, (
% 0.23/0.40 singleton: $i > $i)).
% 0.23/0.40 tff(tptp_fun_D_0_type, type, (
% 0.23/0.40 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.23/0.40 tff(1,plain,
% 0.23/0.40 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.23/0.40 inference(bind,[status(th)],[])).
% 0.23/0.40 tff(2,plain,
% 0.23/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.23/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.40 tff(3,plain,
% 0.23/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.23/0.40 inference(rewrite,[status(thm)],[])).
% 0.23/0.40 tff(4,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.23/0.40 tff(5,plain,
% 0.23/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.40 tff(6,plain,(
% 0.23/0.40 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.23/0.40 inference(skolemize,[status(sab)],[5])).
% 0.23/0.40 tff(7,plain,
% 0.23/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.23/0.40 tff(8,plain,
% 0.23/0.40 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4))),
% 0.23/0.40 inference(quant_inst,[status(thm)],[])).
% 0.23/0.40 tff(9,plain,
% 0.23/0.40 (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4)),
% 0.23/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.23/0.40 tff(10,plain,
% 0.23/0.40 (unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)),
% 0.23/0.40 inference(symmetry,[status(thm)],[9])).
% 0.23/0.40 tff(11,plain,
% 0.23/0.40 (in(A!4, unordered_pair(B!3, A!4)) <=> in(A!4, unordered_pair(A!4, B!3))),
% 0.23/0.40 inference(monotonicity,[status(thm)],[10])).
% 0.23/0.40 tff(12,plain,
% 0.23/0.40 (in(A!4, unordered_pair(A!4, B!3)) <=> in(A!4, unordered_pair(B!3, A!4))),
% 0.23/0.40 inference(symmetry,[status(thm)],[11])).
% 0.23/0.40 tff(13,plain,
% 0.23/0.40 ((~in(A!4, unordered_pair(A!4, B!3))) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.23/0.40 inference(monotonicity,[status(thm)],[12])).
% 0.23/0.40 tff(14,plain,
% 0.23/0.40 (^[A: $i, B: $i] : refl(((set_difference(singleton(A), B) = empty_set) <=> in(A, B)) <=> ((set_difference(singleton(A), B) = empty_set) <=> in(A, B)))),
% 0.23/0.40 inference(bind,[status(th)],[])).
% 0.23/0.40 tff(15,plain,
% 0.23/0.40 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B)) <=> ![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.23/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.23/0.40 tff(16,plain,
% 0.23/0.40 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B)) <=> ![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.23/0.40 inference(rewrite,[status(thm)],[])).
% 0.23/0.40 tff(17,axiom,(![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l36_zfmisc_1')).
% 0.23/0.40 tff(18,plain,
% 0.23/0.40 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.23/0.40 tff(19,plain,(
% 0.23/0.40 ![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.23/0.40 inference(skolemize,[status(sab)],[18])).
% 0.23/0.40 tff(20,plain,
% 0.23/0.40 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.23/0.40 tff(21,plain,
% 0.23/0.40 ((~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))) | ((set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set) <=> in(A!4, unordered_pair(A!4, B!3)))),
% 0.23/0.40 inference(quant_inst,[status(thm)],[])).
% 0.23/0.40 tff(22,plain,
% 0.23/0.40 ((set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set) <=> in(A!4, unordered_pair(A!4, B!3))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.23/0.41 tff(23,plain,
% 0.23/0.41 ((~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)) <=> (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(24,axiom,(~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t22_zfmisc_1')).
% 0.23/0.41 tff(25,plain,
% 0.23/0.41 (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.23/0.41 tff(26,plain,
% 0.23/0.41 (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.23/0.41 tff(27,plain,
% 0.23/0.41 (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.23/0.41 tff(28,plain,
% 0.23/0.41 (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.23/0.41 tff(29,plain,(
% 0.23/0.41 ~(set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set)),
% 0.23/0.41 inference(skolemize,[status(sab)],[28])).
% 0.23/0.41 tff(30,plain,
% 0.23/0.41 ((~((set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set) <=> in(A!4, unordered_pair(A!4, B!3)))) | (set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set) | (~in(A!4, unordered_pair(A!4, B!3)))),
% 0.23/0.41 inference(tautology,[status(thm)],[])).
% 0.23/0.41 tff(31,plain,
% 0.23/0.41 ((~((set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set) <=> in(A!4, unordered_pair(A!4, B!3)))) | (~in(A!4, unordered_pair(A!4, B!3)))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.23/0.41 tff(32,plain,
% 0.23/0.41 (~in(A!4, unordered_pair(A!4, B!3))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[31, 22])).
% 0.23/0.41 tff(33,plain,
% 0.23/0.41 (~in(A!4, unordered_pair(B!3, A!4))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[32, 13])).
% 0.23/0.41 tff(34,plain,
% 0.23/0.41 (^[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)))))))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(35,plain,
% 0.23/0.41 (![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_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))))))))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.23/0.41 tff(36,plain,
% 0.23/0.41 (![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_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))))))))),
% 0.23/0.41 inference(pull_quant,[status(thm)],[])).
% 0.23/0.41 tff(37,plain,
% 0.23/0.41 (^[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))))))))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(38,plain,
% 0.23/0.41 (![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))))))))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.23/0.41 tff(39,plain,
% 0.23/0.41 (![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))))))))),
% 0.23/0.41 inference(transitivity,[status(thm)],[38, 36])).
% 0.23/0.41 tff(40,plain,
% 0.23/0.41 (![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))))))))),
% 0.23/0.41 inference(transitivity,[status(thm)],[39, 35])).
% 0.23/0.41 tff(41,plain,
% 0.23/0.41 (^[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)))))))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(42,plain,
% 0.23/0.41 (![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))))))))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.23/0.41 tff(43,plain,
% 0.23/0.41 (![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))))))))),
% 0.23/0.41 inference(transitivity,[status(thm)],[42, 40])).
% 0.23/0.41 tff(44,plain,
% 0.23/0.41 (^[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))))))))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(45,plain,
% 0.23/0.41 (![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))))))))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.23/0.41 tff(46,plain,
% 0.23/0.41 (![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))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(47,plain,
% 0.23/0.41 (^[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)))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(48,plain,
% 0.23/0.41 (![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))))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.23/0.41 tff(49,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')).
% 0.23/0.41 tff(50,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.23/0.41 tff(51,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.23/0.41 tff(52,plain,(
% 0.23/0.41 ![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))))))),
% 0.23/0.41 inference(skolemize,[status(sab)],[51])).
% 0.23/0.41 tff(53,plain,
% 0.23/0.41 (![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))))))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.23/0.41 tff(54,plain,
% 0.23/0.41 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.23/0.41 tff(55,plain,
% 0.23/0.41 (((~![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | in(A!4, unordered_pair(B!3, A!4))) <=> ((~![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!4, unordered_pair(B!3, A!4)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(56,plain,
% 0.23/0.41 ((~(~in(A!4, unordered_pair(B!3, A!4)))) <=> in(A!4, unordered_pair(B!3, A!4))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(57,plain,
% 0.23/0.41 (((~in(A!4, unordered_pair(B!3, A!4))) | $false) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(58,plain,
% 0.23/0.41 ((~$true) <=> $false),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(59,plain,
% 0.23/0.41 (($true | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))) <=> $true),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(60,plain,
% 0.23/0.41 ((~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))) <=> (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(61,plain,
% 0.23/0.41 ((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) <=> $true),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(62,plain,
% 0.23/0.41 (((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))) <=> ($true | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[61, 60])).
% 0.23/0.41 tff(63,plain,
% 0.23/0.41 (((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))) <=> $true),
% 0.23/0.41 inference(transitivity,[status(thm)],[62, 59])).
% 0.23/0.41 tff(64,plain,
% 0.23/0.41 ((~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))) <=> (~$true)),
% 0.23/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.23/0.41 tff(65,plain,
% 0.23/0.41 ((~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))) <=> $false),
% 0.23/0.41 inference(transitivity,[status(thm)],[64, 58])).
% 0.23/0.41 tff(66,plain,
% 0.23/0.41 ((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(67,plain,
% 0.23/0.41 (((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))))) <=> ((~in(A!4, unordered_pair(B!3, A!4))) | $false)),
% 0.23/0.41 inference(monotonicity,[status(thm)],[66, 65])).
% 0.23/0.41 tff(68,plain,
% 0.23/0.41 (((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))))) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.23/0.42 inference(transitivity,[status(thm)],[67, 57])).
% 0.23/0.42 tff(69,plain,
% 0.23/0.42 ((~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))))) <=> (~(~in(A!4, unordered_pair(B!3, A!4))))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[68])).
% 0.23/0.42 tff(70,plain,
% 0.23/0.42 ((~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))))) <=> in(A!4, unordered_pair(B!3, A!4))),
% 0.23/0.42 inference(transitivity,[status(thm)],[69, 56])).
% 0.23/0.42 tff(71,plain,
% 0.23/0.42 (((~![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))))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))))))) <=> ((~![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!4, unordered_pair(B!3, A!4)))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[70])).
% 0.23/0.42 tff(72,plain,
% 0.23/0.42 (((~![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))))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))))))) <=> ((~![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!4, unordered_pair(B!3, A!4)))),
% 0.23/0.42 inference(transitivity,[status(thm)],[71, 55])).
% 0.23/0.42 tff(73,plain,
% 0.23/0.42 ((~![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))))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))))))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(74,plain,
% 0.23/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | in(A!4, unordered_pair(B!3, A!4))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.23/0.42 tff(75,plain,
% 0.23/0.42 (in(A!4, unordered_pair(B!3, A!4))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[74, 54])).
% 0.23/0.42 tff(76,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[75, 33])).
% 0.23/0.42 % SZS output end Proof
% 0.23/0.42 % E exiting
%------------------------------------------------------------------------------