%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET878+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 05:26:35 AM UTC 2025
% Result : Theorem 0.22s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET878+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.13 % 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 05:49:54 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.39 % SZS status Theorem
% 0.22/0.39 % SZS output start Proof
% 0.22/0.39 tff(tptp_fun_A_4_type, type, (
% 0.22/0.39 tptp_fun_A_4: $i)).
% 0.22/0.39 tff(tptp_fun_D_0_type, type, (
% 0.22/0.39 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.22/0.39 tff(tptp_fun_B_3_type, type, (
% 0.22/0.39 tptp_fun_B_3: $i)).
% 0.22/0.39 tff(unordered_pair_type, type, (
% 0.22/0.39 unordered_pair: ( $i * $i ) > $i)).
% 0.22/0.39 tff(in_type, type, (
% 0.22/0.39 in: ( $i * $i ) > $o)).
% 0.22/0.39 tff(singleton_type, type, (
% 0.22/0.39 singleton: $i > $i)).
% 0.22/0.39 tff(set_intersection2_type, type, (
% 0.22/0.39 set_intersection2: ( $i * $i ) > $i)).
% 0.22/0.39 tff(1,plain,
% 0.22/0.39 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(2,plain,
% 0.22/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.39 tff(3,plain,
% 0.22/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(4,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.22/0.39 tff(5,plain,
% 0.22/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.39 tff(6,plain,(
% 0.22/0.39 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.39 inference(skolemize,[status(sab)],[5])).
% 0.22/0.39 tff(7,plain,
% 0.22/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.39 tff(8,plain,
% 0.22/0.39 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(singleton(A!4), unordered_pair(A!4, B!3)) = set_intersection2(unordered_pair(A!4, B!3), singleton(A!4)))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(9,plain,
% 0.22/0.39 (set_intersection2(singleton(A!4), unordered_pair(A!4, B!3)) = set_intersection2(unordered_pair(A!4, B!3), singleton(A!4))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.22/0.39 tff(10,plain,
% 0.22/0.39 (set_intersection2(unordered_pair(A!4, B!3), singleton(A!4)) = set_intersection2(singleton(A!4), unordered_pair(A!4, B!3))),
% 0.22/0.39 inference(symmetry,[status(thm)],[9])).
% 0.22/0.39 tff(11,plain,
% 0.22/0.39 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(12,plain,
% 0.22/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.22/0.39 tff(13,plain,
% 0.22/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(14,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.22/0.39 tff(15,plain,
% 0.22/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.22/0.39 tff(16,plain,(
% 0.22/0.39 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.22/0.39 inference(skolemize,[status(sab)],[15])).
% 0.22/0.39 tff(17,plain,
% 0.22/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.22/0.39 tff(18,plain,
% 0.22/0.39 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(19,plain,
% 0.22/0.39 (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4)),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.22/0.39 tff(20,plain,
% 0.22/0.39 (unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)),
% 0.22/0.39 inference(symmetry,[status(thm)],[19])).
% 0.22/0.39 tff(21,plain,
% 0.22/0.39 (set_intersection2(unordered_pair(B!3, A!4), singleton(A!4)) = set_intersection2(unordered_pair(A!4, B!3), singleton(A!4))),
% 0.22/0.39 inference(monotonicity,[status(thm)],[20])).
% 0.22/0.39 tff(22,plain,
% 0.22/0.39 (set_intersection2(unordered_pair(B!3, A!4), singleton(A!4)) = set_intersection2(singleton(A!4), unordered_pair(A!4, B!3))),
% 0.22/0.39 inference(transitivity,[status(thm)],[21, 10])).
% 0.22/0.39 tff(23,plain,
% 0.22/0.39 ((set_intersection2(unordered_pair(B!3, A!4), singleton(A!4)) = singleton(A!4)) <=> (set_intersection2(singleton(A!4), unordered_pair(A!4, B!3)) = singleton(A!4))),
% 0.22/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.22/0.39 tff(24,plain,
% 0.22/0.39 ((set_intersection2(singleton(A!4), unordered_pair(A!4, B!3)) = singleton(A!4)) <=> (set_intersection2(unordered_pair(B!3, A!4), singleton(A!4)) = singleton(A!4))),
% 0.22/0.39 inference(symmetry,[status(thm)],[23])).
% 0.22/0.39 tff(25,plain,
% 0.22/0.39 ((~(set_intersection2(singleton(A!4), unordered_pair(A!4, B!3)) = singleton(A!4))) <=> (~(set_intersection2(unordered_pair(B!3, A!4), singleton(A!4)) = singleton(A!4)))),
% 0.22/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.22/0.39 tff(26,plain,
% 0.22/0.39 ((~![A: $i, B: $i] : (set_intersection2(singleton(A), unordered_pair(A, B)) = singleton(A))) <=> (~![A: $i, B: $i] : (set_intersection2(singleton(A), unordered_pair(A, B)) = singleton(A)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(27,axiom,(~![A: $i, B: $i] : (set_intersection2(singleton(A), unordered_pair(A, B)) = singleton(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t19_zfmisc_1')).
% 0.22/0.39 tff(28,plain,
% 0.22/0.39 (~![A: $i, B: $i] : (set_intersection2(singleton(A), unordered_pair(A, B)) = singleton(A))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.22/0.39 tff(29,plain,
% 0.22/0.39 (~![A: $i, B: $i] : (set_intersection2(singleton(A), unordered_pair(A, B)) = singleton(A))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[28, 26])).
% 0.22/0.39 tff(30,plain,
% 0.22/0.39 (~![A: $i, B: $i] : (set_intersection2(singleton(A), unordered_pair(A, B)) = singleton(A))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.22/0.39 tff(31,plain,
% 0.22/0.39 (~![A: $i, B: $i] : (set_intersection2(singleton(A), unordered_pair(A, B)) = singleton(A))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.22/0.39 tff(32,plain,(
% 0.22/0.39 ~(set_intersection2(singleton(A!4), unordered_pair(A!4, B!3)) = singleton(A!4))),
% 0.22/0.39 inference(skolemize,[status(sab)],[31])).
% 0.22/0.39 tff(33,plain,
% 0.22/0.39 (~(set_intersection2(unordered_pair(B!3, A!4), singleton(A!4)) = singleton(A!4))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.22/0.39 tff(34,plain,
% 0.22/0.39 (^[A: $i, B: $i] : refl(((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))) <=> ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(35,plain,
% 0.22/0.39 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.22/0.39 tff(36,plain,
% 0.22/0.39 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(37,plain,
% 0.22/0.39 (^[A: $i, B: $i] : rewrite((in(A, B) => (set_intersection2(B, singleton(A)) = singleton(A))) <=> ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(38,plain,
% 0.22/0.39 (![A: $i, B: $i] : (in(A, B) => (set_intersection2(B, singleton(A)) = singleton(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.22/0.39 tff(39,axiom,(![A: $i, B: $i] : (in(A, B) => (set_intersection2(B, singleton(A)) = singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l32_zfmisc_1')).
% 0.22/0.39 tff(40,plain,
% 0.22/0.39 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.22/0.39 tff(41,plain,
% 0.22/0.39 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.22/0.39 tff(42,plain,(
% 0.22/0.39 ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.22/0.39 inference(skolemize,[status(sab)],[41])).
% 0.22/0.39 tff(43,plain,
% 0.22/0.39 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.22/0.39 tff(44,plain,
% 0.22/0.39 (((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | ((~in(A!4, unordered_pair(B!3, A!4))) | (set_intersection2(unordered_pair(B!3, A!4), singleton(A!4)) = singleton(A!4)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | (~in(A!4, unordered_pair(B!3, A!4))) | (set_intersection2(unordered_pair(B!3, A!4), singleton(A!4)) = singleton(A!4)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(45,plain,
% 0.22/0.39 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | ((~in(A!4, unordered_pair(B!3, A!4))) | (set_intersection2(unordered_pair(B!3, A!4), singleton(A!4)) = singleton(A!4)))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(46,plain,
% 0.22/0.39 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | (~in(A!4, unordered_pair(B!3, A!4))) | (set_intersection2(unordered_pair(B!3, A!4), singleton(A!4)) = singleton(A!4))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.22/0.39 tff(47,plain,
% 0.22/0.39 ((~in(A!4, unordered_pair(B!3, A!4))) | (set_intersection2(unordered_pair(B!3, A!4), singleton(A!4)) = singleton(A!4))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.22/0.39 tff(48,plain,
% 0.22/0.39 (~in(A!4, unordered_pair(B!3, A!4))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[47, 33])).
% 0.22/0.39 tff(49,plain,
% 0.22/0.39 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(50,plain,
% 0.22/0.39 (unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[49, 17])).
% 0.22/0.39 tff(51,plain,
% 0.22/0.39 ((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4)))) | (~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4))),
% 0.22/0.39 inference(tautology,[status(thm)],[])).
% 0.22/0.39 tff(52,plain,
% 0.22/0.39 (~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4)))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[51, 50, 48])).
% 0.22/0.39 tff(53,plain,
% 0.22/0.39 (((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4)))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4))))))) | ((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4)))),
% 0.22/0.39 inference(tautology,[status(thm)],[])).
% 0.22/0.39 tff(54,plain,
% 0.22/0.39 ((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4)))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4))))))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.22/0.39 tff(55,plain,
% 0.22/0.39 (^[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_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)))))))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(56,plain,
% 0.22/0.39 (![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_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))))))))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.22/0.39 tff(57,plain,
% 0.22/0.39 (![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_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))))))))),
% 0.22/0.39 inference(pull_quant,[status(thm)],[])).
% 0.22/0.39 tff(58,plain,
% 0.22/0.39 (^[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_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))))))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(59,plain,
% 0.22/0.40 (![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_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))))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.22/0.40 tff(60,plain,
% 0.22/0.40 (![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_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))))))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[59, 57])).
% 0.22/0.40 tff(61,plain,
% 0.22/0.40 (![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_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))))))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[60, 56])).
% 0.22/0.40 tff(62,plain,
% 0.22/0.40 (^[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)))))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(63,plain,
% 0.22/0.40 (![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_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))))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.22/0.40 tff(64,plain,
% 0.22/0.40 (![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_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))))))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[63, 61])).
% 0.22/0.40 tff(65,plain,
% 0.22/0.40 (^[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))))))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(66,plain,
% 0.22/0.40 (![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_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))))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.22/0.40 tff(67,plain,
% 0.22/0.40 (![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))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(68,plain,
% 0.22/0.40 (^[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)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(69,plain,
% 0.22/0.40 (![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))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.22/0.40 tff(70,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')).
% 0.22/0.40 tff(71,plain,
% 0.22/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.22/0.40 tff(72,plain,
% 0.22/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.22/0.40 tff(73,plain,(
% 0.22/0.40 ![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 0.22/0.40 inference(skolemize,[status(sab)],[72])).
% 0.22/0.40 tff(74,plain,
% 0.22/0.40 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.22/0.40 tff(75,plain,
% 0.22/0.40 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.22/0.40 tff(76,plain,
% 0.22/0.40 (((~![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_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(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4)))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = 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))))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4)))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4)))))))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(77,plain,
% 0.22/0.40 ((~((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = B!3) | (A!4 = A!4))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4)))))))) <=> (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4)))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4))))))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(78,plain,
% 0.22/0.40 (((~![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_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(A!4, B!3))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = B!3) | (A!4 = A!4))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = 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))))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4)))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4)))))))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[77])).
% 0.22/0.41 tff(79,plain,
% 0.22/0.41 (((~![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))))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = B!3) | (A!4 = A!4))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = 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))))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4)))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4)))))))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[78, 76])).
% 0.22/0.41 tff(80,plain,
% 0.22/0.41 ((~![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))))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = B!3) | (A!4 = A!4))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4))))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(81,plain,
% 0.22/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | in(A!4, unordered_pair(B!3, A!4)))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | (~(in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4)) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4))))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.22/0.41 tff(82,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[81, 75, 54])).
% 0.22/0.41 % SZS output end Proof
% 0.22/0.41 % E exiting
%------------------------------------------------------------------------------