%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET872+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 05:26:34 AM UTC 2025
% Result : Theorem 0.15s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.15/0.15 % Problem : SET872+1 : TPTP v9.0.0. Released v3.2.0.
% 0.15/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 05:49:41 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.15/0.41 % SZS status Theorem
% 0.15/0.41 % SZS output start Proof
% 0.15/0.41 tff(in_type, type, (
% 0.15/0.41 in: ( $i * $i ) > $o)).
% 0.15/0.41 tff(unordered_pair_type, type, (
% 0.15/0.41 unordered_pair: ( $i * $i ) > $i)).
% 0.15/0.41 tff(tptp_fun_A_6_type, type, (
% 0.15/0.41 tptp_fun_A_6: $i)).
% 0.15/0.41 tff(tptp_fun_B_5_type, type, (
% 0.15/0.41 tptp_fun_B_5: $i)).
% 0.15/0.41 tff(tptp_fun_C_2_type, type, (
% 0.15/0.41 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.15/0.41 tff(singleton_type, type, (
% 0.15/0.41 singleton: $i > $i)).
% 0.15/0.41 tff(subset_type, type, (
% 0.15/0.41 subset: ( $i * $i ) > $o)).
% 0.15/0.41 tff(tptp_fun_D_1_type, type, (
% 0.15/0.41 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.15/0.41 tff(tptp_fun_C_0_type, type, (
% 0.15/0.41 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.15/0.41 tff(1,plain,
% 0.15/0.41 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(2,plain,
% 0.15/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.15/0.41 tff(3,plain,
% 0.15/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 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')).
% 0.15/0.41 tff(5,plain,
% 0.15/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.15/0.41 tff(6,plain,(
% 0.15/0.41 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.15/0.41 inference(skolemize,[status(sab)],[5])).
% 0.15/0.41 tff(7,plain,
% 0.15/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.15/0.41 tff(8,plain,
% 0.15/0.41 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!6, B!5) = unordered_pair(B!5, A!6))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(9,plain,
% 0.15/0.41 (unordered_pair(A!6, B!5) = unordered_pair(B!5, A!6)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.15/0.41 tff(10,plain,
% 0.15/0.41 (unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5)),
% 0.15/0.41 inference(symmetry,[status(thm)],[9])).
% 0.15/0.41 tff(11,plain,
% 0.15/0.41 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[10])).
% 0.15/0.41 tff(12,plain,
% 0.15/0.41 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)) <=> in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))),
% 0.15/0.41 inference(symmetry,[status(thm)],[11])).
% 0.15/0.41 tff(13,plain,
% 0.15/0.41 ((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))) <=> (~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[12])).
% 0.15/0.41 tff(14,plain,
% 0.15/0.41 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(15,plain,
% 0.15/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.15/0.41 tff(16,plain,
% 0.15/0.41 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(17,plain,
% 0.15/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.15/0.41 tff(18,plain,
% 0.15/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.15/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.15/0.41 tff(19,plain,
% 0.15/0.41 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(20,plain,
% 0.15/0.41 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.15/0.41 tff(21,plain,
% 0.15/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(22,plain,
% 0.15/0.41 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(23,plain,
% 0.15/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.15/0.41 tff(24,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.15/0.41 tff(25,plain,
% 0.15/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.15/0.41 tff(26,plain,
% 0.15/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.15/0.41 tff(27,plain,(
% 0.15/0.41 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 0.15/0.41 inference(skolemize,[status(sab)],[26])).
% 0.15/0.41 tff(28,plain,
% 0.15/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.15/0.41 tff(29,plain,
% 0.15/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.15/0.42 tff(30,plain,
% 0.15/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(singleton(A!6), unordered_pair(A!6, B!5))) | ![C: $i] : ((~in(C, singleton(A!6))) | in(C, unordered_pair(A!6, B!5))))) | (~(subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))))))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(31,plain,
% 0.15/0.42 (~((~((~subset(singleton(A!6), unordered_pair(A!6, B!5))) | ![C: $i] : ((~in(C, singleton(A!6))) | in(C, unordered_pair(A!6, B!5))))) | (~(subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.15/0.42 tff(32,plain,
% 0.15/0.42 (((~((~subset(singleton(A!6), unordered_pair(A!6, B!5))) | ![C: $i] : ((~in(C, singleton(A!6))) | in(C, unordered_pair(A!6, B!5))))) | (~(subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))))))) | (subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(33,plain,
% 0.15/0.42 (subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.15/0.42 tff(34,plain,
% 0.15/0.42 ((~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))) <=> (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B)))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(35,axiom,(~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_zfmisc_1')).
% 0.15/0.42 tff(36,plain,
% 0.15/0.42 (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.15/0.42 tff(37,plain,
% 0.15/0.42 (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.15/0.42 tff(38,plain,
% 0.15/0.42 (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.15/0.42 tff(39,plain,
% 0.15/0.42 (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.15/0.42 tff(40,plain,(
% 0.15/0.42 ~subset(singleton(A!6), unordered_pair(A!6, B!5))),
% 0.15/0.42 inference(skolemize,[status(sab)],[39])).
% 0.15/0.42 tff(41,plain,
% 0.15/0.42 ((~(subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))))) | subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(42,plain,
% 0.15/0.42 ((~(subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))))) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.15/0.42 tff(43,plain,
% 0.15/0.42 (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[42, 33])).
% 0.15/0.42 tff(44,plain,
% 0.15/0.42 (((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(45,plain,
% 0.15/0.42 (~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.15/0.42 tff(46,plain,
% 0.15/0.42 (~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[45, 13])).
% 0.15/0.42 tff(47,plain,
% 0.15/0.42 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(48,plain,
% 0.15/0.42 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.15/0.42 tff(49,plain,
% 0.15/0.42 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.15/0.42 inference(pull_quant,[status(thm)],[])).
% 0.15/0.42 tff(50,plain,
% 0.15/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(51,plain,
% 0.15/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[50])).
% 0.15/0.42 tff(52,plain,
% 0.15/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[51, 49])).
% 0.15/0.42 tff(53,plain,
% 0.15/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[52, 48])).
% 0.15/0.42 tff(54,plain,
% 0.15/0.42 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(55,plain,
% 0.15/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.15/0.42 tff(56,plain,
% 0.15/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[55, 53])).
% 0.15/0.42 tff(57,plain,
% 0.15/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(58,plain,
% 0.15/0.42 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[57])).
% 0.15/0.42 tff(59,plain,
% 0.15/0.42 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(60,plain,
% 0.15/0.42 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(61,plain,
% 0.15/0.42 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.15/0.42 tff(62,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')).
% 0.15/0.42 tff(63,plain,
% 0.15/0.42 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.15/0.42 tff(64,plain,
% 0.15/0.42 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.15/0.42 tff(65,plain,(
% 0.15/0.42 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 0.15/0.42 inference(skolemize,[status(sab)],[64])).
% 0.15/0.42 tff(66,plain,
% 0.15/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.15/0.42 tff(67,plain,
% 0.15/0.42 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.15/0.42 tff(68,plain,
% 0.15/0.42 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(69,plain,
% 0.15/0.42 ((~(~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(70,plain,
% 0.15/0.43 (((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) | $false) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(71,plain,
% 0.15/0.43 ((~$true) <=> $false),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(72,plain,
% 0.15/0.43 (($true | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))) <=> $true),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(73,plain,
% 0.15/0.43 ((~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))) <=> (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(74,plain,
% 0.15/0.43 ((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) <=> $true),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(75,plain,
% 0.15/0.43 (((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))) <=> ($true | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[74, 73])).
% 0.15/0.43 tff(76,plain,
% 0.15/0.43 (((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))) <=> $true),
% 0.15/0.43 inference(transitivity,[status(thm)],[75, 72])).
% 0.15/0.43 tff(77,plain,
% 0.15/0.43 ((~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))) <=> (~$true)),
% 0.15/0.43 inference(monotonicity,[status(thm)],[76])).
% 0.15/0.43 tff(78,plain,
% 0.15/0.43 ((~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))) <=> $false),
% 0.15/0.43 inference(transitivity,[status(thm)],[77, 71])).
% 0.15/0.43 tff(79,plain,
% 0.15/0.43 ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(80,plain,
% 0.15/0.43 (($false | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(81,plain,
% 0.15/0.43 ((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) <=> (~$true)),
% 0.15/0.43 inference(monotonicity,[status(thm)],[74])).
% 0.15/0.43 tff(82,plain,
% 0.15/0.43 ((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) <=> $false),
% 0.15/0.43 inference(transitivity,[status(thm)],[81, 71])).
% 0.15/0.43 tff(83,plain,
% 0.15/0.43 (((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) <=> ($false | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[82])).
% 0.15/0.43 tff(84,plain,
% 0.15/0.43 (((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.15/0.43 inference(transitivity,[status(thm)],[83, 80])).
% 0.15/0.43 tff(85,plain,
% 0.15/0.43 ((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[84])).
% 0.15/0.43 tff(86,plain,
% 0.15/0.43 ((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.15/0.43 inference(transitivity,[status(thm)],[85, 79])).
% 0.15/0.43 tff(87,plain,
% 0.15/0.43 (((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))) <=> ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) | $false)),
% 0.15/0.43 inference(monotonicity,[status(thm)],[86, 78])).
% 0.15/0.43 tff(88,plain,
% 0.15/0.43 (((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.15/0.44 inference(transitivity,[status(thm)],[87, 70])).
% 0.15/0.44 tff(89,plain,
% 0.15/0.44 ((~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))))) <=> (~(~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))))),
% 0.15/0.44 inference(monotonicity,[status(thm)],[88])).
% 0.15/0.44 tff(90,plain,
% 0.15/0.44 ((~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.15/0.44 inference(transitivity,[status(thm)],[89, 69])).
% 0.15/0.44 tff(91,plain,
% 0.15/0.44 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.15/0.44 inference(monotonicity,[status(thm)],[90])).
% 0.15/0.44 tff(92,plain,
% 0.15/0.44 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.15/0.44 inference(transitivity,[status(thm)],[91, 68])).
% 0.15/0.44 tff(93,plain,
% 0.15/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(94,plain,
% 0.15/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.15/0.44 tff(95,plain,
% 0.15/0.44 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[94, 67])).
% 0.15/0.44 tff(96,plain,
% 0.15/0.44 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(97,plain,
% 0.15/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[96])).
% 0.15/0.44 tff(98,plain,
% 0.15/0.44 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.15/0.44 inference(pull_quant,[status(thm)],[])).
% 0.15/0.44 tff(99,plain,
% 0.15/0.44 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(100,plain,
% 0.15/0.44 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[99])).
% 0.15/0.44 tff(101,plain,
% 0.15/0.44 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.15/0.44 inference(transitivity,[status(thm)],[100, 98])).
% 0.15/0.44 tff(102,plain,
% 0.15/0.44 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.15/0.44 inference(transitivity,[status(thm)],[101, 97])).
% 0.15/0.44 tff(103,plain,
% 0.15/0.44 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(104,plain,
% 0.15/0.44 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[103])).
% 0.15/0.44 tff(105,plain,
% 0.15/0.44 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.15/0.44 inference(transitivity,[status(thm)],[104, 102])).
% 0.15/0.44 tff(106,plain,
% 0.15/0.44 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite(((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(107,plain,
% 0.15/0.44 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[106])).
% 0.15/0.44 tff(108,plain,
% 0.15/0.44 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(109,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.15/0.44 tff(110,plain,
% 0.15/0.44 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.15/0.44 tff(111,plain,(
% 0.15/0.44 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.15/0.44 inference(skolemize,[status(sab)],[110])).
% 0.15/0.44 tff(112,plain,
% 0.15/0.44 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.15/0.44 tff(113,plain,
% 0.15/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.15/0.44 tff(114,plain,
% 0.15/0.44 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(115,plain,
% 0.15/0.44 ((~(~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(116,plain,
% 0.15/0.44 (((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) | $false) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(117,plain,
% 0.15/0.44 (($true | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))) <=> $true),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(118,plain,
% 0.15/0.44 ((~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))) <=> (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(119,plain,
% 0.15/0.44 ((singleton(A!6) = singleton(A!6)) <=> $true),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(120,plain,
% 0.15/0.45 (((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))),
% 0.15/0.45 inference(monotonicity,[status(thm)],[119, 118])).
% 0.15/0.45 tff(121,plain,
% 0.15/0.45 (((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))) <=> $true),
% 0.15/0.45 inference(transitivity,[status(thm)],[120, 117])).
% 0.15/0.45 tff(122,plain,
% 0.15/0.45 ((~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))) <=> (~$true)),
% 0.15/0.45 inference(monotonicity,[status(thm)],[121])).
% 0.15/0.45 tff(123,plain,
% 0.15/0.45 ((~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))) <=> $false),
% 0.15/0.45 inference(transitivity,[status(thm)],[122, 71])).
% 0.15/0.45 tff(124,plain,
% 0.15/0.45 ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(125,plain,
% 0.15/0.45 (($false | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(126,plain,
% 0.15/0.45 ((~(singleton(A!6) = singleton(A!6))) <=> (~$true)),
% 0.15/0.45 inference(monotonicity,[status(thm)],[119])).
% 0.15/0.45 tff(127,plain,
% 0.15/0.45 ((~(singleton(A!6) = singleton(A!6))) <=> $false),
% 0.15/0.45 inference(transitivity,[status(thm)],[126, 71])).
% 0.22/0.45 tff(128,plain,
% 0.22/0.45 (((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) <=> ($false | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[127])).
% 0.22/0.45 tff(129,plain,
% 0.22/0.45 (((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.22/0.45 inference(transitivity,[status(thm)],[128, 125])).
% 0.22/0.45 tff(130,plain,
% 0.22/0.45 ((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[129])).
% 0.22/0.45 tff(131,plain,
% 0.22/0.45 ((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[130, 124])).
% 0.22/0.45 tff(132,plain,
% 0.22/0.45 (((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))) <=> ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) | $false)),
% 0.22/0.45 inference(monotonicity,[status(thm)],[131, 123])).
% 0.22/0.45 tff(133,plain,
% 0.22/0.45 (((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[132, 116])).
% 0.22/0.45 tff(134,plain,
% 0.22/0.45 ((~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))))) <=> (~(~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[133])).
% 0.22/0.45 tff(135,plain,
% 0.22/0.45 ((~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.22/0.45 inference(transitivity,[status(thm)],[134, 115])).
% 0.22/0.45 tff(136,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[135])).
% 0.22/0.45 tff(137,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[136, 114])).
% 0.22/0.45 tff(138,plain,
% 0.22/0.45 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(139,plain,
% 0.22/0.45 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.22/0.45 tff(140,plain,
% 0.22/0.45 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[139, 113])).
% 0.22/0.45 tff(141,plain,
% 0.22/0.45 (((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(142,plain,
% 0.22/0.45 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[141, 43])).
% 0.22/0.45 tff(143,plain,
% 0.22/0.45 ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) | (~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(144,plain,
% 0.22/0.45 ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.22/0.45 tff(145,plain,
% 0.22/0.45 (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[144, 140])).
% 0.22/0.45 tff(146,plain,
% 0.22/0.45 (((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)) | (~(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(147,plain,
% 0.22/0.45 ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.22/0.45 tff(148,plain,
% 0.22/0.45 ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) | (~((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(149,plain,
% 0.22/0.45 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[148, 147, 95])).
% 0.22/0.45 tff(150,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[149, 46])).
% 0.22/0.45 % SZS output end Proof
% 0.22/0.46 % E exiting
%------------------------------------------------------------------------------