%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET976+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:26:44 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET976+1 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.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 05:54:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(tptp_fun_D_3_type, type, (
% 0.21/0.39 tptp_fun_D_3: $i)).
% 0.21/0.39 tff(tptp_fun_B_5_type, type, (
% 0.21/0.39 tptp_fun_B_5: $i)).
% 0.21/0.39 tff(in_type, type, (
% 0.21/0.39 in: ( $i * $i ) > $o)).
% 0.21/0.39 tff(singleton_type, type, (
% 0.21/0.39 singleton: $i > $i)).
% 0.21/0.39 tff(tptp_fun_C_4_type, type, (
% 0.21/0.39 tptp_fun_C_4: $i)).
% 0.21/0.39 tff(tptp_fun_A_6_type, type, (
% 0.21/0.39 tptp_fun_A_6: $i)).
% 0.21/0.39 tff(cartesian_product2_type, type, (
% 0.21/0.39 cartesian_product2: ( $i * $i ) > $i)).
% 0.21/0.39 tff(ordered_pair_type, type, (
% 0.21/0.39 ordered_pair: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_C_0_type, type, (
% 0.21/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.21/0.39 tff(1,assumption,(~in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 ((~(~(((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))))) <=> (((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 ((~(((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))))) <=> (~(((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 ((in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) <=> (~((~in(A!6, C!4)) | (~(B!5 = D!3))))) <=> (~(((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 ((in(A!6, C!4) & (B!5 = D!3)) <=> (~((~in(A!6, C!4)) | (~(B!5 = D!3))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 ((in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) <=> (in(A!6, C!4) & (B!5 = D!3))) <=> (in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) <=> (~((~in(A!6, C!4)) | (~(B!5 = D!3)))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 ((in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) <=> (in(A!6, C!4) & (B!5 = D!3))) <=> (~(((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[6, 4])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) <=> (in(A!6, C!4) & (B!5 = D!3))) <=> (~(((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[7, 3])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 ((~(in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) <=> (in(A!6, C!4) & (B!5 = D!3)))) <=> (~(~(((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[8])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 ((~(in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) <=> (in(A!6, C!4) & (B!5 = D!3)))) <=> (((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[9, 2])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 ((~(in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) <=> (in(A!6, C!4) & (B!5 = D!3)))) <=> (~(in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) <=> (in(A!6, C!4) & (B!5 = D!3))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, singleton(D))) <=> (in(A, C) & (B = D)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, singleton(D))) <=> (in(A, C) & (B = D))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(13,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, singleton(D))) <=> (in(A, C) & (B = D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t129_zfmisc_1')).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, singleton(D))) <=> (in(A, C) & (B = D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, singleton(D))) <=> (in(A, C) & (B = D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, singleton(D))) <=> (in(A, C) & (B = D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, singleton(D))) <=> (in(A, C) & (B = D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.39 tff(18,plain,(
% 0.21/0.39 ~(in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) <=> (in(A!6, C!4) & (B!5 = D!3)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[17])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (~(in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) <=> (in(A!6, C!4) & (B!5 = D!3)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[19, 10])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 ((~((~in(A!6, C!4)) | (~(B!5 = D!3)))) | in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))) | (~(((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 ((~((~in(A!6, C!4)) | (~(B!5 = D!3)))) | in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (~((~in(A!6, C!4)) | (~(B!5 = D!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[22, 1])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (((~in(A!6, C!4)) | (~(B!5 = D!3))) | (B!5 = D!3)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (B!5 = D!3),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (D!3 = B!5),
% 0.21/0.39 inference(symmetry,[status(thm)],[25])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (in(D!3, singleton(D!3)) <=> in(B!5, singleton(D!3))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (in(B!5, singleton(D!3)) <=> in(D!3, singleton(D!3))),
% 0.21/0.39 inference(symmetry,[status(thm)],[27])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 ((~in(B!5, singleton(D!3))) <=> (~in(D!3, singleton(D!3)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[28])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(A, C)) | (~in(B, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(35,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l55_zfmisc_1')).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.39 tff(37,plain,(
% 0.21/0.39 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[36])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(A!6, C!4)) | (~in(B!5, singleton(D!3)))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (~(((~in(A!6, C!4)) | (~in(B!5, singleton(D!3)))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 ((((~in(A!6, C!4)) | (~in(B!5, singleton(D!3)))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))) | ((~in(A!6, C!4)) | (~in(B!5, singleton(D!3)))) | in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (((~in(A!6, C!4)) | (~in(B!5, singleton(D!3)))) | in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 ((~in(A!6, C!4)) | (~in(B!5, singleton(D!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[43, 1])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (((~in(A!6, C!4)) | (~(B!5 = D!3))) | in(A!6, C!4)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (in(A!6, C!4)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[45, 23])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 ((~((~in(A!6, C!4)) | (~in(B!5, singleton(D!3))))) | (~in(A!6, C!4)) | (~in(B!5, singleton(D!3)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (~in(B!5, singleton(D!3))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[47, 46, 44])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (~in(D!3, singleton(D!3))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[48, 29])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (^[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))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 (![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)))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (![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)))))))),
% 0.21/0.40 inference(pull_quant,[status(thm)],[])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (^[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)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[54, 52])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[55, 51])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (^[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))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[58, 56])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (^[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)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(63,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.40 tff(65,plain,(
% 0.21/0.40 ![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)))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[64])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (((~![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(D!3, singleton(D!3))) <=> ((~![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(D!3, singleton(D!3)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 ((~(~in(D!3, singleton(D!3)))) <=> in(D!3, singleton(D!3))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 (((~in(D!3, singleton(D!3))) | $false) <=> (~in(D!3, singleton(D!3)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 ((~$true) <=> $false),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (($true | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))) <=> $true),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 ((~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3))) <=> (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 ((singleton(D!3) = singleton(D!3)) <=> $true),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[74, 73])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))) <=> $true),
% 0.21/0.40 inference(transitivity,[status(thm)],[75, 72])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 ((~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3))))) <=> (~$true)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[76])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 ((~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3))))) <=> $false),
% 0.21/0.40 inference(transitivity,[status(thm)],[77, 71])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 ((~((~(singleton(D!3) = singleton(D!3))) | (in(D!3, singleton(D!3)) <=> (D!3 = D!3)))) <=> (~in(D!3, singleton(D!3)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 (((~((~(singleton(D!3) = singleton(D!3))) | (in(D!3, singleton(D!3)) <=> (D!3 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))))) <=> ((~in(D!3, singleton(D!3))) | $false)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[79, 78])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (((~((~(singleton(D!3) = singleton(D!3))) | (in(D!3, singleton(D!3)) <=> (D!3 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))))) <=> (~in(D!3, singleton(D!3)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[80, 70])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 ((~((~((~(singleton(D!3) = singleton(D!3))) | (in(D!3, singleton(D!3)) <=> (D!3 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3))))))) <=> (~(~in(D!3, singleton(D!3))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 ((~((~((~(singleton(D!3) = singleton(D!3))) | (in(D!3, singleton(D!3)) <=> (D!3 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3))))))) <=> in(D!3, singleton(D!3))),
% 0.21/0.40 inference(transitivity,[status(thm)],[82, 69])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (((~![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(D!3) = singleton(D!3))) | (in(D!3, singleton(D!3)) <=> (D!3 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))))))) <=> ((~![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(D!3, singleton(D!3)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (((~![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(D!3) = singleton(D!3))) | (in(D!3, singleton(D!3)) <=> (D!3 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))))))) <=> ((~![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(D!3, singleton(D!3)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[84, 68])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 ((~![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(D!3) = singleton(D!3))) | (in(D!3, singleton(D!3)) <=> (D!3 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | in(D!3, singleton(D!3))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 (in(D!3, singleton(D!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[87, 67])).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[88, 49])).
% 0.21/0.40 tff(90,plain,(in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(91,plain,
% 0.21/0.40 ((((~in(A!6, C!4)) | (~in(B!5, singleton(D!3)))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))) | (~((~in(A!6, C!4)) | (~in(B!5, singleton(D!3))))) | (~in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 ((~((~in(A!6, C!4)) | (~in(B!5, singleton(D!3))))) | (~in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[91, 41])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 (~((~in(A!6, C!4)) | (~in(B!5, singleton(D!3))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[92, 90])).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 (((~in(A!6, C!4)) | (~in(B!5, singleton(D!3)))) | in(B!5, singleton(D!3))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 (in(B!5, singleton(D!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (((~in(A!6, C!4)) | (~(B!5 = D!3))) | (~in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))) | (~(((~in(A!6, C!4)) | (~(B!5 = D!3))) <=> in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (((~in(A!6, C!4)) | (~(B!5 = D!3))) | (~in(ordered_pair(A!6, B!5), cartesian_product2(C!4, singleton(D!3))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[96, 20])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 ((~in(A!6, C!4)) | (~(B!5 = D!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[97, 90])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 (((~in(A!6, C!4)) | (~in(B!5, singleton(D!3)))) | in(A!6, C!4)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 (in(A!6, C!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[99, 93])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 ((~((~in(A!6, C!4)) | (~(B!5 = D!3)))) | (~in(A!6, C!4)) | (~(B!5 = D!3))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 (~(B!5 = D!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[101, 100, 98])).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 ((~(in(B!5, singleton(D!3)) <=> (B!5 = D!3))) | (~in(B!5, singleton(D!3))) | (B!5 = D!3)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 (~(in(B!5, singleton(D!3)) <=> (B!5 = D!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[103, 102, 95])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 (((~![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(B!5, singleton(D!3)) <=> (B!5 = D!3))) <=> ((~![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(B!5, singleton(D!3)) <=> (B!5 = D!3)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 ((~(~(in(B!5, singleton(D!3)) <=> (B!5 = D!3)))) <=> (in(B!5, singleton(D!3)) <=> (B!5 = D!3))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 (((~(in(B!5, singleton(D!3)) <=> (B!5 = D!3))) | $false) <=> (~(in(B!5, singleton(D!3)) <=> (B!5 = D!3)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 ((~(in(B!5, singleton(D!3)) <=> (B!5 = D!3))) <=> (~(in(B!5, singleton(D!3)) <=> (B!5 = D!3)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (($false | (in(B!5, singleton(D!3)) <=> (B!5 = D!3))) <=> (in(B!5, singleton(D!3)) <=> (B!5 = D!3))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 ((~(singleton(D!3) = singleton(D!3))) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 ((~(singleton(D!3) = singleton(D!3))) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[110, 71])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 (((~(singleton(D!3) = singleton(D!3))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3))) <=> ($false | (in(B!5, singleton(D!3)) <=> (B!5 = D!3)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[111])).
% 0.21/0.41 tff(113,plain,
% 0.21/0.41 (((~(singleton(D!3) = singleton(D!3))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3))) <=> (in(B!5, singleton(D!3)) <=> (B!5 = D!3))),
% 0.21/0.41 inference(transitivity,[status(thm)],[112, 109])).
% 0.21/0.41 tff(114,plain,
% 0.21/0.41 ((~((~(singleton(D!3) = singleton(D!3))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3)))) <=> (~(in(B!5, singleton(D!3)) <=> (B!5 = D!3)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[113])).
% 0.21/0.41 tff(115,plain,
% 0.21/0.41 ((~((~(singleton(D!3) = singleton(D!3))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3)))) <=> (~(in(B!5, singleton(D!3)) <=> (B!5 = D!3)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[114, 108])).
% 0.21/0.41 tff(116,plain,
% 0.21/0.41 (((~((~(singleton(D!3) = singleton(D!3))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))))) <=> ((~(in(B!5, singleton(D!3)) <=> (B!5 = D!3))) | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[115, 78])).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 (((~((~(singleton(D!3) = singleton(D!3))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))))) <=> (~(in(B!5, singleton(D!3)) <=> (B!5 = D!3)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[116, 107])).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 ((~((~((~(singleton(D!3) = singleton(D!3))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3))))))) <=> (~(~(in(B!5, singleton(D!3)) <=> (B!5 = D!3))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 ((~((~((~(singleton(D!3) = singleton(D!3))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3))))))) <=> (in(B!5, singleton(D!3)) <=> (B!5 = D!3))),
% 0.21/0.41 inference(transitivity,[status(thm)],[118, 106])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 (((~![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(D!3) = singleton(D!3))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))))))) <=> ((~![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(B!5, singleton(D!3)) <=> (B!5 = D!3)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[119])).
% 0.21/0.41 tff(121,plain,
% 0.21/0.41 (((~![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(D!3) = singleton(D!3))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))))))) <=> ((~![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(B!5, singleton(D!3)) <=> (B!5 = D!3)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[120, 105])).
% 0.21/0.41 tff(122,plain,
% 0.21/0.41 ((~![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(D!3) = singleton(D!3))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3)))) | (~((singleton(D!3) = singleton(D!3)) | (~(in(tptp_fun_C_0(singleton(D!3), D!3), singleton(D!3)) <=> (tptp_fun_C_0(singleton(D!3), D!3) = D!3)))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(123,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(B!5, singleton(D!3)) <=> (B!5 = D!3))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.21/0.41 tff(124,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[123, 67, 104])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------