TSTP Solution File: SET975+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 : Tue Sep 20 05:08:47 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 09:00:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 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(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_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(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,(~((~(A!6 = C!4)) | (~in(B!5, D!3)))), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (((~(A!6 = C!4)) | (~in(B!5, D!3))) | (A!6 = C!4)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (A!6 = C!4),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (C!4 = A!6),
% 0.21/0.39 inference(symmetry,[status(thm)],[3])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (in(C!4, singleton(C!4)) <=> in(A!6, singleton(C!4))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[4])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (in(A!6, singleton(C!4)) <=> in(C!4, singleton(C!4))),
% 0.21/0.39 inference(symmetry,[status(thm)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 ((~in(A!6, singleton(C!4))) <=> (~in(C!4, singleton(C!4)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[6])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (((~(A!6 = C!4)) | (~in(B!5, D!3))) | in(B!5, D!3)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (in(B!5, D!3)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[8, 1])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (((~in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))) <=> (~((~(A!6 = C!4)) | (~in(B!5, D!3))))) <=> (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> ((~(A!6 = C!4)) | (~in(B!5, D!3))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (((A!6 = C!4) & in(B!5, D!3)) <=> (~((~(A!6 = C!4)) | (~in(B!5, D!3))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (((~in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))) <=> ((A!6 = C!4) & in(B!5, D!3))) <=> ((~in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))) <=> (~((~(A!6 = C!4)) | (~in(B!5, D!3)))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[11])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (((~in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))) <=> ((A!6 = C!4) & in(B!5, D!3))) <=> (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> ((~(A!6 = C!4)) | (~in(B!5, D!3))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[12, 10])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 ((~(in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> ((A!6 = C!4) & in(B!5, D!3)))) <=> ((~in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))) <=> ((A!6 = C!4) & in(B!5, D!3)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 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(singleton(C), D)) <=> ((A = C) & in(B, D)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(singleton(C), D)) <=> ((A = C) & in(B, D))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(16,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(singleton(C), D)) <=> ((A = C) & in(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t128_zfmisc_1')).
% 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(singleton(C), D)) <=> ((A = C) & in(B, D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(singleton(C), D)) <=> ((A = C) & in(B, D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(singleton(C), D)) <=> ((A = C) & in(B, D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(singleton(C), D)) <=> ((A = C) & in(B, D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(singleton(C), D)) <=> ((A = C) & in(B, D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(singleton(C), D)) <=> ((A = C) & in(B, D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(singleton(C), D)) <=> ((A = C) & in(B, D)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.21/0.39 tff(24,plain,(
% 0.21/0.39 ~(in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> ((A!6 = C!4) & in(B!5, D!3)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[23])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 ((~in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))) <=> ((A!6 = C!4) & in(B!5, D!3))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> ((~(A!6 = C!4)) | (~in(B!5, D!3)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[25, 13])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 ((~in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))) | ((~(A!6 = C!4)) | (~in(B!5, D!3))) | (~(in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> ((~(A!6 = C!4)) | (~in(B!5, D!3)))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 ((~in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))) | ((~(A!6 = C!4)) | (~in(B!5, D!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (~in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[28, 1])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((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))))))),
% 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(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)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((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))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (![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)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 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')).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.40 tff(37,plain,(
% 0.21/0.40 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[36])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4)))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 ((in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(A!6, singleton(C!4))) | (~in(B!5, D!3))))) <=> (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(A!6, singleton(C!4))) | (~in(B!5, D!3)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4)))))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(A!6, singleton(C!4))) | (~in(B!5, D!3)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[42, 40])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(A!6, singleton(C!4))) | (~in(B!5, D!3)))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[45, 39])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 ((~(in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4))))))) | in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) | ((~in(B!5, D!3)) | (~in(A!6, singleton(C!4))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) | ((~in(B!5, D!3)) | (~in(A!6, singleton(C!4))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 ((~in(B!5, D!3)) | (~in(A!6, singleton(C!4)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[48, 29])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 ((~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4))))) | (~in(B!5, D!3)) | (~in(A!6, singleton(C!4)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (~in(A!6, singleton(C!4))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[50, 49, 9])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (~in(C!4, singleton(C!4))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[51, 7])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (^[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)))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(54,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)))))) <=> ![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] : ![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(56,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(57,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)],[56])).
% 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, 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)],[57, 55])).
% 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, 54])).
% 0.21/0.40 tff(60,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(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)))) | (~((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)],[61, 59])).
% 0.21/0.40 tff(63,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)))), ((((~(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(64,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)],[63])).
% 0.21/0.40 tff(65,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(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))))) <=> ![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)],[65])).
% 0.21/0.40 tff(67,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(68,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(69,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)],[68, 67])).
% 0.21/0.40 tff(70,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)],[69])).
% 0.21/0.40 tff(71,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)],[70, 66])).
% 0.21/0.40 tff(72,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)],[71, 64])).
% 0.21/0.40 tff(73,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)],[72, 62])).
% 0.21/0.40 tff(74,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(C!4, singleton(C!4))) <=> ((~![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(C!4, singleton(C!4)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 ((~(~in(C!4, singleton(C!4)))) <=> in(C!4, singleton(C!4))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (((~in(C!4, singleton(C!4))) | $false) <=> (~in(C!4, singleton(C!4)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 ((~$true) <=> $false),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (($true | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))) <=> $true),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 ((singleton(C!4) = singleton(C!4)) <=> $true),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 (((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))) <=> ($true | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))) <=> $true),
% 0.21/0.40 inference(transitivity,[status(thm)],[80, 78])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 ((~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))) <=> (~$true)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 ((~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))) <=> $false),
% 0.21/0.40 inference(transitivity,[status(thm)],[82, 77])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 ((~((~(singleton(C!4) = singleton(C!4))) | (in(C!4, singleton(C!4)) <=> (C!4 = C!4)))) <=> (~in(C!4, singleton(C!4)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (((~((~(singleton(C!4) = singleton(C!4))) | (in(C!4, singleton(C!4)) <=> (C!4 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))) <=> ((~in(C!4, singleton(C!4))) | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[84, 83])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (((~((~(singleton(C!4) = singleton(C!4))) | (in(C!4, singleton(C!4)) <=> (C!4 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))) <=> (~in(C!4, singleton(C!4)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[85, 76])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 ((~((~((~(singleton(C!4) = singleton(C!4))) | (in(C!4, singleton(C!4)) <=> (C!4 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))))) <=> (~(~in(C!4, singleton(C!4))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[86])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 ((~((~((~(singleton(C!4) = singleton(C!4))) | (in(C!4, singleton(C!4)) <=> (C!4 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))))) <=> in(C!4, singleton(C!4))),
% 0.21/0.41 inference(transitivity,[status(thm)],[87, 75])).
% 0.21/0.41 tff(89,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(C!4) = singleton(C!4))) | (in(C!4, singleton(C!4)) <=> (C!4 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))))) <=> ((~![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(C!4, singleton(C!4)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[88])).
% 0.21/0.41 tff(90,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(C!4) = singleton(C!4))) | (in(C!4, singleton(C!4)) <=> (C!4 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))))) <=> ((~![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(C!4, singleton(C!4)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[89, 74])).
% 0.21/0.41 tff(91,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(C!4) = singleton(C!4))) | (in(C!4, singleton(C!4)) <=> (C!4 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(C!4, singleton(C!4))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (in(C!4, singleton(C!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[92, 73])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[93, 52])).
% 0.21/0.41 tff(95,plain,((~(A!6 = C!4)) | (~in(B!5, D!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) | (~((~(A!6 = C!4)) | (~in(B!5, D!3)))) | (~(in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> ((~(A!6 = C!4)) | (~in(B!5, D!3)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) | (~((~(A!6 = C!4)) | (~in(B!5, D!3))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[96, 26])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 (in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[97, 95])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 ((~(in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3)) <=> (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4))))))) | (~in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))) | (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 ((~in(ordered_pair(A!6, B!5), cartesian_product2(singleton(C!4), D!3))) | (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[99, 46])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 (~((~in(B!5, D!3)) | (~in(A!6, singleton(C!4))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[100, 98])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 (((~in(B!5, D!3)) | (~in(A!6, singleton(C!4)))) | in(A!6, singleton(C!4))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 (in(A!6, singleton(C!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 (((~in(B!5, D!3)) | (~in(A!6, singleton(C!4)))) | in(B!5, D!3)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 (in(B!5, D!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 ((~((~(A!6 = C!4)) | (~in(B!5, D!3)))) | (~(A!6 = C!4)) | (~in(B!5, D!3))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 (~(A!6 = C!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[106, 105, 95])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 ((~(in(A!6, singleton(C!4)) <=> (A!6 = C!4))) | (~in(A!6, singleton(C!4))) | (A!6 = C!4)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (~(in(A!6, singleton(C!4)) <=> (A!6 = C!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[108, 107, 103])).
% 0.21/0.41 tff(110,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(A!6, singleton(C!4)) <=> (A!6 = C!4))) <=> ((~![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(A!6, singleton(C!4)) <=> (A!6 = C!4)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 ((~((~in(A!6, singleton(C!4))) <=> (A!6 = C!4))) <=> (in(A!6, singleton(C!4)) <=> (A!6 = C!4))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 ((((~in(A!6, singleton(C!4))) <=> (A!6 = C!4)) | $false) <=> ((~in(A!6, singleton(C!4))) <=> (A!6 = C!4))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(113,plain,
% 0.21/0.41 ((~(in(A!6, singleton(C!4)) <=> (A!6 = C!4))) <=> ((~in(A!6, singleton(C!4))) <=> (A!6 = C!4))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(114,plain,
% 0.21/0.41 (($false | (in(A!6, singleton(C!4)) <=> (A!6 = C!4))) <=> (in(A!6, singleton(C!4)) <=> (A!6 = C!4))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(115,plain,
% 0.21/0.41 ((~(singleton(C!4) = singleton(C!4))) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.41 tff(116,plain,
% 0.21/0.41 ((~(singleton(C!4) = singleton(C!4))) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[115, 77])).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 (((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4))) <=> ($false | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[116])).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 (((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4))) <=> (in(A!6, singleton(C!4)) <=> (A!6 = C!4))),
% 0.21/0.41 inference(transitivity,[status(thm)],[117, 114])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 ((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) <=> (~(in(A!6, singleton(C!4)) <=> (A!6 = C!4)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 ((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) <=> ((~in(A!6, singleton(C!4))) <=> (A!6 = C!4))),
% 0.21/0.41 inference(transitivity,[status(thm)],[119, 113])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))) <=> (((~in(A!6, singleton(C!4))) <=> (A!6 = C!4)) | $false)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[120, 83])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))) <=> ((~in(A!6, singleton(C!4))) <=> (A!6 = C!4))),
% 0.21/0.42 inference(transitivity,[status(thm)],[121, 112])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 ((~((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))))) <=> (~((~in(A!6, singleton(C!4))) <=> (A!6 = C!4)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[122])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 ((~((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))))) <=> (in(A!6, singleton(C!4)) <=> (A!6 = C!4))),
% 0.21/0.42 inference(transitivity,[status(thm)],[123, 111])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (((~![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(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))))) <=> ((~![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(A!6, singleton(C!4)) <=> (A!6 = C!4)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[124])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (((~![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(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))))) <=> ((~![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(A!6, singleton(C!4)) <=> (A!6 = C!4)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[125, 110])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 ((~![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(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[128, 73, 109])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------