TSTP Solution File: SET954+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET954+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 05:08:44 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % 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 08:52:32 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.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(in_type, type, (
% 0.13/0.39 in: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_D_2_type, type, (
% 0.13/0.39 tptp_fun_D_2: $i)).
% 0.13/0.39 tff(tptp_fun_B_4_type, type, (
% 0.13/0.39 tptp_fun_B_4: $i)).
% 0.13/0.39 tff(tptp_fun_C_3_type, type, (
% 0.13/0.39 tptp_fun_C_3: $i)).
% 0.13/0.39 tff(tptp_fun_A_5_type, type, (
% 0.13/0.39 tptp_fun_A_5: $i)).
% 0.13/0.39 tff(cartesian_product2_type, type, (
% 0.13/0.39 cartesian_product2: ( $i * $i ) > $i)).
% 0.13/0.39 tff(ordered_pair_type, type, (
% 0.13/0.39 ordered_pair: ( $i * $i ) > $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[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))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![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)))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[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))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![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)))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(6,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')).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.39 tff(8,plain,(
% 0.13/0.39 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[7])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2)))))) <=> ((~![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(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ((in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(B!4, D!2)) | (~in(A!5, C!3))))) <=> (in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(B!4, D!2)) | (~in(A!5, C!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(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2))))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(B!4, D!2)) | (~in(A!5, C!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(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[13, 11])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(B!4, D!2)) | (~in(A!5, C!3)))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2)))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[18, 10])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) => in(ordered_pair(B, A), cartesian_product2(D, C)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(22,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) => in(ordered_pair(B, A), cartesian_product2(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t107_zfmisc_1')).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.13/0.40 tff(30,plain,(
% 0.13/0.40 ~((~in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2))) | in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[29])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2))),
% 0.13/0.40 inference(or_elim,[status(thm)],[30])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 ((~(in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2)))))) | (~in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2))) | (~((~in(A!5, C!3)) | (~in(B!4, D!2))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 ((~(in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2)))))) | (~((~in(A!5, C!3)) | (~in(B!4, D!2))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (~((~in(A!5, C!3)) | (~in(B!4, D!2)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[33, 19])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (~in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))),
% 0.13/0.40 inference(or_elim,[status(thm)],[30])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 ((~(in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2)))))) | in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)) | ((~in(A!5, C!3)) | (~in(B!4, D!2)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 ((~(in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)) <=> (~((~in(A!5, C!3)) | (~in(B!4, D!2)))))) | ((~in(A!5, C!3)) | (~in(B!4, D!2)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[37, 34, 17])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------