TSTP Solution File: NUM609+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM609+3 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Sep 18 13:10:52 EDT 2022
% Result : Theorem 0.14s 0.44s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM609+3 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.28 % Computer : n002.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Fri Sep 2 12:32:16 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.29 Usage: tptp [options] [-file:]file
% 0.08/0.29 -h, -? prints this message.
% 0.08/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.29 -m, -model generate model.
% 0.08/0.29 -p, -proof generate proof.
% 0.08/0.29 -c, -core generate unsat core of named formulas.
% 0.08/0.29 -st, -statistics display statistics.
% 0.08/0.29 -t:timeout set timeout (in second).
% 0.08/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.29 -<param>:<value> configuration parameter and value.
% 0.08/0.29 -o:<output-file> file to place output in.
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start Proof
% 0.14/0.44 tff(szmzizndt0_type, type, (
% 0.14/0.44 szmzizndt0: $i > $i)).
% 0.14/0.44 tff(xQ_type, type, (
% 0.14/0.44 xQ: $i)).
% 0.14/0.44 tff(tptp_fun_W0_45_type, type, (
% 0.14/0.44 tptp_fun_W0_45: $i)).
% 0.14/0.44 tff(aElementOf0_type, type, (
% 0.14/0.44 aElementOf0: ( $i * $i ) > $o)).
% 0.14/0.44 tff(aElement0_type, type, (
% 0.14/0.44 aElement0: $i > $o)).
% 0.14/0.44 tff(sdtmndt0_type, type, (
% 0.14/0.44 sdtmndt0: ( $i * $i ) > $i)).
% 0.14/0.44 tff(xP_type, type, (
% 0.14/0.44 xP: $i)).
% 0.14/0.44 tff(aSubsetOf0_type, type, (
% 0.14/0.44 aSubsetOf0: ( $i * $i ) > $o)).
% 0.14/0.44 tff(sdtlseqdt0_type, type, (
% 0.14/0.44 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.14/0.44 tff(aSet0_type, type, (
% 0.14/0.44 aSet0: $i > $o)).
% 0.14/0.44 tff(1,plain,
% 0.14/0.44 ((~![W0: $i] : ((~aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ)))) | aElementOf0(W0, xQ))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ)))) | aElementOf0(W0, xQ)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(2,plain,
% 0.14/0.44 ((~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ)))) | aElementOf0(W0, xQ)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(3,plain,
% 0.14/0.44 ((~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))) <=> (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(4,plain,
% 0.14/0.44 ((~![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xQ))) <=> (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(5,axiom,(~(![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xQ)) | aSubsetOf0(xP, xQ))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.14/0.44 tff(6,plain,
% 0.14/0.44 (~![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xQ))),
% 0.14/0.44 inference(or_elim,[status(thm)],[5])).
% 0.14/0.44 tff(7,plain,
% 0.14/0.44 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[6, 4])).
% 0.14/0.44 tff(8,plain,
% 0.14/0.44 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.44 tff(9,plain,
% 0.14/0.44 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.14/0.44 tff(10,plain,
% 0.14/0.44 (~![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xQ))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.14/0.44 tff(11,plain,
% 0.14/0.44 (~![W0: $i] : ((~aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ)))) | aElementOf0(W0, xQ))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.14/0.44 tff(12,plain,
% 0.14/0.44 (~![W0: $i] : ((~aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ)))) | aElementOf0(W0, xQ))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.14/0.44 tff(13,plain,
% 0.14/0.44 (~![W0: $i] : ((~aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ)))) | aElementOf0(W0, xQ))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.14/0.44 tff(14,plain,
% 0.14/0.44 (~![W0: $i] : ((~aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ)))) | aElementOf0(W0, xQ))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[13, 1])).
% 0.14/0.44 tff(15,plain,(
% 0.14/0.44 ~((~aElementOf0(W0!45, sdtmndt0(xQ, szmzizndt0(xQ)))) | aElementOf0(W0!45, xQ))),
% 0.14/0.44 inference(skolemize,[status(sab)],[14])).
% 0.14/0.44 tff(16,plain,
% 0.14/0.44 (~aElementOf0(W0!45, xQ)),
% 0.14/0.44 inference(or_elim,[status(thm)],[15])).
% 0.14/0.44 tff(17,plain,
% 0.14/0.44 (((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ))) | aElementOf0(W0!45, xQ)),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(18,plain,
% 0.14/0.44 ((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.14/0.44 tff(19,plain,
% 0.14/0.44 (aElementOf0(W0!45, sdtmndt0(xQ, szmzizndt0(xQ)))),
% 0.14/0.44 inference(or_elim,[status(thm)],[15])).
% 0.14/0.44 tff(20,plain,
% 0.14/0.44 ((~(aElementOf0(W0!45, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ)))))) | (~aElementOf0(W0!45, sdtmndt0(xQ, szmzizndt0(xQ)))) | (~((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ))))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(21,plain,
% 0.14/0.44 (~(aElementOf0(W0!45, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ)))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[20, 19, 18])).
% 0.14/0.44 tff(22,plain,
% 0.14/0.44 (^[W0: $i] : refl((aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))))) <=> (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(23,plain,
% 0.14/0.44 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))))) <=> ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ)))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[22])).
% 0.14/0.44 tff(24,plain,
% 0.14/0.44 (^[W0: $i] : rewrite((aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))) <=> (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(25,plain,
% 0.14/0.44 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))) <=> ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ)))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[24])).
% 0.14/0.44 tff(26,plain,
% 0.14/0.44 (^[W0: $i] : rewrite((aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))) <=> (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(27,plain,
% 0.14/0.44 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))) <=> ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[26])).
% 0.14/0.44 tff(28,plain,
% 0.14/0.44 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))) <=> ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(29,plain,
% 0.14/0.44 (^[W0: $i] : rewrite((aElementOf0(W0, xP) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = szmzizndt0(xQ))))) <=> (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(30,plain,
% 0.14/0.44 (![W0: $i] : (aElementOf0(W0, xP) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = szmzizndt0(xQ))))) <=> ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[29])).
% 0.14/0.44 tff(31,axiom,(((aSet0(xP) & ![W0: $i] : (aElementOf0(W0, xQ) => sdtlseqdt0(szmzizndt0(xQ), W0))) & ![W0: $i] : (aElementOf0(W0, xP) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = szmzizndt0(xQ)))))) & (xP = sdtmndt0(xQ, szmzizndt0(xQ)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__5164')).
% 0.14/0.44 tff(32,plain,
% 0.14/0.44 ((aSet0(xP) & ![W0: $i] : (aElementOf0(W0, xQ) => sdtlseqdt0(szmzizndt0(xQ), W0))) & ![W0: $i] : (aElementOf0(W0, xP) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = szmzizndt0(xQ)))))),
% 0.14/0.44 inference(and_elim,[status(thm)],[31])).
% 0.14/0.44 tff(33,plain,
% 0.14/0.44 (![W0: $i] : (aElementOf0(W0, xP) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = szmzizndt0(xQ)))))),
% 0.14/0.44 inference(and_elim,[status(thm)],[32])).
% 0.14/0.44 tff(34,plain,
% 0.14/0.44 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.14/0.44 tff(35,plain,
% 0.14/0.44 (![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[34, 28])).
% 0.14/0.44 tff(36,plain,
% 0.14/0.44 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[35, 27])).
% 0.14/0.44 tff(37,plain,(
% 0.14/0.44 ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = szmzizndt0(xQ)))))),
% 0.14/0.45 inference(skolemize,[status(sab)],[36])).
% 0.14/0.45 tff(38,plain,
% 0.14/0.45 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ)))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[37, 25])).
% 0.14/0.45 tff(39,plain,
% 0.14/0.45 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ)))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[38, 23])).
% 0.14/0.45 tff(40,plain,
% 0.14/0.45 ((~![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = szmzizndt0(xQ)))))) | (aElementOf0(W0!45, sdtmndt0(xQ, szmzizndt0(xQ))) <=> (~((~aElement0(W0!45)) | (~aElementOf0(W0!45, xQ)) | (W0!45 = szmzizndt0(xQ)))))),
% 0.14/0.45 inference(quant_inst,[status(thm)],[])).
% 0.14/0.45 tff(41,plain,
% 0.14/0.45 ($false),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[40, 39, 21])).
% 0.14/0.45 % SZS output end Proof
%------------------------------------------------------------------------------