TSTP Solution File: NUM533+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM533+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 13:10:19 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM533+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 11:28:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(aElementOf0_type, type, (
% 0.20/0.40 aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.40 tff(xB_type, type, (
% 0.20/0.40 xB: $i)).
% 0.20/0.40 tff(tptp_fun_W0_2_type, type, (
% 0.20/0.40 tptp_fun_W0_2: $i)).
% 0.20/0.40 tff(xA_type, type, (
% 0.20/0.40 xA: $i)).
% 0.20/0.40 tff(aSubsetOf0_type, type, (
% 0.20/0.40 aSubsetOf0: ( $i * $i ) > $o)).
% 0.20/0.40 tff(xC_type, type, (
% 0.20/0.40 xC: $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[W0: $i] : refl(((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) <=> ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) <=> ![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) <=> ![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 ((~((((![W0: $i] : (aElementOf0(W0, xA) => aElementOf0(W0, xB)) & aSubsetOf0(xA, xB)) & ![W0: $i] : (aElementOf0(W0, xB) => aElementOf0(W0, xC))) & aSubsetOf0(xB, xC)) => (![W0: $i] : (aElementOf0(W0, xA) => aElementOf0(W0, xC)) | aSubsetOf0(xA, xC)))) <=> (~(aSubsetOf0(xA, xC) | ![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC)) | (~(![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) & aSubsetOf0(xA, xB) & ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) & aSubsetOf0(xB, xC)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(5,axiom,(~((((![W0: $i] : (aElementOf0(W0, xA) => aElementOf0(W0, xB)) & aSubsetOf0(xA, xB)) & ![W0: $i] : (aElementOf0(W0, xB) => aElementOf0(W0, xC))) & aSubsetOf0(xB, xC)) => (![W0: $i] : (aElementOf0(W0, xA) => aElementOf0(W0, xC)) | aSubsetOf0(xA, xC)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (~(aSubsetOf0(xA, xC) | ![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC)) | (~(![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) & aSubsetOf0(xA, xB) & ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) & aSubsetOf0(xB, xC))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB)) & aSubsetOf0(xA, xB) & ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) & aSubsetOf0(xB, xC)),
% 0.20/0.40 inference(or_elim,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.20/0.40 inference(and_elim,[status(thm)],[7])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.20/0.40 tff(10,plain,(
% 0.20/0.40 ![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.20/0.40 inference(skolemize,[status(sab)],[9])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 ((~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))) <=> (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(or_elim,[status(thm)],[6])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.20/0.40 tff(20,plain,(
% 0.20/0.40 ~((~aElementOf0(W0!2, xA)) | aElementOf0(W0!2, xC))),
% 0.20/0.40 inference(skolemize,[status(sab)],[19])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (aElementOf0(W0!2, xA)),
% 0.20/0.40 inference(or_elim,[status(thm)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))) | ((~aElementOf0(W0!2, xA)) | aElementOf0(W0!2, xB))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))) | (~aElementOf0(W0!2, xA)) | aElementOf0(W0!2, xB))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))) | ((~aElementOf0(W0!2, xA)) | aElementOf0(W0!2, xB))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ((~![W0: $i] : ((~aElementOf0(W0, xA)) | aElementOf0(W0, xB))) | (~aElementOf0(W0!2, xA)) | aElementOf0(W0!2, xB)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (aElementOf0(W0!2, xB)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (^[W0: $i] : refl(((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) <=> ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) <=> ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC)) <=> ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(and_elim,[status(thm)],[7])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.40 tff(31,plain,(
% 0.20/0.40 ![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(skolemize,[status(sab)],[30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (~aElementOf0(W0!2, xC)),
% 0.20/0.40 inference(or_elim,[status(thm)],[20])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (((~![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))) | ((~aElementOf0(W0!2, xB)) | aElementOf0(W0!2, xC))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))) | (~aElementOf0(W0!2, xB)) | aElementOf0(W0!2, xC))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((~![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))) | ((~aElementOf0(W0!2, xB)) | aElementOf0(W0!2, xC))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 ((~![W0: $i] : ((~aElementOf0(W0, xB)) | aElementOf0(W0, xC))) | (~aElementOf0(W0!2, xB)) | aElementOf0(W0!2, xC)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[36, 33, 32, 25])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------