TSTP Solution File: NUM631+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM631+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 : 600s
% DateTime : Mon Jul 18 14:28:20 EDT 2022
% Result : Theorem 25.01s 25.23s
% Output : Refutation 25.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of clauses : 61 ( 30 unt; 0 nHn; 61 RR)
% Number of literals : 122 ( 0 equ; 63 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 16 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
aFunction0(xc),
file('NUM631+3.p',unknown),
[] ).
cnf(16,axiom,
aSet0(xQ),
file('NUM631+3.p',unknown),
[] ).
cnf(17,axiom,
aSet0(xP),
file('NUM631+3.p',unknown),
[] ).
cnf(18,axiom,
aSet0(xD),
file('NUM631+3.p',unknown),
[] ).
cnf(20,axiom,
aElementOf0(xK,szNzAzT0),
file('NUM631+3.p',unknown),
[] ).
cnf(22,axiom,
aElementOf0(xk,szNzAzT0),
file('NUM631+3.p',unknown),
[] ).
cnf(30,axiom,
aElementOf0(xp,xQ),
file('NUM631+3.p',unknown),
[] ).
cnf(33,axiom,
aElementOf0(xn,szNzAzT0),
file('NUM631+3.p',unknown),
[] ).
cnf(49,axiom,
equal(sbrdtbr0(xQ),xK),
file('NUM631+3.p',unknown),
[] ).
cnf(51,axiom,
aElementOf0(xQ,szDzozmdt0(xc)),
file('NUM631+3.p',unknown),
[] ).
cnf(52,axiom,
equal(szmzizndt0(xQ),xp),
file('NUM631+3.p',unknown),
[] ).
cnf(53,axiom,
equal(sbrdtbr0(xP),xk),
file('NUM631+3.p',unknown),
[] ).
cnf(68,axiom,
equal(sdtlpdtrp0(xe,xn),xp),
file('NUM631+3.p',unknown),
[] ).
cnf(69,axiom,
aElementOf0(xP,slbdtsldtrb0(xD,xk)),
file('NUM631+3.p',unknown),
[] ).
cnf(74,axiom,
( ~ aFunction0(u)
| aSet0(szDzozmdt0(u)) ),
file('NUM631+3.p',unknown),
[] ).
cnf(81,axiom,
equal(sdtmndt0(xQ,szmzizndt0(xQ)),xP),
file('NUM631+3.p',unknown),
[] ).
cnf(85,axiom,
equal(sdtlpdtrp0(xd,xn),szDzizrdt0(xd)),
file('NUM631+3.p',unknown),
[] ).
cnf(86,axiom,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
file('NUM631+3.p',unknown),
[] ).
cnf(108,axiom,
~ equal(sdtlpdtrp0(xd,xn),sdtlpdtrp0(xc,xQ)),
file('NUM631+3.p',unknown),
[] ).
cnf(120,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM631+3.p',unknown),
[] ).
cnf(136,axiom,
( ~ aSet0(u)
| ~ aElementOf0(sbrdtbr0(u),szNzAzT0)
| isFinite0(u) ),
file('NUM631+3.p',unknown),
[] ).
cnf(169,axiom,
( ~ aElementOf0(u,szNzAzT0)
| equal(szmzizndt0(sdtlpdtrp0(xN,u)),sdtlpdtrp0(xe,u)) ),
file('NUM631+3.p',unknown),
[] ).
cnf(193,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| equal(sdtpldt0(sdtmndt0(u,v),v),u) ),
file('NUM631+3.p',unknown),
[] ).
cnf(203,axiom,
equal(sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))),sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)),
file('NUM631+3.p',unknown),
[] ).
cnf(208,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| ~ equal(w,slbdtsldtrb0(u,v))
| aSet0(w) ),
file('NUM631+3.p',unknown),
[] ).
cnf(385,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| ~ aSubsetOf0(u,sdtlpdtrp0(xN,szszuzczcdt0(v)))
| ~ equal(sbrdtbr0(u),xk)
| equal(sdtlpdtrp0(sdtlpdtrp0(xC,v),u),skf89(v)) ),
file('NUM631+3.p',unknown),
[] ).
cnf(394,axiom,
( ~ aSet0(u)
| ~ equal(sbrdtbr0(u),xk)
| ~ aElementOf0(v,szNzAzT0)
| ~ aSubsetOf0(u,sdtlpdtrp0(xN,szszuzczcdt0(v)))
| equal(sdtlpdtrp0(sdtlpdtrp0(xC,v),u),sdtlpdtrp0(xd,v)) ),
file('NUM631+3.p',unknown),
[] ).
cnf(430,plain,
equal(sdtmndt0(xQ,xp),xP),
inference(rew,[status(thm),theory(equality)],[52,81]),
[iquote('0:Rew:52.0,81.0')] ).
cnf(433,plain,
~ equal(sdtlpdtrp0(xc,xQ),szDzizrdt0(xd)),
inference(rew,[status(thm),theory(equality)],[85,108]),
[iquote('0:Rew:85.0,108.0')] ).
cnf(507,plain,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| ~ aSubsetOf0(u,sdtlpdtrp0(xN,szszuzczcdt0(v)))
| ~ equal(sbrdtbr0(u),xk)
| equal(sdtlpdtrp0(xd,v),skf89(v)) ),
inference(rew,[status(thm),theory(equality)],[385,394]),
[iquote('0:Rew:385.4,394.4')] ).
cnf(688,plain,
( ~ aSet0(szDzozmdt0(xc))
| aElement0(xQ) ),
inference(res,[status(thm),theory(equality)],[51,120]),
[iquote('0:Res:51.0,120.1')] ).
cnf(690,plain,
( ~ aSet0(slbdtsldtrb0(xD,xk))
| aElement0(xP) ),
inference(res,[status(thm),theory(equality)],[69,120]),
[iquote('0:Res:69.0,120.1')] ).
cnf(713,plain,
aElement0(xQ),
inference(ssi,[status(thm)],[688,74,8]),
[iquote('0:SSi:688.0,74.0,8.1')] ).
cnf(782,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xk,szNzAzT0)
| isFinite0(xP) ),
inference(spl,[status(thm),theory(equality)],[53,136]),
[iquote('0:SpL:53.0,136.1')] ).
cnf(783,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(xK,szNzAzT0)
| isFinite0(xQ) ),
inference(spl,[status(thm),theory(equality)],[49,136]),
[iquote('0:SpL:49.0,136.1')] ).
cnf(789,plain,
( ~ aElementOf0(xk,szNzAzT0)
| isFinite0(xP) ),
inference(ssi,[status(thm)],[782,17]),
[iquote('0:SSi:782.0,17.0')] ).
cnf(790,plain,
isFinite0(xP),
inference(mrr,[status(thm)],[789,22]),
[iquote('0:MRR:789.0,22.0')] ).
cnf(791,plain,
( ~ aElementOf0(xK,szNzAzT0)
| isFinite0(xQ) ),
inference(ssi,[status(thm)],[783,16,713]),
[iquote('0:SSi:783.0,16.0,713.0')] ).
cnf(792,plain,
isFinite0(xQ),
inference(mrr,[status(thm)],[791,20]),
[iquote('0:MRR:791.0,20.0')] ).
cnf(1778,plain,
( ~ aElementOf0(xn,szNzAzT0)
| equal(sdtlpdtrp0(xc,sdtpldt0(xP,sdtlpdtrp0(xe,xn))),sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)) ),
inference(spr,[status(thm),theory(equality)],[169,203]),
[iquote('0:SpR:169.1,203.0')] ).
cnf(1814,plain,
( ~ aElementOf0(xn,szNzAzT0)
| equal(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),sdtlpdtrp0(xc,sdtpldt0(xP,xp))) ),
inference(rew,[status(thm),theory(equality)],[68,1778]),
[iquote('0:Rew:68.0,1778.1')] ).
cnf(1815,plain,
equal(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),sdtlpdtrp0(xc,sdtpldt0(xP,xp))),
inference(mrr,[status(thm)],[1814,33]),
[iquote('0:MRR:1814.0,33.0')] ).
cnf(2638,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(xp,xQ)
| equal(sdtpldt0(xP,xp),xQ) ),
inference(spr,[status(thm),theory(equality)],[430,193]),
[iquote('0:SpR:430.0,193.2')] ).
cnf(2641,plain,
( ~ aElementOf0(xp,xQ)
| equal(sdtpldt0(xP,xp),xQ) ),
inference(ssi,[status(thm)],[2638,16,713,792]),
[iquote('0:SSi:2638.0,16.0,713.0,792.0')] ).
cnf(2642,plain,
equal(sdtpldt0(xP,xp),xQ),
inference(mrr,[status(thm)],[2641,30]),
[iquote('0:MRR:2641.0,30.0')] ).
cnf(2649,plain,
equal(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),sdtlpdtrp0(xc,xQ)),
inference(rew,[status(thm),theory(equality)],[2642,1815]),
[iquote('0:Rew:2642.0,1815.0')] ).
cnf(3369,plain,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| aSet0(slbdtsldtrb0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[208]),
[iquote('0:EqR:208.2')] ).
cnf(34118,plain,
( ~ aSet0(xD)
| ~ aElementOf0(xk,szNzAzT0)
| aElement0(xP) ),
inference(sor,[status(thm)],[690,3369]),
[iquote('0:SoR:690.0,3369.2')] ).
cnf(34130,plain,
( ~ aElementOf0(xk,szNzAzT0)
| aElement0(xP) ),
inference(ssi,[status(thm)],[34118,18]),
[iquote('0:SSi:34118.0,18.0')] ).
cnf(34131,plain,
aElement0(xP),
inference(mrr,[status(thm)],[34130,22]),
[iquote('0:MRR:34130.0,22.0')] ).
cnf(36867,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0)
| ~ equal(sbrdtbr0(xP),xk)
| equal(sdtlpdtrp0(xd,xn),skf89(xn)) ),
inference(res,[status(thm),theory(equality)],[86,507]),
[iquote('0:Res:86.0,507.2')] ).
cnf(36873,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0)
| ~ equal(xk,xk)
| equal(skf89(xn),szDzizrdt0(xd)) ),
inference(rew,[status(thm),theory(equality)],[85,36867,53]),
[iquote('0:Rew:85.0,36867.3,53.0,36867.2')] ).
cnf(36874,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0)
| equal(skf89(xn),szDzizrdt0(xd)) ),
inference(obv,[status(thm),theory(equality)],[36873]),
[iquote('0:Obv:36873.2')] ).
cnf(36875,plain,
( ~ aElementOf0(xn,szNzAzT0)
| equal(skf89(xn),szDzizrdt0(xd)) ),
inference(ssi,[status(thm)],[36874,17,790,34131]),
[iquote('0:SSi:36874.0,17.0,790.0,34131.0')] ).
cnf(36876,plain,
equal(skf89(xn),szDzizrdt0(xd)),
inference(mrr,[status(thm)],[36875,33]),
[iquote('0:MRR:36875.0,33.0')] ).
cnf(37362,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0)
| ~ equal(sbrdtbr0(xP),xk)
| equal(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),skf89(xn)) ),
inference(res,[status(thm),theory(equality)],[86,385]),
[iquote('0:Res:86.0,385.2')] ).
cnf(37368,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0)
| ~ equal(xk,xk)
| equal(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),szDzizrdt0(xd)) ),
inference(rew,[status(thm),theory(equality)],[36876,37362,53]),
[iquote('0:Rew:36876.0,37362.3,53.0,37362.2')] ).
cnf(37369,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0)
| equal(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),szDzizrdt0(xd)) ),
inference(obv,[status(thm),theory(equality)],[37368]),
[iquote('0:Obv:37368.2')] ).
cnf(37370,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0)
| equal(sdtlpdtrp0(xc,xQ),szDzizrdt0(xd)) ),
inference(rew,[status(thm),theory(equality)],[2649,37369]),
[iquote('0:Rew:2649.0,37369.2')] ).
cnf(37371,plain,
( ~ aElementOf0(xn,szNzAzT0)
| equal(sdtlpdtrp0(xc,xQ),szDzizrdt0(xd)) ),
inference(ssi,[status(thm)],[37370,17,790,34131]),
[iquote('0:SSi:37370.0,17.0,790.0,34131.0')] ).
cnf(37372,plain,
$false,
inference(mrr,[status(thm)],[37371,33,433]),
[iquote('0:MRR:37371.0,37371.1,33.0,433.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : NUM631+3 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.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 : 600
% 0.13/0.34 % DateTime : Thu Jul 7 15:08:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 25.01/25.23
% 25.01/25.23 SPASS V 3.9
% 25.01/25.23 SPASS beiseite: Proof found.
% 25.01/25.23 % SZS status Theorem
% 25.01/25.23 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.01/25.23 SPASS derived 27103 clauses, backtracked 5841 clauses, performed 38 splits and kept 15961 clauses.
% 25.01/25.23 SPASS allocated 126011 KBytes.
% 25.01/25.23 SPASS spent 0:0:24.12 on the problem.
% 25.01/25.23 0:00:00.04 for the input.
% 25.01/25.23 0:00:00.69 for the FLOTTER CNF translation.
% 25.01/25.23 0:00:00.56 for inferences.
% 25.01/25.23 0:00:01.00 for the backtracking.
% 25.01/25.23 0:0:21.34 for the reduction.
% 25.01/25.23
% 25.01/25.23
% 25.01/25.23 Here is a proof with depth 2, length 61 :
% 25.01/25.23 % SZS output start Refutation
% See solution above
% 25.01/25.23 Formulae used in the proof : m__3453 m__5116 m__5078 m__5164 m__5585 m__3418 m__3533 m__5173 m__5309 m__5147 m__5217 m__5599 mDomSet m__5321 m__5334 m__ mEOfElem mCardNum m__4660 mConsDiff m__5632 mDefSel m__4618 m__4854 m__4730
% 25.01/25.23
%------------------------------------------------------------------------------