TSTP Solution File: RNG090+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG090+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 20:41:26 EDT 2022
% Result : Theorem 3.80s 3.98s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of clauses : 57 ( 19 unt; 0 nHn; 57 RR)
% Number of literals : 142 ( 0 equ; 96 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aIdeal0(xI),
file('RNG090+1.p',unknown),
[] ).
cnf(4,axiom,
aIdeal0(xJ),
file('RNG090+1.p',unknown),
[] ).
cnf(7,axiom,
aElementOf0(xk,xI),
file('RNG090+1.p',unknown),
[] ).
cnf(8,axiom,
aElementOf0(xl,xJ),
file('RNG090+1.p',unknown),
[] ).
cnf(9,axiom,
aElementOf0(xm,xI),
file('RNG090+1.p',unknown),
[] ).
cnf(10,axiom,
aElementOf0(xn,xJ),
file('RNG090+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ aIdeal0(u)
| aSet0(u) ),
file('RNG090+1.p',unknown),
[] ).
cnf(15,axiom,
equal(sdtpldt0(xk,xl),xx),
file('RNG090+1.p',unknown),
[] ).
cnf(16,axiom,
equal(sdtpldt0(xm,xn),xy),
file('RNG090+1.p',unknown),
[] ).
cnf(18,axiom,
aElementOf0(sdtpldt0(xl,xn),xJ),
file('RNG090+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('RNG090+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtpldt0(v,u)) ),
file('RNG090+1.p',unknown),
[] ).
cnf(40,axiom,
~ equal(sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),sdtpldt0(xx,xy)),
file('RNG090+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('RNG090+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('RNG090+1.p',unknown),
[] ).
cnf(91,plain,
( ~ aSet0(xJ)
| aElement0(xn) ),
inference(res,[status(thm),theory(equality)],[10,31]),
[iquote('0:Res:10.0,31.1')] ).
cnf(92,plain,
( ~ aSet0(xJ)
| aElement0(xl) ),
inference(res,[status(thm),theory(equality)],[8,31]),
[iquote('0:Res:8.0,31.1')] ).
cnf(94,plain,
( ~ aSet0(xJ)
| aElement0(sdtpldt0(xl,xn)) ),
inference(res,[status(thm),theory(equality)],[18,31]),
[iquote('0:Res:18.0,31.1')] ).
cnf(95,plain,
( ~ aSet0(xI)
| aElement0(xm) ),
inference(res,[status(thm),theory(equality)],[9,31]),
[iquote('0:Res:9.0,31.1')] ).
cnf(96,plain,
( ~ aSet0(xI)
| aElement0(xk) ),
inference(res,[status(thm),theory(equality)],[7,31]),
[iquote('0:Res:7.0,31.1')] ).
cnf(103,plain,
aElement0(xn),
inference(ssi,[status(thm)],[91,12,4]),
[iquote('0:SSi:91.0,12.0,4.1')] ).
cnf(104,plain,
aElement0(xl),
inference(ssi,[status(thm)],[92,12,4]),
[iquote('0:SSi:92.0,12.0,4.1')] ).
cnf(105,plain,
aElement0(xm),
inference(ssi,[status(thm)],[95,12,3]),
[iquote('0:SSi:95.0,12.0,3.1')] ).
cnf(106,plain,
aElement0(xk),
inference(ssi,[status(thm)],[96,12,3]),
[iquote('0:SSi:96.0,12.0,3.1')] ).
cnf(108,plain,
aElement0(sdtpldt0(xl,xn)),
inference(ssi,[status(thm)],[94,12,4]),
[iquote('0:SSi:94.0,12.0,4.1')] ).
cnf(131,plain,
( ~ aElement0(xn)
| ~ aElement0(xm)
| aElement0(xy) ),
inference(spr,[status(thm),theory(equality)],[16,34]),
[iquote('0:SpR:16.0,34.2')] ).
cnf(137,plain,
aElement0(xy),
inference(ssi,[status(thm)],[131,105,103]),
[iquote('0:SSi:131.1,131.0,105.0,103.0')] ).
cnf(511,plain,
( ~ aElement0(u)
| ~ aElement0(xn)
| ~ aElement0(xm)
| equal(sdtpldt0(xm,sdtpldt0(xn,u)),sdtpldt0(xy,u)) ),
inference(spr,[status(thm),theory(equality)],[16,57]),
[iquote('0:SpR:16.0,57.3')] ).
cnf(512,plain,
( ~ aElement0(u)
| ~ aElement0(xl)
| ~ aElement0(xk)
| equal(sdtpldt0(xk,sdtpldt0(xl,u)),sdtpldt0(xx,u)) ),
inference(spr,[status(thm),theory(equality)],[15,57]),
[iquote('0:SpR:15.0,57.3')] ).
cnf(518,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ aElement0(v)
| ~ aElement0(u)
| equal(sdtpldt0(sdtpldt0(v,u),w),sdtpldt0(u,sdtpldt0(v,w))) ),
inference(spr,[status(thm),theory(equality)],[41,57]),
[iquote('0:SpR:41.2,57.3')] ).
cnf(521,plain,
( ~ aElement0(sdtpldt0(xl,xn))
| ~ aElement0(xm)
| ~ aElement0(xk)
| ~ equal(sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))),sdtpldt0(xx,xy)) ),
inference(spl,[status(thm),theory(equality)],[57,40]),
[iquote('0:SpL:57.3,40.0')] ).
cnf(522,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xm,sdtpldt0(xn,u)),sdtpldt0(xy,u)) ),
inference(ssi,[status(thm)],[511,105,103]),
[iquote('0:SSi:511.2,511.1,105.0,103.0')] ).
cnf(523,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xk,sdtpldt0(xl,u)),sdtpldt0(xx,u)) ),
inference(ssi,[status(thm)],[512,106,104]),
[iquote('0:SSi:512.2,512.1,106.0,104.0')] ).
cnf(528,plain,
~ equal(sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))),sdtpldt0(xx,xy)),
inference(ssi,[status(thm)],[521,106,105,108]),
[iquote('0:SSi:521.2,521.1,521.0,106.0,105.0,108.0')] ).
cnf(538,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(sdtpldt0(v,w),u),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(obv,[status(thm),theory(equality)],[518]),
[iquote('0:Obv:518.1')] ).
cnf(539,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(v,sdtpldt0(w,u)),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[57,538]),
[iquote('0:Rew:57.3,538.3')] ).
cnf(687,plain,
( ~ aElement0(u)
| ~ aElement0(xn)
| ~ aElement0(u)
| equal(sdtpldt0(xm,sdtpldt0(u,xn)),sdtpldt0(xy,u)) ),
inference(spr,[status(thm),theory(equality)],[41,522]),
[iquote('0:SpR:41.2,522.1')] ).
cnf(696,plain,
( ~ aElement0(xn)
| ~ aElement0(u)
| equal(sdtpldt0(xm,sdtpldt0(u,xn)),sdtpldt0(xy,u)) ),
inference(obv,[status(thm),theory(equality)],[687]),
[iquote('0:Obv:687.0')] ).
cnf(697,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xm,sdtpldt0(u,xn)),sdtpldt0(xy,u)) ),
inference(ssi,[status(thm)],[696,103]),
[iquote('0:SSi:696.0,103.0')] ).
cnf(845,plain,
( ~ aElement0(u)
| ~ aElement0(xl)
| ~ aElement0(u)
| equal(sdtpldt0(xk,sdtpldt0(u,xl)),sdtpldt0(xx,u)) ),
inference(spr,[status(thm),theory(equality)],[41,523]),
[iquote('0:SpR:41.2,523.1')] ).
cnf(854,plain,
( ~ aElement0(xl)
| ~ aElement0(u)
| equal(sdtpldt0(xk,sdtpldt0(u,xl)),sdtpldt0(xx,u)) ),
inference(obv,[status(thm),theory(equality)],[845]),
[iquote('0:Obv:845.0')] ).
cnf(855,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xk,sdtpldt0(u,xl)),sdtpldt0(xx,u)) ),
inference(ssi,[status(thm)],[854,104]),
[iquote('0:SSi:854.0,104.0')] ).
cnf(7678,plain,
( ~ aElement0(xn)
| ~ aElement0(u)
| ~ aElement0(xm)
| equal(sdtpldt0(xm,sdtpldt0(u,xn)),sdtpldt0(u,xy)) ),
inference(spr,[status(thm),theory(equality)],[16,539]),
[iquote('0:SpR:16.0,539.3')] ).
cnf(7680,plain,
( ~ aElement0(xl)
| ~ aElement0(u)
| ~ aElement0(xk)
| equal(sdtpldt0(xk,sdtpldt0(u,xl)),sdtpldt0(u,xx)) ),
inference(spr,[status(thm),theory(equality)],[15,539]),
[iquote('0:SpR:15.0,539.3')] ).
cnf(7845,plain,
( ~ aElement0(xn)
| ~ aElement0(xl)
| ~ aElement0(xm)
| ~ equal(sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xm,xn))),sdtpldt0(xx,xy)) ),
inference(spl,[status(thm),theory(equality)],[539,528]),
[iquote('0:SpL:539.3,528.0')] ).
cnf(7846,plain,
( ~ aElement0(xn)
| ~ aElement0(u)
| ~ aElement0(xm)
| equal(sdtpldt0(xy,u),sdtpldt0(u,xy)) ),
inference(rew,[status(thm),theory(equality)],[697,7678]),
[iquote('0:Rew:697.1,7678.3')] ).
cnf(7847,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xy,u),sdtpldt0(u,xy)) ),
inference(ssi,[status(thm)],[7846,105,103]),
[iquote('0:SSi:7846.2,7846.0,105.0,103.0')] ).
cnf(7848,plain,
( ~ aElement0(xl)
| ~ aElement0(u)
| ~ aElement0(xk)
| equal(sdtpldt0(xx,u),sdtpldt0(u,xx)) ),
inference(rew,[status(thm),theory(equality)],[855,7680]),
[iquote('0:Rew:855.1,7680.3')] ).
cnf(7849,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xx,u),sdtpldt0(u,xx)) ),
inference(ssi,[status(thm)],[7848,106,104]),
[iquote('0:SSi:7848.2,7848.0,106.0,104.0')] ).
cnf(7914,plain,
( ~ aElement0(xn)
| ~ aElement0(xl)
| ~ aElement0(xm)
| ~ equal(sdtpldt0(xk,sdtpldt0(xl,xy)),sdtpldt0(xx,xy)) ),
inference(rew,[status(thm),theory(equality)],[16,7845]),
[iquote('0:Rew:16.0,7845.3')] ).
cnf(7915,plain,
( ~ aElement0(xn)
| ~ aElement0(xl)
| ~ aElement0(xm)
| ~ equal(sdtpldt0(xk,sdtpldt0(xy,xl)),sdtpldt0(xx,xy)) ),
inference(rew,[status(thm),theory(equality)],[7847,7914]),
[iquote('0:Rew:7847.1,7914.3')] ).
cnf(7916,plain,
~ equal(sdtpldt0(xk,sdtpldt0(xy,xl)),sdtpldt0(xx,xy)),
inference(ssi,[status(thm)],[7915,105,104,103]),
[iquote('0:SSi:7915.2,7915.1,7915.0,105.0,104.0,103.0')] ).
cnf(11262,plain,
( ~ aElement0(xl)
| ~ aElement0(xy)
| ~ aElement0(xk)
| ~ equal(sdtpldt0(xy,sdtpldt0(xk,xl)),sdtpldt0(xx,xy)) ),
inference(spl,[status(thm),theory(equality)],[539,7916]),
[iquote('0:SpL:539.3,7916.0')] ).
cnf(11267,plain,
( ~ aElement0(xl)
| ~ aElement0(xy)
| ~ aElement0(xk)
| ~ equal(sdtpldt0(xy,xx),sdtpldt0(xx,xy)) ),
inference(rew,[status(thm),theory(equality)],[15,11262]),
[iquote('0:Rew:15.0,11262.3')] ).
cnf(11268,plain,
( ~ aElement0(xl)
| ~ aElement0(xy)
| ~ aElement0(xk)
| ~ equal(sdtpldt0(xx,xy),sdtpldt0(xx,xy)) ),
inference(rew,[status(thm),theory(equality)],[7849,11267]),
[iquote('0:Rew:7849.1,11267.3')] ).
cnf(11269,plain,
( ~ aElement0(xl)
| ~ aElement0(xy)
| ~ aElement0(xk) ),
inference(obv,[status(thm),theory(equality)],[11268]),
[iquote('0:Obv:11268.3')] ).
cnf(11270,plain,
$false,
inference(ssi,[status(thm)],[11269,106,137,104]),
[iquote('0:SSi:11269.2,11269.1,11269.0,106.0,137.0,104.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : RNG090+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon May 30 10:18:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 3.80/3.98
% 3.80/3.98 SPASS V 3.9
% 3.80/3.98 SPASS beiseite: Proof found.
% 3.80/3.98 % SZS status Theorem
% 3.80/3.98 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.80/3.98 SPASS derived 6618 clauses, backtracked 0 clauses, performed 1 splits and kept 1880 clauses.
% 3.80/3.98 SPASS allocated 108598 KBytes.
% 3.80/3.98 SPASS spent 0:00:02.99 on the problem.
% 3.80/3.98 0:00:00.04 for the input.
% 3.80/3.98 0:00:00.10 for the FLOTTER CNF translation.
% 3.80/3.98 0:00:00.07 for inferences.
% 3.80/3.98 0:00:00.01 for the backtracking.
% 3.80/3.98 0:00:02.73 for the reduction.
% 3.80/3.98
% 3.80/3.98
% 3.80/3.98 Here is a proof with depth 3, length 57 :
% 3.80/3.98 % SZS output start Refutation
% See solution above
% 3.80/3.98 Formulae used in the proof : m__870 m__934 m__967 mDefIdeal m__901 m__994 mEOfElem mSortsB m__ mAddComm mAddAsso
% 3.80/3.98
%------------------------------------------------------------------------------