TSTP Solution File: RNG105+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG105+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 20:41:29 EDT 2022
% Result : Theorem 13.25s 13.47s
% Output : Refutation 13.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of clauses : 58 ( 27 unt; 3 nHn; 58 RR)
% Number of literals : 115 ( 0 equ; 66 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aElement0(xc),
file('RNG105+1.p',unknown),
[] ).
cnf(4,axiom,
aElement0(xz),
file('RNG105+1.p',unknown),
[] ).
cnf(5,axiom,
aElement0(xu),
file('RNG105+1.p',unknown),
[] ).
cnf(6,axiom,
aElement0(xv),
file('RNG105+1.p',unknown),
[] ).
cnf(14,axiom,
aElementOf0(xx,slsdtgt0(xc)),
file('RNG105+1.p',unknown),
[] ).
cnf(17,axiom,
equal(sdtasdt0(xc,xu),xx),
file('RNG105+1.p',unknown),
[] ).
cnf(18,axiom,
equal(sdtasdt0(xc,xv),xy),
file('RNG105+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('RNG105+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(u,sz00),sz00) ),
file('RNG105+1.p',unknown),
[] ).
cnf(35,axiom,
equal(sdtasdt0(xc,sdtpldt0(xu,xv)),sdtpldt0(xx,xy)),
file('RNG105+1.p',unknown),
[] ).
cnf(36,axiom,
equal(sdtasdt0(xc,sdtasdt0(xu,xz)),sdtasdt0(xz,xx)),
file('RNG105+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtpldt0(v,u)) ),
file('RNG105+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtasdt0(v,u)) ),
file('RNG105+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('RNG105+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
file('RNG105+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ equal(sdtasdt0(v,u),sz00)
| equal(u,sz00)
| equal(v,sz00) ),
file('RNG105+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ equal(w,slsdtgt0(u))
| ~ equal(sdtasdt0(u,v),x)
| aElementOf0(x,w) ),
file('RNG105+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('RNG105+1.p',unknown),
[] ).
cnf(138,plain,
( ~ aElement0(xu)
| ~ aElement0(xc)
| aElement0(xx) ),
inference(spr,[status(thm),theory(equality)],[17,38]),
[iquote('0:SpR:17.0,38.2')] ).
cnf(148,plain,
aElement0(xx),
inference(ssi,[status(thm)],[138,3,5]),
[iquote('0:SSi:138.1,138.0,3.0,5.0')] ).
cnf(224,plain,
( ~ aElement0(xz)
| ~ aElement0(xx)
| ~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(spl,[status(thm),theory(equality)],[50,53]),
[iquote('0:SpL:50.2,53.0')] ).
cnf(225,plain,
( ~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(ssi,[status(thm)],[224,148,4]),
[iquote('0:SSi:224.1,224.0,148.0,4.0')] ).
cnf(381,plain,
( ~ aElement0(xv)
| ~ aElement0(xc)
| ~ equal(sz00,xy)
| equal(sz00,xv)
| equal(sz00,xc) ),
inference(spl,[status(thm),theory(equality)],[18,66]),
[iquote('0:SpL:18.0,66.2')] ).
cnf(395,plain,
( ~ equal(sz00,xy)
| equal(sz00,xv)
| equal(sz00,xc) ),
inference(ssi,[status(thm)],[381,3,6]),
[iquote('0:SSi:381.1,381.0,3.0,6.0')] ).
cnf(407,plain,
equal(sz00,xv),
inference(spt,[spt(split,[position(s1)])],[395]),
[iquote('1:Spt:395.1')] ).
cnf(411,plain,
( ~ aElement0(u)
| equal(sdtasdt0(u,xv),xv) ),
inference(rew,[status(thm),theory(equality)],[407,25]),
[iquote('1:Rew:407.0,25.1')] ).
cnf(413,plain,
( ~ aElement0(u)
| equal(sdtpldt0(u,xv),u) ),
inference(rew,[status(thm),theory(equality)],[407,21]),
[iquote('1:Rew:407.0,21.1')] ).
cnf(455,plain,
( ~ aElement0(xc)
| equal(xv,xy) ),
inference(spr,[status(thm),theory(equality)],[411,18]),
[iquote('1:SpR:411.1,18.0')] ).
cnf(464,plain,
equal(xv,xy),
inference(ssi,[status(thm)],[455,3]),
[iquote('1:SSi:455.0,3.0')] ).
cnf(467,plain,
equal(sdtasdt0(xc,sdtpldt0(xu,xy)),sdtpldt0(xx,xy)),
inference(rew,[status(thm),theory(equality)],[464,35]),
[iquote('1:Rew:464.0,35.0')] ).
cnf(480,plain,
( ~ aElement0(u)
| equal(sdtpldt0(u,xy),u) ),
inference(rew,[status(thm),theory(equality)],[464,413]),
[iquote('1:Rew:464.0,413.1')] ).
cnf(558,plain,
( ~ aElement0(xu)
| equal(sdtasdt0(xc,xu),sdtpldt0(xx,xy)) ),
inference(spr,[status(thm),theory(equality)],[480,467]),
[iquote('1:SpR:480.1,467.0')] ).
cnf(559,plain,
( ~ aElement0(xu)
| equal(sdtpldt0(xx,xy),xx) ),
inference(rew,[status(thm),theory(equality)],[17,558]),
[iquote('1:Rew:17.0,558.1')] ).
cnf(560,plain,
equal(sdtpldt0(xx,xy),xx),
inference(ssi,[status(thm)],[559,5]),
[iquote('1:SSi:559.0,5.0')] ).
cnf(563,plain,
( ~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc))
| ~ aElementOf0(xx,slsdtgt0(xc)) ),
inference(rew,[status(thm),theory(equality)],[560,225]),
[iquote('1:Rew:560.0,225.1')] ).
cnf(571,plain,
~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc)),
inference(mrr,[status(thm)],[563,14]),
[iquote('1:MRR:563.1,14.0')] ).
cnf(1448,plain,
( ~ aElement0(u)
| ~ aElement0(xu)
| ~ aElement0(xc)
| equal(sdtasdt0(xc,sdtasdt0(xu,u)),sdtasdt0(xx,u)) ),
inference(spr,[status(thm),theory(equality)],[17,78]),
[iquote('0:SpR:17.0,78.3')] ).
cnf(1457,plain,
( ~ aElement0(u)
| equal(sdtasdt0(xc,sdtasdt0(xu,u)),sdtasdt0(xx,u)) ),
inference(ssi,[status(thm)],[1448,3,5]),
[iquote('0:SSi:1448.2,1448.1,3.0,5.0')] ).
cnf(1516,plain,
( ~ aElement0(xz)
| equal(sdtasdt0(xz,xx),sdtasdt0(xx,xz)) ),
inference(spr,[status(thm),theory(equality)],[1457,36]),
[iquote('0:SpR:1457.1,36.0')] ).
cnf(1528,plain,
equal(sdtasdt0(xz,xx),sdtasdt0(xx,xz)),
inference(ssi,[status(thm)],[1516,4]),
[iquote('0:SSi:1516.0,4.0')] ).
cnf(1534,plain,
equal(sdtasdt0(xc,sdtasdt0(xu,xz)),sdtasdt0(xx,xz)),
inference(rew,[status(thm),theory(equality)],[1528,36]),
[iquote('0:Rew:1528.0,36.0')] ).
cnf(1727,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ equal(w,slsdtgt0(u))
| aElementOf0(sdtasdt0(u,v),w) ),
inference(eqr,[status(thm),theory(equality)],[72]),
[iquote('0:EqR:72.3')] ).
cnf(7254,plain,
( ~ aElement0(xc)
| ~ aElement0(sdtasdt0(xu,xz))
| ~ equal(u,slsdtgt0(xc))
| aElementOf0(sdtasdt0(xx,xz),u) ),
inference(spr,[status(thm),theory(equality)],[1534,1727]),
[iquote('0:SpR:1534.0,1727.3')] ).
cnf(7331,plain,
( ~ equal(u,slsdtgt0(xc))
| aElementOf0(sdtasdt0(xx,xz),u) ),
inference(ssi,[status(thm)],[7254,38,5,4,3]),
[iquote('0:SSi:7254.1,7254.0,38.0,5.0,4.0,3.2')] ).
cnf(13593,plain,
~ equal(slsdtgt0(xc),slsdtgt0(xc)),
inference(res,[status(thm),theory(equality)],[7331,571]),
[iquote('1:Res:7331.1,571.0')] ).
cnf(13606,plain,
$false,
inference(obv,[status(thm),theory(equality)],[13593]),
[iquote('1:Obv:13593.0')] ).
cnf(13608,plain,
~ equal(sz00,xv),
inference(spt,[spt(split,[position(sa)])],[13606,407]),
[iquote('1:Spt:13606.0,395.1,407.0')] ).
cnf(13609,plain,
( ~ equal(sz00,xy)
| equal(sz00,xc) ),
inference(spt,[spt(split,[position(s2)])],[395]),
[iquote('1:Spt:13606.0,395.0,395.2')] ).
cnf(13623,plain,
( ~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(rew,[status(thm),theory(equality)],[1528,53]),
[iquote('0:Rew:1528.0,53.0')] ).
cnf(14205,plain,
( ~ aElement0(xc)
| ~ aElement0(sdtpldt0(xu,xv))
| ~ equal(u,slsdtgt0(xc))
| aElementOf0(sdtpldt0(xx,xy),u) ),
inference(spr,[status(thm),theory(equality)],[35,1727]),
[iquote('0:SpR:35.0,1727.3')] ).
cnf(14238,plain,
( ~ equal(u,slsdtgt0(xc))
| aElementOf0(sdtpldt0(xx,xy),u) ),
inference(ssi,[status(thm)],[14205,37,5,6,3]),
[iquote('0:SSi:14205.1,14205.0,37.0,5.0,6.0,3.2')] ).
cnf(14675,plain,
~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc)),
inference(spt,[spt(split,[position(s2s1)])],[13623]),
[iquote('2:Spt:13623.0')] ).
cnf(14679,plain,
~ equal(slsdtgt0(xc),slsdtgt0(xc)),
inference(res,[status(thm),theory(equality)],[7331,14675]),
[iquote('2:Res:7331.1,14675.0')] ).
cnf(14683,plain,
$false,
inference(obv,[status(thm),theory(equality)],[14679]),
[iquote('2:Obv:14679.0')] ).
cnf(14692,plain,
aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc)),
inference(spt,[spt(split,[position(s2sa)])],[14683,14675]),
[iquote('2:Spt:14683.0,13623.0,14675.0')] ).
cnf(14693,plain,
~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)),
inference(spt,[spt(split,[position(s2s2)])],[13623]),
[iquote('2:Spt:14683.0,13623.1')] ).
cnf(26286,plain,
~ equal(slsdtgt0(xc),slsdtgt0(xc)),
inference(res,[status(thm),theory(equality)],[14238,14693]),
[iquote('2:Res:14238.1,14693.0')] ).
cnf(26301,plain,
$false,
inference(obv,[status(thm),theory(equality)],[26286]),
[iquote('2:Obv:26286.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG105+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon May 30 15:08:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 13.25/13.47
% 13.25/13.47 SPASS V 3.9
% 13.25/13.47 SPASS beiseite: Proof found.
% 13.25/13.47 % SZS status Theorem
% 13.25/13.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.25/13.47 SPASS derived 16624 clauses, backtracked 1486 clauses, performed 18 splits and kept 5244 clauses.
% 13.25/13.47 SPASS allocated 118811 KBytes.
% 13.25/13.47 SPASS spent 0:00:09.94 on the problem.
% 13.25/13.47 0:00:00.04 for the input.
% 13.25/13.47 0:00:00.14 for the FLOTTER CNF translation.
% 13.25/13.47 0:00:00.23 for inferences.
% 13.25/13.47 0:00:00.21 for the backtracking.
% 13.25/13.47 0:00:09.23 for the reduction.
% 13.25/13.47
% 13.25/13.47
% 13.25/13.47 Here is a proof with depth 3, length 58 :
% 13.25/13.47 % SZS output start Refutation
% See solution above
% 13.25/13.47 Formulae used in the proof : m__1905 m__1933 m__1956 m__1979 mAddZero mMulZero m__2010 m__2043 mSortsB mSortsB_02 mMulComm m__ mCancel mDefPrIdeal mMulAsso
% 13.25/13.47
%------------------------------------------------------------------------------