TSTP Solution File: RNG092+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG092+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 20:41:27 EDT 2022
% Result : Theorem 0.69s 0.90s
% Output : Refutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of clauses : 57 ( 20 unt; 0 nHn; 57 RR)
% Number of literals : 117 ( 0 equ; 64 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aElement0(skc25),
file('RNG092+2.p',unknown),
[] ).
cnf(3,axiom,
aElement0(sz10),
file('RNG092+2.p',unknown),
[] ).
cnf(4,axiom,
aSet0(xI),
file('RNG092+2.p',unknown),
[] ).
cnf(5,axiom,
aIdeal0(xI),
file('RNG092+2.p',unknown),
[] ).
cnf(6,axiom,
aSet0(xJ),
file('RNG092+2.p',unknown),
[] ).
cnf(7,axiom,
aIdeal0(xJ),
file('RNG092+2.p',unknown),
[] ).
cnf(11,axiom,
aSet0(sdtpldt1(xI,xJ)),
file('RNG092+2.p',unknown),
[] ).
cnf(13,axiom,
aElementOf0(skc24,sdtpldt1(xI,xJ)),
file('RNG092+2.p',unknown),
[] ).
cnf(20,axiom,
aElementOf0(skf29(u),sdtpldt1(xI,xJ)),
file('RNG092+2.p',unknown),
[] ).
cnf(21,axiom,
aElementOf0(skf22(u,v,w),xI),
file('RNG092+2.p',unknown),
[] ).
cnf(22,axiom,
aElementOf0(skf21(u,v,w),xJ),
file('RNG092+2.p',unknown),
[] ).
cnf(26,axiom,
( ~ aElementOf0(u,sdtpldt1(xI,xJ))
| skP3(u) ),
file('RNG092+2.p',unknown),
[] ).
cnf(30,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(sz10,u),u) ),
file('RNG092+2.p',unknown),
[] ).
cnf(36,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('RNG092+2.p',unknown),
[] ).
cnf(39,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtpldt0(v,u)) ),
file('RNG092+2.p',unknown),
[] ).
cnf(43,axiom,
( ~ skP4(skc24)
| ~ aElementOf0(sdtasdt0(skc25,skc24),sdtpldt1(xI,xJ)) ),
file('RNG092+2.p',unknown),
[] ).
cnf(44,axiom,
( ~ aElementOf0(sdtpldt0(u,skf29(u)),sdtpldt1(xI,xJ))
| skP4(u) ),
file('RNG092+2.p',unknown),
[] ).
cnf(48,axiom,
( ~ skP2(u,v,w)
| aElementOf0(sdtasdt0(u,w),sdtpldt1(xI,xJ)) ),
file('RNG092+2.p',unknown),
[] ).
cnf(54,axiom,
( ~ skP3(u)
| ~ skP3(v)
| ~ aElement0(w)
| skP2(w,v,u) ),
file('RNG092+2.p',unknown),
[] ).
cnf(63,axiom,
( ~ skP2(u,v,w)
| equal(sdtpldt0(skf22(u,w,v),skf21(w,u,v)),v) ),
file('RNG092+2.p',unknown),
[] ).
cnf(64,axiom,
( ~ skP2(u,v,w)
| aElementOf0(sdtpldt0(skf20(v,u,w),skf22(u,w,v)),xI) ),
file('RNG092+2.p',unknown),
[] ).
cnf(65,axiom,
( ~ skP2(u,v,w)
| aElementOf0(sdtpldt0(skf19(u,v,w),skf21(w,u,v)),xJ) ),
file('RNG092+2.p',unknown),
[] ).
cnf(68,axiom,
( ~ aElementOf0(u,xJ)
| ~ aElementOf0(v,xI)
| ~ equal(sdtpldt0(v,u),w)
| skP3(w) ),
file('RNG092+2.p',unknown),
[] ).
cnf(89,axiom,
( ~ skP2(u,v,w)
| equal(sdtpldt0(sdtpldt0(skf20(v,u,w),skf22(u,w,v)),sdtpldt0(skf19(u,v,w),skf21(w,u,v))),sdtpldt0(w,v)) ),
file('RNG092+2.p',unknown),
[] ).
cnf(98,plain,
( ~ skP3(u)
| ~ skP3(v)
| skP2(skc25,v,u) ),
inference(res,[status(thm),theory(equality)],[1,54]),
[iquote('0:Res:1.0,54.0')] ).
cnf(144,plain,
( ~ aElementOf0(u,sdtpldt1(xI,xJ))
| aElement0(u) ),
inference(res,[status(thm),theory(equality)],[11,36]),
[iquote('0:Res:11.0,36.0')] ).
cnf(264,plain,
skP3(skc24),
inference(res,[status(thm),theory(equality)],[13,26]),
[iquote('0:Res:13.0,26.0')] ).
cnf(269,plain,
( ~ aSet0(sdtpldt1(xI,xJ))
| aElement0(skc24) ),
inference(res,[status(thm),theory(equality)],[13,36]),
[iquote('0:Res:13.0,36.1')] ).
cnf(298,plain,
aElement0(skc24),
inference(mrr,[status(thm)],[269,11]),
[iquote('0:MRR:269.0,11.0')] ).
cnf(399,plain,
skP3(skf29(u)),
inference(res,[status(thm),theory(equality)],[20,26]),
[iquote('0:Res:20.0,26.0')] ).
cnf(404,plain,
aElement0(skf29(u)),
inference(res,[status(thm),theory(equality)],[20,144]),
[iquote('0:Res:20.0,144.0')] ).
cnf(444,plain,
( ~ aSet0(xJ)
| aElement0(skf21(u,v,w)) ),
inference(res,[status(thm),theory(equality)],[22,36]),
[iquote('0:Res:22.0,36.1')] ).
cnf(450,plain,
( ~ aSet0(xI)
| aElement0(skf22(u,v,w)) ),
inference(res,[status(thm),theory(equality)],[21,36]),
[iquote('0:Res:21.0,36.1')] ).
cnf(456,plain,
aElement0(skf21(u,v,w)),
inference(ssi,[status(thm)],[444,7,6]),
[iquote('0:SSi:444.0,7.0,6.0')] ).
cnf(458,plain,
aElement0(skf22(u,v,w)),
inference(ssi,[status(thm)],[450,5,4]),
[iquote('0:SSi:450.0,5.0,4.0')] ).
cnf(899,plain,
( ~ skP3(u)
| ~ skP3(v)
| ~ aElement0(w)
| aElementOf0(sdtasdt0(w,u),sdtpldt1(xI,xJ)) ),
inference(res,[status(thm),theory(equality)],[54,48]),
[iquote('0:Res:54.3,48.0')] ).
cnf(900,plain,
( ~ skP3(u)
| ~ aElement0(v)
| aElementOf0(sdtasdt0(v,u),sdtpldt1(xI,xJ)) ),
inference(con,[status(thm)],[899]),
[iquote('0:Con:899.1')] ).
cnf(1067,plain,
( ~ aElementOf0(u,xJ)
| ~ aElementOf0(v,xI)
| skP3(sdtpldt0(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[68]),
[iquote('0:EqR:68.2')] ).
cnf(1555,plain,
( ~ aElement0(skf21(u,v,w))
| ~ aElement0(skf22(v,u,w))
| ~ skP2(v,w,u)
| aElement0(w) ),
inference(spr,[status(thm),theory(equality)],[63,39]),
[iquote('0:SpR:63.1,39.2')] ).
cnf(1561,plain,
( ~ skP2(u,v,w)
| aElement0(v) ),
inference(ssi,[status(thm)],[1555,458,456]),
[iquote('0:SSi:1555.1,1555.0,458.0,456.0')] ).
cnf(1665,plain,
( ~ skP3(u)
| ~ skP3(v)
| ~ aElement0(w)
| aElement0(v) ),
inference(res,[status(thm),theory(equality)],[54,1561]),
[iquote('0:Res:54.3,1561.0')] ).
cnf(1666,plain,
( ~ skP3(u)
| ~ aElement0(v)
| aElement0(u) ),
inference(con,[status(thm)],[1665]),
[iquote('0:Con:1665.0')] ).
cnf(1763,plain,
( ~ skP3(u)
| aElement0(u) ),
inference(ems,[status(thm)],[1666,1]),
[iquote('0:EmS:1666.1,1.0')] ).
cnf(2238,plain,
( ~ skP3(u)
| ~ skP3(v)
| aElementOf0(sdtasdt0(skc25,u),sdtpldt1(xI,xJ)) ),
inference(res,[status(thm),theory(equality)],[98,48]),
[iquote('0:Res:98.2,48.0')] ).
cnf(2241,plain,
( ~ skP3(u)
| aElementOf0(sdtasdt0(skc25,u),sdtpldt1(xI,xJ)) ),
inference(con,[status(thm)],[2238]),
[iquote('0:Con:2238.1')] ).
cnf(2257,plain,
( ~ skP3(skc24)
| ~ skP4(skc24) ),
inference(res,[status(thm),theory(equality)],[2241,43]),
[iquote('0:Res:2241.1,43.1')] ).
cnf(2259,plain,
~ skP4(skc24),
inference(ssi,[status(thm)],[2257,264,298]),
[iquote('0:SSi:2257.0,264.0,298.0')] ).
cnf(2718,plain,
( ~ skP2(u,v,w)
| ~ aElementOf0(sdtpldt0(skf19(u,v,w),skf21(w,u,v)),xJ)
| ~ aElementOf0(sdtpldt0(skf20(v,u,w),skf22(u,w,v)),xI)
| skP3(sdtpldt0(w,v)) ),
inference(spr,[status(thm),theory(equality)],[89,1067]),
[iquote('0:SpR:89.1,1067.2')] ).
cnf(2729,plain,
( ~ skP2(u,v,w)
| skP3(sdtpldt0(w,v)) ),
inference(mrr,[status(thm)],[2718,65,64]),
[iquote('0:MRR:2718.1,2718.2,65.1,64.1')] ).
cnf(2749,plain,
( ~ skP3(u)
| ~ skP3(v)
| skP3(sdtpldt0(u,v)) ),
inference(res,[status(thm),theory(equality)],[98,2729]),
[iquote('0:Res:98.2,2729.0')] ).
cnf(3048,plain,
( ~ aElement0(u)
| ~ skP3(u)
| ~ aElement0(sz10)
| aElementOf0(u,sdtpldt1(xI,xJ)) ),
inference(spr,[status(thm),theory(equality)],[30,900]),
[iquote('0:SpR:30.1,900.2')] ).
cnf(3074,plain,
( ~ skP3(u)
| aElementOf0(u,sdtpldt1(xI,xJ)) ),
inference(ssi,[status(thm)],[3048,3,1763]),
[iquote('0:SSi:3048.2,3048.0,3.1,1763.0')] ).
cnf(3096,plain,
( ~ skP3(sdtpldt0(u,skf29(u)))
| skP4(u) ),
inference(res,[status(thm),theory(equality)],[3074,44]),
[iquote('0:Res:3074.1,44.0')] ).
cnf(3166,plain,
( ~ skP3(skf29(u))
| ~ skP3(u)
| skP4(u) ),
inference(sor,[status(thm)],[3096,2749]),
[iquote('0:SoR:3096.0,2749.2')] ).
cnf(3184,plain,
( ~ skP3(u)
| skP4(u) ),
inference(ssi,[status(thm)],[3166,399,404]),
[iquote('0:SSi:3166.0,399.0,404.0')] ).
cnf(3185,plain,
~ skP3(skc24),
inference(res,[status(thm),theory(equality)],[3184,2259]),
[iquote('0:Res:3184.1,2259.0')] ).
cnf(3186,plain,
$false,
inference(ssi,[status(thm)],[3185,264,298]),
[iquote('0:SSi:3185.0,264.0,298.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG092+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 : Mon May 30 20:27:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.69/0.90
% 0.69/0.90 SPASS V 3.9
% 0.69/0.90 SPASS beiseite: Proof found.
% 0.69/0.90 % SZS status Theorem
% 0.69/0.90 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.90 SPASS derived 2197 clauses, backtracked 63 clauses, performed 1 splits and kept 877 clauses.
% 0.69/0.90 SPASS allocated 100358 KBytes.
% 0.69/0.90 SPASS spent 0:00:00.53 on the problem.
% 0.69/0.90 0:00:00.04 for the input.
% 0.69/0.90 0:00:00.17 for the FLOTTER CNF translation.
% 0.69/0.90 0:00:00.03 for inferences.
% 0.69/0.90 0:00:00.00 for the backtracking.
% 0.69/0.90 0:00:00.25 for the reduction.
% 0.69/0.90
% 0.69/0.90
% 0.69/0.90 Here is a proof with depth 5, length 57 :
% 0.69/0.90 % SZS output start Refutation
% See solution above
% 0.69/0.90 Formulae used in the proof : m__ mSortsC_01 m__870 mMulUnit mEOfElem mSortsB
% 0.69/0.90
%------------------------------------------------------------------------------