%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG092+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 3.28s 3.45s
% Output : Refutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 26 ( 8 unt; 4 nHn; 26 RR)
% Number of literals : 65 ( 0 equ; 40 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aElement0(sz10),
file('RNG092+1.p',unknown),
[] ).
cnf(3,axiom,
aIdeal0(xI),
file('RNG092+1.p',unknown),
[] ).
cnf(4,axiom,
aIdeal0(xJ),
file('RNG092+1.p',unknown),
[] ).
cnf(5,axiom,
aElement0(skf23(u)),
file('RNG092+1.p',unknown),
[] ).
cnf(7,axiom,
~ aIdeal0(sdtpldt1(xI,xJ)),
file('RNG092+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ aIdeal0(u)
| aSet0(u) ),
file('RNG092+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ aSet0(u)
| aIdeal0(u)
| aElementOf0(skf21(u),u) ),
file('RNG092+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ equal(w,sdtpldt1(v,u))
| aSet0(w) ),
file('RNG092+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ aElement0(u)
| ~ aElementOf0(v,sdtpldt1(xI,xJ))
| aElementOf0(sdtasdt0(u,v),sdtpldt1(xI,xJ)) ),
file('RNG092+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ aSet0(u)
| ~ aElementOf0(sdtasdt0(skf23(u),skf21(u)),u)
| aIdeal0(u)
| aElementOf0(skf22(u),u) ),
file('RNG092+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ aSet0(u)
| ~ aElementOf0(sdtpldt0(skf21(u),skf22(u)),u)
| ~ aElementOf0(sdtasdt0(skf23(u),skf21(u)),u)
| aIdeal0(u) ),
file('RNG092+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ aElement0(u)
| ~ aElementOf0(v,sdtpldt1(xI,xJ))
| ~ aElementOf0(w,sdtpldt1(xI,xJ))
| aElementOf0(sdtpldt0(w,v),sdtpldt1(xI,xJ)) ),
file('RNG092+1.p',unknown),
[] ).
cnf(85,plain,
( ~ aElementOf0(u,sdtpldt1(xI,xJ))
| ~ aElementOf0(v,sdtpldt1(xI,xJ))
| aElementOf0(sdtpldt0(u,v),sdtpldt1(xI,xJ)) ),
inference(res,[status(thm),theory(equality)],[2,53]),
[iquote('0:Res:2.0,53.0')] ).
cnf(230,plain,
( ~ aSet0(u)
| ~ aSet0(v)
| aSet0(sdtpldt1(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[30]),
[iquote('0:EqR:30.2')] ).
cnf(365,plain,
( ~ aElement0(skf23(sdtpldt1(xI,xJ)))
| ~ aSet0(sdtpldt1(xI,xJ))
| ~ aElementOf0(skf21(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| aIdeal0(sdtpldt1(xI,xJ))
| aElementOf0(skf22(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ)) ),
inference(res,[status(thm),theory(equality)],[37,41]),
[iquote('0:Res:37.2,41.1')] ).
cnf(368,plain,
( ~ aElementOf0(skf21(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| aIdeal0(sdtpldt1(xI,xJ))
| aElementOf0(skf22(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ)) ),
inference(ssi,[status(thm)],[365,230,3,8,4,5]),
[iquote('0:SSi:365.1,365.0,230.1,3.0,8.1,4.0,8.2,5.0,230.1,3.0,8.1,4.0,8.2')] ).
cnf(369,plain,
( ~ aElementOf0(skf21(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| aElementOf0(skf22(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ)) ),
inference(mrr,[status(thm)],[368,7]),
[iquote('0:MRR:368.1,7.0')] ).
cnf(818,plain,
( ~ aElement0(skf23(sdtpldt1(xI,xJ)))
| ~ aSet0(sdtpldt1(xI,xJ))
| ~ aElementOf0(skf21(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(skf21(sdtpldt1(xI,xJ)),skf22(sdtpldt1(xI,xJ))),sdtpldt1(xI,xJ))
| aIdeal0(sdtpldt1(xI,xJ)) ),
inference(res,[status(thm),theory(equality)],[37,50]),
[iquote('0:Res:37.2,50.2')] ).
cnf(821,plain,
( ~ aElementOf0(skf21(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(skf21(sdtpldt1(xI,xJ)),skf22(sdtpldt1(xI,xJ))),sdtpldt1(xI,xJ))
| aIdeal0(sdtpldt1(xI,xJ)) ),
inference(ssi,[status(thm)],[818,230,3,8,4,5]),
[iquote('0:SSi:818.1,818.0,230.1,3.0,8.1,4.0,8.2,5.0,230.1,3.0,8.1,4.0,8.2')] ).
cnf(822,plain,
( ~ aElementOf0(skf21(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(skf21(sdtpldt1(xI,xJ)),skf22(sdtpldt1(xI,xJ))),sdtpldt1(xI,xJ)) ),
inference(mrr,[status(thm)],[821,7]),
[iquote('0:MRR:821.2,7.0')] ).
cnf(10515,plain,
( ~ aElementOf0(skf21(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| ~ aElementOf0(skf22(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| ~ aElementOf0(skf21(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ)) ),
inference(res,[status(thm),theory(equality)],[85,822]),
[iquote('0:Res:85.2,822.1')] ).
cnf(10516,plain,
( ~ aElementOf0(skf22(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| ~ aElementOf0(skf21(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ)) ),
inference(obv,[status(thm),theory(equality)],[10515]),
[iquote('0:Obv:10515.0')] ).
cnf(10517,plain,
~ aElementOf0(skf21(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ)),
inference(mrr,[status(thm)],[10516,369]),
[iquote('0:MRR:10516.0,369.1')] ).
cnf(10928,plain,
( ~ aSet0(sdtpldt1(xI,xJ))
| aIdeal0(sdtpldt1(xI,xJ)) ),
inference(res,[status(thm),theory(equality)],[21,10517]),
[iquote('0:Res:21.2,10517.0')] ).
cnf(10929,plain,
aIdeal0(sdtpldt1(xI,xJ)),
inference(ssi,[status(thm)],[10928,230,3,8,4]),
[iquote('0:SSi:10928.0,230.1,3.0,8.1,4.0,8.2')] ).
cnf(10930,plain,
$false,
inference(mrr,[status(thm)],[10929,7]),
[iquote('0:MRR:10929.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG092+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.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 : 600
% 0.12/0.34 % DateTime : Mon May 30 06:53:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.28/3.45
% 3.28/3.45 SPASS V 3.9
% 3.28/3.45 SPASS beiseite: Proof found.
% 3.28/3.45 % SZS status Theorem
% 3.28/3.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.28/3.45 SPASS derived 6958 clauses, backtracked 149 clauses, performed 4 splits and kept 2111 clauses.
% 3.28/3.45 SPASS allocated 108104 KBytes.
% 3.28/3.45 SPASS spent 0:00:02.69 on the problem.
% 3.28/3.45 0:00:00.03 for the input.
% 3.28/3.45 0:00:00.15 for the FLOTTER CNF translation.
% 3.28/3.45 0:00:00.11 for inferences.
% 3.28/3.45 0:00:00.05 for the backtracking.
% 3.28/3.45 0:00:02.29 for the reduction.
% 3.28/3.45
% 3.28/3.45
% 3.28/3.45 Here is a proof with depth 3, length 26 :
% 3.28/3.45 % SZS output start Refutation
% See solution above
% 3.28/3.45 Formulae used in the proof : mSortsC_01 m__870 mDefIdeal m__ mDefSSum
% 3.28/3.45
%------------------------------------------------------------------------------