TSTP Solution File: NUM555+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM555+1 : 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 14:27:27 EDT 2022
% Result : Theorem 1.21s 1.37s
% Output : Refutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 22 ( 12 unt; 0 nHn; 22 RR)
% Number of literals : 43 ( 0 equ; 22 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
aSet0(xS),
file('NUM555+1.p',unknown),
[] ).
cnf(6,axiom,
aSet0(xQ),
file('NUM555+1.p',unknown),
[] ).
cnf(7,axiom,
isFinite0(xQ),
file('NUM555+1.p',unknown),
[] ).
cnf(8,axiom,
aElement0(xy),
file('NUM555+1.p',unknown),
[] ).
cnf(10,axiom,
aElementOf0(xk,szNzAzT0),
file('NUM555+1.p',unknown),
[] ).
cnf(19,axiom,
~ aElementOf0(xx,xQ),
file('NUM555+1.p',unknown),
[] ).
cnf(20,axiom,
aElementOf0(xx,sdtmndt0(xQ,xy)),
file('NUM555+1.p',unknown),
[] ).
cnf(21,axiom,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('NUM555+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ skP1(u,v,w)
| aElementOf0(w,v) ),
file('NUM555+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM555+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| ~ equal(w,slbdtsldtrb0(u,v))
| aSet0(w) ),
file('NUM555+1.p',unknown),
[] ).
cnf(97,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ aElementOf0(w,x)
| ~ equal(x,sdtmndt0(v,u))
| skP1(u,v,w) ),
file('NUM555+1.p',unknown),
[] ).
cnf(199,plain,
( ~ aSet0(slbdtsldtrb0(xS,xk))
| aElement0(xQ) ),
inference(res,[status(thm),theory(equality)],[21,39]),
[iquote('0:Res:21.0,39.1')] ).
cnf(773,plain,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| aSet0(slbdtsldtrb0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[74]),
[iquote('0:EqR:74.2')] ).
cnf(1145,plain,
( ~ aSet0(xS)
| ~ aElementOf0(xk,szNzAzT0)
| aElement0(xQ) ),
inference(sor,[status(thm)],[199,773]),
[iquote('0:SoR:199.0,773.2')] ).
cnf(1149,plain,
( ~ aElementOf0(xk,szNzAzT0)
| aElement0(xQ) ),
inference(ssi,[status(thm)],[1145,4]),
[iquote('0:SSi:1145.0,4.0')] ).
cnf(1150,plain,
aElement0(xQ),
inference(mrr,[status(thm)],[1149,10]),
[iquote('0:MRR:1149.0,10.0')] ).
cnf(1914,plain,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ aElementOf0(w,sdtmndt0(v,u))
| skP1(u,v,w) ),
inference(eqr,[status(thm),theory(equality)],[97]),
[iquote('0:EqR:97.3')] ).
cnf(5206,plain,
( ~ aElement0(xy)
| ~ aSet0(xQ)
| skP1(xy,xQ,xx) ),
inference(res,[status(thm),theory(equality)],[20,1914]),
[iquote('0:Res:20.0,1914.2')] ).
cnf(5207,plain,
skP1(xy,xQ,xx),
inference(ssi,[status(thm)],[5206,6,1150,7,8]),
[iquote('0:SSi:5206.1,5206.0,6.0,1150.0,7.0,8.0')] ).
cnf(5208,plain,
aElementOf0(xx,xQ),
inference(res,[status(thm),theory(equality)],[5207,35]),
[iquote('0:Res:5207.0,35.0')] ).
cnf(5211,plain,
$false,
inference(mrr,[status(thm)],[5208,19]),
[iquote('0:MRR:5208.0,19.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM555+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % 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 : Wed Jul 6 01:27:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.21/1.37
% 1.21/1.37 SPASS V 3.9
% 1.21/1.37 SPASS beiseite: Proof found.
% 1.21/1.37 % SZS status Theorem
% 1.21/1.37 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.21/1.37 SPASS derived 3739 clauses, backtracked 260 clauses, performed 10 splits and kept 1847 clauses.
% 1.21/1.37 SPASS allocated 102124 KBytes.
% 1.21/1.37 SPASS spent 0:00:00.98 on the problem.
% 1.21/1.37 0:00:00.04 for the input.
% 1.21/1.37 0:00:00.11 for the FLOTTER CNF translation.
% 1.21/1.37 0:00:00.06 for inferences.
% 1.21/1.37 0:00:00.01 for the backtracking.
% 1.21/1.37 0:00:00.71 for the reduction.
% 1.21/1.37
% 1.21/1.37
% 1.21/1.37 Here is a proof with depth 3, length 22 :
% 1.21/1.37 % SZS output start Refutation
% See solution above
% 1.21/1.37 Formulae used in the proof : m__2202_02 m__2291 m__2304 m__2202 m__2338 m__ m__2270 mDefDiff mEOfElem mDefSel
% 1.21/1.37
%------------------------------------------------------------------------------