TSTP Solution File: NUM423+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM423+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 14:26:02 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 8 unt; 7 nHn; 22 RR)
% Number of literals : 63 ( 0 equ; 37 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aInteger0(sz00),
file('NUM423+1.p',unknown),
[] ).
cnf(3,axiom,
aInteger0(xa),
file('NUM423+1.p',unknown),
[] ).
cnf(4,axiom,
aInteger0(xq),
file('NUM423+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(xq,sz00),
file('NUM423+1.p',unknown),
[] ).
cnf(7,axiom,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
file('NUM423+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(u,sz00),sz00) ),
file('NUM423+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('NUM423+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aInteger0(sdtasdt0(v,u)) ),
file('NUM423+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ equal(sdtasdt0(w,v),u)
| aDivisorOf0(w,u)
| equal(w,sz00) ),
file('NUM423+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ aDivisorOf0(u,sdtpldt0(w,smndt0(v)))
| equal(u,sz00)
| sdteqdtlpzmzozddtrp0(w,v,u) ),
file('NUM423+1.p',unknown),
[] ).
cnf(34,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| equal(xq,sz00) ),
inference(res,[status(thm),theory(equality)],[32,7]),
[iquote('0:Res:32.4,7.0')] ).
cnf(35,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xq)
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| equal(xq,sz00) ),
inference(obv,[status(thm),theory(equality)],[34]),
[iquote('0:Obv:34.0')] ).
cnf(36,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xq)
| ~ aDivisorOf0(xq,sz00)
| equal(xq,sz00) ),
inference(rew,[status(thm),theory(equality)],[15,35]),
[iquote('0:Rew:15.1,35.2')] ).
cnf(37,plain,
~ aDivisorOf0(xq,sz00),
inference(mrr,[status(thm)],[36,3,4,6]),
[iquote('0:MRR:36.0,36.1,36.3,3.0,4.0,6.0')] ).
cnf(422,plain,
( ~ aInteger0(sdtasdt0(u,v))
| ~ aInteger0(v)
| ~ aInteger0(u)
| aDivisorOf0(u,sdtasdt0(u,v))
| equal(u,sz00) ),
inference(eqr,[status(thm),theory(equality)],[29]),
[iquote('0:EqR:29.3')] ).
cnf(434,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aDivisorOf0(v,sdtasdt0(v,u))
| equal(v,sz00) ),
inference(ssi,[status(thm)],[422,19]),
[iquote('0:SSi:422.0,19.2')] ).
cnf(619,plain,
( ~ aInteger0(u)
| ~ aInteger0(sz00)
| ~ aInteger0(u)
| aDivisorOf0(u,sz00)
| equal(u,sz00) ),
inference(spr,[status(thm),theory(equality)],[13,434]),
[iquote('0:SpR:13.1,434.2')] ).
cnf(630,plain,
( ~ aInteger0(sz00)
| ~ aInteger0(u)
| aDivisorOf0(u,sz00)
| equal(u,sz00) ),
inference(obv,[status(thm),theory(equality)],[619]),
[iquote('0:Obv:619.0')] ).
cnf(631,plain,
( ~ aInteger0(u)
| aDivisorOf0(u,sz00)
| equal(u,sz00) ),
inference(ssi,[status(thm)],[630,1]),
[iquote('0:SSi:630.0,1.0')] ).
cnf(716,plain,
( ~ aInteger0(xq)
| equal(xq,sz00) ),
inference(res,[status(thm),theory(equality)],[631,37]),
[iquote('0:Res:631.1,37.0')] ).
cnf(720,plain,
equal(xq,sz00),
inference(ssi,[status(thm)],[716,4]),
[iquote('0:SSi:716.0,4.0')] ).
cnf(721,plain,
$false,
inference(mrr,[status(thm)],[720,6]),
[iquote('0:MRR:720.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM423+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 12:03:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.50
% 0.19/0.50 SPASS V 3.9
% 0.19/0.50 SPASS beiseite: Proof found.
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 349 clauses, backtracked 0 clauses, performed 1 splits and kept 141 clauses.
% 0.19/0.50 SPASS allocated 98431 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.50 0:00:00.03 for the input.
% 0.19/0.50 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.50 0:00:00.00 for inferences.
% 0.19/0.50 0:00:00.00 for the backtracking.
% 0.19/0.50 0:00:00.06 for the reduction.
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 Here is a proof with depth 3, length 22 :
% 0.19/0.50 % SZS output start Refutation
% See solution above
% 0.19/0.50 Formulae used in the proof : mIntZero m__671 m__ mMulZero mAddNeg mIntMult mDivisor mEquMod
% 0.19/0.50
%------------------------------------------------------------------------------