%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM457+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 14:26:23 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 8 unt; 1 nHn; 15 RR)
% Number of literals : 33 ( 0 equ; 22 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(sz00),
file('NUM457+1.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xm),
file('NUM457+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xn),
file('NUM457+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(xm,sz00),
file('NUM457+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(xn,sz00),
file('NUM457+1.p',unknown),
[] ).
cnf(8,axiom,
equal(sdtasdt0(xm,xn),sz00),
file('NUM457+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,sz00),sz00) ),
file('NUM457+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtasdt0(w,v),sdtasdt0(w,u))
| equal(v,u)
| equal(w,sz00) ),
file('NUM457+1.p',unknown),
[] ).
cnf(37,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ equal(sdtasdt0(u,xn),sdtasdt0(u,sz00))
| equal(u,sz00) ),
inference(res,[status(thm),theory(equality)],[28,6]),
[iquote('0:Res:28.5,6.0')] ).
cnf(79,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ equal(sdtasdt0(u,xn),sz00)
| equal(u,sz00) ),
inference(rew,[status(thm),theory(equality)],[13,37]),
[iquote('0:Rew:13.1,37.3')] ).
cnf(80,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(u,xn),sz00)
| equal(u,sz00) ),
inference(mrr,[status(thm)],[79,1,4]),
[iquote('0:MRR:79.1,79.2,1.0,4.0')] ).
cnf(85,plain,
( ~ aNaturalNumber0(xm)
| ~ equal(sdtasdt0(xm,xn),sz00) ),
inference(res,[status(thm),theory(equality)],[80,5]),
[iquote('0:Res:80.2,5.0')] ).
cnf(97,plain,
( ~ aNaturalNumber0(xm)
| ~ equal(sz00,sz00) ),
inference(rew,[status(thm),theory(equality)],[8,85]),
[iquote('0:Rew:8.0,85.1')] ).
cnf(98,plain,
~ aNaturalNumber0(xm),
inference(obv,[status(thm),theory(equality)],[97]),
[iquote('0:Obv:97.1')] ).
cnf(99,plain,
$false,
inference(mrr,[status(thm)],[98,3]),
[iquote('0:MRR:98.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM457+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n016.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 : Wed Jul 6 05:48:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 36 clauses, backtracked 0 clauses, performed 0 splits and kept 45 clauses.
% 0.20/0.44 SPASS allocated 103974 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.44 0:00:00.03 for the input.
% 0.20/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.00 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 2, length 15 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : mSortsC m__624 m__ m_MulZero mMulCanc
% 0.20/0.44
%------------------------------------------------------------------------------