TSTP Solution File: NUM435+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM435+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 14:26:10 EDT 2022
% Result : Theorem 1.14s 1.32s
% Output : Refutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 7 unt; 0 nHn; 16 RR)
% Number of literals : 43 ( 0 equ; 31 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
aInteger0(xp),
file('NUM435+1.p',unknown),
[] ).
cnf(6,axiom,
aInteger0(xq),
file('NUM435+1.p',unknown),
[] ).
cnf(7,axiom,
aInteger0(xm),
file('NUM435+1.p',unknown),
[] ).
cnf(26,axiom,
equal(sdtasdt0(sdtasdt0(xp,xq),xm),sdtpldt0(xa,smndt0(xb))),
file('NUM435+1.p',unknown),
[] ).
cnf(27,axiom,
~ equal(sdtasdt0(xq,sdtasdt0(xp,xm)),sdtpldt0(xa,smndt0(xb))),
file('NUM435+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM435+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('NUM435+1.p',unknown),
[] ).
cnf(404,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ aInteger0(xp)
| equal(sdtasdt0(xp,sdtasdt0(xq,xm)),sdtpldt0(xa,smndt0(xb))) ),
inference(spr,[status(thm),theory(equality)],[34,26]),
[iquote('0:SpR:34.3,26.0')] ).
cnf(413,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ aInteger0(v)
| ~ aInteger0(u)
| equal(sdtasdt0(sdtasdt0(v,u),w),sdtasdt0(u,sdtasdt0(v,w))) ),
inference(spr,[status(thm),theory(equality)],[30,34]),
[iquote('0:SpR:30.2,34.3')] ).
cnf(418,plain,
equal(sdtasdt0(xp,sdtasdt0(xq,xm)),sdtpldt0(xa,smndt0(xb))),
inference(ssi,[status(thm)],[404,5,6,7]),
[iquote('0:SSi:404.2,404.1,404.0,5.0,6.0,7.0')] ).
cnf(440,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtasdt0(sdtasdt0(v,w),u),sdtasdt0(w,sdtasdt0(v,u))) ),
inference(obv,[status(thm),theory(equality)],[413]),
[iquote('0:Obv:413.1')] ).
cnf(441,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtasdt0(v,sdtasdt0(w,u)),sdtasdt0(w,sdtasdt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[34,440]),
[iquote('0:Rew:34.3,440.3')] ).
cnf(4671,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ aInteger0(xp)
| ~ equal(sdtasdt0(xp,sdtasdt0(xq,xm)),sdtpldt0(xa,smndt0(xb))) ),
inference(spl,[status(thm),theory(equality)],[441,27]),
[iquote('0:SpL:441.3,27.0')] ).
cnf(4689,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ aInteger0(xp)
| ~ equal(sdtpldt0(xa,smndt0(xb)),sdtpldt0(xa,smndt0(xb))) ),
inference(rew,[status(thm),theory(equality)],[418,4671]),
[iquote('0:Rew:418.0,4671.3')] ).
cnf(4690,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ aInteger0(xp) ),
inference(obv,[status(thm),theory(equality)],[4689]),
[iquote('0:Obv:4689.3')] ).
cnf(4691,plain,
$false,
inference(ssi,[status(thm)],[4690,5,6,7]),
[iquote('0:SSi:4690.2,4690.1,4690.0,5.0,6.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : NUM435+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jul 7 01:07:59 EDT 2022
% 0.15/0.36 % CPUTime :
% 1.14/1.32
% 1.14/1.32 SPASS V 3.9
% 1.14/1.32 SPASS beiseite: Proof found.
% 1.14/1.32 % SZS status Theorem
% 1.14/1.32 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.14/1.32 SPASS derived 2666 clauses, backtracked 16 clauses, performed 4 splits and kept 678 clauses.
% 1.14/1.32 SPASS allocated 102425 KBytes.
% 1.14/1.32 SPASS spent 0:00:00.79 on the problem.
% 1.14/1.32 0:00:00.04 for the input.
% 1.14/1.32 0:00:00.03 for the FLOTTER CNF translation.
% 1.14/1.32 0:00:00.04 for inferences.
% 1.14/1.32 0:00:00.00 for the backtracking.
% 1.14/1.32 0:00:00.65 for the reduction.
% 1.14/1.32
% 1.14/1.32
% 1.14/1.32 Here is a proof with depth 2, length 16 :
% 1.14/1.32 % SZS output start Refutation
% See solution above
% 1.14/1.32 Formulae used in the proof : m__979 m__1032 m__ mMulComm mMulAsso
% 1.14/1.32
%------------------------------------------------------------------------------