TSTP Solution File: NUM434+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM434+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:26:09 EDT 2022
% Result : Theorem 0.96s 1.14s
% Output : Refutation 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of clauses : 41 ( 16 unt; 13 nHn; 41 RR)
% Number of literals : 115 ( 0 equ; 70 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aInteger0(xa),
file('NUM434+1.p',unknown),
[] ).
cnf(4,axiom,
aInteger0(xb),
file('NUM434+1.p',unknown),
[] ).
cnf(5,axiom,
aInteger0(xp),
file('NUM434+1.p',unknown),
[] ).
cnf(6,axiom,
aInteger0(xq),
file('NUM434+1.p',unknown),
[] ).
cnf(7,axiom,
aInteger0(skf1(u,v)),
file('NUM434+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(xp,sz00),
file('NUM434+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(xq,sz00),
file('NUM434+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ aInteger0(u)
| aInteger0(smndt0(u)) ),
file('NUM434+1.p',unknown),
[] ).
cnf(11,axiom,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
file('NUM434+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ aInteger0(u)
| ~ aDivisorOf0(v,u)
| aInteger0(v) ),
file('NUM434+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aInteger0(sdtpldt0(v,u)) ),
file('NUM434+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aInteger0(sdtasdt0(v,u)) ),
file('NUM434+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aInteger0(u)
| ~ aDivisorOf0(v,u)
| ~ equal(v,sz00) ),
file('NUM434+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ aInteger0(u)
| ~ equal(sdtasdt0(sdtasdt0(xp,xq),u),sdtpldt0(xa,smndt0(xb))) ),
file('NUM434+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aInteger0(u)
| ~ aDivisorOf0(v,u)
| equal(sdtasdt0(v,skf1(u,v)),u) ),
file('NUM434+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ equal(sdtasdt0(v,u),sz00)
| equal(u,sz00)
| equal(v,sz00) ),
file('NUM434+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ sdteqdtlpzmzozddtrp0(w,v,u)
| equal(u,sz00)
| sdteqdtlpzmzozddtrp0(v,w,u) ),
file('NUM434+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ equal(sdtasdt0(w,v),u)
| aDivisorOf0(w,u)
| equal(w,sz00) ),
file('NUM434+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ sdteqdtlpzmzozddtrp0(w,v,u)
| equal(u,sz00)
| aDivisorOf0(u,sdtpldt0(w,smndt0(v))) ),
file('NUM434+1.p',unknown),
[] ).
cnf(47,plain,
~ equal(sdtasdt0(sdtasdt0(xp,xq),skf1(u,v)),sdtpldt0(xa,smndt0(xb))),
inference(res,[status(thm),theory(equality)],[7,29]),
[iquote('0:Res:7.0,29.0')] ).
cnf(179,plain,
( ~ aInteger0(u)
| ~ aDivisorOf0(sdtasdt0(xp,xq),u)
| ~ equal(u,sdtpldt0(xa,smndt0(xb))) ),
inference(spl,[status(thm),theory(equality)],[30,47]),
[iquote('0:SpL:30.2,47.0')] ).
cnf(458,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(skf1(u,w))
| ~ aInteger0(w)
| ~ aDivisorOf0(w,u)
| ~ equal(u,v)
| aDivisorOf0(w,v)
| equal(w,sz00) ),
inference(spl,[status(thm),theory(equality)],[30,35]),
[iquote('0:SpL:30.2,35.3')] ).
cnf(472,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ aDivisorOf0(w,u)
| ~ equal(u,v)
| aDivisorOf0(w,v)
| equal(w,sz00) ),
inference(ssi,[status(thm)],[458,7]),
[iquote('0:SSi:458.2,7.0')] ).
cnf(473,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aDivisorOf0(w,u)
| ~ equal(u,v)
| aDivisorOf0(w,v) ),
inference(mrr,[status(thm)],[472,20,25]),
[iquote('0:MRR:472.2,472.6,20.2,25.2')] ).
cnf(511,plain,
( ~ aInteger0(sdtasdt0(xp,xq))
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| equal(sdtasdt0(xp,xq),sz00)
| sdteqdtlpzmzozddtrp0(xb,xa,sdtasdt0(xp,xq)) ),
inference(res,[status(thm),theory(equality)],[11,34]),
[iquote('0:Res:11.0,34.3')] ).
cnf(513,plain,
( equal(sdtasdt0(xp,xq),sz00)
| sdteqdtlpzmzozddtrp0(xb,xa,sdtasdt0(xp,xq)) ),
inference(ssi,[status(thm)],[511,3,4,22,5,6]),
[iquote('0:SSi:511.2,511.1,511.0,3.0,4.0,22.2,5.0,6.0')] ).
cnf(527,plain,
equal(sdtasdt0(xp,xq),sz00),
inference(spt,[spt(split,[position(s1)])],[513]),
[iquote('1:Spt:513.0')] ).
cnf(554,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xp)
| ~ equal(sz00,sz00)
| equal(xq,sz00)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[527,31]),
[iquote('1:SpL:527.0,31.2')] ).
cnf(556,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xp)
| equal(xq,sz00)
| equal(xp,sz00) ),
inference(obv,[status(thm),theory(equality)],[554]),
[iquote('1:Obv:554.2')] ).
cnf(557,plain,
( equal(xq,sz00)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[556,5,6]),
[iquote('1:SSi:556.1,556.0,5.0,6.0')] ).
cnf(558,plain,
$false,
inference(mrr,[status(thm)],[557,9,8]),
[iquote('1:MRR:557.0,557.1,9.0,8.0')] ).
cnf(562,plain,
~ equal(sdtasdt0(xp,xq),sz00),
inference(spt,[spt(split,[position(sa)])],[558,527]),
[iquote('1:Spt:558.0,513.0,527.0')] ).
cnf(563,plain,
sdteqdtlpzmzozddtrp0(xb,xa,sdtasdt0(xp,xq)),
inference(spt,[spt(split,[position(s2)])],[513]),
[iquote('1:Spt:558.0,513.1')] ).
cnf(816,plain,
( ~ aInteger0(sdtasdt0(xp,xq))
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| equal(sdtasdt0(xp,xq),sz00)
| aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
inference(res,[status(thm),theory(equality)],[11,39]),
[iquote('0:Res:11.0,39.3')] ).
cnf(819,plain,
( equal(sdtasdt0(xp,xq),sz00)
| aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
inference(ssi,[status(thm)],[816,3,4,22,5,6]),
[iquote('0:SSi:816.2,816.1,816.0,3.0,4.0,22.2,5.0,6.0')] ).
cnf(820,plain,
aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))),
inference(mrr,[status(thm)],[819,562]),
[iquote('1:MRR:819.0,562.0')] ).
cnf(4370,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(u)
| ~ equal(sdtpldt0(xa,smndt0(xb)),u)
| aDivisorOf0(sdtasdt0(xp,xq),u) ),
inference(res,[status(thm),theory(equality)],[820,473]),
[iquote('1:Res:820.0,473.2')] ).
cnf(4414,plain,
( ~ aInteger0(u)
| ~ equal(sdtpldt0(xa,smndt0(xb)),u)
| aDivisorOf0(sdtasdt0(xp,xq),u) ),
inference(ssi,[status(thm)],[4370,21,3,10,4]),
[iquote('1:SSi:4370.0,21.0,3.1,10.0,4.2')] ).
cnf(4415,plain,
( ~ aInteger0(u)
| ~ equal(sdtpldt0(xa,smndt0(xb)),u) ),
inference(mrr,[status(thm)],[4414,179]),
[iquote('1:MRR:4414.2,179.1')] ).
cnf(4425,plain,
~ aInteger0(sdtpldt0(xa,smndt0(xb))),
inference(eqr,[status(thm),theory(equality)],[4415]),
[iquote('1:EqR:4415.1')] ).
cnf(4428,plain,
$false,
inference(ssi,[status(thm)],[4425,21,3,10,4]),
[iquote('1:SSi:4425.0,21.0,3.1,10.0,4.2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM434+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.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 08:17:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.96/1.14
% 0.96/1.14 SPASS V 3.9
% 0.96/1.14 SPASS beiseite: Proof found.
% 0.96/1.14 % SZS status Theorem
% 0.96/1.14 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.96/1.14 SPASS derived 2387 clauses, backtracked 21 clauses, performed 3 splits and kept 544 clauses.
% 0.96/1.14 SPASS allocated 101742 KBytes.
% 0.96/1.14 SPASS spent 0:00:00.61 on the problem.
% 0.96/1.14 0:00:00.04 for the input.
% 0.96/1.14 0:00:00.03 for the FLOTTER CNF translation.
% 0.96/1.14 0:00:00.03 for inferences.
% 0.96/1.14 0:00:00.00 for the backtracking.
% 0.96/1.14 0:00:00.49 for the reduction.
% 0.96/1.14
% 0.96/1.14
% 0.96/1.14 Here is a proof with depth 3, length 41 :
% 0.96/1.14 % SZS output start Refutation
% See solution above
% 0.96/1.14 Formulae used in the proof : m__979 mDivisor mIntNeg m__1003 mIntPlus mIntMult m__ mZeroDiv mEquModSym mEquMod
% 0.96/1.14
%------------------------------------------------------------------------------