TSTP Solution File: NUM501+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM501+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 14:26:51 EDT 2022
% Result : Theorem 1.20s 1.41s
% Output : Refutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 41 ( 13 unt; 6 nHn; 41 RR)
% Number of literals : 119 ( 0 equ; 81 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM501+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM501+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM501+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM501+1.p',unknown),
[] ).
cnf(7,axiom,
aNaturalNumber0(xr),
file('NUM501+1.p',unknown),
[] ).
cnf(13,axiom,
doDivides0(xr,xk),
file('NUM501+1.p',unknown),
[] ).
cnf(25,axiom,
doDivides0(xp,sdtasdt0(xn,xm)),
file('NUM501+1.p',unknown),
[] ).
cnf(26,axiom,
~ doDivides0(xr,sdtasdt0(xn,xm)),
file('NUM501+1.p',unknown),
[] ).
cnf(28,axiom,
equal(sdtsldt0(sdtasdt0(xn,xm),xp),xk),
file('NUM501+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM501+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ aNaturalNumber0(u)
| ~ isPrime0(u)
| ~ equal(u,sz00) ),
file('NUM501+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM501+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM501+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(v,u)
| ~ doDivides0(w,v)
| doDivides0(w,u) ),
file('NUM501+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM501+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| equal(v,sz00)
| equal(u,sdtasdt0(v,w)) ),
file('NUM501+1.p',unknown),
[] ).
cnf(96,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xr,u)
| ~ doDivides0(u,sdtasdt0(xn,xm)) ),
inference(res,[status(thm),theory(equality)],[63,26]),
[iquote('0:Res:63.5,26.0')] ).
cnf(99,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(u,sdtasdt0(xn,xm))
| ~ doDivides0(xr,u) ),
inference(mrr,[status(thm)],[96,7]),
[iquote('0:MRR:96.0,7.0')] ).
cnf(116,plain,
~ equal(xp,sz00),
inference(ems,[status(thm)],[37,5,6]),
[iquote('0:EmS:37.0,37.1,5.0,6.0')] ).
cnf(446,plain,
( ~ aNaturalNumber0(sdtasdt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[61]),
[iquote('0:EqR:61.3')] ).
cnf(454,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(ssi,[status(thm)],[446,36]),
[iquote('0:SSi:446.0,36.2')] ).
cnf(517,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| doDivides0(v,sdtasdt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[43,454]),
[iquote('0:SpR:43.2,454.2')] ).
cnf(534,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[517]),
[iquote('0:Obv:517.1')] ).
cnf(1305,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[28,69]),
[iquote('0:SpL:28.0,69.3')] ).
cnf(1306,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[1305,6,5,36,3,4]),
[iquote('0:SSi:1305.1,1305.0,6.0,5.0,36.2,3.0,4.0')] ).
cnf(1307,plain,
( ~ equal(u,xk)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[1306,25,116]),
[iquote('0:MRR:1306.0,1306.3,25.0,116.0')] ).
cnf(2344,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
inference(spl,[status(thm),theory(equality)],[28,79]),
[iquote('0:SpL:28.0,79.3')] ).
cnf(2345,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
inference(ssi,[status(thm)],[2344,6,5,36,3,4]),
[iquote('0:SSi:2344.1,2344.0,6.0,5.0,36.2,3.0,4.0')] ).
cnf(2346,plain,
( ~ equal(u,xk)
| equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
inference(mrr,[status(thm)],[2345,25,116]),
[iquote('0:MRR:2345.0,2345.2,25.0,116.0')] ).
cnf(2664,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xk)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spr,[status(thm),theory(equality)],[2346,36]),
[iquote('0:SpR:2346.1,36.2')] ).
cnf(2667,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xk)
| doDivides0(u,sdtasdt0(xn,xm)) ),
inference(spr,[status(thm),theory(equality)],[2346,534]),
[iquote('0:SpR:2346.1,534.2')] ).
cnf(2691,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xk)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(ssi,[status(thm)],[2664,6,5]),
[iquote('0:SSi:2664.1,6.0,5.0')] ).
cnf(2692,plain,
( ~ equal(u,xk)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(mrr,[status(thm)],[2691,1307]),
[iquote('0:MRR:2691.0,1307.1')] ).
cnf(2693,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xk)
| doDivides0(u,sdtasdt0(xn,xm)) ),
inference(ssi,[status(thm)],[2667,6,5]),
[iquote('0:SSi:2667.1,6.0,5.0')] ).
cnf(2694,plain,
( ~ equal(u,xk)
| doDivides0(u,sdtasdt0(xn,xm)) ),
inference(mrr,[status(thm)],[2693,1307]),
[iquote('0:MRR:2693.0,1307.1')] ).
cnf(2779,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(eqr,[status(thm),theory(equality)],[2692]),
[iquote('0:EqR:2692.0')] ).
cnf(2780,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(u,sdtasdt0(xn,xm))
| ~ doDivides0(xr,u) ),
inference(mrr,[status(thm)],[99,2779]),
[iquote('0:MRR:99.1,2779.0')] ).
cnf(3513,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xk)
| ~ doDivides0(xr,u) ),
inference(res,[status(thm),theory(equality)],[2694,2780]),
[iquote('0:Res:2694.1,2780.1')] ).
cnf(3523,plain,
( ~ equal(u,xk)
| ~ doDivides0(xr,u) ),
inference(mrr,[status(thm)],[3513,1307]),
[iquote('0:MRR:3513.0,1307.1')] ).
cnf(3775,plain,
~ equal(xk,xk),
inference(res,[status(thm),theory(equality)],[13,3523]),
[iquote('0:Res:13.0,3523.1')] ).
cnf(3786,plain,
$false,
inference(obv,[status(thm),theory(equality)],[3775]),
[iquote('0:Obv:3775.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM501+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 : Thu Jul 7 16:22:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.20/1.41
% 1.20/1.41 SPASS V 3.9
% 1.20/1.41 SPASS beiseite: Proof found.
% 1.20/1.41 % SZS status Theorem
% 1.20/1.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.20/1.41 SPASS derived 2187 clauses, backtracked 44 clauses, performed 1 splits and kept 1020 clauses.
% 1.20/1.41 SPASS allocated 101351 KBytes.
% 1.20/1.41 SPASS spent 0:00:01.00 on the problem.
% 1.20/1.41 0:00:00.04 for the input.
% 1.20/1.41 0:00:00.04 for the FLOTTER CNF translation.
% 1.20/1.41 0:00:00.03 for inferences.
% 1.20/1.41 0:00:00.00 for the backtracking.
% 1.20/1.41 0:00:00.86 for the reduction.
% 1.20/1.41
% 1.20/1.41
% 1.20/1.41 Here is a proof with depth 5, length 41 :
% 1.20/1.41 % SZS output start Refutation
% See solution above
% 1.20/1.41 Formulae used in the proof : m__1837 m__1860 m__2342 m__ m__2306 mSortsB_02 mDefPrime mMulComm mDefDiv mDivTrans mDefQuot
% 1.20/1.41
%------------------------------------------------------------------------------