TSTP Solution File: NUM514+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM514+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 14:26:59 EDT 2022
% Result : Theorem 18.82s 19.01s
% Output : Refutation 18.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of clauses : 49 ( 19 unt; 9 nHn; 49 RR)
% Number of literals : 127 ( 0 equ; 78 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('NUM514+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM514+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM514+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM514+1.p',unknown),
[] ).
cnf(7,axiom,
aNaturalNumber0(xr),
file('NUM514+1.p',unknown),
[] ).
cnf(8,axiom,
isPrime0(xr),
file('NUM514+1.p',unknown),
[] ).
cnf(13,axiom,
doDivides0(xr,xk),
file('NUM514+1.p',unknown),
[] ).
cnf(29,axiom,
doDivides0(xp,sdtasdt0(xn,xm)),
file('NUM514+1.p',unknown),
[] ).
cnf(35,axiom,
equal(sdtsldt0(sdtasdt0(xn,xm),xp),xk),
file('NUM514+1.p',unknown),
[] ).
cnf(36,axiom,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
file('NUM514+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM514+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ aNaturalNumber0(u)
| ~ isPrime0(u)
| ~ equal(u,sz00) ),
file('NUM514+1.p',unknown),
[] ).
cnf(49,axiom,
equal(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,sdtsldt0(xk,xr))),
file('NUM514+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM514+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM514+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM514+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| equal(v,sz00)
| equal(u,sdtasdt0(v,w)) ),
file('NUM514+1.p',unknown),
[] ).
cnf(101,plain,
~ doDivides0(xp,sdtasdt0(xp,sdtsldt0(xk,xr))),
inference(rew,[status(thm),theory(equality)],[49,36]),
[iquote('0:Rew:49.0,36.0')] ).
cnf(127,plain,
~ equal(xp,sz00),
inference(ems,[status(thm)],[45,5,6]),
[iquote('0:EmS:45.0,45.1,5.0,6.0')] ).
cnf(128,plain,
~ equal(xr,sz00),
inference(ems,[status(thm)],[45,7,8]),
[iquote('0:EmS:45.0,45.1,7.0,8.0')] ).
cnf(509,plain,
( ~ aNaturalNumber0(sdtasdt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[72]),
[iquote('0:EqR:72.3')] ).
cnf(521,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(ssi,[status(thm)],[509,44]),
[iquote('0:SSi:509.0,44.2')] ).
cnf(599,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xk,xr)) ),
inference(res,[status(thm),theory(equality)],[521,101]),
[iquote('0:Res:521.2,101.0')] ).
cnf(602,plain,
~ aNaturalNumber0(sdtsldt0(xk,xr)),
inference(ssi,[status(thm)],[599,6,5]),
[iquote('0:SSi:599.0,6.0,5.0')] ).
cnf(1255,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| aNaturalNumber0(sdtsldt0(u,v))
| equal(v,sz00) ),
inference(eqr,[status(thm),theory(equality)],[80]),
[iquote('0:EqR:80.3')] ).
cnf(2450,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)],[35,90]),
[iquote('0:SpL:35.0,90.3')] ).
cnf(2451,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)],[35,80]),
[iquote('0:SpL:35.0,80.3')] ).
cnf(2453,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[2451,6,5,44,3,4]),
[iquote('0:SSi:2451.1,2451.0,6.0,5.0,44.2,3.0,4.0')] ).
cnf(2454,plain,
( ~ equal(u,xk)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[2453,29,127]),
[iquote('0:MRR:2453.0,2453.3,29.0,127.0')] ).
cnf(2455,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
inference(ssi,[status(thm)],[2450,6,5,44,3,4]),
[iquote('0:SSi:2450.1,2450.0,6.0,5.0,44.2,3.0,4.0')] ).
cnf(2456,plain,
( ~ equal(u,xk)
| equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
inference(mrr,[status(thm)],[2455,29,127]),
[iquote('0:MRR:2455.0,2455.2,29.0,127.0')] ).
cnf(3540,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xk)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spr,[status(thm),theory(equality)],[2456,44]),
[iquote('0:SpR:2456.1,44.2')] ).
cnf(3541,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xk)
| equal(sdtasdt0(xn,xm),sdtasdt0(u,xp)) ),
inference(spr,[status(thm),theory(equality)],[2456,54]),
[iquote('0:SpR:2456.1,54.2')] ).
cnf(3575,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xk)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(ssi,[status(thm)],[3540,6,5]),
[iquote('0:SSi:3540.1,6.0,5.0')] ).
cnf(3576,plain,
( ~ equal(u,xk)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(mrr,[status(thm)],[3575,2454]),
[iquote('0:MRR:3575.0,2454.1')] ).
cnf(3580,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xk)
| equal(sdtasdt0(xn,xm),sdtasdt0(u,xp)) ),
inference(ssi,[status(thm)],[3541,6,5]),
[iquote('0:SSi:3541.1,6.0,5.0')] ).
cnf(3581,plain,
( ~ equal(u,xk)
| equal(sdtasdt0(xn,xm),sdtasdt0(u,xp)) ),
inference(mrr,[status(thm)],[3580,2454]),
[iquote('0:MRR:3580.0,2454.1')] ).
cnf(3637,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(eqr,[status(thm),theory(equality)],[3576]),
[iquote('0:EqR:3576.0')] ).
cnf(4205,plain,
( ~ equal(u,xk)
| aNaturalNumber0(sdtasdt0(u,xp)) ),
inference(spr,[status(thm),theory(equality)],[3581,3637]),
[iquote('0:SpR:3581.1,3637.0')] ).
cnf(4207,plain,
( ~ equal(u,xk)
| doDivides0(xp,sdtasdt0(u,xp)) ),
inference(spr,[status(thm),theory(equality)],[3581,29]),
[iquote('0:SpR:3581.1,29.0')] ).
cnf(4210,plain,
( ~ equal(u,xk)
| equal(sdtsldt0(sdtasdt0(u,xp),xp),xk) ),
inference(spr,[status(thm),theory(equality)],[3581,35]),
[iquote('0:SpR:3581.1,35.0')] ).
cnf(36524,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| ~ doDivides0(xr,xk)
| equal(xr,sz00) ),
inference(sor,[status(thm)],[602,1255]),
[iquote('0:SoR:602.0,1255.3')] ).
cnf(36538,plain,
( ~ aNaturalNumber0(sdtasdt0(u,xp))
| ~ aNaturalNumber0(xp)
| ~ equal(u,xk)
| ~ doDivides0(xp,sdtasdt0(u,xp))
| aNaturalNumber0(xk)
| equal(xp,sz00) ),
inference(spr,[status(thm),theory(equality)],[4210,1255]),
[iquote('0:SpR:4210.1,1255.3')] ).
cnf(36547,plain,
( ~ aNaturalNumber0(xk)
| ~ doDivides0(xr,xk)
| equal(xr,sz00) ),
inference(ssi,[status(thm)],[36524,7,8]),
[iquote('0:SSi:36524.0,7.0,8.0')] ).
cnf(36548,plain,
~ aNaturalNumber0(xk),
inference(mrr,[status(thm)],[36547,13,128]),
[iquote('0:MRR:36547.1,36547.2,13.0,128.0')] ).
cnf(36556,plain,
( ~ aNaturalNumber0(sdtasdt0(u,xp))
| ~ equal(u,xk)
| ~ doDivides0(xp,sdtasdt0(u,xp))
| aNaturalNumber0(xk)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[36538,6,5]),
[iquote('0:SSi:36538.1,6.0,5.0')] ).
cnf(36557,plain,
( ~ equal(u,xk)
| aNaturalNumber0(xk) ),
inference(mrr,[status(thm)],[36556,4205,4207,127]),
[iquote('0:MRR:36556.0,36556.2,36556.4,4205.1,4207.1,127.0')] ).
cnf(36558,plain,
~ equal(u,xk),
inference(mrr,[status(thm)],[36557,36548]),
[iquote('0:MRR:36557.1,36548.0')] ).
cnf(36559,plain,
$false,
inference(unc,[status(thm)],[36558,35]),
[iquote('0:UnC:36558.0,35.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM514+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.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 : Wed Jul 6 18:41:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 18.82/19.01
% 18.82/19.01 SPASS V 3.9
% 18.82/19.01 SPASS beiseite: Proof found.
% 18.82/19.01 % SZS status Theorem
% 18.82/19.01 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.82/19.01 SPASS derived 24693 clauses, backtracked 5055 clauses, performed 17 splits and kept 10632 clauses.
% 18.82/19.01 SPASS allocated 122637 KBytes.
% 18.82/19.01 SPASS spent 0:0:14.21 on the problem.
% 18.82/19.01 0:00:00.04 for the input.
% 18.82/19.01 0:00:00.04 for the FLOTTER CNF translation.
% 18.82/19.01 0:00:00.29 for inferences.
% 18.82/19.01 0:00:00.21 for the backtracking.
% 18.82/19.01 0:0:13.48 for the reduction.
% 18.82/19.01
% 18.82/19.01
% 18.82/19.01 Here is a proof with depth 4, length 49 :
% 18.82/19.01 % SZS output start Refutation
% See solution above
% 18.82/19.01 Formulae used in the proof : m__1837 m__1860 m__2342 m__2306 m__ mSortsB_02 mDefPrime m__2613 mMulComm mDefDiv mDefQuot
% 18.82/19.01
%------------------------------------------------------------------------------