TSTP Solution File: NUM504+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM504+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 14:26:53 EDT 2022
% Result : Theorem 1.08s 1.25s
% Output : Refutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of clauses : 52 ( 16 unt; 6 nHn; 52 RR)
% Number of literals : 156 ( 0 equ; 112 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM504+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM504+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM504+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM504+1.p',unknown),
[] ).
cnf(16,axiom,
~ equal(sz10,sz00),
file('NUM504+1.p',unknown),
[] ).
cnf(27,axiom,
doDivides0(xp,sdtasdt0(xn,xm)),
file('NUM504+1.p',unknown),
[] ).
cnf(30,axiom,
equal(sdtsldt0(sdtasdt0(xn,xm),xp),xk),
file('NUM504+1.p',unknown),
[] ).
cnf(31,axiom,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
file('NUM504+1.p',unknown),
[] ).
cnf(32,axiom,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
file('NUM504+1.p',unknown),
[] ).
cnf(40,axiom,
~ equal(sdtasdt0(xp,xk),sdtasdt0(xp,xm)),
file('NUM504+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM504+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM504+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ aNaturalNumber0(u)
| ~ isPrime0(u)
| ~ equal(u,sz00) ),
file('NUM504+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM504+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ sdtlseqdt0(u,v)
| equal(v,u) ),
file('NUM504+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM504+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM504+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM504+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| equal(v,sz00)
| equal(u,sdtasdt0(v,w)) ),
file('NUM504+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM504+1.p',unknown),
[] ).
cnf(96,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[88,65]),
[iquote('0:MRR:88.3,65.4')] ).
cnf(113,plain,
~ equal(xp,sz00),
inference(ems,[status(thm)],[43,5,6]),
[iquote('0:EmS:43.0,43.1,5.0,6.0')] ).
cnf(142,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp)) ),
inference(spr,[status(thm),theory(equality)],[49,31]),
[iquote('0:SpR:49.2,31.0')] ).
cnf(162,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp)),
inference(ssi,[status(thm)],[142,6,5,4]),
[iquote('0:SSi:142.1,142.0,6.0,5.0,4.0')] ).
cnf(360,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| equal(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) ),
inference(res,[status(thm),theory(equality)],[32,62]),
[iquote('0:Res:32.0,62.2')] ).
cnf(371,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| equal(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) ),
inference(ssi,[status(thm)],[360,42,6,5,4]),
[iquote('0:SSi:360.1,42.0,6.0,5.0,4.2')] ).
cnf(372,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) ),
inference(mrr,[status(thm)],[371,40]),
[iquote('0:MRR:371.2,40.0')] ).
cnf(407,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) ),
inference(sor,[status(thm)],[372,42]),
[iquote('0:SoR:372.0,42.2')] ).
cnf(408,plain,
( ~ aNaturalNumber0(xk)
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) ),
inference(ssi,[status(thm)],[407,6,5]),
[iquote('0:SSi:407.0,6.0,5.0')] ).
cnf(418,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[65]),
[iquote('0:EqR:65.3')] ).
cnf(424,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(ssi,[status(thm)],[418,41]),
[iquote('0:SSi:418.0,41.2')] ).
cnf(802,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[96]),
[iquote('0:EqR:96.3')] ).
cnf(809,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(ssi,[status(thm)],[802,41]),
[iquote('0:SSi:802.0,41.2')] ).
cnf(867,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,sdtpldt0(u,v))
| ~ equal(w,v)
| aNaturalNumber0(w) ),
inference(spl,[status(thm),theory(equality)],[809,66]),
[iquote('0:SpL:809.2,66.3')] ).
cnf(882,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtpldt0(v,u))
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,sdtpldt0(v,u))
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(obv,[status(thm),theory(equality)],[867]),
[iquote('0:Obv:867.0')] ).
cnf(883,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,sdtpldt0(v,u))
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(ssi,[status(thm)],[882,41]),
[iquote('0:SSi:882.1,41.2')] ).
cnf(884,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(mrr,[status(thm)],[883,424]),
[iquote('0:MRR:883.2,424.2')] ).
cnf(1008,plain,
( ~ aNaturalNumber0(u)
| ~ equal(v,u)
| aNaturalNumber0(v) ),
inference(ems,[status(thm)],[884,4]),
[iquote('0:EmS:884.1,4.0')] ).
cnf(1044,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| ~ equal(xk,u) ),
inference(sor,[status(thm)],[408,1008]),
[iquote('0:SoR:408.0,1008.2')] ).
cnf(2831,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)],[30,85]),
[iquote('0:SpL:30.0,85.3')] ).
cnf(2832,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)],[30,75]),
[iquote('0:SpL:30.0,75.3')] ).
cnf(2834,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[2832,6,5,42,3,4]),
[iquote('0:SSi:2832.1,2832.0,6.0,5.0,42.2,3.0,4.0')] ).
cnf(2835,plain,
( ~ equal(u,xk)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[2834,27,113]),
[iquote('0:MRR:2834.0,2834.3,27.0,113.0')] ).
cnf(2838,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| ~ equal(xk,u) ),
inference(mrr,[status(thm)],[1044,2835]),
[iquote('0:MRR:1044.0,2835.1')] ).
cnf(2844,plain,
~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)),
inference(aed,[status(thm),theory(equality)],[16,2838]),
[iquote('0:AED:16.0,2838.1')] ).
cnf(2848,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
inference(ssi,[status(thm)],[2831,6,5,42,3,4]),
[iquote('0:SSi:2831.1,2831.0,6.0,5.0,42.2,3.0,4.0')] ).
cnf(2849,plain,
( ~ equal(u,xk)
| equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
inference(mrr,[status(thm)],[2848,27,113]),
[iquote('0:MRR:2848.0,2848.2,27.0,113.0')] ).
cnf(3031,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xm,xp)) ),
inference(spl,[status(thm),theory(equality)],[49,2844]),
[iquote('0:SpL:49.2,2844.0')] ).
cnf(3041,plain,
~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xm,xp)),
inference(ssi,[status(thm)],[3031,6,5,4]),
[iquote('0:SSi:3031.1,3031.0,6.0,5.0,4.0')] ).
cnf(3136,plain,
( ~ equal(xk,xk)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp)) ),
inference(spl,[status(thm),theory(equality)],[2849,3041]),
[iquote('0:SpL:2849.1,3041.0')] ).
cnf(3147,plain,
~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp)),
inference(obv,[status(thm),theory(equality)],[3136]),
[iquote('0:Obv:3136.0')] ).
cnf(3148,plain,
$false,
inference(mrr,[status(thm)],[3147,162]),
[iquote('0:MRR:3147.0,162.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM504+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % 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 : Wed Jul 6 20:21:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.08/1.25
% 1.08/1.25 SPASS V 3.9
% 1.08/1.25 SPASS beiseite: Proof found.
% 1.08/1.25 % SZS status Theorem
% 1.08/1.25 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.08/1.25 SPASS derived 1830 clauses, backtracked 111 clauses, performed 4 splits and kept 909 clauses.
% 1.08/1.25 SPASS allocated 100670 KBytes.
% 1.08/1.25 SPASS spent 0:00:00.86 on the problem.
% 1.08/1.25 0:00:00.04 for the input.
% 1.08/1.25 0:00:00.04 for the FLOTTER CNF translation.
% 1.08/1.25 0:00:00.03 for inferences.
% 1.08/1.25 0:00:00.00 for the backtracking.
% 1.08/1.25 0:00:00.71 for the reduction.
% 1.08/1.25
% 1.08/1.25
% 1.08/1.25 Here is a proof with depth 6, length 52 :
% 1.08/1.25 % SZS output start Refutation
% See solution above
% 1.08/1.25 Formulae used in the proof : m__1837 m__1860 mSortsC_01 m__2306 m__2414 mSortsB mSortsB_02 mDefPrime m__2342 mMulComm mLEAsym mDefLE mDefDiff mDefQuot
% 1.08/1.25
%------------------------------------------------------------------------------