TSTP Solution File: NUM479+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM479+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:26:37 EDT 2022
% Result : Theorem 2.68s 2.88s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of clauses : 38 ( 16 unt; 7 nHn; 38 RR)
% Number of literals : 101 ( 0 equ; 66 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xl),
file('NUM479+2.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM479+2.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(skc1),
file('NUM479+2.p',unknown),
[] ).
cnf(6,axiom,
aNaturalNumber0(xn),
file('NUM479+2.p',unknown),
[] ).
cnf(8,axiom,
aNaturalNumber0(sdtsldt0(xm,xl)),
file('NUM479+2.p',unknown),
[] ).
cnf(12,axiom,
~ equal(xl,sz00),
file('NUM479+2.p',unknown),
[] ).
cnf(13,axiom,
equal(sdtasdt0(xl,skc1),xm),
file('NUM479+2.p',unknown),
[] ).
cnf(16,axiom,
equal(sdtasdt0(xl,sdtsldt0(xm,xl)),xm),
file('NUM479+2.p',unknown),
[] ).
cnf(25,axiom,
equal(sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),sdtasdt0(xn,xm)),
file('NUM479+2.p',unknown),
[] ).
cnf(29,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM479+2.p',unknown),
[] ).
cnf(35,axiom,
~ equal(sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl))),
file('NUM479+2.p',unknown),
[] ).
cnf(44,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM479+2.p',unknown),
[] ).
cnf(49,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('NUM479+2.p',unknown),
[] ).
cnf(67,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(v,w)
| ~ equal(w,sdtasdt0(v,u))
| equal(u,sdtsldt0(w,v))
| equal(v,sz00) ),
file('NUM479+2.p',unknown),
[] ).
cnf(70,plain,
~ equal(sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)),sdtasdt0(xn,xm)),
inference(rew,[status(thm),theory(equality)],[25,35]),
[iquote('0:Rew:25.0,35.0')] ).
cnf(72,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| equal(v,sz00)
| equal(w,sdtsldt0(u,v)) ),
inference(mrr,[status(thm)],[67,44]),
[iquote('0:MRR:67.3,44.4')] ).
cnf(2384,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(xl)
| equal(sdtasdt0(xl,sdtasdt0(skc1,u)),sdtasdt0(xm,u)) ),
inference(spr,[status(thm),theory(equality)],[13,49]),
[iquote('0:SpR:13.0,49.3')] ).
cnf(2391,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(xl,sdtasdt0(skc1,u)),sdtasdt0(xm,u)) ),
inference(ssi,[status(thm)],[2384,3,5]),
[iquote('0:SSi:2384.2,2384.1,3.0,5.0')] ).
cnf(3256,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(skc1)
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(u,xl),skc1) ),
inference(spl,[status(thm),theory(equality)],[13,72]),
[iquote('0:SpL:13.0,72.3')] ).
cnf(3257,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(xm,xl),sdtsldt0(u,xl)) ),
inference(spl,[status(thm),theory(equality)],[16,72]),
[iquote('0:SpL:16.0,72.3')] ).
cnf(3261,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(u,xl),skc1) ),
inference(ssi,[status(thm)],[3256,5,3]),
[iquote('0:SSi:3256.2,3256.1,5.0,3.0')] ).
cnf(3262,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(sdtsldt0(u,xl),skc1) ),
inference(mrr,[status(thm)],[3261,12]),
[iquote('0:MRR:3261.2,12.0')] ).
cnf(3286,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(xm,xl),skc1) ),
inference(rew,[status(thm),theory(equality)],[3262,3257]),
[iquote('0:Rew:3262.2,3257.5')] ).
cnf(3287,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(xm,xl),skc1) ),
inference(ssi,[status(thm)],[3286,8,3]),
[iquote('0:SSi:3286.2,3286.1,8.0,3.0')] ).
cnf(3288,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(sdtsldt0(xm,xl),skc1) ),
inference(mrr,[status(thm)],[3287,12]),
[iquote('0:MRR:3287.2,12.0')] ).
cnf(4004,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ equal(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xn,xm)) ),
inference(spl,[status(thm),theory(equality)],[49,70]),
[iquote('0:SpL:49.3,70.0')] ).
cnf(4005,plain,
~ equal(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xn,xm)),
inference(ssi,[status(thm)],[4004,3,6,8]),
[iquote('0:SSi:4004.2,4004.1,4004.0,3.0,6.0,8.0')] ).
cnf(4456,plain,
( ~ aNaturalNumber0(xm)
| equal(sdtsldt0(xm,xl),skc1) ),
inference(eqr,[status(thm),theory(equality)],[3288]),
[iquote('0:EqR:3288.1')] ).
cnf(4457,plain,
equal(sdtsldt0(xm,xl),skc1),
inference(ssi,[status(thm)],[4456,4]),
[iquote('0:SSi:4456.0,4.0')] ).
cnf(4479,plain,
~ equal(sdtasdt0(xl,sdtasdt0(xn,skc1)),sdtasdt0(xn,xm)),
inference(rew,[status(thm),theory(equality)],[4457,4005]),
[iquote('0:Rew:4457.0,4005.0')] ).
cnf(4885,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(u)
| equal(sdtasdt0(xl,sdtasdt0(u,skc1)),sdtasdt0(xm,u)) ),
inference(spr,[status(thm),theory(equality)],[29,2391]),
[iquote('0:SpR:29.2,2391.1')] ).
cnf(4907,plain,
( ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(u)
| equal(sdtasdt0(xl,sdtasdt0(u,skc1)),sdtasdt0(xm,u)) ),
inference(obv,[status(thm),theory(equality)],[4885]),
[iquote('0:Obv:4885.0')] ).
cnf(4908,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(xl,sdtasdt0(u,skc1)),sdtasdt0(xm,u)) ),
inference(ssi,[status(thm)],[4907,5]),
[iquote('0:SSi:4907.0,5.0')] ).
cnf(10858,plain,
( ~ aNaturalNumber0(xn)
| ~ equal(sdtasdt0(xn,xm),sdtasdt0(xm,xn)) ),
inference(spl,[status(thm),theory(equality)],[4908,4479]),
[iquote('0:SpL:4908.1,4479.0')] ).
cnf(10871,plain,
~ equal(sdtasdt0(xn,xm),sdtasdt0(xm,xn)),
inference(ssi,[status(thm)],[10858,6]),
[iquote('0:SSi:10858.0,6.0')] ).
cnf(11077,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ equal(sdtasdt0(xm,xn),sdtasdt0(xm,xn)) ),
inference(spl,[status(thm),theory(equality)],[29,10871]),
[iquote('0:SpL:29.2,10871.0')] ).
cnf(11080,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(obv,[status(thm),theory(equality)],[11077]),
[iquote('0:Obv:11077.2')] ).
cnf(11081,plain,
$false,
inference(ssi,[status(thm)],[11080,4,6]),
[iquote('0:SSi:11080.1,11080.0,4.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM479+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jul 7 23:08:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.68/2.88
% 2.68/2.88 SPASS V 3.9
% 2.68/2.88 SPASS beiseite: Proof found.
% 2.68/2.88 % SZS status Theorem
% 2.68/2.88 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.68/2.88 SPASS derived 7272 clauses, backtracked 1349 clauses, performed 22 splits and kept 3657 clauses.
% 2.68/2.88 SPASS allocated 105655 KBytes.
% 2.68/2.88 SPASS spent 0:00:02.12 on the problem.
% 2.68/2.88 0:00:00.03 for the input.
% 2.68/2.88 0:00:00.04 for the FLOTTER CNF translation.
% 2.68/2.88 0:00:00.07 for inferences.
% 2.68/2.88 0:00:00.03 for the backtracking.
% 2.68/2.88 0:00:01.87 for the reduction.
% 2.68/2.88
% 2.68/2.88
% 2.68/2.88 Here is a proof with depth 4, length 38 :
% 2.68/2.88 % SZS output start Refutation
% See solution above
% 2.68/2.88 Formulae used in the proof : m__1524 m__1524_04 m__1553 m__ mMulComm mDefDiv mMulAsso mDefQuot
% 2.68/2.88
%------------------------------------------------------------------------------