TSTP Solution File: NUM478+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM478+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 1.31s 1.51s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 34 ( 13 unt; 7 nHn; 34 RR)
% Number of literals : 94 ( 0 equ; 60 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('NUM478+2.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM478+2.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(skc1),
file('NUM478+2.p',unknown),
[] ).
cnf(6,axiom,
aNaturalNumber0(xn),
file('NUM478+2.p',unknown),
[] ).
cnf(8,axiom,
aNaturalNumber0(sdtsldt0(xm,xl)),
file('NUM478+2.p',unknown),
[] ).
cnf(12,axiom,
~ equal(xl,sz00),
file('NUM478+2.p',unknown),
[] ).
cnf(13,axiom,
equal(sdtasdt0(xl,skc1),xm),
file('NUM478+2.p',unknown),
[] ).
cnf(15,axiom,
equal(sdtasdt0(xl,sdtsldt0(xm,xl)),xm),
file('NUM478+2.p',unknown),
[] ).
cnf(24,axiom,
~ equal(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xn,xm)),
file('NUM478+2.p',unknown),
[] ).
cnf(29,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM478+2.p',unknown),
[] ).
cnf(43,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM478+2.p',unknown),
[] ).
cnf(48,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('NUM478+2.p',unknown),
[] ).
cnf(66,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(v,w)
| ~ equal(w,sdtasdt0(v,u))
| equal(u,sdtsldt0(w,v))
| equal(v,sz00) ),
file('NUM478+2.p',unknown),
[] ).
cnf(70,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| equal(v,sz00)
| equal(w,sdtsldt0(u,v)) ),
inference(mrr,[status(thm)],[66,43]),
[iquote('0:MRR:66.3,43.4')] ).
cnf(1073,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(xl)
| equal(sdtasdt0(xl,sdtasdt0(skc1,u)),sdtasdt0(xm,u)) ),
inference(spr,[status(thm),theory(equality)],[13,48]),
[iquote('0:SpR:13.0,48.3')] ).
cnf(1077,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(xl,sdtasdt0(skc1,u)),sdtasdt0(xm,u)) ),
inference(ssi,[status(thm)],[1073,3,5]),
[iquote('0:SSi:1073.2,1073.1,3.0,5.0')] ).
cnf(1191,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(u)
| equal(sdtasdt0(xl,sdtasdt0(u,skc1)),sdtasdt0(xm,u)) ),
inference(spr,[status(thm),theory(equality)],[29,1077]),
[iquote('0:SpR:29.2,1077.1')] ).
cnf(1204,plain,
( ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(u)
| equal(sdtasdt0(xl,sdtasdt0(u,skc1)),sdtasdt0(xm,u)) ),
inference(obv,[status(thm),theory(equality)],[1191]),
[iquote('0:Obv:1191.0')] ).
cnf(1205,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(xl,sdtasdt0(u,skc1)),sdtasdt0(xm,u)) ),
inference(ssi,[status(thm)],[1204,5]),
[iquote('0:SSi:1204.0,5.0')] ).
cnf(2237,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(skc1)
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(u,xl),skc1) ),
inference(spl,[status(thm),theory(equality)],[13,70]),
[iquote('0:SpL:13.0,70.3')] ).
cnf(2238,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)],[15,70]),
[iquote('0:SpL:15.0,70.3')] ).
cnf(2255,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(u,xl),skc1) ),
inference(ssi,[status(thm)],[2237,5,3]),
[iquote('0:SSi:2237.2,2237.1,5.0,3.0')] ).
cnf(2256,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(sdtsldt0(u,xl),skc1) ),
inference(mrr,[status(thm)],[2255,12]),
[iquote('0:MRR:2255.2,12.0')] ).
cnf(2265,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)],[2256,2238]),
[iquote('0:Rew:2256.2,2238.5')] ).
cnf(2266,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(xm,xl),skc1) ),
inference(ssi,[status(thm)],[2265,8,3]),
[iquote('0:SSi:2265.2,2265.1,8.0,3.0')] ).
cnf(2267,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(sdtsldt0(xm,xl),skc1) ),
inference(mrr,[status(thm)],[2266,12]),
[iquote('0:MRR:2266.2,12.0')] ).
cnf(4027,plain,
( ~ aNaturalNumber0(xm)
| equal(sdtsldt0(xm,xl),skc1) ),
inference(eqr,[status(thm),theory(equality)],[2267]),
[iquote('0:EqR:2267.1')] ).
cnf(4028,plain,
equal(sdtsldt0(xm,xl),skc1),
inference(ssi,[status(thm)],[4027,4]),
[iquote('0:SSi:4027.0,4.0')] ).
cnf(4038,plain,
~ equal(sdtasdt0(xl,sdtasdt0(xn,skc1)),sdtasdt0(xn,xm)),
inference(rew,[status(thm),theory(equality)],[4028,24]),
[iquote('0:Rew:4028.0,24.0')] ).
cnf(5544,plain,
( ~ aNaturalNumber0(xn)
| ~ equal(sdtasdt0(xn,xm),sdtasdt0(xm,xn)) ),
inference(spl,[status(thm),theory(equality)],[1205,4038]),
[iquote('0:SpL:1205.1,4038.0')] ).
cnf(5555,plain,
~ equal(sdtasdt0(xn,xm),sdtasdt0(xm,xn)),
inference(ssi,[status(thm)],[5544,6]),
[iquote('0:SSi:5544.0,6.0')] ).
cnf(5755,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ equal(sdtasdt0(xm,xn),sdtasdt0(xm,xn)) ),
inference(spl,[status(thm),theory(equality)],[29,5555]),
[iquote('0:SpL:29.2,5555.0')] ).
cnf(5758,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(obv,[status(thm),theory(equality)],[5755]),
[iquote('0:Obv:5755.2')] ).
cnf(5759,plain,
$false,
inference(ssi,[status(thm)],[5758,4,6]),
[iquote('0:SSi:5758.1,5758.0,4.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM478+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.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 : Tue Jul 5 10:21:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.31/1.51
% 1.31/1.51 SPASS V 3.9
% 1.31/1.51 SPASS beiseite: Proof found.
% 1.31/1.51 % SZS status Theorem
% 1.31/1.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.31/1.51 SPASS derived 3501 clauses, backtracked 357 clauses, performed 9 splits and kept 1464 clauses.
% 1.31/1.51 SPASS allocated 102130 KBytes.
% 1.31/1.51 SPASS spent 0:00:01.04 on the problem.
% 1.31/1.51 0:00:00.04 for the input.
% 1.31/1.51 0:00:00.04 for the FLOTTER CNF translation.
% 1.31/1.51 0:00:00.04 for inferences.
% 1.31/1.51 0:00:00.01 for the backtracking.
% 1.31/1.51 0:00:00.87 for the reduction.
% 1.31/1.51
% 1.31/1.51
% 1.31/1.51 Here is a proof with depth 4, length 34 :
% 1.31/1.51 % SZS output start Refutation
% See solution above
% 1.31/1.51 Formulae used in the proof : m__1524 m__1524_04 m__1553 m__ mMulComm mDefDiv mMulAsso mDefQuot
% 1.31/1.51
%------------------------------------------------------------------------------