TSTP Solution File: NUM460+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM460+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:26:25 EDT 2022
% Result : Theorem 38.16s 38.37s
% Output : Refutation 38.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 47 ( 12 unt; 0 nHn; 47 RR)
% Number of literals : 136 ( 0 equ; 100 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xm),
file('NUM460+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xn),
file('NUM460+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xl),
file('NUM460+1.p',unknown),
[] ).
cnf(6,axiom,
sdtlseqdt0(xm,xn),
file('NUM460+1.p',unknown),
[] ).
cnf(7,axiom,
sdtlseqdt0(xn,xl),
file('NUM460+1.p',unknown),
[] ).
cnf(8,axiom,
~ sdtlseqdt0(xm,xl),
file('NUM460+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM460+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM460+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM460+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM460+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM460+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| equal(sdtpldt0(v,w),u) ),
file('NUM460+1.p',unknown),
[] ).
cnf(41,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ equal(u,sdtmndt0(xl,xn))
| equal(sdtpldt0(xn,u),xl) ),
inference(res,[status(thm),theory(equality)],[7,33]),
[iquote('0:Res:7.0,33.2')] ).
cnf(42,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ equal(u,sdtmndt0(xl,xn))
| aNaturalNumber0(u) ),
inference(res,[status(thm),theory(equality)],[7,28]),
[iquote('0:Res:7.0,28.2')] ).
cnf(46,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ equal(u,sdtmndt0(xn,xm))
| equal(sdtpldt0(xm,u),xn) ),
inference(res,[status(thm),theory(equality)],[6,33]),
[iquote('0:Res:6.0,33.2')] ).
cnf(47,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ equal(u,sdtmndt0(xn,xm))
| aNaturalNumber0(u) ),
inference(res,[status(thm),theory(equality)],[6,28]),
[iquote('0:Res:6.0,28.2')] ).
cnf(50,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ equal(sdtpldt0(xm,u),xl) ),
inference(res,[status(thm),theory(equality)],[27,8]),
[iquote('0:Res:27.4,8.0')] ).
cnf(55,plain,
( ~ equal(u,sdtmndt0(xl,xn))
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[42,4,5]),
[iquote('0:MRR:42.0,42.1,4.0,5.0')] ).
cnf(56,plain,
( ~ equal(u,sdtmndt0(xn,xm))
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[47,3,4]),
[iquote('0:MRR:47.0,47.1,3.0,4.0')] ).
cnf(57,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(xm,u),xl) ),
inference(mrr,[status(thm)],[50,3,5]),
[iquote('0:MRR:50.1,50.2,3.0,5.0')] ).
cnf(58,plain,
( ~ equal(u,sdtmndt0(xl,xn))
| equal(sdtpldt0(xn,u),xl) ),
inference(mrr,[status(thm)],[41,4,5]),
[iquote('0:MRR:41.0,41.1,4.0,5.0')] ).
cnf(59,plain,
( ~ equal(u,sdtmndt0(xn,xm))
| equal(sdtpldt0(xm,u),xn) ),
inference(mrr,[status(thm)],[46,3,4]),
[iquote('0:MRR:46.0,46.1,3.0,4.0')] ).
cnf(65,plain,
aNaturalNumber0(sdtmndt0(xn,xm)),
inference(eqr,[status(thm),theory(equality)],[56]),
[iquote('0:EqR:56.0')] ).
cnf(68,plain,
aNaturalNumber0(sdtmndt0(xl,xn)),
inference(eqr,[status(thm),theory(equality)],[55]),
[iquote('0:EqR:55.0')] ).
cnf(88,plain,
equal(sdtpldt0(xm,sdtmndt0(xn,xm)),xn),
inference(eqr,[status(thm),theory(equality)],[59]),
[iquote('0:EqR:59.0')] ).
cnf(92,plain,
equal(sdtpldt0(xn,sdtmndt0(xl,xn)),xl),
inference(eqr,[status(thm),theory(equality)],[58]),
[iquote('0:EqR:58.0')] ).
cnf(287,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ aNaturalNumber0(sdtpldt0(w,v))
| ~ aNaturalNumber0(u)
| equal(sdtpldt0(u,sdtpldt0(w,v)),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(spr,[status(thm),theory(equality)],[32,20]),
[iquote('0:SpR:32.3,20.2')] ).
cnf(295,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| equal(sdtpldt0(sdtpldt0(v,u),w),sdtpldt0(u,sdtpldt0(v,w))) ),
inference(spr,[status(thm),theory(equality)],[20,32]),
[iquote('0:SpR:20.2,32.3')] ).
cnf(296,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ~ aNaturalNumber0(xm)
| equal(sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),u)),sdtpldt0(xn,u)) ),
inference(spr,[status(thm),theory(equality)],[88,32]),
[iquote('0:SpR:88.0,32.3')] ).
cnf(308,plain,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),u)),sdtpldt0(xn,u)) ),
inference(ssi,[status(thm)],[296,3,65]),
[iquote('0:SSi:296.2,296.1,3.0,65.0')] ).
cnf(314,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtpldt0(sdtpldt0(v,w),u),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(obv,[status(thm),theory(equality)],[295]),
[iquote('0:Obv:295.1')] ).
cnf(315,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtpldt0(v,sdtpldt0(w,u)),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[32,314]),
[iquote('0:Rew:32.3,314.3')] ).
cnf(320,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(sdtpldt0(v,u))
| ~ aNaturalNumber0(w)
| equal(sdtpldt0(w,sdtpldt0(v,u)),sdtpldt0(v,sdtpldt0(u,w))) ),
inference(obv,[status(thm),theory(equality)],[287]),
[iquote('0:Obv:287.0')] ).
cnf(321,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtpldt0(w,sdtpldt0(v,u)),sdtpldt0(v,sdtpldt0(u,w))) ),
inference(ssi,[status(thm)],[320,18]),
[iquote('0:SSi:320.2,18.2')] ).
cnf(4031,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(v,u))
| ~ equal(sdtpldt0(v,sdtpldt0(xm,u)),xl) ),
inference(spl,[status(thm),theory(equality)],[315,57]),
[iquote('0:SpL:315.3,57.1')] ).
cnf(4057,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(sdtpldt0(v,sdtpldt0(xm,u)),xl) ),
inference(ssi,[status(thm)],[4031,18,3]),
[iquote('0:SSi:4031.3,4031.2,18.0,3.2')] ).
cnf(4370,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| equal(sdtpldt0(sdtmndt0(xn,xm),sdtpldt0(u,xm)),sdtpldt0(u,xn)) ),
inference(spr,[status(thm),theory(equality)],[88,321]),
[iquote('0:SpR:88.0,321.3')] ).
cnf(4424,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| equal(sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),u)),sdtpldt0(u,xn)) ),
inference(rew,[status(thm),theory(equality)],[321,4370]),
[iquote('0:Rew:321.3,4370.3')] ).
cnf(4425,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| equal(sdtpldt0(xn,u),sdtpldt0(u,xn)) ),
inference(rew,[status(thm),theory(equality)],[308,4424]),
[iquote('0:Rew:308.1,4424.3')] ).
cnf(4426,plain,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(xn,u),sdtpldt0(u,xn)) ),
inference(ssi,[status(thm)],[4425,65,3]),
[iquote('0:SSi:4425.2,4425.0,65.0,3.0')] ).
cnf(22246,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(u,xn),xl) ),
inference(spl,[status(thm),theory(equality)],[88,4057]),
[iquote('0:SpL:88.0,4057.2')] ).
cnf(22275,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(u,xn),xl) ),
inference(ssi,[status(thm)],[22246,65]),
[iquote('0:SSi:22246.0,65.0')] ).
cnf(23441,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(xn,u),xl) ),
inference(spl,[status(thm),theory(equality)],[4426,22275]),
[iquote('0:SpL:4426.1,22275.1')] ).
cnf(23449,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(xn,u),xl) ),
inference(obv,[status(thm),theory(equality)],[23441]),
[iquote('0:Obv:23441.0')] ).
cnf(23502,plain,
( ~ aNaturalNumber0(sdtmndt0(xl,xn))
| ~ equal(xl,xl) ),
inference(spl,[status(thm),theory(equality)],[92,23449]),
[iquote('0:SpL:92.0,23449.1')] ).
cnf(23510,plain,
~ aNaturalNumber0(sdtmndt0(xl,xn)),
inference(obv,[status(thm),theory(equality)],[23502]),
[iquote('0:Obv:23502.1')] ).
cnf(23511,plain,
$false,
inference(ssi,[status(thm)],[23510,68]),
[iquote('0:SSi:23510.0,68.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM460+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 02:09:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 38.16/38.37
% 38.16/38.37 SPASS V 3.9
% 38.16/38.37 SPASS beiseite: Proof found.
% 38.16/38.37 % SZS status Theorem
% 38.16/38.37 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.16/38.37 SPASS derived 12704 clauses, backtracked 0 clauses, performed 0 splits and kept 3801 clauses.
% 38.16/38.37 SPASS allocated 125535 KBytes.
% 38.16/38.37 SPASS spent 0:0:32.47 on the problem.
% 38.16/38.37 0:00:00.04 for the input.
% 38.16/38.37 0:00:00.03 for the FLOTTER CNF translation.
% 38.16/38.37 0:00:00.17 for inferences.
% 38.16/38.37 0:00:00.00 for the backtracking.
% 38.16/38.37 0:0:32.18 for the reduction.
% 38.16/38.37
% 38.16/38.37
% 38.16/38.37 Here is a proof with depth 5, length 47 :
% 38.16/38.37 % SZS output start Refutation
% See solution above
% 38.16/38.37 Formulae used in the proof : m__773 m__ mSortsB mAddComm mDefLE mDefDiff mAddAsso
% 38.16/38.37
%------------------------------------------------------------------------------