TSTP Solution File: COM021+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM021+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 : Fri Jul 15 01:44:21 EDT 2022
% Result : Theorem 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 36 ( 16 unt; 4 nHn; 36 RR)
% Number of literals : 100 ( 0 equ; 74 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aRewritingSystem0(xR),
file('COM021+1.p',unknown),
[] ).
cnf(2,axiom,
isLocallyConfluent0(xR),
file('COM021+1.p',unknown),
[] ).
cnf(3,axiom,
isTerminating0(xR),
file('COM021+1.p',unknown),
[] ).
cnf(5,axiom,
aElement0(xb),
file('COM021+1.p',unknown),
[] ).
cnf(9,axiom,
aElement0(xw),
file('COM021+1.p',unknown),
[] ).
cnf(10,axiom,
aElement0(xx),
file('COM021+1.p',unknown),
[] ).
cnf(28,axiom,
aNormalFormOfIn0(xd,xw,xR),
file('COM021+1.p',unknown),
[] ).
cnf(29,axiom,
sdtmndtasgtdt0(xb,xR,xx),
file('COM021+1.p',unknown),
[] ).
cnf(30,axiom,
sdtmndtasgtdt0(xd,xR,xx),
file('COM021+1.p',unknown),
[] ).
cnf(31,axiom,
~ sdtmndtasgtdt0(xb,xR,xd),
file('COM021+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aNormalFormOfIn0(w,v,u)
| aElement0(w) ),
file('COM021+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aNormalFormOfIn0(w,v,u)
| ~ aReductOfIn0(x,w,u) ),
file('COM021+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ equal(w,u)
| sdtmndtasgtdt0(w,v,u) ),
file('COM021+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ sdtmndtasgtdt0(w,v,u)
| equal(w,u)
| sdtmndtplgtdt0(w,v,u) ),
file('COM021+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ sdtmndtplgtdt0(w,v,u)
| aReductOfIn0(u,w,v)
| aReductOfIn0(skf14(u,v,w),w,v) ),
file('COM021+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aRewritingSystem0(w)
| ~ aElement0(x)
| ~ sdtmndtasgtdt0(x,w,v)
| ~ sdtmndtasgtdt0(v,w,u)
| sdtmndtasgtdt0(x,w,u) ),
file('COM021+1.p',unknown),
[] ).
cnf(72,plain,
( ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ aElement0(xd)
| ~ sdtmndtasgtdt0(u,xR,xd)
| ~ sdtmndtasgtdt0(xb,xR,u) ),
inference(res,[status(thm),theory(equality)],[56,31]),
[iquote('0:Res:56.6,31.0')] ).
cnf(76,plain,
( ~ aElement0(u)
| ~ aElement0(xd)
| ~ sdtmndtasgtdt0(u,xR,xd)
| ~ sdtmndtasgtdt0(xb,xR,u) ),
inference(mrr,[status(thm)],[72,5,1]),
[iquote('0:MRR:72.0,72.1,5.0,1.0')] ).
cnf(109,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(xw)
| aElement0(xd) ),
inference(res,[status(thm),theory(equality)],[28,42]),
[iquote('0:Res:28.0,42.2')] ).
cnf(110,plain,
aElement0(xd),
inference(ssi,[status(thm)],[109,9,3,2,1]),
[iquote('0:SSi:109.1,109.0,9.0,3.0,2.0,1.0')] ).
cnf(113,plain,
( ~ aElement0(u)
| ~ sdtmndtasgtdt0(u,xR,xd)
| ~ sdtmndtasgtdt0(xb,xR,u) ),
inference(mrr,[status(thm)],[76,110]),
[iquote('0:MRR:76.1,110.0')] ).
cnf(128,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(xw)
| ~ aReductOfIn0(u,xd,xR) ),
inference(res,[status(thm),theory(equality)],[28,45]),
[iquote('0:Res:28.0,45.2')] ).
cnf(130,plain,
~ aReductOfIn0(u,xd,xR),
inference(ssi,[status(thm)],[128,9,3,2,1]),
[iquote('0:SSi:128.1,128.0,9.0,3.0,2.0,1.0')] ).
cnf(136,plain,
( ~ aElement0(xd)
| ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ aElement0(u)
| ~ equal(u,xd)
| ~ sdtmndtasgtdt0(xb,xR,u) ),
inference(res,[status(thm),theory(equality)],[46,113]),
[iquote('0:Res:46.4,113.1')] ).
cnf(138,plain,
( ~ aElement0(xd)
| ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ equal(u,xd)
| ~ sdtmndtasgtdt0(xb,xR,u) ),
inference(obv,[status(thm),theory(equality)],[136]),
[iquote('0:Obv:136.2')] ).
cnf(139,plain,
( ~ aElement0(u)
| ~ equal(u,xd)
| ~ sdtmndtasgtdt0(xb,xR,u) ),
inference(ssi,[status(thm)],[138,3,2,1,110]),
[iquote('0:SSi:138.1,138.0,3.0,2.0,1.0,110.0')] ).
cnf(140,plain,
( ~ aElement0(xx)
| ~ equal(xx,xd) ),
inference(res,[status(thm),theory(equality)],[29,139]),
[iquote('0:Res:29.0,139.2')] ).
cnf(143,plain,
~ equal(xx,xd),
inference(ssi,[status(thm)],[140,10]),
[iquote('0:SSi:140.0,10.0')] ).
cnf(207,plain,
( ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xd)
| equal(xx,xd)
| sdtmndtplgtdt0(xd,xR,xx) ),
inference(res,[status(thm),theory(equality)],[30,52]),
[iquote('0:Res:30.0,52.3')] ).
cnf(219,plain,
( equal(xx,xd)
| sdtmndtplgtdt0(xd,xR,xx) ),
inference(ssi,[status(thm)],[207,110,3,2,1,10]),
[iquote('0:SSi:207.2,207.1,207.0,110.0,3.0,2.0,1.0,10.0')] ).
cnf(220,plain,
sdtmndtplgtdt0(xd,xR,xx),
inference(mrr,[status(thm)],[219,143]),
[iquote('0:MRR:219.0,143.0')] ).
cnf(339,plain,
( ~ aElement0(u)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xd)
| ~ sdtmndtplgtdt0(xd,xR,u)
| aReductOfIn0(u,xd,xR) ),
inference(res,[status(thm),theory(equality)],[55,130]),
[iquote('0:Res:55.5,130.0')] ).
cnf(342,plain,
( ~ aElement0(u)
| ~ sdtmndtplgtdt0(xd,xR,u)
| aReductOfIn0(u,xd,xR) ),
inference(ssi,[status(thm)],[339,110,3,2,1]),
[iquote('0:SSi:339.2,339.1,110.0,3.0,2.0,1.0')] ).
cnf(343,plain,
( ~ aElement0(u)
| ~ sdtmndtplgtdt0(xd,xR,u) ),
inference(mrr,[status(thm)],[342,130]),
[iquote('0:MRR:342.2,130.0')] ).
cnf(533,plain,
~ aElement0(xx),
inference(res,[status(thm),theory(equality)],[220,343]),
[iquote('0:Res:220.0,343.1')] ).
cnf(536,plain,
$false,
inference(ssi,[status(thm)],[533,10]),
[iquote('0:SSi:533.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : COM021+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 18:26:44 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.53
% 0.21/0.53 SPASS V 3.9
% 0.21/0.53 SPASS beiseite: Proof found.
% 0.21/0.53 % SZS status Theorem
% 0.21/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.53 SPASS derived 308 clauses, backtracked 102 clauses, performed 7 splits and kept 327 clauses.
% 0.21/0.53 SPASS allocated 104602 KBytes.
% 0.21/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.21/0.53 0:00:00.03 for the input.
% 0.21/0.53 0:00:00.08 for the FLOTTER CNF translation.
% 0.21/0.53 0:00:00.00 for inferences.
% 0.21/0.53 0:00:00.00 for the backtracking.
% 0.21/0.53 0:00:00.03 for the reduction.
% 0.21/0.53
% 0.21/0.53
% 0.21/0.53 Here is a proof with depth 3, length 36 :
% 0.21/0.53 % SZS output start Refutation
% See solution above
% 0.21/0.53 Formulae used in the proof : m__656 m__656_01 m__731 m__799 m__850 m__818 m__ mNFRDef mTCRDef mTCDef mTCRTrans
% 0.21/0.53
%------------------------------------------------------------------------------