TSTP Solution File: COM019+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM019+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 01:44:20 EDT 2022
% Result : Theorem 190.79s 190.96s
% Output : Refutation 190.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of clauses : 58 ( 20 unt; 5 nHn; 58 RR)
% Number of literals : 191 ( 0 equ; 133 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aRewritingSystem0(xR),
file('COM019+1.p',unknown),
[] ).
cnf(2,axiom,
isLocallyConfluent0(xR),
file('COM019+1.p',unknown),
[] ).
cnf(3,axiom,
isTerminating0(xR),
file('COM019+1.p',unknown),
[] ).
cnf(4,axiom,
aElement0(xa),
file('COM019+1.p',unknown),
[] ).
cnf(5,axiom,
aElement0(xb),
file('COM019+1.p',unknown),
[] ).
cnf(7,axiom,
aElement0(xu),
file('COM019+1.p',unknown),
[] ).
cnf(9,axiom,
aElement0(xw),
file('COM019+1.p',unknown),
[] ).
cnf(18,axiom,
aElement0(skf31(u,v)),
file('COM019+1.p',unknown),
[] ).
cnf(21,axiom,
aReductOfIn0(xu,xa,xR),
file('COM019+1.p',unknown),
[] ).
cnf(22,axiom,
sdtmndtasgtdt0(xu,xR,xb),
file('COM019+1.p',unknown),
[] ).
cnf(25,axiom,
sdtmndtasgtdt0(xu,xR,xw),
file('COM019+1.p',unknown),
[] ).
cnf(27,axiom,
aNormalFormOfIn0(xd,xw,xR),
file('COM019+1.p',unknown),
[] ).
cnf(28,axiom,
~ sdtmndtasgtdt0(xb,xR,xd),
file('COM019+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aReductOfIn0(w,v,u)
| aElement0(w) ),
file('COM019+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aNormalFormOfIn0(w,v,u)
| aElement0(w) ),
file('COM019+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aNormalFormOfIn0(w,v,u)
| sdtmndtasgtdt0(v,u,w) ),
file('COM019+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aNormalFormOfIn0(w,v,u)
| ~ aReductOfIn0(x,w,u) ),
file('COM019+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ aReductOfIn0(w,u,v)
| sdtmndtplgtdt0(u,v,w) ),
file('COM019+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ isTerminating0(u)
| ~ sdtmndtplgtdt0(w,u,v)
| iLess0(v,w) ),
file('COM019+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ sdtmndtasgtdt0(w,v,u)
| equal(w,u)
| sdtmndtplgtdt0(w,v,u) ),
file('COM019+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ sdtmndtplgtdt0(w,v,u)
| aReductOfIn0(u,w,v)
| aReductOfIn0(skf14(u,v,w),w,v) ),
file('COM019+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aRewritingSystem0(w)
| ~ aElement0(x)
| ~ sdtmndtasgtdt0(x,w,v)
| ~ sdtmndtasgtdt0(v,w,u)
| sdtmndtasgtdt0(x,w,u) ),
file('COM019+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ iLess0(w,xa)
| ~ sdtmndtasgtdt0(w,xR,u)
| ~ sdtmndtasgtdt0(w,xR,v)
| sdtmndtasgtdt0(u,xR,skf31(u,v)) ),
file('COM019+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ iLess0(w,xa)
| ~ sdtmndtasgtdt0(w,xR,u)
| ~ sdtmndtasgtdt0(w,xR,v)
| sdtmndtasgtdt0(v,xR,skf31(u,v)) ),
file('COM019+1.p',unknown),
[] ).
cnf(62,plain,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aReductOfIn0(w,v,u)
| sdtmndtplgtdt0(v,u,w) ),
inference(mrr,[status(thm)],[44,38]),
[iquote('0:MRR:44.2,38.3')] ).
cnf(105,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(xw)
| aElement0(xd) ),
inference(res,[status(thm),theory(equality)],[27,39]),
[iquote('0:Res:27.0,39.2')] ).
cnf(106,plain,
aElement0(xd),
inference(ssi,[status(thm)],[105,9,3,2,1]),
[iquote('0:SSi:105.1,105.0,9.0,3.0,2.0,1.0')] ).
cnf(120,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(xw)
| sdtmndtasgtdt0(xw,xR,xd) ),
inference(res,[status(thm),theory(equality)],[27,40]),
[iquote('0:Res:27.0,40.2')] ).
cnf(122,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(ssi,[status(thm)],[120,9,3,2,1]),
[iquote('0:SSi:120.1,120.0,9.0,3.0,2.0,1.0')] ).
cnf(126,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(xw)
| ~ aReductOfIn0(u,xd,xR) ),
inference(res,[status(thm),theory(equality)],[27,42]),
[iquote('0:Res:27.0,42.2')] ).
cnf(128,plain,
~ aReductOfIn0(u,xd,xR),
inference(ssi,[status(thm)],[126,9,3,2,1]),
[iquote('0:SSi:126.1,126.0,9.0,3.0,2.0,1.0')] ).
cnf(195,plain,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aRewritingSystem0(u)
| ~ aElement0(w)
| ~ aElement0(v)
| ~ isTerminating0(u)
| ~ aReductOfIn0(w,v,u)
| iLess0(w,v) ),
inference(res,[status(thm),theory(equality)],[62,46]),
[iquote('0:Res:62.3,46.4')] ).
cnf(198,plain,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ isTerminating0(u)
| ~ aReductOfIn0(v,w,u)
| iLess0(v,w) ),
inference(obv,[status(thm),theory(equality)],[195]),
[iquote('0:Obv:195.1')] ).
cnf(199,plain,
( ~ aRewritingSystem0(u)
| ~ aElement0(v)
| ~ isTerminating0(u)
| ~ aReductOfIn0(w,v,u)
| iLess0(w,v) ),
inference(mrr,[status(thm)],[198,38]),
[iquote('0:MRR:198.1,38.3')] ).
cnf(316,plain,
( ~ aElement0(u)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xd)
| ~ sdtmndtplgtdt0(xd,xR,u)
| aReductOfIn0(u,xd,xR) ),
inference(res,[status(thm),theory(equality)],[52,128]),
[iquote('0:Res:52.5,128.0')] ).
cnf(320,plain,
( ~ aElement0(u)
| ~ sdtmndtplgtdt0(xd,xR,u)
| aReductOfIn0(u,xd,xR) ),
inference(ssi,[status(thm)],[316,106,3,2,1]),
[iquote('0:SSi:316.2,316.1,106.0,3.0,2.0,1.0')] ).
cnf(321,plain,
( ~ aElement0(u)
| ~ sdtmndtplgtdt0(xd,xR,u) ),
inference(mrr,[status(thm)],[320,128]),
[iquote('0:MRR:320.2,128.0')] ).
cnf(536,plain,
( ~ aElement0(xb)
| ~ aElement0(u)
| ~ aElement0(xu)
| ~ iLess0(xu,xa)
| ~ sdtmndtasgtdt0(xu,xR,u)
| sdtmndtasgtdt0(u,xR,skf31(xb,u)) ),
inference(res,[status(thm),theory(equality)],[22,57]),
[iquote('0:Res:22.0,57.4')] ).
cnf(544,plain,
( ~ aElement0(u)
| ~ iLess0(xu,xa)
| ~ sdtmndtasgtdt0(xu,xR,u)
| sdtmndtasgtdt0(u,xR,skf31(xb,u)) ),
inference(ssi,[status(thm)],[536,7,5]),
[iquote('0:SSi:536.2,536.0,7.0,5.0')] ).
cnf(599,plain,
( ~ aElement0(xb)
| ~ aElement0(u)
| ~ aElement0(xu)
| ~ iLess0(xu,xa)
| ~ sdtmndtasgtdt0(xu,xR,u)
| sdtmndtasgtdt0(xb,xR,skf31(xb,u)) ),
inference(res,[status(thm),theory(equality)],[22,56]),
[iquote('0:Res:22.0,56.4')] ).
cnf(610,plain,
( ~ aElement0(u)
| ~ iLess0(xu,xa)
| ~ sdtmndtasgtdt0(xu,xR,u)
| sdtmndtasgtdt0(xb,xR,skf31(xb,u)) ),
inference(ssi,[status(thm)],[599,7,5]),
[iquote('0:SSi:599.2,599.0,7.0,5.0')] ).
cnf(838,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(xa)
| ~ isTerminating0(xR)
| iLess0(xu,xa) ),
inference(res,[status(thm),theory(equality)],[21,199]),
[iquote('0:Res:21.0,199.3')] ).
cnf(842,plain,
iLess0(xu,xa),
inference(ssi,[status(thm)],[838,3,2,1,4]),
[iquote('0:SSi:838.2,838.1,838.0,3.0,2.0,1.0,4.0,3.0,2.0,1.0')] ).
cnf(843,plain,
( ~ aElement0(u)
| ~ sdtmndtasgtdt0(xu,xR,u)
| sdtmndtasgtdt0(u,xR,skf31(xb,u)) ),
inference(mrr,[status(thm)],[544,842]),
[iquote('0:MRR:544.1,842.0')] ).
cnf(848,plain,
( ~ aElement0(u)
| ~ sdtmndtasgtdt0(xu,xR,u)
| sdtmndtasgtdt0(xb,xR,skf31(xb,u)) ),
inference(mrr,[status(thm)],[610,842]),
[iquote('0:MRR:610.1,842.0')] ).
cnf(942,plain,
( ~ aElement0(u)
| ~ aElement0(skf31(xb,u))
| ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ sdtmndtasgtdt0(xu,xR,u)
| equal(skf31(xb,u),u)
| sdtmndtplgtdt0(u,xR,skf31(xb,u)) ),
inference(res,[status(thm),theory(equality)],[843,49]),
[iquote('0:Res:843.2,49.3')] ).
cnf(945,plain,
( ~ aElement0(skf31(xb,u))
| ~ aRewritingSystem0(xR)
| ~ aElement0(u)
| ~ sdtmndtasgtdt0(xu,xR,u)
| equal(skf31(xb,u),u)
| sdtmndtplgtdt0(u,xR,skf31(xb,u)) ),
inference(obv,[status(thm),theory(equality)],[942]),
[iquote('0:Obv:942.0')] ).
cnf(946,plain,
( ~ aElement0(u)
| ~ sdtmndtasgtdt0(xu,xR,u)
| equal(skf31(xb,u),u)
| sdtmndtplgtdt0(u,xR,skf31(xb,u)) ),
inference(ssi,[status(thm)],[945,3,2,1,18,5]),
[iquote('0:SSi:945.1,945.0,3.0,2.0,1.0,18.0,5.0')] ).
cnf(78918,plain,
( ~ aElement0(xd)
| ~ aElement0(skf31(xb,xd))
| ~ sdtmndtasgtdt0(xu,xR,xd)
| equal(skf31(xb,xd),xd) ),
inference(res,[status(thm),theory(equality)],[946,321]),
[iquote('0:Res:946.3,321.1')] ).
cnf(78938,plain,
( ~ sdtmndtasgtdt0(xu,xR,xd)
| equal(skf31(xb,xd),xd) ),
inference(ssi,[status(thm)],[78918,18,5,106]),
[iquote('0:SSi:78918.1,78918.0,18.0,5.0,106.0,106.0')] ).
cnf(81992,plain,
( ~ aElement0(u)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xu)
| ~ sdtmndtasgtdt0(xw,xR,u)
| sdtmndtasgtdt0(xu,xR,u) ),
inference(res,[status(thm),theory(equality)],[25,53]),
[iquote('0:Res:25.0,53.4')] ).
cnf(81996,plain,
( ~ aElement0(u)
| ~ sdtmndtasgtdt0(xw,xR,u)
| sdtmndtasgtdt0(xu,xR,u) ),
inference(ssi,[status(thm)],[81992,7,3,2,1,9]),
[iquote('0:SSi:81992.3,81992.2,81992.1,7.0,3.0,2.0,1.0,9.0')] ).
cnf(84588,plain,
( ~ aElement0(xd)
| sdtmndtasgtdt0(xu,xR,xd) ),
inference(res,[status(thm),theory(equality)],[122,81996]),
[iquote('0:Res:122.0,81996.1')] ).
cnf(84595,plain,
sdtmndtasgtdt0(xu,xR,xd),
inference(ssi,[status(thm)],[84588,106]),
[iquote('0:SSi:84588.0,106.0')] ).
cnf(84596,plain,
equal(skf31(xb,xd),xd),
inference(mrr,[status(thm)],[78938,84595]),
[iquote('0:MRR:78938.0,84595.0')] ).
cnf(84675,plain,
( ~ aElement0(xd)
| ~ sdtmndtasgtdt0(xu,xR,xd)
| sdtmndtasgtdt0(xb,xR,xd) ),
inference(spr,[status(thm),theory(equality)],[84596,848]),
[iquote('0:SpR:84596.0,848.2')] ).
cnf(84677,plain,
( ~ sdtmndtasgtdt0(xu,xR,xd)
| sdtmndtasgtdt0(xb,xR,xd) ),
inference(ssi,[status(thm)],[84675,106]),
[iquote('0:SSi:84675.0,106.0')] ).
cnf(84678,plain,
$false,
inference(mrr,[status(thm)],[84677,84595,28]),
[iquote('0:MRR:84677.0,84677.1,84595.0,28.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : COM019+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 20:08:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 190.79/190.96
% 190.79/190.96 SPASS V 3.9
% 190.79/190.96 SPASS beiseite: Proof found.
% 190.79/190.96 % SZS status Theorem
% 190.79/190.96 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 190.79/190.96 SPASS derived 57042 clauses, backtracked 27926 clauses, performed 218 splits and kept 48122 clauses.
% 190.79/190.96 SPASS allocated 169764 KBytes.
% 190.79/190.96 SPASS spent 0:1:22.27 on the problem.
% 190.79/190.96 0:00:00.04 for the input.
% 190.79/190.96 0:00:00.08 for the FLOTTER CNF translation.
% 190.79/190.96 0:00:00.82 for inferences.
% 190.79/190.96 0:00:04.40 for the backtracking.
% 190.79/190.96 0:1:16.39 for the reduction.
% 190.79/190.96
% 190.79/190.96
% 190.79/190.96 Here is a proof with depth 4, length 58 :
% 190.79/190.96 % SZS output start Refutation
% See solution above
% 190.79/190.96 Formulae used in the proof : m__656 m__656_01 m__731 m__755 m__799 m__715 m__818 m__ mReduct mNFRDef mTCDef mTermin mTCRDef mTCRTrans
% 190.79/190.96
%------------------------------------------------------------------------------