TSTP Solution File: COM019+1 by SPASS---3.9

View Problem - 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  
%------------------------------------------------------------------------------