TSTP Solution File: COM020+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COM020+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 1.50s 1.69s
% Output   : Refutation 1.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   21
% Syntax   : Number of clauses     :   47 (  18 unt;   0 nHn;  47 RR)
%            Number of literals    :  146 (   0 equ; 105 neg)
%            Maximal clause size   :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    aRewritingSystem0(xR),
    file('COM020+1.p',unknown),
    [] ).

cnf(2,axiom,
    isLocallyConfluent0(xR),
    file('COM020+1.p',unknown),
    [] ).

cnf(3,axiom,
    isTerminating0(xR),
    file('COM020+1.p',unknown),
    [] ).

cnf(4,axiom,
    aElement0(xa),
    file('COM020+1.p',unknown),
    [] ).

cnf(5,axiom,
    aElement0(xb),
    file('COM020+1.p',unknown),
    [] ).

cnf(7,axiom,
    aElement0(xu),
    file('COM020+1.p',unknown),
    [] ).

cnf(9,axiom,
    aElement0(xw),
    file('COM020+1.p',unknown),
    [] ).

cnf(18,axiom,
    aElement0(skf31(u,v)),
    file('COM020+1.p',unknown),
    [] ).

cnf(21,axiom,
    aReductOfIn0(xu,xa,xR),
    file('COM020+1.p',unknown),
    [] ).

cnf(22,axiom,
    sdtmndtasgtdt0(xu,xR,xb),
    file('COM020+1.p',unknown),
    [] ).

cnf(25,axiom,
    sdtmndtasgtdt0(xu,xR,xw),
    file('COM020+1.p',unknown),
    [] ).

cnf(27,axiom,
    aNormalFormOfIn0(xd,xw,xR),
    file('COM020+1.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ aElement0(u)
    | ~ sdtmndtasgtdt0(xd,xR,u)
    | ~ sdtmndtasgtdt0(xb,xR,u) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ aRewritingSystem0(u)
    | ~ aElement0(v)
    | ~ aReductOfIn0(w,v,u)
    | aElement0(w) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ aRewritingSystem0(u)
    | ~ aElement0(v)
    | ~ aNormalFormOfIn0(w,v,u)
    | aElement0(w) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(40,axiom,
    ( ~ aRewritingSystem0(u)
    | ~ aElement0(v)
    | ~ aNormalFormOfIn0(w,v,u)
    | sdtmndtasgtdt0(v,u,w) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(44,axiom,
    ( ~ aElement0(u)
    | ~ aRewritingSystem0(v)
    | ~ aElement0(w)
    | ~ aReductOfIn0(w,u,v)
    | sdtmndtplgtdt0(u,v,w) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ aRewritingSystem0(u)
    | ~ aElement0(v)
    | ~ aElement0(w)
    | ~ isTerminating0(u)
    | ~ sdtmndtplgtdt0(w,u,v)
    | iLess0(v,w) ),
    file('COM020+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('COM020+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('COM020+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('COM020+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(115,plain,
    ( ~ aRewritingSystem0(xR)
    | ~ aElement0(xw)
    | aElement0(xd) ),
    inference(res,[status(thm),theory(equality)],[27,39]),
    [iquote('0:Res:27.0,39.2')] ).

cnf(116,plain,
    aElement0(xd),
    inference(ssi,[status(thm)],[115,9,3,2,1]),
    [iquote('0:SSi:115.1,115.0,9.0,3.0,2.0,1.0')] ).

cnf(125,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(127,plain,
    sdtmndtasgtdt0(xw,xR,xd),
    inference(ssi,[status(thm)],[125,9,3,2,1]),
    [iquote('0:SSi:125.1,125.0,9.0,3.0,2.0,1.0')] ).

cnf(249,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(252,plain,
    ( ~ aRewritingSystem0(u)
    | ~ aElement0(v)
    | ~ aElement0(w)
    | ~ isTerminating0(u)
    | ~ aReductOfIn0(v,w,u)
    | iLess0(v,w) ),
    inference(obv,[status(thm),theory(equality)],[249]),
    [iquote('0:Obv:249.1')] ).

cnf(253,plain,
    ( ~ aRewritingSystem0(u)
    | ~ aElement0(v)
    | ~ isTerminating0(u)
    | ~ aReductOfIn0(w,v,u)
    | iLess0(w,v) ),
    inference(mrr,[status(thm)],[252,38]),
    [iquote('0:MRR:252.1,38.3')] ).

cnf(874,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(875,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(883,plain,
    ( ~ aElement0(u)
    | ~ iLess0(xu,xa)
    | ~ sdtmndtasgtdt0(xu,xR,u)
    | sdtmndtasgtdt0(u,xR,skf31(xb,u)) ),
    inference(ssi,[status(thm)],[875,7,5]),
    [iquote('0:SSi:875.2,875.0,7.0,5.0')] ).

cnf(884,plain,
    ( ~ aElement0(u)
    | ~ iLess0(xu,xa)
    | ~ sdtmndtasgtdt0(xu,xR,u)
    | sdtmndtasgtdt0(xb,xR,skf31(xb,u)) ),
    inference(ssi,[status(thm)],[874,7,5]),
    [iquote('0:SSi:874.2,874.0,7.0,5.0')] ).

cnf(2208,plain,
    ( ~ aRewritingSystem0(xR)
    | ~ aElement0(xa)
    | ~ isTerminating0(xR)
    | iLess0(xu,xa) ),
    inference(res,[status(thm),theory(equality)],[21,253]),
    [iquote('0:Res:21.0,253.3')] ).

cnf(2212,plain,
    iLess0(xu,xa),
    inference(ssi,[status(thm)],[2208,3,2,1,4]),
    [iquote('0:SSi:2208.2,2208.1,2208.0,3.0,2.0,1.0,4.0,3.0,2.0,1.0')] ).

cnf(2215,plain,
    ( ~ aElement0(u)
    | ~ sdtmndtasgtdt0(xu,xR,u)
    | sdtmndtasgtdt0(u,xR,skf31(xb,u)) ),
    inference(mrr,[status(thm)],[883,2212]),
    [iquote('0:MRR:883.1,2212.0')] ).

cnf(2216,plain,
    ( ~ aElement0(u)
    | ~ sdtmndtasgtdt0(xu,xR,u)
    | sdtmndtasgtdt0(xb,xR,skf31(xb,u)) ),
    inference(mrr,[status(thm)],[884,2212]),
    [iquote('0:MRR:884.1,2212.0')] ).

cnf(2387,plain,
    ( ~ aElement0(xd)
    | ~ aElement0(skf31(xb,xd))
    | ~ sdtmndtasgtdt0(xu,xR,xd)
    | ~ sdtmndtasgtdt0(xb,xR,skf31(xb,xd)) ),
    inference(res,[status(thm),theory(equality)],[2215,37]),
    [iquote('0:Res:2215.2,37.1')] ).

cnf(2392,plain,
    ( ~ sdtmndtasgtdt0(xu,xR,xd)
    | ~ sdtmndtasgtdt0(xb,xR,skf31(xb,xd)) ),
    inference(ssi,[status(thm)],[2387,18,5,116]),
    [iquote('0:SSi:2387.1,2387.0,18.0,5.0,116.0,116.0')] ).

cnf(2753,plain,
    ( ~ aElement0(xd)
    | ~ sdtmndtasgtdt0(xu,xR,xd)
    | ~ sdtmndtasgtdt0(xu,xR,xd) ),
    inference(res,[status(thm),theory(equality)],[2216,2392]),
    [iquote('0:Res:2216.2,2392.1')] ).

cnf(2756,plain,
    ( ~ aElement0(xd)
    | ~ sdtmndtasgtdt0(xu,xR,xd) ),
    inference(obv,[status(thm),theory(equality)],[2753]),
    [iquote('0:Obv:2753.1')] ).

cnf(2757,plain,
    ~ sdtmndtasgtdt0(xu,xR,xd),
    inference(ssi,[status(thm)],[2756,116]),
    [iquote('0:SSi:2756.0,116.0')] ).

cnf(4056,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(4058,plain,
    ( ~ aElement0(u)
    | ~ sdtmndtasgtdt0(xw,xR,u)
    | sdtmndtasgtdt0(xu,xR,u) ),
    inference(ssi,[status(thm)],[4056,7,3,2,1,9]),
    [iquote('0:SSi:4056.3,4056.2,4056.1,7.0,3.0,2.0,1.0,9.0')] ).

cnf(5371,plain,
    ( ~ aElement0(xd)
    | sdtmndtasgtdt0(xu,xR,xd) ),
    inference(res,[status(thm),theory(equality)],[127,4058]),
    [iquote('0:Res:127.0,4058.1')] ).

cnf(5379,plain,
    sdtmndtasgtdt0(xu,xR,xd),
    inference(ssi,[status(thm)],[5371,116]),
    [iquote('0:SSi:5371.0,116.0')] ).

cnf(5380,plain,
    $false,
    inference(mrr,[status(thm)],[5379,2757]),
    [iquote('0:MRR:5379.0,2757.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : COM020+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n008.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 19:53:07 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.50/1.69  
% 1.50/1.69  SPASS V 3.9 
% 1.50/1.69  SPASS beiseite: Proof found.
% 1.50/1.69  % SZS status Theorem
% 1.50/1.69  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.50/1.69  SPASS derived 3709 clauses, backtracked 1580 clauses, performed 52 splits and kept 3253 clauses.
% 1.50/1.69  SPASS allocated 107906 KBytes.
% 1.50/1.69  SPASS spent	0:00:01.26 on the problem.
% 1.50/1.69  		0:00:00.04 for the input.
% 1.50/1.69  		0:00:00.10 for the FLOTTER CNF translation.
% 1.50/1.69  		0:00:00.08 for inferences.
% 1.50/1.69  		0:00:00.03 for the backtracking.
% 1.50/1.69  		0:00:00.95 for the reduction.
% 1.50/1.69  
% 1.50/1.69  
% 1.50/1.69  Here is a proof with depth 3, length 47 :
% 1.50/1.69  % SZS output start Refutation
% See solution above
% 1.50/1.69  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 mTCRTrans
% 1.50/1.69  
%------------------------------------------------------------------------------