TSTP Solution File: SWC222+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC222+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 : Tue Jul 19 22:02:35 EDT 2022

% Result   : Theorem 29.83s 30.07s
% Output   : Refutation 29.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   27
% Syntax   : Number of clauses     :   43 (  15 unt;   6 nHn;  43 RR)
%            Number of literals    :   97 (   0 equ;  54 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    ssList(skc7),
    file('SWC222+1.p',unknown),
    [] ).

cnf(8,axiom,
    ssList(nil),
    file('SWC222+1.p',unknown),
    [] ).

cnf(9,axiom,
    cyclefreeP(nil),
    file('SWC222+1.p',unknown),
    [] ).

cnf(10,axiom,
    totalorderP(nil),
    file('SWC222+1.p',unknown),
    [] ).

cnf(11,axiom,
    strictorderP(nil),
    file('SWC222+1.p',unknown),
    [] ).

cnf(12,axiom,
    totalorderedP(nil),
    file('SWC222+1.p',unknown),
    [] ).

cnf(13,axiom,
    strictorderedP(nil),
    file('SWC222+1.p',unknown),
    [] ).

cnf(14,axiom,
    duplicatefreeP(nil),
    file('SWC222+1.p',unknown),
    [] ).

cnf(15,axiom,
    equalelemsP(nil),
    file('SWC222+1.p',unknown),
    [] ).

cnf(54,axiom,
    ~ equal(skc7,nil),
    file('SWC222+1.p',unknown),
    [] ).

cnf(62,axiom,
    ssItem(skf44(u,v,w)),
    file('SWC222+1.p',unknown),
    [] ).

cnf(71,axiom,
    ( ~ ssItem(u)
    | ~ memberP(nil,u) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(84,axiom,
    ( ~ ssList(u)
    | ssItem(hd(u))
    | equal(nil,u) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(85,axiom,
    ( ~ ssList(u)
    | ssList(tl(u))
    | equal(nil,u) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(89,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ssList(cons(u,v)) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(117,axiom,
    ( ~ ssList(u)
    | equal(nil,u)
    | equal(cons(hd(u),tl(u)),u) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(120,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(166,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(cons(u,v),w),cons(u,app(v,w))) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(189,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ equal(app(app(v,cons(w,nil)),u),skc7)
    | memberP(v,skf44(w,u,v)) ),
    file('SWC222+1.p',unknown),
    [] ).

cnf(255,plain,
    ( equal(skc7,nil)
    | equal(cons(hd(skc7),tl(skc7)),skc7) ),
    inference(res,[status(thm),theory(equality)],[5,117]),
    [iquote('0:Res:5.0,117.0')] ).

cnf(280,plain,
    ( equal(skc7,nil)
    | ssItem(hd(skc7)) ),
    inference(res,[status(thm),theory(equality)],[5,84]),
    [iquote('0:Res:5.0,84.0')] ).

cnf(281,plain,
    ( equal(skc7,nil)
    | ssList(tl(skc7)) ),
    inference(res,[status(thm),theory(equality)],[5,85]),
    [iquote('0:Res:5.0,85.0')] ).

cnf(565,plain,
    ssItem(hd(skc7)),
    inference(mrr,[status(thm)],[280,54]),
    [iquote('0:MRR:280.0,54.0')] ).

cnf(566,plain,
    ssList(tl(skc7)),
    inference(mrr,[status(thm)],[281,54]),
    [iquote('0:MRR:281.0,54.0')] ).

cnf(571,plain,
    equal(cons(hd(skc7),tl(skc7)),skc7),
    inference(mrr,[status(thm)],[255,54]),
    [iquote('0:MRR:255.0,54.0')] ).

cnf(1977,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[120]),
    [iquote('0:EqR:120.2')] ).

cnf(1980,plain,
    ( ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(ssi,[status(thm)],[1977,89,15,14,11,10,9,13,12,8,78,77,74,73,72,76,75]),
    [iquote('0:SSi:1977.0,89.1,15.1,14.1,11.1,10.1,9.1,13.1,12.0,8.0,78.0,77.0,74.0,73.0,72.0,76.0,75.2')] ).

cnf(6220,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ ssItem(u)
    | ~ equal(app(cons(u,nil),v),skc7)
    | memberP(nil,skf44(u,v,nil)) ),
    inference(spl,[status(thm),theory(equality)],[80,189]),
    [iquote('0:SpL:80.1,189.3')] ).

cnf(6236,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ ssItem(u)
    | ~ equal(cons(u,v),skc7)
    | memberP(nil,skf44(u,v,nil)) ),
    inference(rew,[status(thm),theory(equality)],[80,6220,166]),
    [iquote('0:Rew:80.1,6220.4,166.3,6220.4')] ).

cnf(6237,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc7)
    | memberP(nil,skf44(v,u,nil)) ),
    inference(ssi,[status(thm)],[6236,15,14,11,10,9,13,12,8,89,78,77,74,73,72,76,75,1980]),
    [iquote('0:SSi:6236.2,6236.0,15.1,14.1,11.1,10.1,9.1,13.1,12.1,8.1,89.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.2,78.0,77.0,74.0,73.0,72.0,76.0,75.0,1980.0')] ).

cnf(22257,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssItem(skf44(v,u,nil))
    | ~ equal(cons(v,u),skc7) ),
    inference(res,[status(thm),theory(equality)],[6237,71]),
    [iquote('0:Res:6237.3,71.1')] ).

cnf(22260,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc7) ),
    inference(ssi,[status(thm)],[22257,62,15,14,11,10,9,13,12,8]),
    [iquote('0:SSi:22257.2,62.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.0')] ).

cnf(29359,plain,
    ( ~ ssList(tl(skc7))
    | ~ ssItem(hd(skc7))
    | ~ equal(skc7,skc7) ),
    inference(spl,[status(thm),theory(equality)],[571,22260]),
    [iquote('0:SpL:571.0,22260.2')] ).

cnf(29427,plain,
    ( ~ ssList(tl(skc7))
    | ~ ssItem(hd(skc7)) ),
    inference(obv,[status(thm),theory(equality)],[29359]),
    [iquote('0:Obv:29359.2')] ).

cnf(29428,plain,
    $false,
    inference(ssi,[status(thm)],[29427,565,566]),
    [iquote('0:SSi:29427.1,29427.0,565.0,566.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SWC222+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.31  % Computer : n028.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit : 300
% 0.12/0.31  % WCLimit  : 600
% 0.12/0.31  % DateTime : Sun Jun 12 08:31:21 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 29.83/30.07  
% 29.83/30.07  SPASS V 3.9 
% 29.83/30.07  SPASS beiseite: Proof found.
% 29.83/30.07  % SZS status Theorem
% 29.83/30.07  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 29.83/30.07  SPASS derived 18170 clauses, backtracked 2628 clauses, performed 26 splits and kept 7436 clauses.
% 29.83/30.07  SPASS allocated 124878 KBytes.
% 29.83/30.07  SPASS spent	0:0:25.30 on the problem.
% 29.83/30.07  		0:00:00.04 for the input.
% 29.83/30.07  		0:00:00.07 for the FLOTTER CNF translation.
% 29.83/30.07  		0:00:00.29 for inferences.
% 29.83/30.07  		0:00:00.75 for the backtracking.
% 29.83/30.07  		0:0:23.84 for the reduction.
% 29.83/30.07  
% 29.83/30.07  
% 29.83/30.07  Here is a proof with depth 3, length 43 :
% 29.83/30.07  % SZS output start Refutation
% See solution above
% 29.83/30.07  Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax78 ax4 ax27
% 29.83/30.07  
%------------------------------------------------------------------------------