TSTP Solution File: SWC236+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC236+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 22:02:42 EDT 2022

% Result   : Theorem 28.00s 28.18s
% Output   : Refutation 28.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   29
% Syntax   : Number of clauses     :   55 (  21 unt;  10 nHn;  55 RR)
%            Number of literals    :  123 (   0 equ;  67 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(4,axiom,
    ssList(skc6),
    file('SWC236+1.p',unknown),
    [] ).

cnf(5,axiom,
    totalorderedP(skc6),
    file('SWC236+1.p',unknown),
    [] ).

cnf(8,axiom,
    ssList(nil),
    file('SWC236+1.p',unknown),
    [] ).

cnf(9,axiom,
    cyclefreeP(nil),
    file('SWC236+1.p',unknown),
    [] ).

cnf(10,axiom,
    totalorderP(nil),
    file('SWC236+1.p',unknown),
    [] ).

cnf(11,axiom,
    strictorderP(nil),
    file('SWC236+1.p',unknown),
    [] ).

cnf(12,axiom,
    totalorderedP(nil),
    file('SWC236+1.p',unknown),
    [] ).

cnf(13,axiom,
    strictorderedP(nil),
    file('SWC236+1.p',unknown),
    [] ).

cnf(14,axiom,
    duplicatefreeP(nil),
    file('SWC236+1.p',unknown),
    [] ).

cnf(15,axiom,
    equalelemsP(nil),
    file('SWC236+1.p',unknown),
    [] ).

cnf(54,axiom,
    ~ equal(skc6,nil),
    file('SWC236+1.p',unknown),
    [] ).

cnf(62,axiom,
    ssItem(skf44(u,v,w)),
    file('SWC236+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ ssItem(u)
    | ~ memberP(nil,u) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(85,axiom,
    ( ~ ssList(u)
    | ssItem(hd(u))
    | equal(nil,u) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(86,axiom,
    ( ~ ssList(u)
    | ssList(tl(u))
    | equal(nil,u) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(90,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ssList(cons(u,v)) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(117,axiom,
    ( ~ ssList(u)
    | equal(nil,u)
    | equal(cons(hd(u),tl(u)),u) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(120,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(130,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ totalorderedP(cons(v,u))
    | totalorderedP(u)
    | equal(nil,u) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(166,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(cons(u,v),w),cons(u,app(v,w))) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(188,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ equal(app(app(v,cons(w,nil)),u),skc6)
    | memberP(v,skf44(w,u,v)) ),
    file('SWC236+1.p',unknown),
    [] ).

cnf(258,plain,
    ( equal(skc6,nil)
    | equal(cons(hd(skc6),tl(skc6)),skc6) ),
    inference(res,[status(thm),theory(equality)],[4,117]),
    [iquote('0:Res:4.0,117.0')] ).

cnf(283,plain,
    ( equal(skc6,nil)
    | ssItem(hd(skc6)) ),
    inference(res,[status(thm),theory(equality)],[4,85]),
    [iquote('0:Res:4.0,85.0')] ).

cnf(284,plain,
    ( equal(skc6,nil)
    | ssList(tl(skc6)) ),
    inference(res,[status(thm),theory(equality)],[4,86]),
    [iquote('0:Res:4.0,86.0')] ).

cnf(576,plain,
    ssItem(hd(skc6)),
    inference(mrr,[status(thm)],[283,54]),
    [iquote('0:MRR:283.0,54.0')] ).

cnf(577,plain,
    ssList(tl(skc6)),
    inference(mrr,[status(thm)],[284,54]),
    [iquote('0:MRR:284.0,54.0')] ).

cnf(582,plain,
    equal(cons(hd(skc6),tl(skc6)),skc6),
    inference(mrr,[status(thm)],[258,54]),
    [iquote('0:MRR:258.0,54.0')] ).

cnf(2032,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[120]),
    [iquote('0:EqR:120.2')] ).

cnf(2035,plain,
    ( ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(ssi,[status(thm)],[2032,90,15,14,10,11,9,12,13,8,79,78,74,75,73,76,77]),
    [iquote('0:SSi:2032.0,90.1,15.1,14.1,10.1,11.1,9.1,12.1,13.0,8.0,79.0,78.0,74.0,75.0,73.0,76.0,77.2')] ).

cnf(2391,plain,
    ( ~ ssList(tl(skc6))
    | ~ ssItem(hd(skc6))
    | ~ totalorderedP(skc6)
    | totalorderedP(tl(skc6))
    | equal(tl(skc6),nil) ),
    inference(spl,[status(thm),theory(equality)],[582,130]),
    [iquote('0:SpL:582.0,130.2')] ).

cnf(2403,plain,
    ( ~ totalorderedP(skc6)
    | totalorderedP(tl(skc6))
    | equal(tl(skc6),nil) ),
    inference(ssi,[status(thm)],[2391,576,577]),
    [iquote('0:SSi:2391.1,2391.0,576.0,577.0')] ).

cnf(2404,plain,
    ( totalorderedP(tl(skc6))
    | equal(tl(skc6),nil) ),
    inference(mrr,[status(thm)],[2403,5]),
    [iquote('0:MRR:2403.0,5.0')] ).

cnf(2408,plain,
    equal(tl(skc6),nil),
    inference(spt,[spt(split,[position(s1)])],[2404]),
    [iquote('1:Spt:2404.1')] ).

cnf(2410,plain,
    equal(cons(hd(skc6),nil),skc6),
    inference(rew,[status(thm),theory(equality)],[2408,582]),
    [iquote('1:Rew:2408.0,582.0')] ).

cnf(6718,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ ssItem(u)
    | ~ equal(app(cons(u,nil),v),skc6)
    | memberP(nil,skf44(u,v,nil)) ),
    inference(spl,[status(thm),theory(equality)],[81,188]),
    [iquote('0:SpL:81.1,188.3')] ).

cnf(6732,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ ssItem(u)
    | ~ equal(cons(u,v),skc6)
    | memberP(nil,skf44(u,v,nil)) ),
    inference(rew,[status(thm),theory(equality)],[81,6718,166]),
    [iquote('0:Rew:81.1,6718.4,166.3,6718.4')] ).

cnf(6733,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc6)
    | memberP(nil,skf44(v,u,nil)) ),
    inference(ssi,[status(thm)],[6732,15,14,10,11,9,12,13,8,90,79,78,74,75,73,76,77,2035]),
    [iquote('0:SSi:6732.2,6732.0,15.1,14.1,10.1,11.1,9.1,12.1,13.1,8.1,90.0,15.0,14.0,10.0,11.0,9.0,12.0,13.0,8.2,79.0,78.0,74.0,75.0,73.0,76.0,77.0,2035.0')] ).

cnf(22546,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssItem(skf44(v,u,nil))
    | ~ equal(cons(v,u),skc6) ),
    inference(res,[status(thm),theory(equality)],[6733,72]),
    [iquote('0:Res:6733.3,72.1')] ).

cnf(22549,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc6) ),
    inference(ssi,[status(thm)],[22546,62,15,14,10,11,9,12,13,8]),
    [iquote('0:SSi:22546.2,62.0,15.0,14.0,10.0,11.0,9.0,12.0,13.0,8.0')] ).

cnf(27222,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(skc6))
    | ~ equal(skc6,skc6) ),
    inference(spl,[status(thm),theory(equality)],[2410,22549]),
    [iquote('1:SpL:2410.0,22549.2')] ).

cnf(27224,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(skc6)) ),
    inference(obv,[status(thm),theory(equality)],[27222]),
    [iquote('1:Obv:27222.2')] ).

cnf(27225,plain,
    $false,
    inference(ssi,[status(thm)],[27224,576,15,14,10,11,9,12,13,8]),
    [iquote('1:SSi:27224.1,27224.0,576.0,15.0,14.0,10.0,11.0,9.0,12.0,13.0,8.0')] ).

cnf(27234,plain,
    ~ equal(tl(skc6),nil),
    inference(spt,[spt(split,[position(sa)])],[27225,2408]),
    [iquote('1:Spt:27225.0,2404.1,2408.0')] ).

cnf(27235,plain,
    totalorderedP(tl(skc6)),
    inference(spt,[spt(split,[position(s2)])],[2404]),
    [iquote('1:Spt:27225.0,2404.0')] ).

cnf(28423,plain,
    ( ~ ssList(tl(skc6))
    | ~ ssItem(hd(skc6))
    | ~ equal(skc6,skc6) ),
    inference(spl,[status(thm),theory(equality)],[582,22549]),
    [iquote('0:SpL:582.0,22549.2')] ).

cnf(28446,plain,
    ( ~ ssList(tl(skc6))
    | ~ ssItem(hd(skc6)) ),
    inference(obv,[status(thm),theory(equality)],[28423]),
    [iquote('0:Obv:28423.2')] ).

cnf(28447,plain,
    $false,
    inference(ssi,[status(thm)],[28446,576,27235,577]),
    [iquote('1:SSi:28446.1,28446.0,576.0,27235.0,577.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC236+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jun 12 23:23:12 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 28.00/28.18  
% 28.00/28.18  SPASS V 3.9 
% 28.00/28.18  SPASS beiseite: Proof found.
% 28.00/28.18  % SZS status Theorem
% 28.00/28.18  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 28.00/28.18  SPASS derived 17698 clauses, backtracked 1633 clauses, performed 22 splits and kept 6601 clauses.
% 28.00/28.18  SPASS allocated 124460 KBytes.
% 28.00/28.18  SPASS spent	0:0:23.76 on the problem.
% 28.00/28.18  		0:00:00.04 for the input.
% 28.00/28.18  		0:00:00.07 for the FLOTTER CNF translation.
% 28.00/28.18  		0:00:00.32 for inferences.
% 28.00/28.18  		0:00:00.70 for the backtracking.
% 28.00/28.18  		0:0:22.32 for the reduction.
% 28.00/28.18  
% 28.00/28.18  
% 28.00/28.18  Here is a proof with depth 3, length 55 :
% 28.00/28.18  % SZS output start Refutation
% See solution above
% 28.00/28.18  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 ax67 ax27
% 28.00/28.18  
%------------------------------------------------------------------------------