TSTP Solution File: SWC251+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC251+1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Tue Jul 19 22:02:50 EDT 2022

% Result   : Theorem 39.14s 39.34s
% Output   : Refutation 39.14s
% 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('SWC251+1.p',unknown),
    [] ).

cnf(5,axiom,
    strictorderedP(skc6),
    file('SWC251+1.p',unknown),
    [] ).

cnf(8,axiom,
    ssList(nil),
    file('SWC251+1.p',unknown),
    [] ).

cnf(9,axiom,
    cyclefreeP(nil),
    file('SWC251+1.p',unknown),
    [] ).

cnf(10,axiom,
    totalorderP(nil),
    file('SWC251+1.p',unknown),
    [] ).

cnf(11,axiom,
    strictorderP(nil),
    file('SWC251+1.p',unknown),
    [] ).

cnf(12,axiom,
    totalorderedP(nil),
    file('SWC251+1.p',unknown),
    [] ).

cnf(13,axiom,
    strictorderedP(nil),
    file('SWC251+1.p',unknown),
    [] ).

cnf(14,axiom,
    duplicatefreeP(nil),
    file('SWC251+1.p',unknown),
    [] ).

cnf(15,axiom,
    equalelemsP(nil),
    file('SWC251+1.p',unknown),
    [] ).

cnf(54,axiom,
    ~ equal(skc6,nil),
    file('SWC251+1.p',unknown),
    [] ).

cnf(62,axiom,
    ssItem(skf44(u,v,w)),
    file('SWC251+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ ssItem(u)
    | ~ memberP(nil,u) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(85,axiom,
    ( ~ ssList(u)
    | ssItem(hd(u))
    | equal(nil,u) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(86,axiom,
    ( ~ ssList(u)
    | ssList(tl(u))
    | equal(nil,u) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(90,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ssList(cons(u,v)) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(117,axiom,
    ( ~ ssList(u)
    | equal(nil,u)
    | equal(cons(hd(u),tl(u)),u) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(120,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(131,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ strictorderedP(cons(v,u))
    | strictorderedP(u)
    | equal(nil,u) ),
    file('SWC251+1.p',unknown),
    [] ).

cnf(166,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(cons(u,v),w),cons(u,app(v,w))) ),
    file('SWC251+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('SWC251+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(2088,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[120]),
    [iquote('0:EqR:120.2')] ).

cnf(2091,plain,
    ( ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(ssi,[status(thm)],[2088,90,15,14,11,10,9,13,12,8,79,78,75,74,73,77,76]),
    [iquote('0:SSi:2088.0,90.1,15.1,14.1,11.1,10.1,9.1,13.1,12.0,8.0,79.0,78.0,75.0,74.0,73.0,77.0,76.2')] ).

cnf(2420,plain,
    ( ~ ssList(tl(skc6))
    | ~ ssItem(hd(skc6))
    | ~ strictorderedP(skc6)
    | strictorderedP(tl(skc6))
    | equal(tl(skc6),nil) ),
    inference(spl,[status(thm),theory(equality)],[582,131]),
    [iquote('0:SpL:582.0,131.2')] ).

cnf(2432,plain,
    ( ~ strictorderedP(skc6)
    | strictorderedP(tl(skc6))
    | equal(tl(skc6),nil) ),
    inference(ssi,[status(thm)],[2420,576,577]),
    [iquote('0:SSi:2420.1,2420.0,576.0,577.0')] ).

cnf(2433,plain,
    ( strictorderedP(tl(skc6))
    | equal(tl(skc6),nil) ),
    inference(mrr,[status(thm)],[2432,5]),
    [iquote('0:MRR:2432.0,5.0')] ).

cnf(2437,plain,
    equal(tl(skc6),nil),
    inference(spt,[spt(split,[position(s1)])],[2433]),
    [iquote('1:Spt:2433.1')] ).

cnf(2439,plain,
    equal(cons(hd(skc6),nil),skc6),
    inference(rew,[status(thm),theory(equality)],[2437,582]),
    [iquote('1:Rew:2437.0,582.0')] ).

cnf(6791,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(6805,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)],[81,6791,166]),
    [iquote('0:Rew:81.1,6791.4,166.3,6791.4')] ).

cnf(6806,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc6)
    | memberP(nil,skf44(v,u,nil)) ),
    inference(ssi,[status(thm)],[6805,15,14,11,10,9,13,12,8,90,79,78,75,74,73,77,76,2091]),
    [iquote('0:SSi:6805.2,6805.0,15.1,14.1,11.1,10.1,9.1,13.1,12.1,8.1,90.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.2,79.0,78.0,75.0,74.0,73.0,77.0,76.0,2091.0')] ).

cnf(22387,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssItem(skf44(v,u,nil))
    | ~ equal(cons(v,u),skc6) ),
    inference(res,[status(thm),theory(equality)],[6806,72]),
    [iquote('0:Res:6806.3,72.1')] ).

cnf(22390,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc6) ),
    inference(ssi,[status(thm)],[22387,62,15,14,11,10,9,13,12,8]),
    [iquote('0:SSi:22387.2,62.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.0')] ).

cnf(27237,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(skc6))
    | ~ equal(skc6,skc6) ),
    inference(spl,[status(thm),theory(equality)],[2439,22390]),
    [iquote('1:SpL:2439.0,22390.2')] ).

cnf(27239,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(skc6)) ),
    inference(obv,[status(thm),theory(equality)],[27237]),
    [iquote('1:Obv:27237.2')] ).

cnf(27240,plain,
    $false,
    inference(ssi,[status(thm)],[27239,576,15,14,11,10,9,13,12,8]),
    [iquote('1:SSi:27239.1,27239.0,576.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.0')] ).

cnf(27249,plain,
    ~ equal(tl(skc6),nil),
    inference(spt,[spt(split,[position(sa)])],[27240,2437]),
    [iquote('1:Spt:27240.0,2433.1,2437.0')] ).

cnf(27250,plain,
    strictorderedP(tl(skc6)),
    inference(spt,[spt(split,[position(s2)])],[2433]),
    [iquote('1:Spt:27240.0,2433.0')] ).

cnf(28440,plain,
    ( ~ ssList(tl(skc6))
    | ~ ssItem(hd(skc6))
    | ~ equal(skc6,skc6) ),
    inference(spl,[status(thm),theory(equality)],[582,22390]),
    [iquote('0:SpL:582.0,22390.2')] ).

cnf(28463,plain,
    ( ~ ssList(tl(skc6))
    | ~ ssItem(hd(skc6)) ),
    inference(obv,[status(thm),theory(equality)],[28440]),
    [iquote('0:Obv:28440.2')] ).

cnf(28464,plain,
    $false,
    inference(ssi,[status(thm)],[28463,576,27250,577]),
    [iquote('1:SSi:28463.1,28463.0,576.0,27250.0,577.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SWC251+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.11/0.32  % Computer : n008.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sun Jun 12 02:44:37 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 39.14/39.34  
% 39.14/39.34  SPASS V 3.9 
% 39.14/39.34  SPASS beiseite: Proof found.
% 39.14/39.34  % SZS status Theorem
% 39.14/39.34  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 39.14/39.34  SPASS derived 17713 clauses, backtracked 1635 clauses, performed 22 splits and kept 6628 clauses.
% 39.14/39.34  SPASS allocated 124407 KBytes.
% 39.14/39.34  SPASS spent	0:0:34.56 on the problem.
% 39.14/39.34  		0:00:00.03 for the input.
% 39.14/39.34  		0:00:00.04 for the FLOTTER CNF translation.
% 39.14/39.34  		0:00:00.43 for inferences.
% 39.14/39.34  		0:00:00.82 for the backtracking.
% 39.14/39.34  		0:0:32.85 for the reduction.
% 39.14/39.34  
% 39.14/39.34  
% 39.14/39.34  Here is a proof with depth 3, length 55 :
% 39.14/39.34  % SZS output start Refutation
% See solution above
% 39.14/39.34  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 ax70 ax27
% 39.14/39.34  
%------------------------------------------------------------------------------