TSTP Solution File: SWC404+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC404+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 22:03:51 EDT 2022

% Result   : Theorem 29.50s 29.68s
% Output   : Refutation 29.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   22
% Syntax   : Number of clauses     :   53 (  28 unt;   4 nHn;  53 RR)
%            Number of literals    :  125 (   0 equ;  79 neg)
%            Maximal clause size   :    9 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  12 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssItem(skc11),
    file('SWC404+1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(skc10),
    file('SWC404+1.p',unknown),
    [] ).

cnf(3,axiom,
    ssList(skc9),
    file('SWC404+1.p',unknown),
    [] ).

cnf(5,axiom,
    ssList(skc7),
    file('SWC404+1.p',unknown),
    [] ).

cnf(6,axiom,
    strictorderedP(skc7),
    file('SWC404+1.p',unknown),
    [] ).

cnf(17,axiom,
    memberP(skc7,skc11),
    file('SWC404+1.p',unknown),
    [] ).

cnf(34,axiom,
    ssList(skf69(u)),
    file('SWC404+1.p',unknown),
    [] ).

cnf(35,axiom,
    ssList(skf68(u)),
    file('SWC404+1.p',unknown),
    [] ).

cnf(36,axiom,
    ssList(skf67(u)),
    file('SWC404+1.p',unknown),
    [] ).

cnf(37,axiom,
    ssItem(skf66(u)),
    file('SWC404+1.p',unknown),
    [] ).

cnf(38,axiom,
    ssItem(skf65(u)),
    file('SWC404+1.p',unknown),
    [] ).

cnf(56,axiom,
    ~ memberP(skc8,skc11),
    file('SWC404+1.p',unknown),
    [] ).

cnf(72,axiom,
    equal(app(app(skc9,skc7),skc10),skc8),
    file('SWC404+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ equal(skc7,nil)
    | equal(skc8,nil) ),
    file('SWC404+1.p',unknown),
    [] ).

cnf(93,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(v,u)) ),
    file('SWC404+1.p',unknown),
    [] ).

cnf(104,axiom,
    ( ~ ssList(u)
    | ~ leq(skf65(u),skf66(u))
    | totalorderedP(u) ),
    file('SWC404+1.p',unknown),
    [] ).

cnf(120,axiom,
    ( ~ ssItem(u)
    | ~ ssItem(v)
    | ~ lt(v,u)
    | leq(v,u) ),
    file('SWC404+1.p',unknown),
    [] ).

cnf(147,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ memberP(v,w)
    | memberP(app(v,u),w) ),
    file('SWC404+1.p',unknown),
    [] ).

cnf(148,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ memberP(u,w)
    | memberP(app(v,u),w) ),
    file('SWC404+1.p',unknown),
    [] ).

cnf(153,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ totalorderedP(cons(v,u))
    | leq(v,hd(u))
    | equal(nil,u) ),
    file('SWC404+1.p',unknown),
    [] ).

cnf(175,axiom,
    ( ~ ssList(u)
    | totalorderedP(u)
    | equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u) ),
    file('SWC404+1.p',unknown),
    [] ).

cnf(193,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ ssItem(y)
    | ~ ssItem(z)
    | ~ strictorderedP(u)
    | ~ equal(app(app(x,cons(z,w)),cons(y,v)),u)
    | lt(z,y) ),
    file('SWC404+1.p',unknown),
    [] ).

cnf(226,plain,
    ( totalorderedP(skc7)
    | equal(app(app(skf67(skc7),cons(skf65(skc7),skf68(skc7))),cons(skf66(skc7),skf69(skc7))),skc7) ),
    inference(res,[status(thm),theory(equality)],[5,175]),
    [iquote('0:Res:5.0,175.0')] ).

cnf(267,plain,
    ( ~ leq(skf65(skc7),skf66(skc7))
    | totalorderedP(skc7) ),
    inference(res,[status(thm),theory(equality)],[5,104]),
    [iquote('0:Res:5.0,104.0')] ).

cnf(315,plain,
    ( ~ ssItem(u)
    | ~ totalorderedP(cons(u,skc7))
    | leq(u,hd(skc7))
    | equal(skc7,nil) ),
    inference(res,[status(thm),theory(equality)],[5,153]),
    [iquote('0:Res:5.0,153.1')] ).

cnf(333,plain,
    ( ~ ssList(u)
    | ssList(app(u,skc7)) ),
    inference(res,[status(thm),theory(equality)],[5,93]),
    [iquote('0:Res:5.0,93.1')] ).

cnf(568,plain,
    equal(skc7,nil),
    inference(spt,[spt(split,[position(s1)])],[315]),
    [iquote('1:Spt:315.3')] ).

cnf(575,plain,
    ( ~ equal(nil,nil)
    | equal(skc8,nil) ),
    inference(rew,[status(thm),theory(equality)],[568,73]),
    [iquote('1:Rew:568.0,73.0')] ).

cnf(680,plain,
    memberP(nil,skc11),
    inference(rew,[status(thm),theory(equality)],[568,17]),
    [iquote('1:Rew:568.0,17.0')] ).

cnf(729,plain,
    equal(skc8,nil),
    inference(obv,[status(thm),theory(equality)],[575]),
    [iquote('1:Obv:575.0')] ).

cnf(839,plain,
    ~ memberP(nil,skc11),
    inference(rew,[status(thm),theory(equality)],[729,56]),
    [iquote('1:Rew:729.0,56.0')] ).

cnf(881,plain,
    $false,
    inference(mrr,[status(thm)],[839,680]),
    [iquote('1:MRR:839.0,680.0')] ).

cnf(1081,plain,
    ~ equal(skc7,nil),
    inference(spt,[spt(split,[position(sa)])],[881,568]),
    [iquote('1:Spt:881.0,315.3,568.0')] ).

cnf(1082,plain,
    ( ~ ssItem(u)
    | ~ totalorderedP(cons(u,skc7))
    | leq(u,hd(skc7)) ),
    inference(spt,[spt(split,[position(s2)])],[315]),
    [iquote('1:Spt:881.0,315.0,315.1,315.2')] ).

cnf(1904,plain,
    totalorderedP(skc7),
    inference(spt,[spt(split,[position(s2s1)])],[226]),
    [iquote('2:Spt:226.0')] ).

cnf(3650,plain,
    ( ~ ssList(skc10)
    | ~ ssList(app(skc9,skc7))
    | ~ ssItem(u)
    | ~ memberP(app(skc9,skc7),u)
    | memberP(skc8,u) ),
    inference(spr,[status(thm),theory(equality)],[72,147]),
    [iquote('0:SpR:72.0,147.4')] ).

cnf(3657,plain,
    ( ~ ssItem(u)
    | ~ memberP(app(skc9,skc7),u)
    | memberP(skc8,u) ),
    inference(ssi,[status(thm)],[3650,333,3,2]),
    [iquote('0:SSi:3650.1,3650.0,333.0,3.0,2.1')] ).

cnf(12157,plain,
    ( ~ ssList(skc7)
    | ~ ssList(skc9)
    | ~ ssItem(u)
    | ~ ssItem(u)
    | ~ memberP(skc7,u)
    | memberP(skc8,u) ),
    inference(res,[status(thm),theory(equality)],[148,3657]),
    [iquote('0:Res:148.4,3657.1')] ).

cnf(12159,plain,
    ( ~ ssList(skc7)
    | ~ ssList(skc9)
    | ~ ssItem(u)
    | ~ memberP(skc7,u)
    | memberP(skc8,u) ),
    inference(obv,[status(thm),theory(equality)],[12157]),
    [iquote('0:Obv:12157.2')] ).

cnf(21177,plain,
    ( ~ ssItem(u)
    | ~ memberP(skc7,u)
    | memberP(skc8,u) ),
    inference(ssi,[status(thm)],[12159,3,5,6,1904]),
    [iquote('2:SSi:12159.1,12159.0,3.0,5.0,6.0,1904.0')] ).

cnf(25421,plain,
    ( ~ ssItem(skc11)
    | ~ memberP(skc7,skc11) ),
    inference(res,[status(thm),theory(equality)],[21177,56]),
    [iquote('2:Res:21177.2,56.0')] ).

cnf(25422,plain,
    ~ memberP(skc7,skc11),
    inference(ssi,[status(thm)],[25421,1]),
    [iquote('2:SSi:25421.0,1.0')] ).

cnf(25423,plain,
    $false,
    inference(mrr,[status(thm)],[25422,17]),
    [iquote('2:MRR:25422.0,17.0')] ).

cnf(25424,plain,
    ~ totalorderedP(skc7),
    inference(spt,[spt(split,[position(s2sa)])],[25423,1904]),
    [iquote('2:Spt:25423.0,226.0,1904.0')] ).

cnf(25425,plain,
    equal(app(app(skf67(skc7),cons(skf65(skc7),skf68(skc7))),cons(skf66(skc7),skf69(skc7))),skc7),
    inference(spt,[spt(split,[position(s2s2)])],[226]),
    [iquote('2:Spt:25423.0,226.1')] ).

cnf(25426,plain,
    ~ leq(skf65(skc7),skf66(skc7)),
    inference(mrr,[status(thm)],[267,25424]),
    [iquote('2:MRR:267.1,25424.0')] ).

cnf(25547,plain,
    ( ~ ssList(u)
    | ~ ssList(skf69(skc7))
    | ~ ssList(skf68(skc7))
    | ~ ssList(skf67(skc7))
    | ~ ssItem(skf66(skc7))
    | ~ ssItem(skf65(skc7))
    | ~ strictorderedP(u)
    | ~ equal(skc7,u)
    | lt(skf65(skc7),skf66(skc7)) ),
    inference(spl,[status(thm),theory(equality)],[25425,193]),
    [iquote('2:SpL:25425.0,193.7')] ).

cnf(25568,plain,
    ( ~ ssList(u)
    | ~ strictorderedP(u)
    | ~ equal(skc7,u)
    | lt(skf65(skc7),skf66(skc7)) ),
    inference(ssi,[status(thm)],[25547,38,5,6,37,36,35,34]),
    [iquote('2:SSi:25547.5,25547.4,25547.3,25547.2,25547.1,38.0,5.0,6.0,37.0,5.0,6.0,36.0,5.0,6.0,35.0,5.0,6.0,34.0,5.0,6.0')] ).

cnf(25621,plain,
    ( ~ ssItem(skf66(skc7))
    | ~ ssItem(skf65(skc7))
    | ~ lt(skf65(skc7),skf66(skc7)) ),
    inference(res,[status(thm),theory(equality)],[120,25426]),
    [iquote('2:Res:120.3,25426.0')] ).

cnf(32565,plain,
    ~ lt(skf65(skc7),skf66(skc7)),
    inference(ssi,[status(thm)],[25621,38,5,6,37]),
    [iquote('2:SSi:25621.1,25621.0,38.0,5.0,6.0,37.0,5.0,6.0')] ).

cnf(32566,plain,
    ( ~ ssList(u)
    | ~ strictorderedP(u)
    | ~ equal(skc7,u) ),
    inference(mrr,[status(thm)],[25568,32565]),
    [iquote('2:MRR:25568.3,32565.0')] ).

cnf(35578,plain,
    ~ equal(skc7,skc7),
    inference(ems,[status(thm)],[32566,5,6]),
    [iquote('2:EmS:32566.0,32566.1,5.0,6.0')] ).

cnf(35580,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[35578]),
    [iquote('2:Obv:35578.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWC404+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jun 12 13:42:05 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 29.50/29.68  
% 29.50/29.68  SPASS V 3.9 
% 29.50/29.68  SPASS beiseite: Proof found.
% 29.50/29.68  % SZS status Theorem
% 29.50/29.68  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 29.50/29.68  SPASS derived 24692 clauses, backtracked 6250 clauses, performed 84 splits and kept 13032 clauses.
% 29.50/29.68  SPASS allocated 126238 KBytes.
% 29.50/29.68  SPASS spent	0:0:24.66 on the problem.
% 29.50/29.68  		0:00:00.04 for the input.
% 29.50/29.68  		0:00:00.06 for the FLOTTER CNF translation.
% 29.50/29.68  		0:00:00.30 for inferences.
% 29.50/29.68  		0:00:00.52 for the backtracking.
% 29.50/29.68  		0:0:23.36 for the reduction.
% 29.50/29.68  
% 29.50/29.68  
% 29.50/29.68  Here is a proof with depth 4, length 53 :
% 29.50/29.68  % SZS output start Refutation
% See solution above
% 29.50/29.68  Formulae used in the proof : co1 ax11 ax2 ax17 ax26 ax93 ax36 ax67 ax12
% 29.50/29.68  
%------------------------------------------------------------------------------