TSTP Solution File: SWC106+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC106+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n032.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 22:01:46 EDT 2022

% Result   : Theorem 1.21s 1.39s
% Output   : Refutation 1.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   23
% Syntax   : Number of clauses     :   50 (  21 unt;  13 nHn;  50 RR)
%            Number of literals    :  104 (   0 equ;  50 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   15 (  14 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ssList(skc4),
    file('SWC106+1.p',unknown),
    [] ).

cnf(5,axiom,
    ssList(nil),
    file('SWC106+1.p',unknown),
    [] ).

cnf(6,axiom,
    cyclefreeP(nil),
    file('SWC106+1.p',unknown),
    [] ).

cnf(7,axiom,
    totalorderP(nil),
    file('SWC106+1.p',unknown),
    [] ).

cnf(8,axiom,
    strictorderP(nil),
    file('SWC106+1.p',unknown),
    [] ).

cnf(9,axiom,
    totalorderedP(nil),
    file('SWC106+1.p',unknown),
    [] ).

cnf(10,axiom,
    strictorderedP(nil),
    file('SWC106+1.p',unknown),
    [] ).

cnf(11,axiom,
    duplicatefreeP(nil),
    file('SWC106+1.p',unknown),
    [] ).

cnf(12,axiom,
    equalelemsP(nil),
    file('SWC106+1.p',unknown),
    [] ).

cnf(51,axiom,
    ssList(skf46(u,v)),
    file('SWC106+1.p',unknown),
    [] ).

cnf(52,axiom,
    ssItem(skf45(u,v)),
    file('SWC106+1.p',unknown),
    [] ).

cnf(60,axiom,
    ( skP0(u,v)
    | neq(v,nil) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ skP0(skc4,skc5)
    | neq(skc5,nil) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ neq(skc5,nil)
    | ~ skP0(skc4,skc5) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(86,axiom,
    ( skP0(u,v)
    | equal(cons(skf45(u,v),nil),u) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(90,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ssList(cons(u,v)) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(91,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(v,u)) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(98,axiom,
    ( ~ rearsegP(u,v)
    | ~ neq(v,nil)
    | skP0(v,u) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(108,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | neq(v,u)
    | equal(v,u) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(110,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ equal(cons(u,v),nil) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(120,axiom,
    ( equal(app(skf46(u,v),cons(skf45(v,u),nil)),u)
    | skP0(v,u) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(145,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(w,u),v)
    | rearsegP(v,u) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(153,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ totalorderedP(cons(v,u))
    | leq(v,hd(u))
    | equal(nil,u) ),
    file('SWC106+1.p',unknown),
    [] ).

cnf(197,plain,
    neq(skc5,nil),
    inference(mrr,[status(thm)],[69,60]),
    [iquote('0:MRR:69.0,60.1')] ).

cnf(198,plain,
    ~ skP0(skc4,skc5),
    inference(mrr,[status(thm)],[79,197]),
    [iquote('0:MRR:79.0,197.0')] ).

cnf(199,plain,
    ( skP0(u,v)
    | equal(app(skf46(v,u),u),v) ),
    inference(rew,[status(thm),theory(equality)],[86,120]),
    [iquote('0:Rew:86.0,120.0')] ).

cnf(255,plain,
    ( ~ ssList(u)
    | neq(skc4,u)
    | equal(skc4,u) ),
    inference(res,[status(thm),theory(equality)],[2,108]),
    [iquote('0:Res:2.0,108.0')] ).

cnf(257,plain,
    ( ~ ssItem(u)
    | ~ equal(cons(u,skc4),nil) ),
    inference(res,[status(thm),theory(equality)],[2,110]),
    [iquote('0:Res:2.0,110.0')] ).

cnf(310,plain,
    ( ~ ssItem(u)
    | ~ totalorderedP(cons(u,skc4))
    | leq(u,hd(skc4))
    | equal(skc4,nil) ),
    inference(res,[status(thm),theory(equality)],[2,153]),
    [iquote('0:Res:2.0,153.1')] ).

cnf(1464,plain,
    equal(skc4,nil),
    inference(spt,[spt(split,[position(s1)])],[310]),
    [iquote('1:Spt:310.3')] ).

cnf(1472,plain,
    ~ skP0(nil,skc5),
    inference(rew,[status(thm),theory(equality)],[1464,198]),
    [iquote('1:Rew:1464.0,198.0')] ).

cnf(1504,plain,
    ( ~ ssItem(u)
    | ~ equal(cons(u,nil),nil) ),
    inference(rew,[status(thm),theory(equality)],[1464,257]),
    [iquote('1:Rew:1464.0,257.1')] ).

cnf(1806,plain,
    ( ~ ssItem(skf45(u,v))
    | ~ ssList(nil)
    | skP0(u,v)
    | ssList(u) ),
    inference(spr,[status(thm),theory(equality)],[86,90]),
    [iquote('0:SpR:86.1,90.2')] ).

cnf(1808,plain,
    ( ~ ssItem(skf45(u,v))
    | ~ equal(u,nil)
    | skP0(u,v) ),
    inference(spl,[status(thm),theory(equality)],[86,1504]),
    [iquote('1:SpL:86.1,1504.1')] ).

cnf(1818,plain,
    ( ~ equal(u,nil)
    | skP0(u,v) ),
    inference(ssi,[status(thm)],[1808,52]),
    [iquote('1:SSi:1808.0,52.0')] ).

cnf(1850,plain,
    ~ equal(nil,nil),
    inference(res,[status(thm),theory(equality)],[1818,1472]),
    [iquote('1:Res:1818.1,1472.0')] ).

cnf(1851,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[1850]),
    [iquote('1:Obv:1850.0')] ).

cnf(1852,plain,
    ~ equal(skc4,nil),
    inference(spt,[spt(split,[position(sa)])],[1851,1464]),
    [iquote('1:Spt:1851.0,310.3,1464.0')] ).

cnf(1853,plain,
    ( ~ ssItem(u)
    | ~ totalorderedP(cons(u,skc4))
    | leq(u,hd(skc4)) ),
    inference(spt,[spt(split,[position(s2)])],[310]),
    [iquote('1:Spt:1851.0,310.0,310.1,310.2')] ).

cnf(1867,plain,
    ( skP0(u,v)
    | ssList(u) ),
    inference(ssi,[status(thm)],[1806,12,11,8,7,6,10,9,5,52]),
    [iquote('0:SSi:1806.1,1806.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0,52.0')] ).

cnf(4052,plain,
    ( ~ ssList(u)
    | ~ ssList(app(v,u))
    | ~ ssList(v)
    | rearsegP(app(v,u),u) ),
    inference(eqr,[status(thm),theory(equality)],[145]),
    [iquote('0:EqR:145.3')] ).

cnf(4066,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | rearsegP(app(v,u),u) ),
    inference(ssi,[status(thm)],[4052,91]),
    [iquote('0:SSi:4052.1,91.2')] ).

cnf(4151,plain,
    ( ~ ssList(u)
    | ~ ssList(skf46(v,u))
    | skP0(u,v)
    | rearsegP(v,u) ),
    inference(spr,[status(thm),theory(equality)],[199,4066]),
    [iquote('0:SpR:199.1,4066.2')] ).

cnf(4162,plain,
    ( ~ ssList(u)
    | skP0(u,v)
    | rearsegP(v,u) ),
    inference(ssi,[status(thm)],[4151,51]),
    [iquote('0:SSi:4151.1,51.0')] ).

cnf(4163,plain,
    ( skP0(u,v)
    | rearsegP(v,u) ),
    inference(mrr,[status(thm)],[4162,1867]),
    [iquote('0:MRR:4162.0,1867.1')] ).

cnf(4164,plain,
    ( ~ neq(u,nil)
    | skP0(u,v) ),
    inference(mrr,[status(thm)],[98,4163]),
    [iquote('0:MRR:98.0,4163.1')] ).

cnf(4175,plain,
    ~ neq(skc4,nil),
    inference(res,[status(thm),theory(equality)],[4164,198]),
    [iquote('0:Res:4164.1,198.0')] ).

cnf(4176,plain,
    ( ~ ssList(nil)
    | equal(skc4,nil) ),
    inference(res,[status(thm),theory(equality)],[255,4175]),
    [iquote('0:Res:255.1,4175.0')] ).

cnf(4179,plain,
    equal(skc4,nil),
    inference(ssi,[status(thm)],[4176,12,11,8,7,6,10,9,5]),
    [iquote('0:SSi:4176.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0')] ).

cnf(4180,plain,
    $false,
    inference(mrr,[status(thm)],[4179,1852]),
    [iquote('1:MRR:4179.0,1852.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SWC106+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.10  % Command  : run_spass %d %s
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 600
% 0.09/0.28  % DateTime : Sun Jun 12 00:41:25 EDT 2022
% 0.09/0.28  % CPUTime  : 
% 1.21/1.39  
% 1.21/1.39  SPASS V 3.9 
% 1.21/1.39  SPASS beiseite: Proof found.
% 1.21/1.39  % SZS status Theorem
% 1.21/1.39  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.21/1.39  SPASS derived 2847 clauses, backtracked 670 clauses, performed 25 splits and kept 2093 clauses.
% 1.21/1.39  SPASS allocated 101262 KBytes.
% 1.21/1.39  SPASS spent	0:00:01.06 on the problem.
% 1.21/1.39  		0:00:00.03 for the input.
% 1.21/1.39  		0:00:00.04 for the FLOTTER CNF translation.
% 1.21/1.39  		0:00:00.03 for inferences.
% 1.21/1.39  		0:00:00.02 for the backtracking.
% 1.21/1.39  		0:00:00.78 for the reduction.
% 1.21/1.39  
% 1.21/1.39  
% 1.21/1.39  Here is a proof with depth 3, length 50 :
% 1.21/1.39  % SZS output start Refutation
% See solution above
% 1.21/1.39  Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax16 ax26 ax15 ax21 ax6 ax67
% 1.21/1.39  
%------------------------------------------------------------------------------