TSTP Solution File: SWC240+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC240+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 22:02:44 EDT 2022

% Result   : Theorem 38.25s 38.49s
% Output   : Refutation 38.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   31
% Syntax   : Number of clauses     :   58 (  18 unt;  10 nHn;  58 RR)
%            Number of literals    :  146 (   0 equ;  84 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    :   12 (  12 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssItem(skc7),
    file('SWC240+1.p',unknown),
    [] ).

cnf(3,axiom,
    ssList(skc5),
    file('SWC240+1.p',unknown),
    [] ).

cnf(6,axiom,
    ssList(nil),
    file('SWC240+1.p',unknown),
    [] ).

cnf(7,axiom,
    cyclefreeP(nil),
    file('SWC240+1.p',unknown),
    [] ).

cnf(8,axiom,
    totalorderP(nil),
    file('SWC240+1.p',unknown),
    [] ).

cnf(9,axiom,
    strictorderP(nil),
    file('SWC240+1.p',unknown),
    [] ).

cnf(10,axiom,
    totalorderedP(nil),
    file('SWC240+1.p',unknown),
    [] ).

cnf(11,axiom,
    strictorderedP(nil),
    file('SWC240+1.p',unknown),
    [] ).

cnf(12,axiom,
    duplicatefreeP(nil),
    file('SWC240+1.p',unknown),
    [] ).

cnf(13,axiom,
    equalelemsP(nil),
    file('SWC240+1.p',unknown),
    [] ).

cnf(52,axiom,
    ~ equal(skc5,nil),
    file('SWC240+1.p',unknown),
    [] ).

cnf(60,axiom,
    ssItem(skf44(u,v,w)),
    file('SWC240+1.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ ssItem(u)
    | ~ memberP(nil,u) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(70,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(71,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(82,axiom,
    ( ~ ssList(u)
    | ssItem(hd(u))
    | equal(nil,u) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ ssList(u)
    | ssList(tl(u))
    | equal(nil,u) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(84,axiom,
    ( ~ ssItem(u)
    | ~ memberP(skc5,u)
    | equal(skc7,u) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(88,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ssList(cons(u,v)) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(89,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(v,u)) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(115,axiom,
    ( ~ ssList(u)
    | equal(nil,u)
    | equal(cons(hd(u),tl(u)),u) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(118,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(164,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(cons(u,v),w),cons(u,app(v,w))) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(183,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ equal(app(x,cons(u,w)),v)
    | memberP(v,u) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(186,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ equal(app(app(v,cons(w,nil)),u),skc5)
    | memberP(v,skf44(w,u,v)) ),
    file('SWC240+1.p',unknown),
    [] ).

cnf(250,plain,
    ( equal(skc5,nil)
    | equal(cons(hd(skc5),tl(skc5)),skc5) ),
    inference(res,[status(thm),theory(equality)],[3,115]),
    [iquote('0:Res:3.0,115.0')] ).

cnf(275,plain,
    ( equal(skc5,nil)
    | ssItem(hd(skc5)) ),
    inference(res,[status(thm),theory(equality)],[3,82]),
    [iquote('0:Res:3.0,82.0')] ).

cnf(276,plain,
    ( equal(skc5,nil)
    | ssList(tl(skc5)) ),
    inference(res,[status(thm),theory(equality)],[3,83]),
    [iquote('0:Res:3.0,83.0')] ).

cnf(560,plain,
    ssItem(hd(skc5)),
    inference(mrr,[status(thm)],[275,52]),
    [iquote('0:MRR:275.0,52.0')] ).

cnf(561,plain,
    ssList(tl(skc5)),
    inference(mrr,[status(thm)],[276,52]),
    [iquote('0:MRR:276.0,52.0')] ).

cnf(566,plain,
    equal(cons(hd(skc5),tl(skc5)),skc5),
    inference(mrr,[status(thm)],[250,52]),
    [iquote('0:MRR:250.0,52.0')] ).

cnf(1988,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[118]),
    [iquote('0:EqR:118.2')] ).

cnf(1991,plain,
    ( ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(ssi,[status(thm)],[1988,88,13,12,9,8,7,11,10,6,76,75,72,71,70,74,73]),
    [iquote('0:SSi:1988.0,88.1,13.1,12.1,9.1,8.1,7.1,11.1,10.0,6.0,76.0,75.0,72.0,71.0,70.0,74.0,73.2')] ).

cnf(5624,plain,
    ( ~ ssItem(u)
    | ~ ssList(app(v,cons(u,w)))
    | ~ ssList(w)
    | ~ ssList(v)
    | memberP(app(v,cons(u,w)),u) ),
    inference(eqr,[status(thm),theory(equality)],[183]),
    [iquote('0:EqR:183.4')] ).

cnf(5650,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | memberP(app(w,cons(u,v)),u) ),
    inference(ssi,[status(thm)],[5624,89,88]),
    [iquote('0:SSi:5624.1,89.2,88.2')] ).

cnf(6062,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ ssItem(u)
    | ~ equal(app(cons(u,nil),v),skc5)
    | memberP(nil,skf44(u,v,nil)) ),
    inference(spl,[status(thm),theory(equality)],[78,186]),
    [iquote('0:SpL:78.1,186.3')] ).

cnf(6078,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ ssItem(u)
    | ~ equal(cons(u,v),skc5)
    | memberP(nil,skf44(u,v,nil)) ),
    inference(rew,[status(thm),theory(equality)],[78,6062,164]),
    [iquote('0:Rew:78.1,6062.4,164.3,6062.4')] ).

cnf(6079,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc5)
    | memberP(nil,skf44(v,u,nil)) ),
    inference(ssi,[status(thm)],[6078,13,12,9,8,7,11,10,6,88,76,75,72,71,70,74,73,1991]),
    [iquote('0:SSi:6078.2,6078.0,13.1,12.1,9.1,8.1,7.1,11.1,10.1,6.1,88.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.2,76.0,75.0,72.0,71.0,70.0,74.0,73.0,1991.0')] ).

cnf(15846,plain,
    ( ~ ssList(cons(u,v))
    | ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(nil)
    | memberP(cons(u,v),u) ),
    inference(spr,[status(thm),theory(equality)],[78,5650]),
    [iquote('0:SpR:78.1,5650.3')] ).

cnf(15875,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | memberP(cons(u,v),u) ),
    inference(ssi,[status(thm)],[15846,13,12,9,8,7,11,10,6,88]),
    [iquote('0:SSi:15846.3,15846.0,13.2,12.0,9.0,8.0,7.0,11.0,10.0,6.0,88.0')] ).

cnf(17851,plain,
    ( ~ ssList(u)
    | ~ ssItem(hd(u))
    | ~ ssList(tl(u))
    | equal(nil,u)
    | memberP(u,hd(u)) ),
    inference(spr,[status(thm),theory(equality)],[115,15875]),
    [iquote('0:SpR:115.2,15875.2')] ).

cnf(17862,plain,
    ( ~ ssList(u)
    | equal(nil,u)
    | memberP(u,hd(u)) ),
    inference(mrr,[status(thm)],[17851,82,83]),
    [iquote('0:MRR:17851.1,17851.2,82.1,83.1')] ).

cnf(17946,plain,
    ( ~ ssList(skc5)
    | ~ ssItem(hd(skc5))
    | equal(skc5,nil)
    | equal(hd(skc5),skc7) ),
    inference(res,[status(thm),theory(equality)],[17862,84]),
    [iquote('0:Res:17862.2,84.1')] ).

cnf(22661,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssItem(skf44(v,u,nil))
    | ~ equal(cons(v,u),skc5) ),
    inference(res,[status(thm),theory(equality)],[6079,69]),
    [iquote('0:Res:6079.3,69.1')] ).

cnf(22664,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc5) ),
    inference(ssi,[status(thm)],[22661,60,13,12,9,8,7,11,10,6]),
    [iquote('0:SSi:22661.2,60.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0')] ).

cnf(31973,plain,
    ( ~ ssItem(hd(skc5))
    | equal(skc5,nil)
    | equal(hd(skc5),skc7) ),
    inference(ssi,[status(thm)],[17946,3]),
    [iquote('0:SSi:17946.0,3.0')] ).

cnf(31974,plain,
    ( ~ ssItem(hd(skc5))
    | equal(hd(skc5),skc7) ),
    inference(mrr,[status(thm)],[31973,52]),
    [iquote('0:MRR:31973.1,52.0')] ).

cnf(31975,plain,
    equal(hd(skc5),skc7),
    inference(mrr,[status(thm)],[31974,560]),
    [iquote('0:MRR:31974.0,560.0')] ).

cnf(31977,plain,
    equal(cons(skc7,tl(skc5)),skc5),
    inference(rew,[status(thm),theory(equality)],[31975,566]),
    [iquote('0:Rew:31975.0,566.0')] ).

cnf(32579,plain,
    ( ~ ssList(tl(skc5))
    | ~ ssItem(skc7)
    | ~ equal(skc5,skc5) ),
    inference(spl,[status(thm),theory(equality)],[31977,22664]),
    [iquote('0:SpL:31977.0,22664.2')] ).

cnf(32601,plain,
    ( ~ ssList(tl(skc5))
    | ~ ssItem(skc7) ),
    inference(obv,[status(thm),theory(equality)],[32579]),
    [iquote('0:Obv:32579.2')] ).

cnf(32602,plain,
    $false,
    inference(ssi,[status(thm)],[32601,1,561]),
    [iquote('0:SSi:32601.1,32601.0,1.0,561.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC240+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n015.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jun 12 00:10:21 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 38.25/38.49  
% 38.25/38.49  SPASS V 3.9 
% 38.25/38.49  SPASS beiseite: Proof found.
% 38.25/38.49  % SZS status Theorem
% 38.25/38.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 38.25/38.49  SPASS derived 18545 clauses, backtracked 5079 clauses, performed 50 splits and kept 9300 clauses.
% 38.25/38.49  SPASS allocated 126434 KBytes.
% 38.25/38.49  SPASS spent	0:0:32.83 on the problem.
% 38.25/38.49  		0:00:00.04 for the input.
% 38.25/38.49  		0:00:00.07 for the FLOTTER CNF translation.
% 38.25/38.49  		0:00:00.32 for inferences.
% 38.25/38.49  		0:00:00.98 for the backtracking.
% 38.25/38.49  		0:0:31.07 for the reduction.
% 38.25/38.49  
% 38.25/38.49  
% 38.25/38.49  Here is a proof with depth 4, length 58 :
% 38.25/38.49  % SZS output start Refutation
% See solution above
% 38.25/38.49  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 ax26 ax78 ax4 ax27 ax3
% 38.25/38.49  
%------------------------------------------------------------------------------