TSTP Solution File: SWC214-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC214-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 22:02:32 EDT 2022

% Result   : Unsatisfiable 9.14s 9.33s
% Output   : Refutation 9.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   29
% Syntax   : Number of clauses     :   88 (  36 unt;   6 nHn;  88 RR)
%            Number of literals    :  198 (   0 equ; 123 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   15 (  14 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(sk1),
    file('SWC214-1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(sk2),
    file('SWC214-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(sk4,sk2),
    file('SWC214-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(sk3,sk1),
    file('SWC214-1.p',unknown),
    [] ).

cnf(7,axiom,
    neq(sk2,nil),
    file('SWC214-1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ ssList(u)
    | ~ strictorderedP(u)
    | ~ frontsegP(sk4,u)
    | ~ segmentP(u,sk3)
    | ~ neq(sk3,u) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(11,axiom,
    ~ neq(sk1,nil),
    file('SWC214-1.p',unknown),
    [] ).

cnf(24,axiom,
    ssList(skaf82(u)),
    file('SWC214-1.p',unknown),
    [] ).

cnf(58,axiom,
    ssItem(skaf44(u)),
    file('SWC214-1.p',unknown),
    [] ).

cnf(67,axiom,
    ( ~ ssList(u)
    | segmentP(u,nil) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ ssList(u)
    | ssItem(v)
    | duplicatefreeP(u) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(96,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(u,v)) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(97,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ssList(cons(v,u)) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(110,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),u) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(113,axiom,
    ( ~ ssItem(u)
    | ~ ssItem(v)
    | equal(u,v)
    | neq(u,v) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(120,axiom,
    ( ~ ssList(u)
    | equal(nil,u)
    | equal(cons(skaf83(u),skaf82(u)),u) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(127,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(128,axiom,
    ( ~ ssItem(u)
    | ~ ssItem(v)
    | ~ neq(u,v)
    | ~ equal(u,v) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(131,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | equal(app(cons(v,nil),u),cons(v,u)) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(155,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(v,w),u)
    | frontsegP(u,v) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(168,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | equal(app(cons(w,v),u),cons(w,app(v,u))) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(190,axiom,
    ( ~ ssList(u)
    | ~ duplicatefreeP(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ ssList(y)
    | ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
    file('SWC214-1.p',unknown),
    [] ).

cnf(202,plain,
    ( ~ strictorderedP(u)
    | ~ ssList(u)
    | ~ segmentP(u,sk1)
    | ~ neq(sk1,u)
    | ~ frontsegP(sk2,u) ),
    inference(rew,[status(thm),theory(equality)],[6,10,5]),
    [iquote('0:Rew:6.0,10.4,6.0,10.3,5.0,10.2')] ).

cnf(266,plain,
    ( equal(nil,sk2)
    | equal(cons(skaf83(sk2),skaf82(sk2)),sk2) ),
    inference(res,[status(thm),theory(equality)],[2,120]),
    [iquote('0:Res:2.0,120.0')] ).

cnf(345,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,sk2)) ),
    inference(res,[status(thm),theory(equality)],[2,97]),
    [iquote('0:Res:2.0,97.1')] ).

cnf(514,plain,
    ( ~ ssItem(u)
    | ~ equal(cons(u,sk1),sk1) ),
    inference(res,[status(thm),theory(equality)],[1,110]),
    [iquote('0:Res:1.0,110.1')] ).

cnf(517,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,sk1)) ),
    inference(res,[status(thm),theory(equality)],[1,97]),
    [iquote('0:Res:1.0,97.1')] ).

cnf(559,plain,
    ssItem(u),
    inference(spt,[spt(split,[position(s1)])],[83]),
    [iquote('1:Spt:83.1')] ).

cnf(562,plain,
    ssList(cons(u,sk1)),
    inference(mrr,[status(thm)],[517,559]),
    [iquote('1:MRR:517.0,559.0')] ).

cnf(565,plain,
    cyclefreeP(cons(u,nil)),
    inference(mrr,[status(thm)],[81,559]),
    [iquote('1:MRR:81.0,559.0')] ).

cnf(566,plain,
    totalorderP(cons(u,nil)),
    inference(mrr,[status(thm)],[80,559]),
    [iquote('1:MRR:80.0,559.0')] ).

cnf(567,plain,
    strictorderP(cons(u,nil)),
    inference(mrr,[status(thm)],[79,559]),
    [iquote('1:MRR:79.0,559.0')] ).

cnf(568,plain,
    totalorderedP(cons(u,nil)),
    inference(mrr,[status(thm)],[78,559]),
    [iquote('1:MRR:78.0,559.0')] ).

cnf(569,plain,
    strictorderedP(cons(u,nil)),
    inference(mrr,[status(thm)],[77,559]),
    [iquote('1:MRR:77.0,559.0')] ).

cnf(570,plain,
    duplicatefreeP(cons(u,nil)),
    inference(mrr,[status(thm)],[76,559]),
    [iquote('1:MRR:76.0,559.0')] ).

cnf(571,plain,
    equalelemsP(cons(u,nil)),
    inference(mrr,[status(thm)],[75,559]),
    [iquote('1:MRR:75.0,559.0')] ).

cnf(573,plain,
    ~ equal(cons(u,sk1),sk1),
    inference(mrr,[status(thm)],[514,559]),
    [iquote('1:MRR:514.0,559.0')] ).

cnf(590,plain,
    ( equal(u,v)
    | neq(u,v) ),
    inference(mrr,[status(thm)],[113,559]),
    [iquote('1:MRR:113.1,113.0,559.0')] ).

cnf(599,plain,
    ( ~ neq(u,v)
    | ~ equal(u,v) ),
    inference(mrr,[status(thm)],[128,559]),
    [iquote('1:MRR:128.1,128.0,559.0')] ).

cnf(687,plain,
    ( ~ ssList(u)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    inference(mrr,[status(thm)],[127,559]),
    [iquote('1:MRR:127.1,559.0')] ).

cnf(688,plain,
    ( ~ ssList(u)
    | equal(app(cons(v,nil),u),cons(v,u)) ),
    inference(mrr,[status(thm)],[131,559]),
    [iquote('1:MRR:131.1,559.0')] ).

cnf(1981,plain,
    equal(nil,sk1),
    inference(res,[status(thm),theory(equality)],[590,11]),
    [iquote('1:Res:590.1,11.0')] ).

cnf(1999,plain,
    neq(sk2,sk1),
    inference(rew,[status(thm),theory(equality)],[1981,7]),
    [iquote('1:Rew:1981.0,7.0')] ).

cnf(2002,plain,
    cyclefreeP(cons(u,sk1)),
    inference(rew,[status(thm),theory(equality)],[1981,565]),
    [iquote('1:Rew:1981.0,565.0')] ).

cnf(2003,plain,
    totalorderP(cons(u,sk1)),
    inference(rew,[status(thm),theory(equality)],[1981,566]),
    [iquote('1:Rew:1981.0,566.0')] ).

cnf(2004,plain,
    strictorderP(cons(u,sk1)),
    inference(rew,[status(thm),theory(equality)],[1981,567]),
    [iquote('1:Rew:1981.0,567.0')] ).

cnf(2005,plain,
    totalorderedP(cons(u,sk1)),
    inference(rew,[status(thm),theory(equality)],[1981,568]),
    [iquote('1:Rew:1981.0,568.0')] ).

cnf(2006,plain,
    strictorderedP(cons(u,sk1)),
    inference(rew,[status(thm),theory(equality)],[1981,569]),
    [iquote('1:Rew:1981.0,569.0')] ).

cnf(2007,plain,
    duplicatefreeP(cons(u,sk1)),
    inference(rew,[status(thm),theory(equality)],[1981,570]),
    [iquote('1:Rew:1981.0,570.0')] ).

cnf(2008,plain,
    equalelemsP(cons(u,sk1)),
    inference(rew,[status(thm),theory(equality)],[1981,571]),
    [iquote('1:Rew:1981.0,571.0')] ).

cnf(2019,plain,
    ( ~ ssList(u)
    | segmentP(u,sk1) ),
    inference(rew,[status(thm),theory(equality)],[1981,67]),
    [iquote('1:Rew:1981.0,67.1')] ).

cnf(2051,plain,
    ( ~ ssList(u)
    | ~ equal(cons(v,sk1),u)
    | singletonP(u) ),
    inference(rew,[status(thm),theory(equality)],[1981,687]),
    [iquote('1:Rew:1981.0,687.1')] ).

cnf(2052,plain,
    ( ~ ssList(u)
    | equal(app(cons(v,sk1),u),cons(v,u)) ),
    inference(rew,[status(thm),theory(equality)],[1981,688]),
    [iquote('1:Rew:1981.0,688.1')] ).

cnf(2074,plain,
    ( ~ strictorderedP(u)
    | ~ ssList(u)
    | ~ neq(sk1,u)
    | ~ frontsegP(sk2,u) ),
    inference(mrr,[status(thm)],[202,2019]),
    [iquote('1:MRR:202.2,2019.1')] ).

cnf(2113,plain,
    ( equal(sk2,sk1)
    | equal(cons(skaf83(sk2),skaf82(sk2)),sk2) ),
    inference(rew,[status(thm),theory(equality)],[1981,266]),
    [iquote('1:Rew:1981.0,266.0')] ).

cnf(2645,plain,
    ~ equal(sk2,sk1),
    inference(res,[status(thm),theory(equality)],[1999,599]),
    [iquote('1:Res:1999.0,599.0')] ).

cnf(2802,plain,
    ( ~ ssList(cons(u,sk1))
    | singletonP(cons(u,sk1)) ),
    inference(eqr,[status(thm),theory(equality)],[2051]),
    [iquote('1:EqR:2051.1')] ).

cnf(2803,plain,
    singletonP(cons(u,sk1)),
    inference(ssi,[status(thm)],[2802,562,2002,2003,2004,2005,2006,2007,2008]),
    [iquote('1:SSi:2802.0,562.0,2002.0,2003.0,2004.0,2005.0,2006.0,2007.0,2008.0')] ).

cnf(4680,plain,
    ( ~ ssList(app(u,v))
    | ~ ssList(u)
    | ~ ssList(v)
    | frontsegP(app(u,v),u) ),
    inference(eqr,[status(thm),theory(equality)],[155]),
    [iquote('0:EqR:155.3')] ).

cnf(4695,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | frontsegP(app(u,v),u) ),
    inference(ssi,[status(thm)],[4680,96]),
    [iquote('0:SSi:4680.0,96.2')] ).

cnf(4834,plain,
    ( ~ ssList(u)
    | ~ ssList(cons(v,sk1))
    | ~ ssList(u)
    | frontsegP(cons(v,u),cons(v,sk1)) ),
    inference(spr,[status(thm),theory(equality)],[2052,4695]),
    [iquote('1:SpR:2052.1,4695.2')] ).

cnf(4852,plain,
    ( ~ ssList(cons(u,sk1))
    | ~ ssList(v)
    | frontsegP(cons(u,v),cons(u,sk1)) ),
    inference(obv,[status(thm),theory(equality)],[4834]),
    [iquote('1:Obv:4834.0')] ).

cnf(4853,plain,
    ( ~ ssList(u)
    | frontsegP(cons(v,u),cons(v,sk1)) ),
    inference(ssi,[status(thm)],[4852,562,2002,2003,2004,2005,2006,2007,2008,2803]),
    [iquote('1:SSi:4852.0,562.0,2002.0,2003.0,2004.0,2005.0,2006.0,2007.0,2008.0,2803.0')] ).

cnf(5106,plain,
    equal(cons(skaf83(sk2),skaf82(sk2)),sk2),
    inference(mrr,[status(thm)],[2113,2645]),
    [iquote('1:MRR:2113.0,2645.0')] ).

cnf(5406,plain,
    ( ~ ssList(skaf82(sk2))
    | frontsegP(sk2,cons(skaf83(sk2),sk1)) ),
    inference(spr,[status(thm),theory(equality)],[5106,4853]),
    [iquote('1:SpR:5106.0,4853.1')] ).

cnf(6174,plain,
    frontsegP(sk2,cons(skaf83(sk2),sk1)),
    inference(ssi,[status(thm)],[5406,24,2]),
    [iquote('1:SSi:5406.0,24.0,2.0')] ).

cnf(6451,plain,
    ( ~ strictorderedP(cons(skaf83(sk2),sk1))
    | ~ ssList(cons(skaf83(sk2),sk1))
    | ~ neq(sk1,cons(skaf83(sk2),sk1)) ),
    inference(res,[status(thm),theory(equality)],[6174,2074]),
    [iquote('1:Res:6174.0,2074.3')] ).

cnf(6452,plain,
    ~ neq(sk1,cons(skaf83(sk2),sk1)),
    inference(ssi,[status(thm)],[6451,562,2002,2003,2004,2005,2006,2007,2008,2803]),
    [iquote('1:SSi:6451.1,6451.0,562.0,2002.0,2003.0,2004.0,2005.0,2006.0,2007.0,2008.0,2803.0,562.0,2002.0,2003.0,2004.0,2005.0,2006.0,2007.0,2008.0,2803.0')] ).

cnf(6484,plain,
    equal(cons(skaf83(sk2),sk1),sk1),
    inference(res,[status(thm),theory(equality)],[590,6452]),
    [iquote('1:Res:590.1,6452.0')] ).

cnf(6485,plain,
    $false,
    inference(mrr,[status(thm)],[6484,573]),
    [iquote('1:MRR:6484.0,573.0')] ).

cnf(6486,plain,
    ( ~ ssList(u)
    | duplicatefreeP(u) ),
    inference(spt,[spt(split,[position(s2)])],[83]),
    [iquote('1:Spt:6485.0,83.0,83.2')] ).

cnf(6499,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ ssList(y)
    | ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
    inference(mrr,[status(thm)],[190,6486]),
    [iquote('1:MRR:190.1,6486.1')] ).

cnf(18586,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ ssList(cons(w,v))
    | ~ ssList(u)
    | ssList(cons(w,app(v,u))) ),
    inference(spr,[status(thm),theory(equality)],[168,96]),
    [iquote('0:SpR:168.3,96.2')] ).

cnf(18631,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(cons(v,u))
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(obv,[status(thm),theory(equality)],[18586]),
    [iquote('0:Obv:18586.0')] ).

cnf(18632,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(ssi,[status(thm)],[18631,97]),
    [iquote('0:SSi:18631.2,97.2')] ).

cnf(19795,plain,
    ( ~ ssList(app(app(u,cons(v,w)),cons(v,x)))
    | ~ ssItem(v)
    | ~ ssList(u)
    | ~ ssList(w)
    | ~ ssList(x) ),
    inference(eqr,[status(thm),theory(equality)],[6499]),
    [iquote('1:EqR:6499.5')] ).

cnf(19823,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x) ),
    inference(ssi,[status(thm)],[19795,96,97]),
    [iquote('1:SSi:19795.0,96.2,96.2,97.2,97.2')] ).

cnf(19824,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w) ),
    inference(mrr,[status(thm)],[18632,19823]),
    [iquote('1:MRR:18632.3,19823.1')] ).

cnf(19827,plain,
    ( ~ ssList(u)
    | ~ ssItem(v) ),
    inference(con,[status(thm)],[19824]),
    [iquote('1:Con:19824.2')] ).

cnf(19829,plain,
    ~ ssItem(u),
    inference(mrr,[status(thm)],[345,19827]),
    [iquote('1:MRR:345.1,19827.0')] ).

cnf(19831,plain,
    $false,
    inference(unc,[status(thm)],[19829,58]),
    [iquote('1:UnC:19829.0,58.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SWC214-1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n007.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 08:52:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 9.14/9.33  
% 9.14/9.33  SPASS V 3.9 
% 9.14/9.33  SPASS beiseite: Proof found.
% 9.14/9.33  % SZS status Theorem
% 9.14/9.33  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 9.14/9.33  SPASS derived 12908 clauses, backtracked 6934 clauses, performed 138 splits and kept 12093 clauses.
% 9.14/9.33  SPASS allocated 89999 KBytes.
% 9.14/9.33  SPASS spent	0:00:07.35 on the problem.
% 9.14/9.33  		0:00:00.04 for the input.
% 9.14/9.33  		0:00:00.00 for the FLOTTER CNF translation.
% 9.14/9.33  		0:00:00.11 for inferences.
% 9.14/9.33  		0:00:00.19 for the backtracking.
% 9.14/9.33  		0:00:06.78 for the reduction.
% 9.14/9.33  
% 9.14/9.33  
% 9.14/9.33  Here is a proof with depth 5, length 88 :
% 9.14/9.33  % SZS output start Refutation
% See solution above
% 9.14/9.33  Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_10 co1_11 clause13 clause47 clause56 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause85 clause86 clause99 clause102 clause109 clause116 clause117 clause120 clause144 clause157 clause179
% 9.14/9.33  
%------------------------------------------------------------------------------