TSTP Solution File: SWC224-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC224-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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 22:02:36 EDT 2022

% Result   : Unsatisfiable 16.80s 16.97s
% Output   : Refutation 16.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   30
% Syntax   : Number of clauses     :   66 (  27 unt;   2 nHn;  66 RR)
%            Number of literals    :  154 (   0 equ;  97 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   8 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(sk1),
    file('SWC224-1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(sk2),
    file('SWC224-1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(nil,sk1),
    file('SWC224-1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ equal(app(app(v,cons(w,nil)),u),sk1)
    | memberP(v,sk5(u,v,w)) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(18,axiom,
    equalelemsP(nil),
    file('SWC224-1.p',unknown),
    [] ).

cnf(19,axiom,
    duplicatefreeP(nil),
    file('SWC224-1.p',unknown),
    [] ).

cnf(20,axiom,
    strictorderedP(nil),
    file('SWC224-1.p',unknown),
    [] ).

cnf(21,axiom,
    totalorderedP(nil),
    file('SWC224-1.p',unknown),
    [] ).

cnf(22,axiom,
    strictorderP(nil),
    file('SWC224-1.p',unknown),
    [] ).

cnf(23,axiom,
    totalorderP(nil),
    file('SWC224-1.p',unknown),
    [] ).

cnf(24,axiom,
    cyclefreeP(nil),
    file('SWC224-1.p',unknown),
    [] ).

cnf(25,axiom,
    ssList(nil),
    file('SWC224-1.p',unknown),
    [] ).

cnf(30,axiom,
    ssList(skaf82(u)),
    file('SWC224-1.p',unknown),
    [] ).

cnf(64,axiom,
    ssItem(skaf44(u)),
    file('SWC224-1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(82,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(84,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(85,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(86,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(87,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(88,axiom,
    ( ~ ssItem(u)
    | ~ memberP(nil,u) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(89,axiom,
    ( ~ ssList(u)
    | ssItem(v)
    | duplicatefreeP(u) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(91,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(102,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(u,v)) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(103,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ssList(cons(v,u)) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(126,axiom,
    ( ~ ssList(u)
    | equal(nil,u)
    | equal(cons(skaf83(u),skaf82(u)),u) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(133,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(174,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | equal(app(cons(w,v),u),cons(w,app(v,u))) ),
    file('SWC224-1.p',unknown),
    [] ).

cnf(196,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('SWC224-1.p',unknown),
    [] ).

cnf(539,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,sk2)) ),
    inference(res,[status(thm),theory(equality)],[2,103]),
    [iquote('0:Res:2.0,103.1')] ).

cnf(581,plain,
    ssItem(u),
    inference(spt,[spt(split,[position(s1)])],[89]),
    [iquote('1:Spt:89.1')] ).

cnf(586,plain,
    ~ memberP(nil,u),
    inference(mrr,[status(thm)],[88,581]),
    [iquote('1:MRR:88.0,581.0')] ).

cnf(587,plain,
    cyclefreeP(cons(u,nil)),
    inference(mrr,[status(thm)],[87,581]),
    [iquote('1:MRR:87.0,581.0')] ).

cnf(588,plain,
    totalorderP(cons(u,nil)),
    inference(mrr,[status(thm)],[86,581]),
    [iquote('1:MRR:86.0,581.0')] ).

cnf(589,plain,
    strictorderP(cons(u,nil)),
    inference(mrr,[status(thm)],[85,581]),
    [iquote('1:MRR:85.0,581.0')] ).

cnf(590,plain,
    totalorderedP(cons(u,nil)),
    inference(mrr,[status(thm)],[84,581]),
    [iquote('1:MRR:84.0,581.0')] ).

cnf(591,plain,
    strictorderedP(cons(u,nil)),
    inference(mrr,[status(thm)],[83,581]),
    [iquote('1:MRR:83.0,581.0')] ).

cnf(592,plain,
    duplicatefreeP(cons(u,nil)),
    inference(mrr,[status(thm)],[82,581]),
    [iquote('1:MRR:82.0,581.0')] ).

cnf(593,plain,
    equalelemsP(cons(u,nil)),
    inference(mrr,[status(thm)],[81,581]),
    [iquote('1:MRR:81.0,581.0')] ).

cnf(706,plain,
    ( ~ ssList(u)
    | ssList(cons(v,u)) ),
    inference(mrr,[status(thm)],[103,581]),
    [iquote('1:MRR:103.1,581.0')] ).

cnf(711,plain,
    ( ~ ssList(u)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    inference(mrr,[status(thm)],[133,581]),
    [iquote('1:MRR:133.1,581.0')] ).

cnf(793,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | equal(app(cons(w,v),u),cons(w,app(v,u))) ),
    inference(mrr,[status(thm)],[174,581]),
    [iquote('1:MRR:174.2,581.0')] ).

cnf(799,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(app(app(v,cons(w,nil)),u),sk1)
    | memberP(v,sk5(u,v,w)) ),
    inference(mrr,[status(thm)],[9,581]),
    [iquote('1:MRR:9.2,581.0')] ).

cnf(3216,plain,
    ( ~ ssList(cons(u,nil))
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[711]),
    [iquote('1:EqR:711.1')] ).

cnf(3217,plain,
    singletonP(cons(u,nil)),
    inference(ssi,[status(thm)],[3216,706,25,24,23,22,21,20,19,18,593,592,591,590,589,588,587]),
    [iquote('1:SSi:3216.0,706.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.0,593.0,592.0,591.0,590.0,589.0,588.0,587.1')] ).

cnf(7020,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ equal(app(cons(u,nil),v),sk1)
    | memberP(nil,sk5(v,nil,u)) ),
    inference(spl,[status(thm),theory(equality)],[91,799]),
    [iquote('1:SpL:91.1,799.2')] ).

cnf(7033,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ equal(cons(u,v),sk1)
    | memberP(nil,sk5(v,nil,u)) ),
    inference(rew,[status(thm),theory(equality)],[91,7020,793]),
    [iquote('1:Rew:91.1,7020.3,793.2,7020.3')] ).

cnf(7034,plain,
    ( ~ ssList(u)
    | ~ equal(cons(v,u),sk1)
    | memberP(nil,sk5(u,nil,v)) ),
    inference(ssi,[status(thm)],[7033,25,24,23,22,21,20,19,18,706,593,592,591,590,589,588,587,3217]),
    [iquote('1:SSi:7033.2,7033.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.0,706.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.1,593.0,592.0,591.0,590.0,589.0,588.0,587.0,3217.0')] ).

cnf(7035,plain,
    ( ~ ssList(u)
    | ~ equal(cons(v,u),sk1) ),
    inference(mrr,[status(thm)],[7034,586]),
    [iquote('1:MRR:7034.2,586.0')] ).

cnf(8205,plain,
    ( ~ ssList(u)
    | ~ ssList(skaf82(u))
    | ~ equal(u,sk1)
    | equal(nil,u) ),
    inference(spl,[status(thm),theory(equality)],[126,7035]),
    [iquote('1:SpL:126.2,7035.1')] ).

cnf(8216,plain,
    ( ~ ssList(u)
    | ~ equal(u,sk1)
    | equal(nil,u) ),
    inference(ssi,[status(thm)],[8205,30]),
    [iquote('1:SSi:8205.1,30.0')] ).

cnf(10308,plain,
    ( ~ equal(sk1,sk1)
    | equal(nil,sk1) ),
    inference(ems,[status(thm)],[8216,1]),
    [iquote('1:EmS:8216.0,1.0')] ).

cnf(10309,plain,
    equal(nil,sk1),
    inference(obv,[status(thm),theory(equality)],[10308]),
    [iquote('1:Obv:10308.0')] ).

cnf(10310,plain,
    $false,
    inference(mrr,[status(thm)],[10309,7]),
    [iquote('1:MRR:10309.0,7.0')] ).

cnf(10384,plain,
    ( ~ ssList(u)
    | duplicatefreeP(u) ),
    inference(spt,[spt(split,[position(s2)])],[89]),
    [iquote('1:Spt:10310.0,89.0,89.2')] ).

cnf(10429,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)],[196,10384]),
    [iquote('1:MRR:196.1,10384.1')] ).

cnf(28043,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)],[174,102]),
    [iquote('0:SpR:174.3,102.2')] ).

cnf(28099,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(cons(v,u))
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(obv,[status(thm),theory(equality)],[28043]),
    [iquote('0:Obv:28043.0')] ).

cnf(28100,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(ssi,[status(thm)],[28099,103]),
    [iquote('0:SSi:28099.2,103.2')] ).

cnf(29917,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)],[10429]),
    [iquote('1:EqR:10429.5')] ).

cnf(29947,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x) ),
    inference(ssi,[status(thm)],[29917,102,103]),
    [iquote('1:SSi:29917.0,102.2,102.2,103.2,103.2')] ).

cnf(29949,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w) ),
    inference(mrr,[status(thm)],[28100,29947]),
    [iquote('1:MRR:28100.3,29947.1')] ).

cnf(29952,plain,
    ( ~ ssList(u)
    | ~ ssItem(v) ),
    inference(con,[status(thm)],[29949]),
    [iquote('1:Con:29949.2')] ).

cnf(29954,plain,
    ~ ssItem(u),
    inference(mrr,[status(thm)],[539,29952]),
    [iquote('1:MRR:539.1,29952.0')] ).

cnf(29957,plain,
    $false,
    inference(unc,[status(thm)],[29954,64]),
    [iquote('1:UnC:29954.0,64.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC224-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 20:35:41 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 16.80/16.97  
% 16.80/16.97  SPASS V 3.9 
% 16.80/16.97  SPASS beiseite: Proof found.
% 16.80/16.97  % SZS status Theorem
% 16.80/16.97  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 16.80/16.97  SPASS derived 19992 clauses, backtracked 6564 clauses, performed 90 splits and kept 15237 clauses.
% 16.80/16.97  SPASS allocated 97259 KBytes.
% 16.80/16.97  SPASS spent	0:0:12.81 on the problem.
% 16.80/16.97  		0:00:00.04 for the input.
% 16.80/16.97  		0:00:00.00 for the FLOTTER CNF translation.
% 16.80/16.97  		0:00:00.18 for inferences.
% 16.80/16.97  		0:00:00.39 for the backtracking.
% 16.80/16.97  		0:0:11.83 for the reduction.
% 16.80/16.97  
% 16.80/16.97  
% 16.80/16.97  Here is a proof with depth 3, length 66 :
% 16.80/16.97  % SZS output start Refutation
% See solution above
% 16.80/16.97  Formulae used in the proof : co1_1 co1_2 co1_7 co1_9 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause13 clause47 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause74 clause85 clause86 clause109 clause116 clause157 clause179
% 16.80/16.97  
%------------------------------------------------------------------------------