TSTP Solution File: SWC247-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC247-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 22:02:47 EDT 2022

% Result   : Unsatisfiable 8.02s 8.18s
% Output   : Refutation 8.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   31
% Syntax   : Number of clauses     :   68 (  30 unt;   3 nHn;  68 RR)
%            Number of literals    :  152 (   0 equ;  94 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    :   13 (  13 usr;   8 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(sk1),
    file('SWC247-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(sk3,sk1),
    file('SWC247-1.p',unknown),
    [] ).

cnf(8,axiom,
    totalorderedP(sk3),
    file('SWC247-1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(nil,sk1),
    file('SWC247-1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ equal(app(app(v,cons(w,nil)),u),sk1)
    | memberP(v,sk5(u,v,w)) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(16,axiom,
    equalelemsP(nil),
    file('SWC247-1.p',unknown),
    [] ).

cnf(17,axiom,
    duplicatefreeP(nil),
    file('SWC247-1.p',unknown),
    [] ).

cnf(18,axiom,
    strictorderedP(nil),
    file('SWC247-1.p',unknown),
    [] ).

cnf(19,axiom,
    totalorderedP(nil),
    file('SWC247-1.p',unknown),
    [] ).

cnf(20,axiom,
    strictorderP(nil),
    file('SWC247-1.p',unknown),
    [] ).

cnf(21,axiom,
    totalorderP(nil),
    file('SWC247-1.p',unknown),
    [] ).

cnf(22,axiom,
    cyclefreeP(nil),
    file('SWC247-1.p',unknown),
    [] ).

cnf(23,axiom,
    ssList(nil),
    file('SWC247-1.p',unknown),
    [] ).

cnf(27,axiom,
    ssItem(skaf83(u)),
    file('SWC247-1.p',unknown),
    [] ).

cnf(28,axiom,
    ssList(skaf82(u)),
    file('SWC247-1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(82,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(84,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(85,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(86,axiom,
    ( ~ ssItem(u)
    | ~ memberP(nil,u) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(87,axiom,
    ( ~ ssList(u)
    | ssItem(v)
    | duplicatefreeP(u) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(89,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(100,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(u,v)) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(101,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ssList(cons(v,u)) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(124,axiom,
    ( ~ ssList(u)
    | equal(nil,u)
    | equal(cons(skaf83(u),skaf82(u)),u) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(131,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(172,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | equal(app(cons(w,v),u),cons(w,app(v,u))) ),
    file('SWC247-1.p',unknown),
    [] ).

cnf(194,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('SWC247-1.p',unknown),
    [] ).

cnf(201,plain,
    totalorderedP(sk1),
    inference(rew,[status(thm),theory(equality)],[6,8]),
    [iquote('0:Rew:6.0,8.0')] ).

cnf(452,plain,
    ( equal(cons(skaf83(sk1),skaf82(sk1)),sk1)
    | equal(nil,sk1) ),
    inference(res,[status(thm),theory(equality)],[1,124]),
    [iquote('0:Res:1.0,124.0')] ).

cnf(536,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,sk1)) ),
    inference(res,[status(thm),theory(equality)],[1,101]),
    [iquote('0:Res:1.0,101.1')] ).

cnf(581,plain,
    equal(cons(skaf83(sk1),skaf82(sk1)),sk1),
    inference(mrr,[status(thm)],[452,9]),
    [iquote('0:MRR:452.1,9.0')] ).

cnf(597,plain,
    ssItem(u),
    inference(spt,[spt(split,[position(s1)])],[87]),
    [iquote('1:Spt:87.1')] ).

cnf(602,plain,
    ~ memberP(nil,u),
    inference(mrr,[status(thm)],[86,597]),
    [iquote('1:MRR:86.0,597.0')] ).

cnf(603,plain,
    cyclefreeP(cons(u,nil)),
    inference(mrr,[status(thm)],[85,597]),
    [iquote('1:MRR:85.0,597.0')] ).

cnf(604,plain,
    totalorderP(cons(u,nil)),
    inference(mrr,[status(thm)],[84,597]),
    [iquote('1:MRR:84.0,597.0')] ).

cnf(605,plain,
    strictorderP(cons(u,nil)),
    inference(mrr,[status(thm)],[83,597]),
    [iquote('1:MRR:83.0,597.0')] ).

cnf(606,plain,
    totalorderedP(cons(u,nil)),
    inference(mrr,[status(thm)],[82,597]),
    [iquote('1:MRR:82.0,597.0')] ).

cnf(607,plain,
    strictorderedP(cons(u,nil)),
    inference(mrr,[status(thm)],[81,597]),
    [iquote('1:MRR:81.0,597.0')] ).

cnf(608,plain,
    duplicatefreeP(cons(u,nil)),
    inference(mrr,[status(thm)],[80,597]),
    [iquote('1:MRR:80.0,597.0')] ).

cnf(609,plain,
    equalelemsP(cons(u,nil)),
    inference(mrr,[status(thm)],[79,597]),
    [iquote('1:MRR:79.0,597.0')] ).

cnf(718,plain,
    ( ~ ssList(u)
    | ssList(cons(v,u)) ),
    inference(mrr,[status(thm)],[101,597]),
    [iquote('1:MRR:101.1,597.0')] ).

cnf(723,plain,
    ( ~ ssList(u)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    inference(mrr,[status(thm)],[131,597]),
    [iquote('1:MRR:131.1,597.0')] ).

cnf(802,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | equal(app(cons(w,v),u),cons(w,app(v,u))) ),
    inference(mrr,[status(thm)],[172,597]),
    [iquote('1:MRR:172.2,597.0')] ).

cnf(807,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(app(app(v,cons(w,nil)),u),sk1)
    | memberP(v,sk5(u,v,w)) ),
    inference(mrr,[status(thm)],[12,597]),
    [iquote('1:MRR:12.2,597.0')] ).

cnf(1232,plain,
    ( ~ ssList(cons(u,nil))
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[723]),
    [iquote('1:EqR:723.1')] ).

cnf(1233,plain,
    singletonP(cons(u,nil)),
    inference(ssi,[status(thm)],[1232,718,16,17,18,19,20,21,22,23,609,608,607,606,605,604,603]),
    [iquote('1:SSi:1232.0,718.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.0,609.0,608.0,607.0,606.0,605.0,604.0,603.1')] ).

cnf(4494,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)],[89,807]),
    [iquote('1:SpL:89.1,807.2')] ).

cnf(4508,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)],[89,4494,802]),
    [iquote('1:Rew:89.1,4494.3,802.2,4494.3')] ).

cnf(4509,plain,
    ( ~ ssList(u)
    | ~ equal(cons(v,u),sk1)
    | memberP(nil,sk5(u,nil,v)) ),
    inference(ssi,[status(thm)],[4508,16,17,18,19,20,21,22,23,718,609,608,607,606,605,604,603,1233]),
    [iquote('1:SSi:4508.2,4508.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.0,718.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.1,609.0,608.0,607.0,606.0,605.0,604.0,603.0,1233.0')] ).

cnf(4510,plain,
    ( ~ ssList(u)
    | ~ equal(cons(v,u),sk1) ),
    inference(mrr,[status(thm)],[4509,602]),
    [iquote('1:MRR:4509.2,602.0')] ).

cnf(4912,plain,
    ( ~ ssList(skaf82(sk1))
    | ~ equal(sk1,sk1) ),
    inference(spl,[status(thm),theory(equality)],[581,4510]),
    [iquote('1:SpL:581.0,4510.1')] ).

cnf(5110,plain,
    ~ ssList(skaf82(sk1)),
    inference(obv,[status(thm),theory(equality)],[4912]),
    [iquote('1:Obv:4912.1')] ).

cnf(5111,plain,
    $false,
    inference(ssi,[status(thm)],[5110,28,201,1]),
    [iquote('1:SSi:5110.0,28.0,201.0,1.0')] ).

cnf(5189,plain,
    ( ~ ssList(u)
    | duplicatefreeP(u) ),
    inference(spt,[spt(split,[position(s2)])],[87]),
    [iquote('1:Spt:5111.0,87.0,87.2')] ).

cnf(5203,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)],[194,5189]),
    [iquote('1:MRR:194.1,5189.1')] ).

cnf(15685,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)],[172,100]),
    [iquote('0:SpR:172.3,100.2')] ).

cnf(15736,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(cons(v,u))
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(obv,[status(thm),theory(equality)],[15685]),
    [iquote('0:Obv:15685.0')] ).

cnf(15737,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(ssi,[status(thm)],[15736,101]),
    [iquote('0:SSi:15736.2,101.2')] ).

cnf(17877,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)],[5203]),
    [iquote('1:EqR:5203.5')] ).

cnf(17905,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x) ),
    inference(ssi,[status(thm)],[17877,100,101]),
    [iquote('1:SSi:17877.0,100.2,100.2,101.2,101.2')] ).

cnf(17907,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w) ),
    inference(mrr,[status(thm)],[15737,17905]),
    [iquote('1:MRR:15737.3,17905.1')] ).

cnf(17913,plain,
    ( ~ ssList(u)
    | ~ ssItem(v) ),
    inference(con,[status(thm)],[17907]),
    [iquote('1:Con:17907.2')] ).

cnf(17914,plain,
    ~ ssItem(u),
    inference(mrr,[status(thm)],[536,17913]),
    [iquote('1:MRR:536.1,17913.0')] ).

cnf(17917,plain,
    $false,
    inference(unc,[status(thm)],[17914,27]),
    [iquote('1:UnC:17914.0,27.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWC247-1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n017.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
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jun 12 14:49:52 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 8.02/8.18  
% 8.02/8.18  SPASS V 3.9 
% 8.02/8.18  SPASS beiseite: Proof found.
% 8.02/8.18  % SZS status Theorem
% 8.02/8.18  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 8.02/8.18  SPASS derived 11660 clauses, backtracked 2677 clauses, performed 52 splits and kept 7430 clauses.
% 8.02/8.18  SPASS allocated 89553 KBytes.
% 8.02/8.18  SPASS spent	0:00:06.63 on the problem.
% 8.02/8.18  		0:00:00.04 for the input.
% 8.02/8.18  		0:00:00.00 for the FLOTTER CNF translation.
% 8.02/8.18  		0:00:00.13 for inferences.
% 8.02/8.18  		0:00:00.15 for the backtracking.
% 8.02/8.18  		0:00:06.06 for the reduction.
% 8.02/8.18  
% 8.02/8.18  
% 8.02/8.18  Here is a proof with depth 2, length 68 :
% 8.02/8.18  % SZS output start Refutation
% See solution above
% 8.02/8.18  Formulae used in the proof : co1_1 co1_6 co1_8 co1_9 co1_12 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause12 clause13 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause74 clause85 clause86 clause109 clause116 clause157 clause179
% 8.02/8.18  
%------------------------------------------------------------------------------