TSTP Solution File: SWC153-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC153-1 : 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 22:02:06 EDT 2022

% Result   : Unsatisfiable 34.33s 34.57s
% Output   : Refutation 34.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   20
% Syntax   : Number of clauses     :   62 (  20 unt;   1 nHn;  62 RR)
%            Number of literals    :  206 (   0 equ; 154 neg)
%            Maximal clause size   :   10 (   3 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  15 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    equal(sk1,sk3),
    file('SWC153-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssItem(x)
    | ~ ssItem(y)
    | ~ leq(x,y)
    | ~ equal(app(app(app(app(w,cons(y,nil)),v),cons(x,nil)),u),sk3)
    | leq(y,x) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ ssItem(y)
    | ~ ssItem(z)
    | ~ memberP(w,u)
    | ~ leq(y,z)
    | ~ equal(app(app(app(app(x,cons(z,nil)),w),cons(y,nil)),v),sk3)
    | leq(z,u) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ ssItem(y)
    | ~ ssItem(z)
    | ~ memberP(w,u)
    | ~ leq(y,z)
    | ~ equal(app(app(app(app(x,cons(z,nil)),w),cons(y,nil)),v),sk3)
    | leq(u,y) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(12,axiom,
    ssList(sk7),
    file('SWC153-1.p',unknown),
    [] ).

cnf(13,axiom,
    ssList(sk8),
    file('SWC153-1.p',unknown),
    [] ).

cnf(14,axiom,
    ssList(sk9),
    file('SWC153-1.p',unknown),
    [] ).

cnf(15,axiom,
    equal(app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9),sk1),
    file('SWC153-1.p',unknown),
    [] ).

cnf(16,axiom,
    leq(sk6,sk5),
    file('SWC153-1.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ leq(sk5,sk6)
    | memberP(sk8,sk10) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ leq(sk5,sk6)
    | ~ leq(sk5,sk10)
    | ~ leq(sk10,sk6) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(31,axiom,
    ssItem(skaf83(u)),
    file('SWC153-1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ ssItem(u)
    | leq(u,u) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(91,axiom,
    ( ~ ssList(u)
    | ssItem(v)
    | duplicatefreeP(u) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(104,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(u,v)) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(105,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ssList(cons(v,u)) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(149,axiom,
    ( ~ ssItem(u)
    | ~ ssItem(v)
    | ~ leq(u,v)
    | ~ leq(v,u)
    | equal(u,v) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(175,axiom,
    ( ~ ssItem(u)
    | ~ ssItem(v)
    | ~ ssItem(w)
    | ~ leq(u,v)
    | ~ leq(v,w)
    | leq(u,w) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(176,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | equal(app(cons(w,v),u),cons(w,app(v,u))) ),
    file('SWC153-1.p',unknown),
    [] ).

cnf(198,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('SWC153-1.p',unknown),
    [] ).

cnf(207,plain,
    equal(app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9),sk3),
    inference(rew,[status(thm),theory(equality)],[6,15]),
    [iquote('0:Rew:6.0,15.0')] ).

cnf(349,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,sk9)) ),
    inference(res,[status(thm),theory(equality)],[14,105]),
    [iquote('0:Res:14.0,105.1')] ).

cnf(572,plain,
    ssItem(u),
    inference(spt,[spt(split,[position(s1)])],[91]),
    [iquote('1:Spt:91.1')] ).

cnf(573,plain,
    leq(u,u),
    inference(mrr,[status(thm)],[81,572]),
    [iquote('1:MRR:81.0,572.0')] ).

cnf(641,plain,
    ( ~ leq(u,v)
    | ~ leq(v,u)
    | equal(u,v) ),
    inference(mrr,[status(thm)],[149,572]),
    [iquote('1:MRR:149.1,149.0,572.0')] ).

cnf(669,plain,
    ( ~ leq(u,v)
    | ~ leq(v,w)
    | leq(u,w) ),
    inference(mrr,[status(thm)],[175,572]),
    [iquote('1:MRR:175.2,175.1,175.0,572.0')] ).

cnf(709,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ memberP(v,x)
    | ~ leq(y,z)
    | ~ equal(app(app(app(app(w,cons(z,nil)),v),cons(y,nil)),u),sk3)
    | leq(x,y) ),
    inference(mrr,[status(thm)],[9,572]),
    [iquote('1:MRR:9.5,9.4,9.0,572.0')] ).

cnf(710,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ memberP(v,x)
    | ~ leq(y,z)
    | ~ equal(app(app(app(app(w,cons(z,nil)),v),cons(y,nil)),u),sk3)
    | leq(z,x) ),
    inference(mrr,[status(thm)],[8,572]),
    [iquote('1:MRR:8.5,8.4,8.0,572.0')] ).

cnf(788,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ leq(x,y)
    | ~ equal(app(app(app(app(w,cons(y,nil)),v),cons(x,nil)),u),sk3)
    | leq(y,x) ),
    inference(mrr,[status(thm)],[7,572]),
    [iquote('1:MRR:7.4,7.3,572.0')] ).

cnf(789,plain,
    ( ~ leq(sk5,sk10)
    | ~ leq(sk10,sk6) ),
    inference(mrr,[status(thm)],[19,669]),
    [iquote('1:MRR:19.0,669.2')] ).

cnf(2754,plain,
    ( ~ leq(sk5,sk6)
    | equal(sk6,sk5) ),
    inference(res,[status(thm),theory(equality)],[16,641]),
    [iquote('1:Res:16.0,641.0')] ).

cnf(6567,plain,
    ( ~ ssList(sk9)
    | ~ ssList(sk8)
    | ~ ssList(sk7)
    | ~ leq(sk6,sk5)
    | ~ equal(sk3,sk3)
    | leq(sk5,sk6) ),
    inference(spl,[status(thm),theory(equality)],[207,788]),
    [iquote('1:SpL:207.0,788.4')] ).

cnf(6570,plain,
    ( ~ ssList(sk9)
    | ~ ssList(sk8)
    | ~ ssList(sk7)
    | ~ leq(sk6,sk5)
    | leq(sk5,sk6) ),
    inference(obv,[status(thm),theory(equality)],[6567]),
    [iquote('1:Obv:6567.4')] ).

cnf(22744,plain,
    ( ~ leq(sk6,sk5)
    | leq(sk5,sk6) ),
    inference(ssi,[status(thm)],[6570,12,13,14]),
    [iquote('1:SSi:6570.2,6570.1,6570.0,12.0,13.0,14.0')] ).

cnf(22745,plain,
    leq(sk5,sk6),
    inference(mrr,[status(thm)],[22744,16]),
    [iquote('1:MRR:22744.0,16.0')] ).

cnf(22746,plain,
    memberP(sk8,sk10),
    inference(mrr,[status(thm)],[18,22745]),
    [iquote('1:MRR:18.0,22745.0')] ).

cnf(22747,plain,
    equal(sk6,sk5),
    inference(mrr,[status(thm)],[2754,22745]),
    [iquote('1:MRR:2754.0,22745.0')] ).

cnf(22753,plain,
    ( ~ leq(sk5,sk10)
    | ~ leq(sk10,sk5) ),
    inference(rew,[status(thm),theory(equality)],[22747,789]),
    [iquote('1:Rew:22747.0,789.1')] ).

cnf(22764,plain,
    equal(app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9),sk3),
    inference(rew,[status(thm),theory(equality)],[22747,207]),
    [iquote('1:Rew:22747.0,207.0')] ).

cnf(23020,plain,
    ( ~ ssList(sk9)
    | ~ ssList(sk8)
    | ~ ssList(sk7)
    | ~ memberP(sk8,u)
    | ~ leq(sk5,sk5)
    | ~ equal(sk3,sk3)
    | leq(sk5,u) ),
    inference(spl,[status(thm),theory(equality)],[22764,710]),
    [iquote('1:SpL:22764.0,710.5')] ).

cnf(23021,plain,
    ( ~ ssList(sk9)
    | ~ ssList(sk8)
    | ~ ssList(sk7)
    | ~ memberP(sk8,u)
    | ~ leq(sk5,sk5)
    | ~ equal(sk3,sk3)
    | leq(u,sk5) ),
    inference(spl,[status(thm),theory(equality)],[22764,709]),
    [iquote('1:SpL:22764.0,709.5')] ).

cnf(23030,plain,
    ( ~ ssList(sk9)
    | ~ ssList(sk8)
    | ~ ssList(sk7)
    | ~ memberP(sk8,u)
    | ~ leq(sk5,sk5)
    | leq(u,sk5) ),
    inference(obv,[status(thm),theory(equality)],[23021]),
    [iquote('1:Obv:23021.5')] ).

cnf(23033,plain,
    ( ~ ssList(sk9)
    | ~ ssList(sk8)
    | ~ ssList(sk7)
    | ~ memberP(sk8,u)
    | ~ leq(sk5,sk5)
    | leq(sk5,u) ),
    inference(obv,[status(thm),theory(equality)],[23020]),
    [iquote('1:Obv:23020.5')] ).

cnf(25066,plain,
    ( ~ memberP(sk8,u)
    | ~ leq(sk5,sk5)
    | leq(sk5,u) ),
    inference(ssi,[status(thm)],[23033,12,13,14]),
    [iquote('1:SSi:23033.2,23033.1,23033.0,12.0,13.0,14.0')] ).

cnf(25067,plain,
    ( ~ memberP(sk8,u)
    | leq(sk5,u) ),
    inference(mrr,[status(thm)],[25066,573]),
    [iquote('1:MRR:25066.1,573.0')] ).

cnf(25068,plain,
    ( ~ memberP(sk8,u)
    | ~ leq(sk5,sk5)
    | leq(u,sk5) ),
    inference(ssi,[status(thm)],[23030,12,13,14]),
    [iquote('1:SSi:23030.2,23030.1,23030.0,12.0,13.0,14.0')] ).

cnf(25069,plain,
    ( ~ memberP(sk8,u)
    | leq(u,sk5) ),
    inference(mrr,[status(thm)],[25068,573]),
    [iquote('1:MRR:25068.1,573.0')] ).

cnf(25175,plain,
    leq(sk5,sk10),
    inference(res,[status(thm),theory(equality)],[22746,25067]),
    [iquote('1:Res:22746.0,25067.0')] ).

cnf(25176,plain,
    ~ leq(sk10,sk5),
    inference(mrr,[status(thm)],[22753,25175]),
    [iquote('1:MRR:22753.0,25175.0')] ).

cnf(25180,plain,
    leq(sk10,sk5),
    inference(res,[status(thm),theory(equality)],[22746,25069]),
    [iquote('1:Res:22746.0,25069.0')] ).

cnf(25181,plain,
    $false,
    inference(mrr,[status(thm)],[25180,25176]),
    [iquote('1:MRR:25180.0,25176.0')] ).

cnf(25182,plain,
    ( ~ ssList(u)
    | duplicatefreeP(u) ),
    inference(spt,[spt(split,[position(s2)])],[91]),
    [iquote('1:Spt:25181.0,91.0,91.2')] ).

cnf(25200,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)],[198,25182]),
    [iquote('1:MRR:198.1,25182.1')] ).

cnf(43560,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)],[176,104]),
    [iquote('0:SpR:176.3,104.2')] ).

cnf(43612,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(cons(v,u))
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(obv,[status(thm),theory(equality)],[43560]),
    [iquote('0:Obv:43560.0')] ).

cnf(43613,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(ssi,[status(thm)],[43612,105]),
    [iquote('0:SSi:43612.2,105.2')] ).

cnf(45181,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)],[25200]),
    [iquote('1:EqR:25200.5')] ).

cnf(45219,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x) ),
    inference(ssi,[status(thm)],[45181,104,105]),
    [iquote('1:SSi:45181.0,104.2,104.2,105.2,105.2')] ).

cnf(45220,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w) ),
    inference(mrr,[status(thm)],[43613,45219]),
    [iquote('1:MRR:43613.3,45219.1')] ).

cnf(45223,plain,
    ( ~ ssList(u)
    | ~ ssItem(v) ),
    inference(con,[status(thm)],[45220]),
    [iquote('1:Con:45220.2')] ).

cnf(45225,plain,
    ~ ssItem(u),
    inference(mrr,[status(thm)],[349,45223]),
    [iquote('1:MRR:349.1,45223.0')] ).

cnf(45227,plain,
    $false,
    inference(unc,[status(thm)],[45225,31]),
    [iquote('1:UnC:45225.0,31.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SWC153-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n015.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 23:52:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 34.33/34.57  
% 34.33/34.57  SPASS V 3.9 
% 34.33/34.57  SPASS beiseite: Proof found.
% 34.33/34.57  % SZS status Theorem
% 34.33/34.57  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 34.33/34.57  SPASS derived 29813 clauses, backtracked 16234 clauses, performed 331 splits and kept 22577 clauses.
% 34.33/34.57  SPASS allocated 108196 KBytes.
% 34.33/34.57  SPASS spent	0:0:25.41 on the problem.
% 34.33/34.57  		0:00:00.04 for the input.
% 34.33/34.57  		0:00:00.00 for the FLOTTER CNF translation.
% 34.33/34.57  		0:00:00.30 for inferences.
% 34.33/34.57  		0:00:00.71 for the backtracking.
% 34.33/34.57  		0:0:23.96 for the reduction.
% 34.33/34.57  
% 34.33/34.57  
% 34.33/34.57  Here is a proof with depth 2, length 62 :
% 34.33/34.57  % SZS output start Refutation
% See solution above
% 34.33/34.57  Formulae used in the proof : co1_6 co1_7 co1_8 co1_9 co1_12 co1_13 co1_14 co1_15 co1_16 co1_18 co1_19 clause12 clause62 clause72 clause85 clause86 clause130 clause156 clause157 clause179
% 34.33/34.57  
%------------------------------------------------------------------------------