TSTP Solution File: SWC261-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC261-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 22:02:54 EDT 2022

% Result   : Unsatisfiable 69.94s 70.14s
% Output   : Refutation 69.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   20
% Syntax   : Number of clauses     :   59 (  15 unt;  12 nHn;  59 RR)
%            Number of literals    :  172 (   0 equ; 109 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(sk1),
    file('SWC261-1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(sk2),
    file('SWC261-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(sk3,sk1),
    file('SWC261-1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ ssItem(u)
    | ~ memberP(sk3,u)
    | equal(sk5,u) ),
    file('SWC261-1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ totalorderedP(sk1),
    file('SWC261-1.p',unknown),
    [] ).

cnf(36,axiom,
    ssList(skaf68(u)),
    file('SWC261-1.p',unknown),
    [] ).

cnf(37,axiom,
    ssList(skaf67(u)),
    file('SWC261-1.p',unknown),
    [] ).

cnf(38,axiom,
    ssList(skaf66(u)),
    file('SWC261-1.p',unknown),
    [] ).

cnf(56,axiom,
    ssItem(skaf44(u)),
    file('SWC261-1.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ ssItem(u)
    | geq(u,u) ),
    file('SWC261-1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ ssList(u)
    | ssItem(v)
    | duplicatefreeP(u) ),
    file('SWC261-1.p',unknown),
    [] ).

cnf(94,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(u,v)) ),
    file('SWC261-1.p',unknown),
    [] ).

cnf(95,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ssList(cons(v,u)) ),
    file('SWC261-1.p',unknown),
    [] ).

cnf(100,axiom,
    ( ~ ssList(u)
    | ~ leq(skaf64(u),skaf65(u))
    | totalorderedP(u) ),
    file('SWC261-1.p',unknown),
    [] ).

cnf(116,axiom,
    ( ~ ssItem(u)
    | ~ ssItem(v)
    | ~ geq(u,v)
    | leq(v,u) ),
    file('SWC261-1.p',unknown),
    [] ).

cnf(149,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ memberP(v,u)
    | memberP(app(v,w),u) ),
    file('SWC261-1.p',unknown),
    [] ).

cnf(166,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | equal(app(cons(w,v),u),cons(w,app(v,u))) ),
    file('SWC261-1.p',unknown),
    [] ).

cnf(173,axiom,
    ( ~ ssList(u)
    | totalorderedP(u)
    | equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u) ),
    file('SWC261-1.p',unknown),
    [] ).

cnf(184,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ equal(app(w,cons(v,x)),u)
    | memberP(u,v) ),
    file('SWC261-1.p',unknown),
    [] ).

cnf(188,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('SWC261-1.p',unknown),
    [] ).

cnf(197,plain,
    ( ~ ssItem(u)
    | ~ memberP(sk1,u)
    | equal(sk5,u) ),
    inference(rew,[status(thm),theory(equality)],[6,8]),
    [iquote('0:Rew:6.0,8.1')] ).

cnf(442,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,sk2)) ),
    inference(res,[status(thm),theory(equality)],[2,95]),
    [iquote('0:Res:2.0,95.1')] ).

cnf(478,plain,
    ssItem(u),
    inference(spt,[spt(split,[position(s1)])],[81]),
    [iquote('1:Spt:81.1')] ).

cnf(480,plain,
    geq(u,u),
    inference(mrr,[status(thm)],[64,478]),
    [iquote('1:MRR:64.0,478.0')] ).

cnf(507,plain,
    ( ~ memberP(sk1,u)
    | equal(sk5,u) ),
    inference(mrr,[status(thm)],[197,478]),
    [iquote('1:MRR:197.0,478.0')] ).

cnf(524,plain,
    ( ~ geq(u,v)
    | leq(v,u) ),
    inference(mrr,[status(thm)],[116,478]),
    [iquote('1:MRR:116.1,116.0,478.0')] ).

cnf(577,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ memberP(u,w)
    | memberP(app(u,v),w) ),
    inference(mrr,[status(thm)],[149,478]),
    [iquote('1:MRR:149.0,478.0')] ).

cnf(614,plain,
    ( ~ ssList(u)
    | ssList(cons(v,u)) ),
    inference(mrr,[status(thm)],[95,478]),
    [iquote('1:MRR:95.1,478.0')] ).

cnf(628,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(v,cons(x,w)),u)
    | memberP(u,x) ),
    inference(mrr,[status(thm)],[184,478]),
    [iquote('1:MRR:184.1,478.0')] ).

cnf(1317,plain,
    ( ~ ssList(u)
    | ~ geq(skaf65(u),skaf64(u))
    | totalorderedP(u) ),
    inference(res,[status(thm),theory(equality)],[524,100]),
    [iquote('1:Res:524.1,100.1')] ).

cnf(3493,plain,
    ( ~ ssList(app(u,cons(v,w)))
    | ~ ssList(u)
    | ~ ssList(w)
    | memberP(app(u,cons(v,w)),v) ),
    inference(eqr,[status(thm),theory(equality)],[628]),
    [iquote('1:EqR:628.3')] ).

cnf(3508,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | memberP(app(u,cons(w,v)),w) ),
    inference(ssi,[status(thm)],[3493,94,614]),
    [iquote('1:SSi:3493.0,94.1,614.2')] ).

cnf(4177,plain,
    ( ~ ssList(u)
    | ~ ssList(app(skaf66(u),cons(skaf64(u),skaf67(u))))
    | ~ ssList(cons(skaf65(u),skaf68(u)))
    | ~ memberP(app(skaf66(u),cons(skaf64(u),skaf67(u))),v)
    | totalorderedP(u)
    | memberP(u,v) ),
    inference(spr,[status(thm),theory(equality)],[173,577]),
    [iquote('1:SpR:173.2,577.3')] ).

cnf(4206,plain,
    ( ~ ssList(u)
    | ~ memberP(app(skaf66(u),cons(skaf64(u),skaf67(u))),v)
    | totalorderedP(u)
    | memberP(u,v) ),
    inference(ssi,[status(thm)],[4177,614,36,94,38,37]),
    [iquote('1:SSi:4177.2,4177.1,614.0,36.1,94.0,38.2,614.0,37.1')] ).

cnf(6816,plain,
    ( ~ ssList(u)
    | ~ ssList(app(skaf66(u),cons(skaf64(u),skaf67(u))))
    | ~ ssList(skaf68(u))
    | totalorderedP(u)
    | memberP(u,skaf65(u)) ),
    inference(spr,[status(thm),theory(equality)],[173,3508]),
    [iquote('1:SpR:173.2,3508.2')] ).

cnf(6838,plain,
    ( ~ ssList(u)
    | totalorderedP(u)
    | memberP(u,skaf65(u)) ),
    inference(ssi,[status(thm)],[6816,36,94,38,614,37]),
    [iquote('1:SSi:6816.2,6816.1,36.0,94.1,38.0,614.2,37.0')] ).

cnf(7687,plain,
    ( ~ ssList(sk1)
    | totalorderedP(sk1)
    | equal(skaf65(sk1),sk5) ),
    inference(res,[status(thm),theory(equality)],[6838,507]),
    [iquote('1:Res:6838.2,507.0')] ).

cnf(23238,plain,
    ( ~ ssList(skaf66(u))
    | ~ ssList(skaf67(u))
    | ~ ssList(u)
    | totalorderedP(u)
    | memberP(u,skaf64(u)) ),
    inference(res,[status(thm),theory(equality)],[3508,4206]),
    [iquote('1:Res:3508.2,4206.1')] ).

cnf(23256,plain,
    ( ~ ssList(u)
    | totalorderedP(u)
    | memberP(u,skaf64(u)) ),
    inference(ssi,[status(thm)],[23238,37,38]),
    [iquote('1:SSi:23238.1,23238.0,37.0,38.0')] ).

cnf(31761,plain,
    ( ~ ssList(sk1)
    | totalorderedP(sk1)
    | equal(skaf64(sk1),sk5) ),
    inference(res,[status(thm),theory(equality)],[23256,507]),
    [iquote('1:Res:23256.2,507.0')] ).

cnf(32043,plain,
    ( totalorderedP(sk1)
    | equal(skaf65(sk1),sk5) ),
    inference(ssi,[status(thm)],[7687,1]),
    [iquote('1:SSi:7687.0,1.0')] ).

cnf(32044,plain,
    equal(skaf65(sk1),sk5),
    inference(mrr,[status(thm)],[32043,9]),
    [iquote('1:MRR:32043.0,9.0')] ).

cnf(32049,plain,
    ( totalorderedP(sk1)
    | equal(skaf64(sk1),sk5) ),
    inference(ssi,[status(thm)],[31761,1]),
    [iquote('1:SSi:31761.0,1.0')] ).

cnf(32050,plain,
    equal(skaf64(sk1),sk5),
    inference(mrr,[status(thm)],[32049,9]),
    [iquote('1:MRR:32049.0,9.0')] ).

cnf(32182,plain,
    ( ~ ssList(sk1)
    | ~ geq(sk5,skaf64(sk1))
    | totalorderedP(sk1) ),
    inference(spl,[status(thm),theory(equality)],[32044,1317]),
    [iquote('1:SpL:32044.0,1317.1')] ).

cnf(32188,plain,
    ( ~ ssList(sk1)
    | ~ geq(sk5,sk5)
    | totalorderedP(sk1) ),
    inference(rew,[status(thm),theory(equality)],[32050,32182]),
    [iquote('1:Rew:32050.0,32182.1')] ).

cnf(32189,plain,
    ( ~ geq(sk5,sk5)
    | totalorderedP(sk1) ),
    inference(ssi,[status(thm)],[32188,1]),
    [iquote('1:SSi:32188.0,1.0')] ).

cnf(32190,plain,
    $false,
    inference(mrr,[status(thm)],[32189,480,9]),
    [iquote('1:MRR:32189.0,32189.1,480.0,9.0')] ).

cnf(32203,plain,
    ( ~ ssList(u)
    | duplicatefreeP(u) ),
    inference(spt,[spt(split,[position(s2)])],[81]),
    [iquote('1:Spt:32190.0,81.0,81.2')] ).

cnf(32443,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)],[188,32203]),
    [iquote('1:MRR:188.1,32203.1')] ).

cnf(46252,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)],[166,94]),
    [iquote('0:SpR:166.3,94.2')] ).

cnf(46293,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(cons(v,u))
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(obv,[status(thm),theory(equality)],[46252]),
    [iquote('0:Obv:46252.0')] ).

cnf(46294,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(ssi,[status(thm)],[46293,95]),
    [iquote('0:SSi:46293.2,95.2')] ).

cnf(47249,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)],[32443]),
    [iquote('1:EqR:32443.5')] ).

cnf(47277,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x) ),
    inference(ssi,[status(thm)],[47249,94,95]),
    [iquote('1:SSi:47249.0,94.2,94.2,95.2,95.2')] ).

cnf(47278,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w) ),
    inference(mrr,[status(thm)],[46294,47277]),
    [iquote('1:MRR:46294.3,47277.1')] ).

cnf(47281,plain,
    ( ~ ssList(u)
    | ~ ssItem(v) ),
    inference(con,[status(thm)],[47278]),
    [iquote('1:Con:47278.2')] ).

cnf(47282,plain,
    ~ ssItem(u),
    inference(mrr,[status(thm)],[442,47281]),
    [iquote('1:MRR:442.1,47281.0')] ).

cnf(47283,plain,
    $false,
    inference(unc,[status(thm)],[47282,56]),
    [iquote('1:UnC:47282.0,56.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC261-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jun 11 21:47:25 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 69.94/70.14  
% 69.94/70.14  SPASS V 3.9 
% 69.94/70.14  SPASS beiseite: Proof found.
% 69.94/70.14  % SZS status Theorem
% 69.94/70.14  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 69.94/70.14  SPASS derived 28677 clauses, backtracked 7658 clauses, performed 101 splits and kept 18125 clauses.
% 69.94/70.14  SPASS allocated 113758 KBytes.
% 69.94/70.14  SPASS spent	0:0:58.29 on the problem.
% 69.94/70.14  		0:00:00.04 for the input.
% 69.94/70.14  		0:00:00.00 for the FLOTTER CNF translation.
% 69.94/70.14  		0:00:00.47 for inferences.
% 69.94/70.14  		0:00:02.89 for the backtracking.
% 69.94/70.14  		0:0:54.38 for the reduction.
% 69.94/70.14  
% 69.94/70.14  
% 69.94/70.14  Here is a proof with depth 4, length 59 :
% 69.94/70.14  % SZS output start Refutation
% See solution above
% 69.94/70.14  Formulae used in the proof : co1_1 co1_2 co1_6 co1_8 co1_9 clause27 clause28 clause29 clause47 clause55 clause72 clause85 clause86 clause91 clause107 clause140 clause157 clause164 clause175 clause179
% 69.94/70.14  
%------------------------------------------------------------------------------