TSTP Solution File: SET995+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET995+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.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 05:30:18 EDT 2022

% Result   : Theorem 0.36s 0.57s
% Output   : Refutation 0.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   30 (  14 unt;   2 nHn;  30 RR)
%            Number of literals    :   80 (   0 equ;  51 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    function(skc10),
    file('SET995+1.p',unknown),
    [] ).

cnf(2,axiom,
    relation(skc10),
    file('SET995+1.p',unknown),
    [] ).

cnf(3,axiom,
    function(skc9),
    file('SET995+1.p',unknown),
    [] ).

cnf(4,axiom,
    relation(skc9),
    file('SET995+1.p',unknown),
    [] ).

cnf(23,axiom,
    ~ equal(skc10,skc9),
    file('SET995+1.p',unknown),
    [] ).

cnf(27,axiom,
    equal(relation_rng(skc9),singleton(skc11)),
    file('SET995+1.p',unknown),
    [] ).

cnf(28,axiom,
    equal(relation_rng(skc10),singleton(skc11)),
    file('SET995+1.p',unknown),
    [] ).

cnf(29,axiom,
    equal(relation_dom(skc10),relation_dom(skc9)),
    file('SET995+1.p',unknown),
    [] ).

cnf(50,axiom,
    ( ~ in(u,v)
    | ~ equal(v,singleton(w))
    | equal(u,w) ),
    file('SET995+1.p',unknown),
    [] ).

cnf(60,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,relation_dom(u))
    | ~ equal(w,relation_rng(u))
    | ~ equal(x,apply(u,v))
    | in(x,w) ),
    file('SET995+1.p',unknown),
    [] ).

cnf(61,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ function(v)
    | ~ relation(v)
    | ~ equal(relation_dom(v),relation_dom(u))
    | equal(v,u)
    | in(skf16(v,w),relation_dom(v)) ),
    file('SET995+1.p',unknown),
    [] ).

cnf(62,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ function(v)
    | ~ relation(v)
    | ~ equal(relation_dom(v),relation_dom(u))
    | ~ equal(apply(v,skf16(v,u)),apply(u,skf16(v,u)))
    | equal(v,u) ),
    file('SET995+1.p',unknown),
    [] ).

cnf(114,plain,
    ( ~ relation(skc9)
    | ~ function(skc9)
    | ~ relation(skc10)
    | ~ function(skc10)
    | ~ equal(apply(skc10,skf16(skc9,skc10)),apply(skc9,skf16(skc9,skc10)))
    | equal(skc10,skc9) ),
    inference(res,[status(thm),theory(equality)],[29,62]),
    [iquote('0:Res:29.0,62.5')] ).

cnf(115,plain,
    ( ~ relation(skc9)
    | ~ function(skc9)
    | ~ relation(skc10)
    | ~ function(skc10)
    | in(skf16(skc9,u),relation_dom(skc9))
    | equal(skc10,skc9) ),
    inference(res,[status(thm),theory(equality)],[29,61]),
    [iquote('0:Res:29.0,61.4')] ).

cnf(123,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | ~ in(u,relation_dom(skc10))
    | ~ equal(v,apply(skc10,u))
    | in(v,singleton(skc11)) ),
    inference(res,[status(thm),theory(equality)],[28,60]),
    [iquote('0:Res:28.0,60.2')] ).

cnf(130,plain,
    ( ~ relation(skc9)
    | ~ function(skc9)
    | ~ in(u,relation_dom(skc9))
    | ~ equal(v,apply(skc9,u))
    | in(v,singleton(skc11)) ),
    inference(res,[status(thm),theory(equality)],[27,60]),
    [iquote('0:Res:27.0,60.2')] ).

cnf(161,plain,
    ( ~ in(u,relation_dom(skc9))
    | ~ equal(v,apply(skc9,u))
    | in(v,singleton(skc11)) ),
    inference(mrr,[status(thm)],[130,4,3]),
    [iquote('0:MRR:130.0,130.1,4.0,3.0')] ).

cnf(162,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | ~ in(u,relation_dom(skc9))
    | ~ equal(v,apply(skc10,u))
    | in(v,singleton(skc11)) ),
    inference(rew,[status(thm),theory(equality)],[29,123]),
    [iquote('0:Rew:29.0,123.2')] ).

cnf(163,plain,
    ( ~ in(u,relation_dom(skc9))
    | ~ equal(v,apply(skc10,u))
    | in(v,singleton(skc11)) ),
    inference(mrr,[status(thm)],[162,2,1]),
    [iquote('0:MRR:162.0,162.1,2.0,1.0')] ).

cnf(164,plain,
    in(skf16(skc9,u),relation_dom(skc9)),
    inference(mrr,[status(thm)],[115,4,3,2,1,23]),
    [iquote('0:MRR:115.0,115.1,115.2,115.3,115.5,4.0,3.0,2.0,1.0,23.0')] ).

cnf(187,plain,
    ~ equal(apply(skc10,skf16(skc9,skc10)),apply(skc9,skf16(skc9,skc10))),
    inference(mrr,[status(thm)],[114,4,3,2,1,23]),
    [iquote('0:MRR:114.0,114.1,114.2,114.3,114.5,4.0,3.0,2.0,1.0,23.0')] ).

cnf(360,plain,
    ( ~ in(u,singleton(v))
    | equal(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[50]),
    [iquote('0:EqR:50.1')] ).

cnf(862,plain,
    ( ~ in(u,relation_dom(skc9))
    | in(apply(skc10,u),singleton(skc11)) ),
    inference(eqr,[status(thm),theory(equality)],[163]),
    [iquote('0:EqR:163.1')] ).

cnf(873,plain,
    ( ~ in(u,relation_dom(skc9))
    | equal(apply(skc10,u),skc11) ),
    inference(res,[status(thm),theory(equality)],[862,360]),
    [iquote('0:Res:862.1,360.0')] ).

cnf(888,plain,
    equal(apply(skc10,skf16(skc9,u)),skc11),
    inference(res,[status(thm),theory(equality)],[164,873]),
    [iquote('0:Res:164.0,873.0')] ).

cnf(898,plain,
    ~ equal(apply(skc9,skf16(skc9,skc10)),skc11),
    inference(rew,[status(thm),theory(equality)],[888,187]),
    [iquote('0:Rew:888.0,187.0')] ).

cnf(1124,plain,
    ( ~ in(u,relation_dom(skc9))
    | in(apply(skc9,u),singleton(skc11)) ),
    inference(eqr,[status(thm),theory(equality)],[161]),
    [iquote('0:EqR:161.1')] ).

cnf(1172,plain,
    ( ~ in(u,relation_dom(skc9))
    | equal(apply(skc9,u),skc11) ),
    inference(res,[status(thm),theory(equality)],[1124,360]),
    [iquote('0:Res:1124.1,360.0')] ).

cnf(1189,plain,
    equal(apply(skc9,skf16(skc9,u)),skc11),
    inference(res,[status(thm),theory(equality)],[164,1172]),
    [iquote('0:Res:164.0,1172.0')] ).

cnf(1198,plain,
    $false,
    inference(unc,[status(thm)],[1189,898]),
    [iquote('0:UnC:1189.0,898.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET995+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n013.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 : Sat Jul  9 17:26:29 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.36/0.57  
% 0.36/0.57  SPASS V 3.9 
% 0.36/0.57  SPASS beiseite: Proof found.
% 0.36/0.57  % SZS status Theorem
% 0.36/0.57  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.36/0.57  SPASS derived 917 clauses, backtracked 50 clauses, performed 4 splits and kept 550 clauses.
% 0.36/0.57  SPASS allocated 98585 KBytes.
% 0.36/0.57  SPASS spent	0:00:00.22 on the problem.
% 0.36/0.57  		0:00:00.03 for the input.
% 0.36/0.57  		0:00:00.05 for the FLOTTER CNF translation.
% 0.36/0.57  		0:00:00.01 for inferences.
% 0.36/0.57  		0:00:00.00 for the backtracking.
% 0.36/0.57  		0:00:00.09 for the reduction.
% 0.36/0.57  
% 0.36/0.57  
% 0.36/0.57  Here is a proof with depth 4, length 30 :
% 0.36/0.57  % SZS output start Refutation
% See solution above
% 0.36/0.57  Formulae used in the proof : t17_funct_1 d1_tarski antisymmetry_r2_hidden d5_funct_1 t9_funct_1
% 0.36/0.57  
%------------------------------------------------------------------------------