TSTP Solution File: SEU003+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU003+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 14:33:30 EDT 2022

% Result   : Theorem 12.26s 12.49s
% Output   : Refutation 12.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   33 (  13 unt;   4 nHn;  33 RR)
%            Number of literals    :   86 (   0 equ;  54 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    relation(skc9),
    file('SEU003+1.p',unknown),
    [] ).

cnf(2,axiom,
    relation(skc8),
    file('SEU003+1.p',unknown),
    [] ).

cnf(3,axiom,
    function(skc8),
    file('SEU003+1.p',unknown),
    [] ).

cnf(4,axiom,
    function(skc9),
    file('SEU003+1.p',unknown),
    [] ).

cnf(23,axiom,
    element(skf12(u),u),
    file('SEU003+1.p',unknown),
    [] ).

cnf(29,axiom,
    ~ subset(relation_rng(skc9),relation_dom(skc8)),
    file('SEU003+1.p',unknown),
    [] ).

cnf(30,axiom,
    ~ in(skf7(u,v),u),
    file('SEU003+1.p',unknown),
    [] ).

cnf(37,axiom,
    equal(relation_dom(relation_composition(skc9,skc8)),relation_dom(skc9)),
    file('SEU003+1.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ empty(u)
    | ~ in(v,u) ),
    file('SEU003+1.p',unknown),
    [] ).

cnf(41,axiom,
    ( subset(u,v)
    | in(skf7(v,u),u) ),
    file('SEU003+1.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ element(u,v)
    | empty(v)
    | in(u,v) ),
    file('SEU003+1.p',unknown),
    [] ).

cnf(60,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,w)
    | ~ equal(w,relation_rng(u))
    | in(skf8(u,x),relation_dom(u)) ),
    file('SEU003+1.p',unknown),
    [] ).

cnf(61,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,w)
    | ~ equal(w,relation_rng(u))
    | equal(apply(u,skf8(u,v)),v) ),
    file('SEU003+1.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ relation(u)
    | ~ function(u)
    | ~ relation(v)
    | ~ function(v)
    | ~ in(w,relation_dom(relation_composition(v,u)))
    | in(apply(v,w),relation_dom(u)) ),
    file('SEU003+1.p',unknown),
    [] ).

cnf(73,plain,
    ( ~ relation(skc9)
    | ~ in(u,v)
    | ~ equal(v,relation_rng(skc9))
    | in(skf8(skc9,w),relation_dom(skc9)) ),
    inference(res,[status(thm),theory(equality)],[4,60]),
    [iquote('0:Res:4.0,60.1')] ).

cnf(106,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ function(skc8)
    | ~ in(v,relation_dom(relation_composition(u,skc8)))
    | in(apply(u,v),relation_dom(skc8)) ),
    inference(res,[status(thm),theory(equality)],[2,64]),
    [iquote('0:Res:2.0,64.3')] ).

cnf(139,plain,
    ( ~ in(u,v)
    | ~ equal(v,relation_rng(skc9))
    | in(skf8(skc9,w),relation_dom(skc9)) ),
    inference(mrr,[status(thm)],[73,1]),
    [iquote('0:MRR:73.0,1.0')] ).

cnf(154,plain,
    ( ~ relation(u)
    | ~ function(u)
    | ~ in(v,relation_dom(relation_composition(u,skc8)))
    | in(apply(u,v),relation_dom(skc8)) ),
    inference(mrr,[status(thm)],[106,3]),
    [iquote('0:MRR:106.2,3.0')] ).

cnf(395,plain,
    ( ~ empty(u)
    | subset(u,v) ),
    inference(res,[status(thm),theory(equality)],[41,39]),
    [iquote('0:Res:41.1,39.1')] ).

cnf(440,plain,
    ~ empty(relation_rng(skc9)),
    inference(res,[status(thm),theory(equality)],[395,29]),
    [iquote('0:Res:395.1,29.0')] ).

cnf(507,plain,
    ( empty(u)
    | in(skf12(u),u) ),
    inference(res,[status(thm),theory(equality)],[23,46]),
    [iquote('0:Res:23.0,46.0')] ).

cnf(711,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,relation_rng(u))
    | equal(apply(u,skf8(u,v)),v) ),
    inference(eqr,[status(thm),theory(equality)],[61]),
    [iquote('0:EqR:61.3')] ).

cnf(1268,plain,
    ( ~ in(u,relation_rng(skc9))
    | in(skf8(skc9,v),relation_dom(skc9)) ),
    inference(eqr,[status(thm),theory(equality)],[139]),
    [iquote('0:EqR:139.1')] ).

cnf(2162,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ relation(u)
    | ~ function(u)
    | ~ in(v,relation_rng(u))
    | ~ in(skf8(u,v),relation_dom(relation_composition(u,skc8)))
    | in(v,relation_dom(skc8)) ),
    inference(spr,[status(thm),theory(equality)],[711,154]),
    [iquote('0:SpR:711.3,154.3')] ).

cnf(2179,plain,
    ( ~ relation(u)
    | ~ function(u)
    | ~ in(v,relation_rng(u))
    | ~ in(skf8(u,v),relation_dom(relation_composition(u,skc8)))
    | in(v,relation_dom(skc8)) ),
    inference(obv,[status(thm),theory(equality)],[2162]),
    [iquote('0:Obv:2162.1')] ).

cnf(3766,plain,
    ( empty(relation_rng(skc9))
    | in(skf8(skc9,u),relation_dom(skc9)) ),
    inference(res,[status(thm),theory(equality)],[507,1268]),
    [iquote('0:Res:507.1,1268.0')] ).

cnf(3788,plain,
    in(skf8(skc9,u),relation_dom(skc9)),
    inference(mrr,[status(thm)],[3766,440]),
    [iquote('0:MRR:3766.0,440.0')] ).

cnf(18510,plain,
    ( ~ relation(skc9)
    | ~ function(skc9)
    | ~ in(u,relation_rng(skc9))
    | ~ in(skf8(skc9,u),relation_dom(skc9))
    | in(u,relation_dom(skc8)) ),
    inference(spl,[status(thm),theory(equality)],[37,2179]),
    [iquote('0:SpL:37.0,2179.3')] ).

cnf(18514,plain,
    ( ~ in(u,relation_rng(skc9))
    | ~ in(skf8(skc9,u),relation_dom(skc9))
    | in(u,relation_dom(skc8)) ),
    inference(ssi,[status(thm)],[18510,4,1]),
    [iquote('0:SSi:18510.1,18510.0,4.0,1.0,4.0,1.0')] ).

cnf(18515,plain,
    ( ~ in(u,relation_rng(skc9))
    | in(u,relation_dom(skc8)) ),
    inference(mrr,[status(thm)],[18514,3788]),
    [iquote('0:MRR:18514.1,3788.0')] ).

cnf(18524,plain,
    ~ in(skf7(relation_dom(skc8),u),relation_rng(skc9)),
    inference(res,[status(thm),theory(equality)],[18515,30]),
    [iquote('0:Res:18515.1,30.0')] ).

cnf(18542,plain,
    subset(relation_rng(skc9),relation_dom(skc8)),
    inference(res,[status(thm),theory(equality)],[41,18524]),
    [iquote('0:Res:41.1,18524.0')] ).

cnf(18544,plain,
    $false,
    inference(mrr,[status(thm)],[18542,29]),
    [iquote('0:MRR:18542.0,29.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU003+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n022.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 : Sat Jun 18 21:24:17 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 12.26/12.49  
% 12.26/12.49  SPASS V 3.9 
% 12.26/12.49  SPASS beiseite: Proof found.
% 12.26/12.49  % SZS status Theorem
% 12.26/12.49  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 12.26/12.49  SPASS derived 15249 clauses, backtracked 862 clauses, performed 9 splits and kept 7751 clauses.
% 12.26/12.49  SPASS allocated 115477 KBytes.
% 12.26/12.49  SPASS spent	0:0:11.73 on the problem.
% 12.26/12.49  		0:00:00.04 for the input.
% 12.26/12.49  		0:00:00.05 for the FLOTTER CNF translation.
% 12.26/12.49  		0:00:00.19 for inferences.
% 12.26/12.49  		0:00:00.48 for the backtracking.
% 12.26/12.49  		0:0:10.86 for the reduction.
% 12.26/12.49  
% 12.26/12.49  
% 12.26/12.49  Here is a proof with depth 5, length 33 :
% 12.26/12.49  % SZS output start Refutation
% See solution above
% 12.26/12.49  Formulae used in the proof : t27_funct_1 existence_m1_subset_1 d3_tarski antisymmetry_r2_hidden t7_boole t2_subset d5_funct_1 t21_funct_1
% 12.26/12.49  
%------------------------------------------------------------------------------