TSTP Solution File: SET681+3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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 05:28:03 EDT 2022

% Result   : Theorem 18.48s 18.69s
% Output   : Refutation 18.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   45 (  14 unt;   3 nHn;  45 RR)
%            Number of literals    :  106 (   0 equ;  73 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  12 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    ilf_type(u,set_type),
    file('SET681+3.p',unknown),
    [] ).

cnf(12,axiom,
    ilf_type(skc8,relation_type(skc7,skc6)),
    file('SET681+3.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ relation_like(u)
    | ~ ilf_type(u,set_type)
    | ilf_type(u,binary_relation_type) ),
    file('SET681+3.p',unknown),
    [] ).

cnf(28,axiom,
    ( member(ordered_pair(skc10,skc9),skc8)
    | member(skc9,range__dfg(skc7,skc6,skc8)) ),
    file('SET681+3.p',unknown),
    [] ).

cnf(34,axiom,
    ( ~ empty(u)
    | ~ ilf_type(v,set_type)
    | ~ member(v,u)
    | ~ ilf_type(u,set_type) ),
    file('SET681+3.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(w,subset_type(cross_product(u,v)))
    | relation_like(w) ),
    file('SET681+3.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ member(skc9,range__dfg(skc7,skc6,skc8))
    | ~ ilf_type(u,member_type(skc7))
    | ~ member(ordered_pair(u,skc9),skc8) ),
    file('SET681+3.p',unknown),
    [] ).

cnf(40,axiom,
    ( ~ member(u,v)
    | ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | ilf_type(u,member_type(v))
    | empty(v) ),
    file('SET681+3.p',unknown),
    [] ).

cnf(44,axiom,
    ( ~ ilf_type(u,relation_type(v,w))
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(w,set_type)
    | ilf_type(u,subset_type(cross_product(v,w))) ),
    file('SET681+3.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ member(u,range_of(v))
    | ~ ilf_type(u,set_type)
    | ~ ilf_type(v,binary_relation_type)
    | member(ordered_pair(skf10(v,u),u),v) ),
    file('SET681+3.p',unknown),
    [] ).

cnf(48,axiom,
    ( ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(w,relation_type(u,v))
    | equal(range__dfg(u,v,w),range_of(w)) ),
    file('SET681+3.p',unknown),
    [] ).

cnf(54,axiom,
    ( ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(w,binary_relation_type)
    | ~ member(ordered_pair(u,v),w)
    | member(v,range_of(w)) ),
    file('SET681+3.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(w,set_type)
    | ~ ilf_type(x,set_type)
    | ~ ilf_type(y,relation_type(u,v))
    | ~ member(ordered_pair(w,x),y)
    | member(w,u) ),
    file('SET681+3.p',unknown),
    [] ).

cnf(69,plain,
    ( ~ relation_like(u)
    | ilf_type(u,binary_relation_type) ),
    inference(mrr,[status(thm)],[26,6]),
    [iquote('0:MRR:26.1,6.0')] ).

cnf(74,plain,
    ( ~ empty(u)
    | ~ member(v,u) ),
    inference(mrr,[status(thm)],[34,6]),
    [iquote('0:MRR:34.1,34.3,6.0,6.0')] ).

cnf(76,plain,
    ( ~ ilf_type(u,subset_type(cross_product(v,w)))
    | relation_like(u) ),
    inference(mrr,[status(thm)],[37,6]),
    [iquote('0:MRR:37.0,37.1,6.0,6.0')] ).

cnf(81,plain,
    ( ~ member(u,v)
    | ilf_type(u,member_type(v)) ),
    inference(mrr,[status(thm)],[40,6,74]),
    [iquote('0:MRR:40.1,40.2,40.4,6.0,6.0,74.0')] ).

cnf(83,plain,
    ( ~ ilf_type(u,relation_type(v,w))
    | ilf_type(u,subset_type(cross_product(v,w))) ),
    inference(mrr,[status(thm)],[44,6]),
    [iquote('0:MRR:44.1,44.2,6.0,6.0')] ).

cnf(85,plain,
    ( ~ ilf_type(u,binary_relation_type)
    | ~ member(v,range_of(u))
    | member(ordered_pair(skf10(u,v),v),u) ),
    inference(mrr,[status(thm)],[46,6]),
    [iquote('0:MRR:46.1,6.0')] ).

cnf(87,plain,
    ( ~ ilf_type(u,relation_type(v,w))
    | equal(range__dfg(v,w,u),range_of(u)) ),
    inference(mrr,[status(thm)],[48,6]),
    [iquote('0:MRR:48.0,48.1,6.0,6.0')] ).

cnf(95,plain,
    ( ~ ilf_type(u,binary_relation_type)
    | ~ member(ordered_pair(v,w),u)
    | member(w,range_of(u)) ),
    inference(mrr,[status(thm)],[54,6]),
    [iquote('0:MRR:54.0,54.1,6.0,6.0')] ).

cnf(105,plain,
    ( ~ ilf_type(u,relation_type(v,w))
    | ~ member(ordered_pair(x,y),u)
    | member(x,v) ),
    inference(mrr,[status(thm)],[64,6]),
    [iquote('0:MRR:64.0,64.1,64.2,64.3,6.0,6.0,6.0,6.0')] ).

cnf(113,plain,
    ( ~ member(ordered_pair(u,v),skc8)
    | member(u,skc7) ),
    inference(res,[status(thm),theory(equality)],[12,105]),
    [iquote('0:Res:12.0,105.0')] ).

cnf(118,plain,
    equal(range__dfg(skc7,skc6,skc8),range_of(skc8)),
    inference(res,[status(thm),theory(equality)],[12,87]),
    [iquote('0:Res:12.0,87.0')] ).

cnf(119,plain,
    ilf_type(skc8,subset_type(cross_product(skc7,skc6))),
    inference(res,[status(thm),theory(equality)],[12,83]),
    [iquote('0:Res:12.0,83.0')] ).

cnf(121,plain,
    ( ~ ilf_type(u,member_type(skc7))
    | ~ member(skc9,range_of(skc8))
    | ~ member(ordered_pair(u,skc9),skc8) ),
    inference(rew,[status(thm),theory(equality)],[118,38]),
    [iquote('0:Rew:118.0,38.0')] ).

cnf(122,plain,
    ( member(skc9,range_of(skc8))
    | member(ordered_pair(skc10,skc9),skc8) ),
    inference(rew,[status(thm),theory(equality)],[118,28]),
    [iquote('0:Rew:118.0,28.1')] ).

cnf(125,plain,
    ~ member(skc9,range_of(skc8)),
    inference(spt,[spt(split,[position(s1)])],[121]),
    [iquote('1:Spt:121.1')] ).

cnf(127,plain,
    member(ordered_pair(skc10,skc9),skc8),
    inference(mrr,[status(thm)],[122,125]),
    [iquote('1:MRR:122.0,125.0')] ).

cnf(156,plain,
    relation_like(skc8),
    inference(res,[status(thm),theory(equality)],[119,76]),
    [iquote('0:Res:119.0,76.0')] ).

cnf(303,plain,
    ( ~ ilf_type(skc8,binary_relation_type)
    | member(skc9,range_of(skc8)) ),
    inference(res,[status(thm),theory(equality)],[127,95]),
    [iquote('1:Res:127.0,95.1')] ).

cnf(307,plain,
    ~ ilf_type(skc8,binary_relation_type),
    inference(mrr,[status(thm)],[303,125]),
    [iquote('1:MRR:303.1,125.0')] ).

cnf(308,plain,
    ~ relation_like(skc8),
    inference(res,[status(thm),theory(equality)],[69,307]),
    [iquote('1:Res:69.1,307.0')] ).

cnf(309,plain,
    $false,
    inference(ssi,[status(thm)],[308,156]),
    [iquote('1:SSi:308.0,156.0')] ).

cnf(310,plain,
    member(skc9,range_of(skc8)),
    inference(spt,[spt(split,[position(sa)])],[309,125]),
    [iquote('1:Spt:309.0,121.1,125.0')] ).

cnf(311,plain,
    ( ~ ilf_type(u,member_type(skc7))
    | ~ member(ordered_pair(u,skc9),skc8) ),
    inference(spt,[spt(split,[position(s2)])],[121]),
    [iquote('1:Spt:309.0,121.0,121.2')] ).

cnf(817,plain,
    ( ~ ilf_type(skc8,binary_relation_type)
    | ~ member(u,range_of(skc8))
    | member(skf10(skc8,u),skc7) ),
    inference(res,[status(thm),theory(equality)],[85,113]),
    [iquote('0:Res:85.2,113.0')] ).

cnf(819,plain,
    ( ~ ilf_type(skc8,binary_relation_type)
    | ~ member(skc9,range_of(skc8))
    | ~ ilf_type(skf10(skc8,skc9),member_type(skc7)) ),
    inference(res,[status(thm),theory(equality)],[85,311]),
    [iquote('1:Res:85.2,311.1')] ).

cnf(828,plain,
    ( ~ ilf_type(skc8,binary_relation_type)
    | ~ ilf_type(skf10(skc8,skc9),member_type(skc7)) ),
    inference(mrr,[status(thm)],[819,310]),
    [iquote('1:MRR:819.1,310.0')] ).

cnf(989,plain,
    ( ~ member(skf10(skc8,skc9),skc7)
    | ~ ilf_type(skc8,binary_relation_type) ),
    inference(res,[status(thm),theory(equality)],[81,828]),
    [iquote('1:Res:81.1,828.1')] ).

cnf(15827,plain,
    ( ~ ilf_type(skc8,binary_relation_type)
    | ~ member(skc9,range_of(skc8))
    | ~ ilf_type(skc8,binary_relation_type) ),
    inference(res,[status(thm),theory(equality)],[817,989]),
    [iquote('1:Res:817.2,989.0')] ).

cnf(15828,plain,
    ( ~ member(skc9,range_of(skc8))
    | ~ ilf_type(skc8,binary_relation_type) ),
    inference(obv,[status(thm),theory(equality)],[15827]),
    [iquote('1:Obv:15827.0')] ).

cnf(15829,plain,
    ~ ilf_type(skc8,binary_relation_type),
    inference(mrr,[status(thm)],[15828,310]),
    [iquote('1:MRR:15828.0,310.0')] ).

cnf(15830,plain,
    ~ relation_like(skc8),
    inference(res,[status(thm),theory(equality)],[69,15829]),
    [iquote('1:Res:69.1,15829.0')] ).

cnf(15831,plain,
    $false,
    inference(ssi,[status(thm)],[15830,156]),
    [iquote('1:SSi:15830.0,156.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n003.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 Jul 10 18:18:14 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 18.48/18.69  
% 18.48/18.69  SPASS V 3.9 
% 18.48/18.69  SPASS beiseite: Proof found.
% 18.48/18.69  % SZS status Theorem
% 18.48/18.69  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 18.48/18.69  SPASS derived 15207 clauses, backtracked 175 clauses, performed 7 splits and kept 12654 clauses.
% 18.48/18.69  SPASS allocated 112306 KBytes.
% 18.48/18.69  SPASS spent	0:0:18.11 on the problem.
% 18.48/18.69  		0:00:00.03 for the input.
% 18.48/18.69  		0:00:00.05 for the FLOTTER CNF translation.
% 18.48/18.69  		0:00:00.13 for inferences.
% 18.48/18.69  		0:00:00.57 for the backtracking.
% 18.48/18.69  		0:0:17.23 for the reduction.
% 18.48/18.69  
% 18.48/18.69  
% 18.48/18.69  Here is a proof with depth 5, length 45 :
% 18.48/18.69  % SZS output start Refutation
% See solution above
% 18.48/18.69  Formulae used in the proof : p31 prove_relset_1_48 p17 p10 p26 p8 p6 p1 p29 p2 p3
% 18.48/18.69  
%------------------------------------------------------------------------------