TSTP Solution File: SEU159+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 14:34:29 EDT 2022

% Result   : Theorem 0.37s 0.54s
% Output   : Refutation 0.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   39 (  10 unt;  11 nHn;  39 RR)
%            Number of literals    :   85 (   0 equ;  41 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SEU159+1.p',unknown),
    [] ).

cnf(3,axiom,
    ( in(skc3,skc5)
    | subset(unordered_pair(skc3,skc4),skc5) ),
    file('SEU159+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( in(skc4,skc5)
    | subset(unordered_pair(skc3,skc4),skc5) ),
    file('SEU159+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( subset(u,v)
    | in(skf3(v,u),u) ),
    file('SEU159+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ in(skf3(u,v),u)
    | subset(w,u) ),
    file('SEU159+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ in(u,v)
    | ~ subset(v,w)
    | in(u,w) ),
    file('SEU159+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,unordered_pair(x,v))
    | in(u,w) ),
    file('SEU159+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ in(skc4,skc5)
    | ~ in(skc3,skc5)
    | ~ subset(unordered_pair(skc3,skc4),skc5) ),
    file('SEU159+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ in(u,v)
    | ~ equal(v,unordered_pair(w,x))
    | equal(u,x)
    | equal(u,w) ),
    file('SEU159+1.p',unknown),
    [] ).

cnf(16,plain,
    subset(unordered_pair(skc3,skc4),skc5),
    inference(spt,[spt(split,[position(s1)])],[4]),
    [iquote('1:Spt:4.1')] ).

cnf(17,plain,
    ( ~ in(skc4,skc5)
    | ~ in(skc3,skc5) ),
    inference(mrr,[status(thm)],[11,16]),
    [iquote('1:MRR:11.2,16.0')] ).

cnf(30,plain,
    ( ~ equal(u,v)
    | in(u,unordered_pair(w,v)) ),
    inference(eqr,[status(thm),theory(equality)],[10]),
    [iquote('0:EqR:10.1')] ).

cnf(33,plain,
    ( ~ equal(u,v)
    | in(u,unordered_pair(v,w)) ),
    inference(spr,[status(thm),theory(equality)],[2,30]),
    [iquote('0:SpR:2.0,30.1')] ).

cnf(35,plain,
    ( ~ equal(u,v)
    | ~ subset(unordered_pair(w,v),x)
    | in(u,x) ),
    inference(res,[status(thm),theory(equality)],[30,8]),
    [iquote('0:Res:30.1,8.0')] ).

cnf(40,plain,
    ( ~ equal(u,v)
    | ~ subset(unordered_pair(v,w),x)
    | in(u,x) ),
    inference(res,[status(thm),theory(equality)],[33,8]),
    [iquote('0:Res:33.1,8.0')] ).

cnf(69,plain,
    ( ~ in(u,unordered_pair(v,w))
    | equal(u,w)
    | equal(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[12]),
    [iquote('0:EqR:12.1')] ).

cnf(86,plain,
    ( subset(unordered_pair(u,v),w)
    | equal(skf3(w,unordered_pair(u,v)),v)
    | equal(skf3(w,unordered_pair(u,v)),u) ),
    inference(res,[status(thm),theory(equality)],[6,69]),
    [iquote('0:Res:6.1,69.0')] ).

cnf(94,plain,
    ( ~ equal(u,skc4)
    | in(u,skc5) ),
    inference(res,[status(thm),theory(equality)],[16,35]),
    [iquote('1:Res:16.0,35.1')] ).

cnf(96,plain,
    ( ~ equal(skc4,skc4)
    | ~ in(skc3,skc5) ),
    inference(res,[status(thm),theory(equality)],[94,17]),
    [iquote('1:Res:94.1,17.0')] ).

cnf(103,plain,
    ~ in(skc3,skc5),
    inference(obv,[status(thm),theory(equality)],[96]),
    [iquote('1:Obv:96.0')] ).

cnf(131,plain,
    ( ~ equal(u,skc3)
    | in(u,skc5) ),
    inference(res,[status(thm),theory(equality)],[16,40]),
    [iquote('1:Res:16.0,40.1')] ).

cnf(149,plain,
    ~ equal(skc3,skc3),
    inference(res,[status(thm),theory(equality)],[131,103]),
    [iquote('1:Res:131.1,103.0')] ).

cnf(150,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[149]),
    [iquote('1:Obv:149.0')] ).

cnf(151,plain,
    ~ subset(unordered_pair(skc3,skc4),skc5),
    inference(spt,[spt(split,[position(sa)])],[150,16]),
    [iquote('1:Spt:150.0,4.1,16.0')] ).

cnf(152,plain,
    in(skc4,skc5),
    inference(spt,[spt(split,[position(s2)])],[4]),
    [iquote('1:Spt:150.0,4.0')] ).

cnf(153,plain,
    in(skc3,skc5),
    inference(mrr,[status(thm)],[3,151]),
    [iquote('1:MRR:3.1,151.0')] ).

cnf(170,plain,
    ( subset(unordered_pair(u,u),v)
    | equal(skf3(v,unordered_pair(u,u)),u) ),
    inference(fac,[status(thm)],[86]),
    [iquote('0:Fac:86.1,86.2')] ).

cnf(186,plain,
    ( ~ in(u,v)
    | subset(unordered_pair(w,u),v)
    | equal(skf3(v,unordered_pair(w,u)),w)
    | subset(x,v) ),
    inference(spl,[status(thm),theory(equality)],[86,7]),
    [iquote('0:SpL:86.1,7.0')] ).

cnf(202,plain,
    ( ~ in(u,v)
    | subset(unordered_pair(w,u),v)
    | equal(skf3(v,unordered_pair(w,u)),w) ),
    inference(con,[status(thm)],[186]),
    [iquote('0:Con:186.3')] ).

cnf(235,plain,
    ( ~ in(u,v)
    | subset(unordered_pair(u,u),v)
    | subset(w,v) ),
    inference(spl,[status(thm),theory(equality)],[170,7]),
    [iquote('0:SpL:170.1,7.0')] ).

cnf(241,plain,
    ( ~ in(u,v)
    | subset(unordered_pair(u,u),v) ),
    inference(con,[status(thm)],[235]),
    [iquote('0:Con:235.2')] ).

cnf(253,plain,
    ( ~ in(u,v)
    | ~ equal(w,u)
    | in(w,v) ),
    inference(res,[status(thm),theory(equality)],[241,35]),
    [iquote('0:Res:241.1,35.1')] ).

cnf(315,plain,
    ( ~ equal(u,skc3)
    | in(u,skc5) ),
    inference(res,[status(thm),theory(equality)],[153,253]),
    [iquote('1:Res:153.0,253.0')] ).

cnf(330,plain,
    ( ~ equal(skf3(skc5,u),skc3)
    | subset(v,skc5) ),
    inference(res,[status(thm),theory(equality)],[315,7]),
    [iquote('1:Res:315.1,7.0')] ).

cnf(710,plain,
    ( ~ in(u,skc5)
    | ~ equal(v,skc3)
    | subset(unordered_pair(v,u),skc5)
    | subset(w,skc5) ),
    inference(spl,[status(thm),theory(equality)],[202,330]),
    [iquote('1:SpL:202.2,330.0')] ).

cnf(719,plain,
    ( ~ in(u,skc5)
    | ~ equal(v,skc3)
    | subset(unordered_pair(v,u),skc5) ),
    inference(con,[status(thm)],[710]),
    [iquote('1:Con:710.3')] ).

cnf(745,plain,
    ( ~ in(skc4,skc5)
    | ~ equal(skc3,skc3) ),
    inference(res,[status(thm),theory(equality)],[719,151]),
    [iquote('1:Res:719.2,151.0')] ).

cnf(749,plain,
    ~ in(skc4,skc5),
    inference(obv,[status(thm),theory(equality)],[745]),
    [iquote('1:Obv:745.1')] ).

cnf(750,plain,
    $false,
    inference(mrr,[status(thm)],[749,152]),
    [iquote('1:MRR:749.0,152.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n024.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 22:55:17 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.37/0.54  
% 0.37/0.54  SPASS V 3.9 
% 0.37/0.54  SPASS beiseite: Proof found.
% 0.37/0.54  % SZS status Theorem
% 0.37/0.54  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.37/0.54  SPASS derived 554 clauses, backtracked 4 clauses, performed 1 splits and kept 250 clauses.
% 0.37/0.54  SPASS allocated 85842 KBytes.
% 0.37/0.54  SPASS spent	0:00:00.20 on the problem.
% 0.37/0.54  		0:00:00.03 for the input.
% 0.37/0.54  		0:00:00.03 for the FLOTTER CNF translation.
% 0.37/0.54  		0:00:00.01 for inferences.
% 0.37/0.54  		0:00:00.00 for the backtracking.
% 0.37/0.54  		0:00:00.09 for the reduction.
% 0.37/0.54  
% 0.37/0.54  
% 0.37/0.54  Here is a proof with depth 9, length 39 :
% 0.37/0.54  % SZS output start Refutation
% See solution above
% 0.37/0.54  Formulae used in the proof : commutativity_k2_tarski t38_zfmisc_1 d3_tarski d2_tarski
% 0.37/0.54  
%------------------------------------------------------------------------------