TSTP Solution File: SEU281+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n004.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 14:35:48 EDT 2022

% Result   : Theorem 0.18s 0.48s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   39 (  14 unt;   7 nHn;  39 RR)
%            Number of literals    :   87 (   0 equ;  49 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(19,axiom,
    ( in(skf8(u),u)
    | in(skf9(v),skc7) ),
    file('SEU281+1.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ equal(skf15(u),skf15(u))
    | skP0(v) ),
    file('SEU281+1.p',unknown),
    [] ).

cnf(23,axiom,
    ( in(skf8(u),u)
    | in(skf8(u),cartesian_product2(skc7,skc6)) ),
    file('SEU281+1.p',unknown),
    [] ).

cnf(26,axiom,
    ( in(skf8(u),u)
    | equal(ordered_pair(skf9(u),singleton(skf9(u))),skf8(u)) ),
    file('SEU281+1.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ skP0(u)
    | ~ in(v,skf13(w,u))
    | in(v,cartesian_product2(u,w)) ),
    file('SEU281+1.p',unknown),
    [] ).

cnf(28,axiom,
    ( ~ skP0(u)
    | ~ in(v,skf13(w,u))
    | in(skf14(u,x),u) ),
    file('SEU281+1.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ skP0(u)
    | ~ in(v,skf13(w,u))
    | equal(ordered_pair(skf14(u,v),singleton(skf14(u,v))),v) ),
    file('SEU281+1.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ in(u,v)
    | ~ in(w,cartesian_product2(v,x))
    | ~ equal(ordered_pair(u,singleton(u)),w)
    | in(w,skf13(x,v)) ),
    file('SEU281+1.p',unknown),
    [] ).

cnf(31,axiom,
    ( ~ in(u,skc7)
    | ~ in(skf8(v),v)
    | ~ in(skf8(v),cartesian_product2(skc7,skc6))
    | ~ equal(ordered_pair(u,singleton(u)),skf8(v)) ),
    file('SEU281+1.p',unknown),
    [] ).

cnf(32,plain,
    skP0(u),
    inference(obv,[status(thm),theory(equality)],[22]),
    [iquote('0:Obv:22.0')] ).

cnf(33,plain,
    ( ~ in(u,skf13(v,w))
    | in(skf14(w,x),w) ),
    inference(mrr,[status(thm)],[28,32]),
    [iquote('0:MRR:28.0,32.0')] ).

cnf(34,plain,
    ( ~ in(u,skf13(v,w))
    | in(u,cartesian_product2(w,v)) ),
    inference(mrr,[status(thm)],[27,32]),
    [iquote('0:MRR:27.0,32.0')] ).

cnf(35,plain,
    ( ~ in(u,skf13(v,w))
    | equal(ordered_pair(skf14(w,u),singleton(skf14(w,u))),u) ),
    inference(mrr,[status(thm)],[29,32]),
    [iquote('0:MRR:29.0,32.0')] ).

cnf(36,plain,
    in(skf8(u),u),
    inference(spt,[spt(split,[position(s1)])],[19]),
    [iquote('1:Spt:19.0')] ).

cnf(37,plain,
    ( ~ in(u,skc7)
    | ~ in(skf8(v),cartesian_product2(skc7,skc6))
    | ~ equal(ordered_pair(u,singleton(u)),skf8(v)) ),
    inference(mrr,[status(thm)],[31,36]),
    [iquote('1:MRR:31.1,36.0')] ).

cnf(39,plain,
    in(skf8(skf13(u,v)),cartesian_product2(v,u)),
    inference(res,[status(thm),theory(equality)],[36,34]),
    [iquote('1:Res:36.0,34.0')] ).

cnf(41,plain,
    in(skf14(u,v),u),
    inference(res,[status(thm),theory(equality)],[36,33]),
    [iquote('1:Res:36.0,33.0')] ).

cnf(42,plain,
    equal(ordered_pair(skf14(u,skf8(skf13(v,u))),singleton(skf14(u,skf8(skf13(v,u))))),skf8(skf13(v,u))),
    inference(res,[status(thm),theory(equality)],[36,35]),
    [iquote('1:Res:36.0,35.0')] ).

cnf(49,plain,
    ( ~ in(skf14(u,skf8(skf13(v,u))),skc7)
    | ~ in(skf8(w),cartesian_product2(skc7,skc6))
    | ~ equal(skf8(skf13(v,u)),skf8(w)) ),
    inference(spl,[status(thm),theory(equality)],[42,37]),
    [iquote('1:SpL:42.0,37.2')] ).

cnf(67,plain,
    ( ~ in(skf8(u),cartesian_product2(skc7,skc6))
    | ~ equal(skf8(skf13(v,skc7)),skf8(u)) ),
    inference(res,[status(thm),theory(equality)],[41,49]),
    [iquote('1:Res:41.0,49.0')] ).

cnf(68,plain,
    ~ in(skf8(skf13(u,skc7)),cartesian_product2(skc7,skc6)),
    inference(eqr,[status(thm),theory(equality)],[67]),
    [iquote('1:EqR:67.1')] ).

cnf(69,plain,
    $false,
    inference(unc,[status(thm)],[68,39]),
    [iquote('1:UnC:68.0,39.0')] ).

cnf(70,plain,
    in(skf9(u),skc7),
    inference(spt,[spt(split,[position(s2)])],[19]),
    [iquote('1:Spt:69.0,19.1')] ).

cnf(75,plain,
    ( in(skf8(skf13(u,v)),cartesian_product2(skc7,skc6))
    | in(skf8(skf13(u,v)),cartesian_product2(v,u)) ),
    inference(res,[status(thm),theory(equality)],[23,34]),
    [iquote('0:Res:23.0,34.0')] ).

cnf(83,plain,
    ( ~ in(skf9(u),v)
    | ~ in(w,cartesian_product2(v,x))
    | ~ equal(skf8(u),w)
    | in(skf8(u),u)
    | in(w,skf13(x,v)) ),
    inference(spl,[status(thm),theory(equality)],[26,30]),
    [iquote('0:SpL:26.1,30.2')] ).

cnf(91,plain,
    ( ~ in(skf9(u),skc7)
    | ~ in(skf8(v),v)
    | ~ in(skf8(v),cartesian_product2(skc7,skc6))
    | ~ equal(skf8(u),skf8(v))
    | in(skf8(u),u) ),
    inference(spl,[status(thm),theory(equality)],[26,31]),
    [iquote('0:SpL:26.1,31.3')] ).

cnf(92,plain,
    ( ~ in(skf8(u),u)
    | ~ in(skf8(u),cartesian_product2(skc7,skc6))
    | ~ equal(skf8(v),skf8(u))
    | in(skf8(v),v) ),
    inference(mrr,[status(thm)],[91,70]),
    [iquote('1:MRR:91.0,70.0')] ).

cnf(98,plain,
    in(skf8(skf13(skc6,skc7)),cartesian_product2(skc7,skc6)),
    inference(fac,[status(thm)],[75]),
    [iquote('0:Fac:75.0,75.1')] ).

cnf(115,plain,
    ( ~ in(skf8(skf13(skc6,skc7)),skf13(skc6,skc7))
    | ~ equal(skf8(u),skf8(skf13(skc6,skc7)))
    | in(skf8(u),u) ),
    inference(res,[status(thm),theory(equality)],[98,92]),
    [iquote('1:Res:98.0,92.1')] ).

cnf(127,plain,
    ( ~ in(skf9(u),skc7)
    | ~ equal(skf8(u),skf8(skf13(skc6,skc7)))
    | in(skf8(u),u)
    | in(skf8(skf13(skc6,skc7)),skf13(skc6,skc7)) ),
    inference(res,[status(thm),theory(equality)],[98,83]),
    [iquote('0:Res:98.0,83.1')] ).

cnf(130,plain,
    ( ~ equal(skf8(u),skf8(skf13(skc6,skc7)))
    | in(skf8(u),u)
    | in(skf8(skf13(skc6,skc7)),skf13(skc6,skc7)) ),
    inference(mrr,[status(thm)],[127,70]),
    [iquote('1:MRR:127.0,70.0')] ).

cnf(131,plain,
    ( ~ equal(skf8(u),skf8(skf13(skc6,skc7)))
    | in(skf8(u),u) ),
    inference(mrr,[status(thm)],[130,115]),
    [iquote('1:MRR:130.2,115.0')] ).

cnf(136,plain,
    in(skf8(skf13(skc6,skc7)),skf13(skc6,skc7)),
    inference(eqr,[status(thm),theory(equality)],[131]),
    [iquote('1:EqR:131.0')] ).

cnf(138,plain,
    in(skf14(skc7,u),skc7),
    inference(res,[status(thm),theory(equality)],[136,33]),
    [iquote('1:Res:136.0,33.0')] ).

cnf(139,plain,
    equal(ordered_pair(skf14(skc7,skf8(skf13(skc6,skc7))),singleton(skf14(skc7,skf8(skf13(skc6,skc7))))),skf8(skf13(skc6,skc7))),
    inference(res,[status(thm),theory(equality)],[136,35]),
    [iquote('1:Res:136.0,35.0')] ).

cnf(176,plain,
    ( ~ in(skf14(skc7,skf8(skf13(skc6,skc7))),skc7)
    | ~ in(skf8(u),u)
    | ~ in(skf8(u),cartesian_product2(skc7,skc6))
    | ~ equal(skf8(skf13(skc6,skc7)),skf8(u)) ),
    inference(spl,[status(thm),theory(equality)],[139,31]),
    [iquote('1:SpL:139.0,31.3')] ).

cnf(177,plain,
    ( ~ in(skf8(u),cartesian_product2(skc7,skc6))
    | ~ equal(skf8(skf13(skc6,skc7)),skf8(u)) ),
    inference(mrr,[status(thm)],[176,138,131]),
    [iquote('1:MRR:176.0,176.1,138.0,131.1')] ).

cnf(190,plain,
    ~ equal(skf8(skf13(skc6,skc7)),skf8(skf13(skc6,skc7))),
    inference(res,[status(thm),theory(equality)],[98,177]),
    [iquote('1:Res:98.0,177.0')] ).

cnf(191,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[190]),
    [iquote('1:Obv:190.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n004.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 Jun 19 02:43:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.48  
% 0.18/0.48  SPASS V 3.9 
% 0.18/0.48  SPASS beiseite: Proof found.
% 0.18/0.48  % SZS status Theorem
% 0.18/0.48  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.48  SPASS derived 132 clauses, backtracked 5 clauses, performed 1 splits and kept 141 clauses.
% 0.18/0.48  SPASS allocated 97973 KBytes.
% 0.18/0.48  SPASS spent	0:00:00.13 on the problem.
% 0.18/0.48  		0:00:00.03 for the input.
% 0.18/0.48  		0:00:00.05 for the FLOTTER CNF translation.
% 0.18/0.48  		0:00:00.01 for inferences.
% 0.18/0.48  		0:00:00.00 for the backtracking.
% 0.18/0.48  		0:00:00.02 for the reduction.
% 0.18/0.48  
% 0.18/0.48  
% 0.18/0.48  Here is a proof with depth 7, length 39 :
% 0.18/0.48  % SZS output start Refutation
% See solution above
% 0.18/0.48  Formulae used in the proof : s1_xboole_0__e16_22__wellord2__1 antisymmetry_r2_hidden s1_tarski__e16_22__wellord2__2
% 0.18/0.48  
%------------------------------------------------------------------------------