TSTP Solution File: SEU283+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU283+1 : TPTP v8.1.0. Released v3.3.0.
% 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 14:35:49 EDT 2022

% Result   : Theorem 0.53s 0.74s
% Output   : Refutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   44 (   9 unt;   4 nHn;  44 RR)
%            Number of literals    :  119 (   0 equ;  80 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(15,axiom,
    relation(skf9(u)),
    file('SEU283+1.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ skP0(u)
    | function(skf9(u)) ),
    file('SEU283+1.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ equal(singleton(skf10(u)),singleton(skf10(u)))
    | skP0(v) ),
    file('SEU283+1.p',unknown),
    [] ).

cnf(40,axiom,
    ( ~ skP0(u)
    | ~ in(ordered_pair(v,w),skf9(u))
    | in(v,u) ),
    file('SEU283+1.p',unknown),
    [] ).

cnf(42,axiom,
    ( ~ skP0(u)
    | ~ in(ordered_pair(v,w),skf9(u))
    | equal(w,singleton(v)) ),
    file('SEU283+1.p',unknown),
    [] ).

cnf(43,axiom,
    ( ~ in(skf13(u,v),v)
    | ~ in(ordered_pair(skf13(u,v),w),u) ),
    file('SEU283+1.p',unknown),
    [] ).

cnf(44,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(relation_dom(u),skc7)
    | in(skf8(v),skc7) ),
    file('SEU283+1.p',unknown),
    [] ).

cnf(45,axiom,
    ( ~ relation(u)
    | ~ equal(v,relation_dom(u))
    | ~ in(ordered_pair(w,x),u)
    | in(w,v) ),
    file('SEU283+1.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ skP0(u)
    | ~ in(v,u)
    | ~ equal(w,singleton(v))
    | in(ordered_pair(v,w),skf9(u)) ),
    file('SEU283+1.p',unknown),
    [] ).

cnf(50,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(relation_dom(u),skc7)
    | ~ equal(apply(u,skf8(u)),singleton(skf8(u))) ),
    file('SEU283+1.p',unknown),
    [] ).

cnf(51,axiom,
    ( ~ relation(u)
    | equal(v,relation_dom(u))
    | in(skf13(u,v),v)
    | in(ordered_pair(skf13(u,v),skf14(v,u)),u) ),
    file('SEU283+1.p',unknown),
    [] ).

cnf(53,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,relation_dom(u))
    | ~ equal(w,apply(u,v))
    | in(ordered_pair(v,w),u) ),
    file('SEU283+1.p',unknown),
    [] ).

cnf(55,plain,
    skP0(u),
    inference(obv,[status(thm),theory(equality)],[37]),
    [iquote('0:Obv:37.0')] ).

cnf(56,plain,
    function(skf9(u)),
    inference(mrr,[status(thm)],[24,55]),
    [iquote('0:MRR:24.0,55.0')] ).

cnf(57,plain,
    ( ~ in(ordered_pair(u,v),skf9(w))
    | in(u,w) ),
    inference(mrr,[status(thm)],[40,55]),
    [iquote('0:MRR:40.0,55.0')] ).

cnf(58,plain,
    ( ~ in(ordered_pair(u,v),skf9(w))
    | equal(v,singleton(u)) ),
    inference(mrr,[status(thm)],[42,55]),
    [iquote('0:MRR:42.0,55.0')] ).

cnf(59,plain,
    ( ~ in(u,v)
    | ~ equal(w,singleton(u))
    | in(ordered_pair(u,w),skf9(v)) ),
    inference(mrr,[status(thm)],[46,55]),
    [iquote('0:MRR:46.0,55.0')] ).

cnf(78,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(relation_dom(u),skc7) ),
    inference(spt,[spt(split,[position(s1)])],[44]),
    [iquote('1:Spt:44.0,44.1,44.2')] ).

cnf(163,plain,
    ( ~ in(skf13(skf9(u),v),u)
    | ~ equal(w,singleton(skf13(skf9(u),v)))
    | ~ in(skf13(skf9(u),v),v) ),
    inference(res,[status(thm),theory(equality)],[59,43]),
    [iquote('0:Res:59.2,43.1')] ).

cnf(168,plain,
    ( ~ in(skf13(skf9(u),v),u)
    | ~ in(skf13(skf9(u),v),v) ),
    inference(aed,[status(thm),theory(equality)],[163]),
    [iquote('0:AED:163.1')] ).

cnf(180,plain,
    ( ~ relation(skf9(u))
    | ~ in(v,u)
    | ~ equal(w,singleton(v))
    | ~ equal(x,relation_dom(skf9(u)))
    | in(v,x) ),
    inference(res,[status(thm),theory(equality)],[59,45]),
    [iquote('0:Res:59.2,45.2')] ).

cnf(181,plain,
    ( ~ relation(skf9(u))
    | ~ in(v,u)
    | ~ equal(w,relation_dom(skf9(u)))
    | in(v,w) ),
    inference(aed,[status(thm),theory(equality)],[180]),
    [iquote('0:AED:180.2')] ).

cnf(182,plain,
    ( ~ in(u,v)
    | ~ equal(w,relation_dom(skf9(v)))
    | in(u,w) ),
    inference(ssi,[status(thm)],[181,56,15]),
    [iquote('0:SSi:181.0,56.0,15.0')] ).

cnf(237,plain,
    ( ~ relation(skf9(u))
    | equal(v,relation_dom(skf9(u)))
    | in(skf13(skf9(u),v),v)
    | in(skf13(skf9(u),v),u) ),
    inference(res,[status(thm),theory(equality)],[51,57]),
    [iquote('0:Res:51.3,57.0')] ).

cnf(240,plain,
    ( equal(u,relation_dom(skf9(v)))
    | in(skf13(skf9(v),u),u)
    | in(skf13(skf9(v),u),v) ),
    inference(ssi,[status(thm)],[237,56,15]),
    [iquote('0:SSi:237.0,56.0,15.0')] ).

cnf(260,plain,
    ( ~ function(skf9(u))
    | ~ relation(skf9(u))
    | ~ in(v,relation_dom(skf9(u)))
    | ~ equal(w,apply(skf9(u),v))
    | equal(w,singleton(v)) ),
    inference(res,[status(thm),theory(equality)],[53,58]),
    [iquote('0:Res:53.4,58.0')] ).

cnf(270,plain,
    ( ~ in(u,relation_dom(skf9(v)))
    | ~ equal(w,apply(skf9(v),u))
    | equal(w,singleton(u)) ),
    inference(ssi,[status(thm)],[260,56,15]),
    [iquote('0:SSi:260.1,260.0,56.0,15.0,56.0,15.0')] ).

cnf(829,plain,
    ( ~ in(u,relation_dom(skf9(v)))
    | equal(apply(skf9(v),u),singleton(u)) ),
    inference(eqr,[status(thm),theory(equality)],[270]),
    [iquote('0:EqR:270.1')] ).

cnf(911,plain,
    ( equal(relation_dom(skf9(u)),u)
    | in(skf13(skf9(u),u),u) ),
    inference(fac,[status(thm)],[240]),
    [iquote('0:Fac:240.1,240.2')] ).

cnf(969,plain,
    ( ~ in(skf13(skf9(u),u),u)
    | equal(relation_dom(skf9(u)),u) ),
    inference(res,[status(thm),theory(equality)],[911,168]),
    [iquote('0:Res:911.1,168.0')] ).

cnf(980,plain,
    equal(relation_dom(skf9(u)),u),
    inference(mrr,[status(thm)],[969,911]),
    [iquote('0:MRR:969.0,911.1')] ).

cnf(990,plain,
    ( ~ in(u,v)
    | ~ equal(w,v)
    | in(u,w) ),
    inference(rew,[status(thm),theory(equality)],[980,182]),
    [iquote('0:Rew:980.0,182.1')] ).

cnf(1053,plain,
    ( ~ in(u,v)
    | equal(apply(skf9(v),u),singleton(u)) ),
    inference(rew,[status(thm),theory(equality)],[980,829]),
    [iquote('0:Rew:980.0,829.0')] ).

cnf(1233,plain,
    ( ~ function(skf9(u))
    | ~ relation(skf9(u))
    | ~ equal(u,skc7) ),
    inference(spl,[status(thm),theory(equality)],[980,78]),
    [iquote('1:SpL:980.0,78.2')] ).

cnf(1241,plain,
    ~ equal(u,skc7),
    inference(ssi,[status(thm)],[1233,56,15]),
    [iquote('1:SSi:1233.1,1233.0,56.0,15.0,56.0,15.0')] ).

cnf(1242,plain,
    $false,
    inference(unc,[status(thm)],[1241,980]),
    [iquote('1:UnC:1241.0,980.0')] ).

cnf(1244,plain,
    in(skf8(u),skc7),
    inference(spt,[spt(split,[position(s2)])],[44]),
    [iquote('1:Spt:1242.0,44.3')] ).

cnf(1289,plain,
    ( ~ equal(u,skc7)
    | in(skf8(v),u) ),
    inference(res,[status(thm),theory(equality)],[1244,990]),
    [iquote('1:Res:1244.0,990.0')] ).

cnf(1633,plain,
    ( ~ function(skf9(u))
    | ~ relation(skf9(u))
    | ~ in(skf8(skf9(u)),u)
    | ~ equal(relation_dom(skf9(u)),skc7)
    | ~ equal(singleton(skf8(skf9(u))),singleton(skf8(skf9(u)))) ),
    inference(spl,[status(thm),theory(equality)],[1053,50]),
    [iquote('0:SpL:1053.1,50.3')] ).

cnf(1634,plain,
    ( ~ function(skf9(u))
    | ~ relation(skf9(u))
    | ~ in(skf8(skf9(u)),u)
    | ~ equal(relation_dom(skf9(u)),skc7) ),
    inference(obv,[status(thm),theory(equality)],[1633]),
    [iquote('0:Obv:1633.4')] ).

cnf(1635,plain,
    ( ~ function(skf9(u))
    | ~ relation(skf9(u))
    | ~ in(skf8(skf9(u)),u)
    | ~ equal(u,skc7) ),
    inference(rew,[status(thm),theory(equality)],[980,1634]),
    [iquote('0:Rew:980.0,1634.3')] ).

cnf(1636,plain,
    ( ~ in(skf8(skf9(u)),u)
    | ~ equal(u,skc7) ),
    inference(ssi,[status(thm)],[1635,56,15]),
    [iquote('0:SSi:1635.1,1635.0,56.0,15.0,56.0,15.0')] ).

cnf(1637,plain,
    ~ equal(u,skc7),
    inference(mrr,[status(thm)],[1636,1289]),
    [iquote('1:MRR:1636.0,1289.1')] ).

cnf(1638,plain,
    $false,
    inference(unc,[status(thm)],[1637,980]),
    [iquote('1:UnC:1637.0,980.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU283+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jun 18 20:28:13 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.53/0.74  
% 0.53/0.74  SPASS V 3.9 
% 0.53/0.74  SPASS beiseite: Proof found.
% 0.53/0.74  % SZS status Theorem
% 0.53/0.74  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.53/0.74  SPASS derived 1218 clauses, backtracked 13 clauses, performed 1 splits and kept 623 clauses.
% 0.53/0.74  SPASS allocated 98985 KBytes.
% 0.53/0.74  SPASS spent	0:00:00.37 on the problem.
% 0.53/0.74  		0:00:00.04 for the input.
% 0.53/0.74  		0:00:00.05 for the FLOTTER CNF translation.
% 0.53/0.74  		0:00:00.02 for inferences.
% 0.53/0.74  		0:00:00.00 for the backtracking.
% 0.53/0.74  		0:00:00.24 for the reduction.
% 0.53/0.74  
% 0.53/0.74  
% 0.53/0.74  Here is a proof with depth 4, length 44 :
% 0.53/0.74  % SZS output start Refutation
% See solution above
% 0.53/0.74  Formulae used in the proof : s1_funct_1__e16_22__wellord2__1 rc3_relat_1 d4_relat_1 antisymmetry_r2_hidden s2_funct_1__e16_22__wellord2__1 d4_funct_1
% 0.53/0.74  
%------------------------------------------------------------------------------