TSTP Solution File: SEU293+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU293+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 14:35:55 EDT 2022

% Result   : Theorem 0.47s 0.64s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   44 (  19 unt;   3 nHn;  44 RR)
%            Number of literals    :   97 (   0 equ;  57 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;  10 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    function(skc15),
    file('SEU293+1.p',unknown),
    [] ).

cnf(33,axiom,
    relation_of2_as_subset(skc15,skc17,skc16),
    file('SEU293+1.p',unknown),
    [] ).

cnf(34,axiom,
    quasi_total(skc15,skc17,skc16),
    file('SEU293+1.p',unknown),
    [] ).

cnf(35,axiom,
    ~ equal(skc16,empty_set),
    file('SEU293+1.p',unknown),
    [] ).

cnf(46,axiom,
    ( skP0(u,v)
    | equal(v,empty_set) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(59,axiom,
    ( in(skc19,skc17)
    | in(skc19,relation_inverse_image(skc15,skc18)) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ element(u,powerset(cartesian_product2(v,w)))
    | relation(u) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(66,axiom,
    ( ~ relation_of2_as_subset(u,v,w)
    | relation_of2(u,v,w) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(70,axiom,
    ( in(skc19,relation_inverse_image(skc15,skc18))
    | in(apply(skc15,skc19),skc18) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ relation_of2_as_subset(u,v,w)
    | element(u,powerset(cartesian_product2(v,w))) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ relation_of2(u,v,w)
    | equal(relation_dom_as_subset(v,w,u),relation_dom(u)) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ in(skc19,skc17)
    | ~ in(skc19,relation_inverse_image(skc15,skc18))
    | ~ in(apply(skc15,skc19),skc18) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ skP0(u,v)
    | ~ relation_of2_as_subset(w,u,v)
    | ~ quasi_total(w,u,v)
    | equal(relation_dom_as_subset(u,v,w),u) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(82,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,w)
    | ~ equal(w,relation_inverse_image(u,x))
    | in(v,relation_dom(u)) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,w)
    | ~ equal(w,relation_inverse_image(u,x))
    | in(apply(u,v),x) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(87,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,relation_dom(u))
    | ~ equal(w,relation_inverse_image(u,x))
    | ~ in(apply(u,v),x)
    | in(v,w) ),
    file('SEU293+1.p',unknown),
    [] ).

cnf(94,plain,
    ( ~ relation(skc15)
    | ~ in(u,v)
    | ~ equal(v,relation_inverse_image(skc15,w))
    | in(u,relation_dom(skc15)) ),
    inference(res,[status(thm),theory(equality)],[1,82]),
    [iquote('0:Res:1.0,82.1')] ).

cnf(96,plain,
    skP0(u,skc16),
    inference(res,[status(thm),theory(equality)],[46,35]),
    [iquote('0:Res:46.0,35.0')] ).

cnf(102,plain,
    ( ~ skP0(skc17,skc16)
    | ~ relation_of2_as_subset(skc15,skc17,skc16)
    | equal(relation_dom_as_subset(skc17,skc16,skc15),skc17) ),
    inference(res,[status(thm),theory(equality)],[34,81]),
    [iquote('0:Res:34.0,81.0')] ).

cnf(106,plain,
    element(skc15,powerset(cartesian_product2(skc17,skc16))),
    inference(res,[status(thm),theory(equality)],[33,72]),
    [iquote('0:Res:33.0,72.0')] ).

cnf(107,plain,
    relation_of2(skc15,skc17,skc16),
    inference(res,[status(thm),theory(equality)],[33,66]),
    [iquote('0:Res:33.0,66.0')] ).

cnf(110,plain,
    equal(relation_dom_as_subset(skc17,skc16,skc15),skc17),
    inference(mrr,[status(thm)],[102,96,33]),
    [iquote('0:MRR:102.0,102.1,96.0,33.0')] ).

cnf(113,plain,
    in(skc19,relation_inverse_image(skc15,skc18)),
    inference(spt,[spt(split,[position(s1)])],[59]),
    [iquote('1:Spt:59.1')] ).

cnf(114,plain,
    ( ~ in(skc19,skc17)
    | ~ in(apply(skc15,skc19),skc18) ),
    inference(mrr,[status(thm)],[77,113]),
    [iquote('1:MRR:77.1,113.0')] ).

cnf(156,plain,
    relation(skc15),
    inference(res,[status(thm),theory(equality)],[106,63]),
    [iquote('0:Res:106.0,63.0')] ).

cnf(159,plain,
    ( ~ in(u,v)
    | ~ equal(v,relation_inverse_image(skc15,w))
    | in(u,relation_dom(skc15)) ),
    inference(mrr,[status(thm)],[94,156]),
    [iquote('0:MRR:94.0,156.0')] ).

cnf(266,plain,
    ( ~ relation_of2(skc15,skc17,skc16)
    | equal(relation_dom(skc15),skc17) ),
    inference(spr,[status(thm),theory(equality)],[74,110]),
    [iquote('0:SpR:74.1,110.0')] ).

cnf(268,plain,
    equal(relation_dom(skc15),skc17),
    inference(mrr,[status(thm)],[266,107]),
    [iquote('0:MRR:266.0,107.0')] ).

cnf(276,plain,
    ( ~ in(u,v)
    | ~ equal(v,relation_inverse_image(skc15,w))
    | in(u,skc17) ),
    inference(rew,[status(thm),theory(equality)],[268,159]),
    [iquote('0:Rew:268.0,159.2')] ).

cnf(361,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,relation_inverse_image(u,w))
    | in(apply(u,v),w) ),
    inference(eqr,[status(thm),theory(equality)],[83]),
    [iquote('0:EqR:83.3')] ).

cnf(456,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,relation_dom(u))
    | ~ in(apply(u,v),w)
    | in(v,relation_inverse_image(u,w)) ),
    inference(eqr,[status(thm),theory(equality)],[87]),
    [iquote('0:EqR:87.3')] ).

cnf(812,plain,
    ( ~ in(u,relation_inverse_image(skc15,v))
    | in(u,skc17) ),
    inference(eqr,[status(thm),theory(equality)],[276]),
    [iquote('0:EqR:276.1')] ).

cnf(838,plain,
    in(skc19,skc17),
    inference(res,[status(thm),theory(equality)],[113,812]),
    [iquote('1:Res:113.0,812.0')] ).

cnf(846,plain,
    ~ in(apply(skc15,skc19),skc18),
    inference(mrr,[status(thm)],[114,838]),
    [iquote('1:MRR:114.0,838.0')] ).

cnf(1127,plain,
    ( ~ function(skc15)
    | ~ relation(skc15)
    | ~ in(skc19,relation_inverse_image(skc15,skc18)) ),
    inference(res,[status(thm),theory(equality)],[361,846]),
    [iquote('1:Res:361.3,846.0')] ).

cnf(1130,plain,
    ~ in(skc19,relation_inverse_image(skc15,skc18)),
    inference(ssi,[status(thm)],[1127,1,156]),
    [iquote('1:SSi:1127.1,1127.0,1.0,156.0,1.0,156.0')] ).

cnf(1131,plain,
    $false,
    inference(mrr,[status(thm)],[1130,113]),
    [iquote('1:MRR:1130.0,113.0')] ).

cnf(1133,plain,
    ~ in(skc19,relation_inverse_image(skc15,skc18)),
    inference(spt,[spt(split,[position(sa)])],[1131,113]),
    [iquote('1:Spt:1131.0,59.1,113.0')] ).

cnf(1134,plain,
    in(skc19,skc17),
    inference(spt,[spt(split,[position(s2)])],[59]),
    [iquote('1:Spt:1131.0,59.0')] ).

cnf(1136,plain,
    in(apply(skc15,skc19),skc18),
    inference(mrr,[status(thm)],[70,1133]),
    [iquote('1:MRR:70.0,1133.0')] ).

cnf(1618,plain,
    ( ~ function(skc15)
    | ~ relation(skc15)
    | ~ in(skc19,relation_dom(skc15))
    | in(skc19,relation_inverse_image(skc15,skc18)) ),
    inference(res,[status(thm),theory(equality)],[1136,456]),
    [iquote('1:Res:1136.0,456.3')] ).

cnf(1620,plain,
    ( ~ function(skc15)
    | ~ relation(skc15)
    | ~ in(skc19,skc17)
    | in(skc19,relation_inverse_image(skc15,skc18)) ),
    inference(rew,[status(thm),theory(equality)],[268,1618]),
    [iquote('1:Rew:268.0,1618.2')] ).

cnf(1621,plain,
    ( ~ in(skc19,skc17)
    | in(skc19,relation_inverse_image(skc15,skc18)) ),
    inference(ssi,[status(thm)],[1620,1,156]),
    [iquote('1:SSi:1620.1,1620.0,1.0,156.0,1.0,156.0')] ).

cnf(1622,plain,
    $false,
    inference(mrr,[status(thm)],[1621,1134,1133]),
    [iquote('1:MRR:1621.0,1621.1,1134.0,1133.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU293+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n023.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jun 20 13:25:33 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.47/0.64  
% 0.47/0.64  SPASS V 3.9 
% 0.47/0.64  SPASS beiseite: Proof found.
% 0.47/0.64  % SZS status Theorem
% 0.47/0.64  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.47/0.64  SPASS derived 1237 clauses, backtracked 8 clauses, performed 1 splits and kept 721 clauses.
% 0.47/0.64  SPASS allocated 99115 KBytes.
% 0.47/0.64  SPASS spent	0:00:00.27 on the problem.
% 0.47/0.64  		0:00:00.04 for the input.
% 0.47/0.64  		0:00:00.04 for the FLOTTER CNF translation.
% 0.47/0.64  		0:00:00.02 for inferences.
% 0.47/0.64  		0:00:00.00 for the backtracking.
% 0.47/0.64  		0:00:00.15 for the reduction.
% 0.47/0.64  
% 0.47/0.64  
% 0.47/0.64  Here is a proof with depth 3, length 44 :
% 0.47/0.64  % SZS output start Refutation
% See solution above
% 0.47/0.64  Formulae used in the proof : t46_funct_2 d1_funct_2 cc1_relset_1 redefinition_m2_relset_1 dt_m2_relset_1 redefinition_k4_relset_1 d13_funct_1 antisymmetry_r2_hidden
% 0.47/0.64  
%------------------------------------------------------------------------------