TSTP Solution File: SEU061+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU061+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 14:33:47 EDT 2022

% Result   : Theorem 138.76s 139.05s
% Output   : Refutation 138.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   18
% Syntax   : Number of clauses     :   61 (  19 unt;  13 nHn;  61 RR)
%            Number of literals    :  149 (   0 equ;  76 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    :   18 (  18 usr;   8 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    relation(skc10),
    file('SEU061+1.p',unknown),
    [] ).

cnf(6,axiom,
    empty(empty_set),
    file('SEU061+1.p',unknown),
    [] ).

cnf(23,axiom,
    empty(skf23(u)),
    file('SEU061+1.p',unknown),
    [] ).

cnf(26,axiom,
    element(skf21(u),u),
    file('SEU061+1.p',unknown),
    [] ).

cnf(34,axiom,
    element(skf23(u),powerset(u)),
    file('SEU061+1.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ empty(u)
    | equal(u,empty_set) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(42,axiom,
    ( ~ empty(u)
    | ~ in(v,u) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(48,axiom,
    ( ~ element(u,v)
    | empty(v)
    | in(u,v) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(51,axiom,
    ( ~ equal(relation_inverse_image(skc10,singleton(skc11)),empty_set)
    | in(skc11,relation_rng(skc10)) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(52,axiom,
    ( ~ in(skc11,relation_rng(skc10))
    | equal(relation_inverse_image(skc10,singleton(skc11)),empty_set) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(55,axiom,
    ( ~ in(u,v)
    | ~ equal(v,singleton(w))
    | equal(u,w) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(56,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,singleton(v))
    | in(u,w) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(58,axiom,
    ( ~ empty(u)
    | ~ in(v,w)
    | ~ element(w,powerset(u)) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(61,axiom,
    ( ~ relation(u)
    | ~ equal(v,relation_rng(u))
    | ~ in(ordered_pair(w,x),u)
    | in(x,v) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ relation(u)
    | ~ in(v,w)
    | ~ equal(w,relation_rng(u))
    | in(ordered_pair(skf17(u,v),v),u) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ relation(u)
    | equal(v,relation_inverse_image(u,w))
    | in(skf13(w,u,v),v)
    | in(skf14(w,x,y),w) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ relation(u)
    | ~ in(v,w)
    | ~ equal(x,relation_inverse_image(u,w))
    | ~ in(ordered_pair(y,v),u)
    | in(y,x) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ relation(u)
    | equal(v,relation_inverse_image(u,w))
    | in(ordered_pair(skf13(w,u,v),skf14(w,v,u)),u)
    | in(skf13(w,u,v),v) ),
    file('SEU061+1.p',unknown),
    [] ).

cnf(73,plain,
    ( ~ in(u,v)
    | ~ equal(w,relation_inverse_image(skc10,v))
    | ~ in(ordered_pair(x,u),skc10)
    | in(x,w) ),
    inference(res,[status(thm),theory(equality)],[1,68]),
    [iquote('0:Res:1.0,68.0')] ).

cnf(78,plain,
    ( ~ in(u,v)
    | ~ equal(v,relation_rng(skc10))
    | in(ordered_pair(skf17(skc10,u),u),skc10) ),
    inference(res,[status(thm),theory(equality)],[1,63]),
    [iquote('0:Res:1.0,63.0')] ).

cnf(79,plain,
    ( ~ equal(u,relation_rng(skc10))
    | ~ in(ordered_pair(v,w),skc10)
    | in(w,u) ),
    inference(res,[status(thm),theory(equality)],[1,61]),
    [iquote('0:Res:1.0,61.0')] ).

cnf(81,plain,
    equal(skf23(u),empty_set),
    inference(ems,[status(thm)],[38,23]),
    [iquote('0:EmS:38.0,23.0')] ).

cnf(93,plain,
    element(empty_set,powerset(u)),
    inference(rew,[status(thm),theory(equality)],[81,34]),
    [iquote('0:Rew:81.0,34.0')] ).

cnf(121,plain,
    ( empty(u)
    | in(skf21(u),u) ),
    inference(res,[status(thm),theory(equality)],[26,48]),
    [iquote('0:Res:26.0,48.0')] ).

cnf(143,plain,
    ~ in(skc11,relation_rng(skc10)),
    inference(spt,[spt(split,[position(s1)])],[52]),
    [iquote('1:Spt:52.0')] ).

cnf(144,plain,
    ~ equal(relation_inverse_image(skc10,singleton(skc11)),empty_set),
    inference(mrr,[status(thm)],[51,143]),
    [iquote('1:MRR:51.1,143.0')] ).

cnf(169,plain,
    ( ~ empty(u)
    | ~ in(v,empty_set) ),
    inference(res,[status(thm),theory(equality)],[93,58]),
    [iquote('0:Res:93.0,58.2')] ).

cnf(174,plain,
    ~ in(u,empty_set),
    inference(ems,[status(thm)],[169,6]),
    [iquote('0:EmS:169.0,6.0')] ).

cnf(218,plain,
    ( ~ equal(u,v)
    | in(u,singleton(v)) ),
    inference(eqr,[status(thm),theory(equality)],[56]),
    [iquote('0:EqR:56.1')] ).

cnf(220,plain,
    ( ~ empty(singleton(u))
    | ~ equal(v,u) ),
    inference(res,[status(thm),theory(equality)],[218,42]),
    [iquote('0:Res:218.1,42.1')] ).

cnf(224,plain,
    ~ empty(singleton(u)),
    inference(aed,[status(thm),theory(equality)],[220]),
    [iquote('0:AED:220.1')] ).

cnf(232,plain,
    ( ~ in(u,singleton(v))
    | equal(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[55]),
    [iquote('0:EqR:55.1')] ).

cnf(239,plain,
    ( empty(singleton(u))
    | equal(skf21(singleton(u)),u) ),
    inference(res,[status(thm),theory(equality)],[121,232]),
    [iquote('0:Res:121.1,232.0')] ).

cnf(242,plain,
    equal(skf21(singleton(u)),u),
    inference(mrr,[status(thm)],[239,224]),
    [iquote('0:MRR:239.0,224.0')] ).

cnf(246,plain,
    ( empty(singleton(u))
    | in(u,singleton(u)) ),
    inference(spr,[status(thm),theory(equality)],[242,121]),
    [iquote('0:SpR:242.0,121.1')] ).

cnf(249,plain,
    in(u,singleton(u)),
    inference(mrr,[status(thm)],[246,224]),
    [iquote('0:MRR:246.0,224.0')] ).

cnf(313,plain,
    ( ~ relation(u)
    | ~ in(v,relation_rng(u))
    | in(ordered_pair(skf17(u,v),v),u) ),
    inference(eqr,[status(thm),theory(equality)],[63]),
    [iquote('0:EqR:63.2')] ).

cnf(394,plain,
    ( ~ relation(u)
    | equal(v,relation_inverse_image(u,singleton(w)))
    | in(skf13(singleton(w),u,v),v)
    | equal(skf14(singleton(w),x,y),w) ),
    inference(res,[status(thm),theory(equality)],[64,232]),
    [iquote('0:Res:64.3,232.0')] ).

cnf(518,plain,
    ( ~ relation(u)
    | ~ relation(u)
    | ~ equal(v,relation_rng(u))
    | equal(w,relation_inverse_image(u,x))
    | in(skf13(x,u,w),w)
    | in(skf14(x,w,u),v) ),
    inference(res,[status(thm),theory(equality)],[69,61]),
    [iquote('0:Res:69.2,61.2')] ).

cnf(529,plain,
    ( ~ relation(u)
    | ~ equal(v,relation_rng(u))
    | equal(w,relation_inverse_image(u,x))
    | in(skf13(x,u,w),w)
    | in(skf14(x,w,u),v) ),
    inference(obv,[status(thm),theory(equality)],[518]),
    [iquote('0:Obv:518.0')] ).

cnf(1064,plain,
    ( ~ relation(skc10)
    | ~ in(u,relation_rng(skc10))
    | ~ equal(v,relation_rng(skc10))
    | in(u,v) ),
    inference(res,[status(thm),theory(equality)],[313,79]),
    [iquote('0:Res:313.2,79.1')] ).

cnf(1067,plain,
    ( ~ in(u,relation_rng(skc10))
    | ~ equal(v,relation_rng(skc10))
    | in(u,v) ),
    inference(ssi,[status(thm)],[1064,1]),
    [iquote('0:SSi:1064.0,1.0')] ).

cnf(1222,plain,
    ( ~ in(u,relation_rng(skc10))
    | in(ordered_pair(skf17(skc10,u),u),skc10) ),
    inference(eqr,[status(thm),theory(equality)],[78]),
    [iquote('0:EqR:78.1')] ).

cnf(1991,plain,
    ( ~ in(u,v)
    | ~ in(ordered_pair(w,u),skc10)
    | in(w,relation_inverse_image(skc10,v)) ),
    inference(eqr,[status(thm),theory(equality)],[73]),
    [iquote('0:EqR:73.1')] ).

cnf(2310,plain,
    ( ~ relation(u)
    | equal(v,relation_inverse_image(u,w))
    | in(skf13(w,u,v),v)
    | in(skf14(w,v,u),relation_rng(u)) ),
    inference(eqr,[status(thm),theory(equality)],[529]),
    [iquote('0:EqR:529.1')] ).

cnf(4791,plain,
    ( ~ in(u,relation_rng(skc10))
    | ~ in(u,v)
    | in(skf17(skc10,u),relation_inverse_image(skc10,v)) ),
    inference(res,[status(thm),theory(equality)],[1222,1991]),
    [iquote('0:Res:1222.1,1991.1')] ).

cnf(13903,plain,
    ( ~ relation(u)
    | ~ relation(v)
    | equal(w,relation_inverse_image(u,singleton(x)))
    | in(skf13(singleton(x),u,w),w)
    | equal(y,relation_inverse_image(v,singleton(x)))
    | in(skf13(singleton(x),v,y),y)
    | in(x,relation_rng(v)) ),
    inference(spr,[status(thm),theory(equality)],[394,2310]),
    [iquote('0:SpR:394.3,2310.3')] ).

cnf(14009,plain,
    ( ~ relation(u)
    | equal(v,relation_inverse_image(u,singleton(w)))
    | in(skf13(singleton(w),u,v),v)
    | in(w,relation_rng(u)) ),
    inference(con,[status(thm)],[13903]),
    [iquote('0:Con:13903.0')] ).

cnf(43422,plain,
    ( ~ relation(u)
    | equal(relation_inverse_image(u,singleton(v)),empty_set)
    | in(v,relation_rng(u)) ),
    inference(res,[status(thm),theory(equality)],[14009,174]),
    [iquote('0:Res:14009.2,174.0')] ).

cnf(43629,plain,
    ( ~ relation(skc10)
    | ~ equal(empty_set,empty_set)
    | in(skc11,relation_rng(skc10)) ),
    inference(spl,[status(thm),theory(equality)],[43422,144]),
    [iquote('1:SpL:43422.1,144.0')] ).

cnf(43644,plain,
    ( ~ relation(skc10)
    | in(skc11,relation_rng(skc10)) ),
    inference(obv,[status(thm),theory(equality)],[43629]),
    [iquote('1:Obv:43629.1')] ).

cnf(43645,plain,
    in(skc11,relation_rng(skc10)),
    inference(ssi,[status(thm)],[43644,1]),
    [iquote('1:SSi:43644.0,1.0')] ).

cnf(43646,plain,
    $false,
    inference(mrr,[status(thm)],[43645,143]),
    [iquote('1:MRR:43645.0,143.0')] ).

cnf(43662,plain,
    in(skc11,relation_rng(skc10)),
    inference(spt,[spt(split,[position(sa)])],[43646,143]),
    [iquote('1:Spt:43646.0,52.0,143.0')] ).

cnf(43663,plain,
    equal(relation_inverse_image(skc10,singleton(skc11)),empty_set),
    inference(spt,[spt(split,[position(s2)])],[52]),
    [iquote('1:Spt:43646.0,52.1')] ).

cnf(43802,plain,
    ( ~ in(u,relation_rng(skc10))
    | ~ in(u,singleton(skc11))
    | in(skf17(skc10,u),empty_set) ),
    inference(spr,[status(thm),theory(equality)],[43663,4791]),
    [iquote('1:SpR:43663.0,4791.2')] ).

cnf(43825,plain,
    ( ~ in(u,relation_rng(skc10))
    | ~ in(u,singleton(skc11)) ),
    inference(mrr,[status(thm)],[43802,174]),
    [iquote('1:MRR:43802.2,174.0')] ).

cnf(43833,plain,
    ( ~ equal(u,relation_rng(skc10))
    | in(skc11,u) ),
    inference(res,[status(thm),theory(equality)],[43662,1067]),
    [iquote('1:Res:43662.0,1067.0')] ).

cnf(46816,plain,
    ( ~ equal(relation_rng(skc10),relation_rng(skc10))
    | ~ in(skc11,singleton(skc11)) ),
    inference(res,[status(thm),theory(equality)],[43833,43825]),
    [iquote('1:Res:43833.1,43825.0')] ).

cnf(46899,plain,
    ~ in(skc11,singleton(skc11)),
    inference(obv,[status(thm),theory(equality)],[46816]),
    [iquote('1:Obv:46816.0')] ).

cnf(46900,plain,
    $false,
    inference(mrr,[status(thm)],[46899,249]),
    [iquote('1:MRR:46899.0,249.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SEU061+1 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.11  % Command  : run_spass %d %s
% 0.11/0.32  % Computer : n015.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sun Jun 19 20:02:30 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 138.76/139.05  
% 138.76/139.05  SPASS V 3.9 
% 138.76/139.05  SPASS beiseite: Proof found.
% 138.76/139.05  % SZS status Theorem
% 138.76/139.05  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 138.76/139.05  SPASS derived 38950 clauses, backtracked 2230 clauses, performed 6 splits and kept 22049 clauses.
% 138.76/139.05  SPASS allocated 139097 KBytes.
% 138.76/139.05  SPASS spent	0:2:16.05 on the problem.
% 138.76/139.05  		0:00:00.03 for the input.
% 138.76/139.05  		0:00:00.05 for the FLOTTER CNF translation.
% 138.76/139.05  		0:00:00.89 for inferences.
% 138.76/139.05  		0:00:06.01 for the backtracking.
% 138.76/139.05  		0:02:08.31 for the reduction.
% 138.76/139.05  
% 138.76/139.05  
% 138.76/139.05  Here is a proof with depth 5, length 61 :
% 138.76/139.05  % SZS output start Refutation
% See solution above
% 138.76/139.05  Formulae used in the proof : t142_funct_1 fc4_relat_1 rc2_subset_1 existence_m1_subset_1 t6_boole t7_boole t2_subset d1_tarski antisymmetry_r2_hidden t5_subset d5_relat_1 d14_relat_1
% 138.76/139.05  
%------------------------------------------------------------------------------