TSTP Solution File: SEU203+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU203+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 14:34:58 EDT 2022

% Result   : Theorem 1.01s 1.18s
% Output   : Refutation 1.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   18
% Syntax   : Number of clauses     :   60 (  16 unt;   9 nHn;  60 RR)
%            Number of literals    :  145 (   0 equ;  93 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  11 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    relation(skc8),
    file('SEU203+1.p',unknown),
    [] ).

cnf(3,axiom,
    empty(empty_set),
    file('SEU203+1.p',unknown),
    [] ).

cnf(4,axiom,
    relation(empty_set),
    file('SEU203+1.p',unknown),
    [] ).

cnf(11,axiom,
    element(skf15(u),u),
    file('SEU203+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ empty(u)
    | relation(u) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ empty(u)
    | empty(relation_dom(u)) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ empty(u)
    | equal(u,empty_set) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ empty(u)
    | ~ in(v,u) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(22,axiom,
    ( in(skc11,skc9)
    | in(skc10,relation_image(skc8,skc9)) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ element(u,v)
    | empty(v)
    | in(u,v) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(28,axiom,
    ( in(skc10,relation_image(skc8,skc9))
    | in(ordered_pair(skc11,skc10),skc8) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(31,axiom,
    ( ~ relation(u)
    | ~ equal(v,relation_dom(u))
    | ~ in(ordered_pair(w,x),u)
    | in(w,v) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(32,axiom,
    ( ~ relation(u)
    | ~ in(v,w)
    | ~ equal(w,relation_image(u,x))
    | in(skf7(x,y,z),x) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ relation(u)
    | ~ in(v,w)
    | ~ equal(w,relation_dom(u))
    | in(ordered_pair(v,skf11(u,v)),u) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(36,axiom,
    ( ~ relation(u)
    | equal(v,relation_dom(u))
    | in(skf13(u,v),v)
    | in(ordered_pair(skf13(u,v),skf14(v,u)),u) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ relation(u)
    | ~ in(v,w)
    | ~ equal(w,relation_image(u,x))
    | in(ordered_pair(skf7(x,u,v),v),u) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ in(u,skc9)
    | ~ in(u,relation_dom(skc8))
    | ~ in(skc10,relation_image(skc8,skc9))
    | ~ in(ordered_pair(u,skc10),skc8) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ relation(u)
    | ~ in(v,w)
    | ~ equal(x,relation_image(u,w))
    | ~ in(ordered_pair(v,y),u)
    | in(y,x) ),
    file('SEU203+1.p',unknown),
    [] ).

cnf(43,plain,
    ( ~ in(u,v)
    | ~ equal(w,relation_image(skc8,v))
    | ~ in(ordered_pair(u,x),skc8)
    | in(x,w) ),
    inference(res,[status(thm),theory(equality)],[1,39]),
    [iquote('0:Res:1.0,39.0')] ).

cnf(47,plain,
    ( ~ in(u,v)
    | ~ equal(v,relation_image(skc8,w))
    | in(skf7(w,x,y),w) ),
    inference(res,[status(thm),theory(equality)],[1,32]),
    [iquote('0:Res:1.0,32.0')] ).

cnf(49,plain,
    ( ~ equal(u,relation_dom(skc8))
    | ~ in(ordered_pair(v,w),skc8)
    | in(v,u) ),
    inference(res,[status(thm),theory(equality)],[1,31]),
    [iquote('0:Res:1.0,31.0')] ).

cnf(51,plain,
    in(skc10,relation_image(skc8,skc9)),
    inference(spt,[spt(split,[position(s1)])],[22]),
    [iquote('1:Spt:22.1')] ).

cnf(52,plain,
    ( ~ in(u,skc9)
    | ~ in(u,relation_dom(skc8))
    | ~ in(ordered_pair(u,skc10),skc8) ),
    inference(mrr,[status(thm)],[38,51]),
    [iquote('1:MRR:38.2,51.0')] ).

cnf(61,plain,
    ( ~ empty(u)
    | equal(relation_dom(u),empty_set) ),
    inference(ems,[status(thm)],[18,16]),
    [iquote('0:EmS:18.0,16.1')] ).

cnf(77,plain,
    ( empty(u)
    | in(skf15(u),u) ),
    inference(res,[status(thm),theory(equality)],[11,26]),
    [iquote('0:Res:11.0,26.0')] ).

cnf(166,plain,
    ( ~ relation(u)
    | ~ in(v,relation_dom(u))
    | in(ordered_pair(v,skf11(u,v)),u) ),
    inference(eqr,[status(thm),theory(equality)],[33]),
    [iquote('0:EqR:33.2')] ).

cnf(167,plain,
    ( ~ empty(u)
    | ~ relation(u)
    | ~ in(v,w)
    | ~ equal(w,empty_set)
    | in(ordered_pair(v,skf11(u,v)),u) ),
    inference(spl,[status(thm),theory(equality)],[61,33]),
    [iquote('0:SpL:61.1,33.2')] ).

cnf(168,plain,
    ( ~ empty(u)
    | ~ in(v,w)
    | ~ equal(w,empty_set)
    | in(ordered_pair(v,skf11(u,v)),u) ),
    inference(ssi,[status(thm)],[167,13]),
    [iquote('0:SSi:167.1,13.1')] ).

cnf(169,plain,
    ( ~ empty(u)
    | ~ in(v,w)
    | ~ equal(w,empty_set) ),
    inference(mrr,[status(thm)],[168,21]),
    [iquote('0:MRR:168.3,21.1')] ).

cnf(170,plain,
    ( ~ in(u,v)
    | ~ equal(v,empty_set) ),
    inference(ems,[status(thm)],[169,3]),
    [iquote('0:EmS:169.0,3.0')] ).

cnf(171,plain,
    ~ equal(relation_image(skc8,skc9),empty_set),
    inference(res,[status(thm),theory(equality)],[51,170]),
    [iquote('1:Res:51.0,170.0')] ).

cnf(261,plain,
    ( ~ relation(u)
    | ~ in(v,relation_image(u,w))
    | in(ordered_pair(skf7(w,u,v),v),u) ),
    inference(eqr,[status(thm),theory(equality)],[37]),
    [iquote('0:EqR:37.2')] ).

cnf(440,plain,
    ( ~ relation(u)
    | ~ empty(u)
    | ~ in(v,relation_dom(u)) ),
    inference(res,[status(thm),theory(equality)],[166,21]),
    [iquote('0:Res:166.2,21.1')] ).

cnf(448,plain,
    ( ~ relation(u)
    | ~ empty(u)
    | ~ in(v,empty_set) ),
    inference(rew,[status(thm),theory(equality)],[61,440]),
    [iquote('0:Rew:61.1,440.2')] ).

cnf(449,plain,
    ( ~ empty(u)
    | ~ in(v,empty_set) ),
    inference(ssi,[status(thm)],[448,13]),
    [iquote('0:SSi:448.0,13.1')] ).

cnf(452,plain,
    ~ in(u,empty_set),
    inference(ems,[status(thm)],[449,3]),
    [iquote('0:EmS:449.0,3.0')] ).

cnf(456,plain,
    ( ~ relation(empty_set)
    | equal(u,relation_dom(empty_set))
    | in(skf13(empty_set,u),u) ),
    inference(res,[status(thm),theory(equality)],[36,452]),
    [iquote('0:Res:36.3,452.0')] ).

cnf(457,plain,
    ( ~ relation(empty_set)
    | ~ in(u,relation_dom(empty_set)) ),
    inference(res,[status(thm),theory(equality)],[166,452]),
    [iquote('0:Res:166.2,452.0')] ).

cnf(463,plain,
    ~ in(u,relation_dom(empty_set)),
    inference(ssi,[status(thm)],[457,4,3]),
    [iquote('0:SSi:457.0,4.0,3.0')] ).

cnf(545,plain,
    ( equal(u,relation_dom(empty_set))
    | in(skf13(empty_set,u),u) ),
    inference(ssi,[status(thm)],[456,4,3]),
    [iquote('0:SSi:456.0,4.0,3.0')] ).

cnf(624,plain,
    empty(relation_dom(empty_set)),
    inference(res,[status(thm),theory(equality)],[77,463]),
    [iquote('0:Res:77.1,463.0')] ).

cnf(646,plain,
    equal(relation_dom(empty_set),empty_set),
    inference(ems,[status(thm)],[18,624]),
    [iquote('0:EmS:18.0,624.0')] ).

cnf(652,plain,
    ( equal(u,empty_set)
    | in(skf13(empty_set,u),u) ),
    inference(rew,[status(thm),theory(equality)],[646,545]),
    [iquote('0:Rew:646.0,545.0')] ).

cnf(750,plain,
    ( ~ in(u,relation_image(skc8,v))
    | in(skf7(v,w,x),v) ),
    inference(eqr,[status(thm),theory(equality)],[47]),
    [iquote('0:EqR:47.1')] ).

cnf(880,plain,
    ( ~ relation(skc8)
    | ~ in(u,relation_image(skc8,v))
    | ~ equal(w,relation_dom(skc8))
    | in(skf7(v,skc8,u),w) ),
    inference(res,[status(thm),theory(equality)],[261,49]),
    [iquote('0:Res:261.2,49.1')] ).

cnf(881,plain,
    ( ~ relation(skc8)
    | ~ in(skc10,relation_image(skc8,u))
    | ~ in(skf7(u,skc8,skc10),skc9)
    | ~ in(skf7(u,skc8,skc10),relation_dom(skc8)) ),
    inference(res,[status(thm),theory(equality)],[261,52]),
    [iquote('1:Res:261.2,52.2')] ).

cnf(885,plain,
    ( ~ in(u,relation_image(skc8,v))
    | ~ equal(w,relation_dom(skc8))
    | in(skf7(v,skc8,u),w) ),
    inference(ssi,[status(thm)],[880,1]),
    [iquote('0:SSi:880.0,1.0')] ).

cnf(887,plain,
    ( ~ in(skc10,relation_image(skc8,u))
    | ~ in(skf7(u,skc8,skc10),skc9)
    | ~ in(skf7(u,skc8,skc10),relation_dom(skc8)) ),
    inference(ssi,[status(thm)],[881,1]),
    [iquote('1:SSi:881.0,1.0')] ).

cnf(1013,plain,
    ( equal(relation_image(skc8,u),empty_set)
    | in(skf7(u,v,w),u) ),
    inference(res,[status(thm),theory(equality)],[652,750]),
    [iquote('0:Res:652.1,750.0')] ).

cnf(1225,plain,
    ( ~ in(u,v)
    | ~ in(ordered_pair(u,w),skc8)
    | in(w,relation_image(skc8,v)) ),
    inference(eqr,[status(thm),theory(equality)],[43]),
    [iquote('0:EqR:43.1')] ).

cnf(3191,plain,
    ( ~ in(skc10,relation_image(skc8,u))
    | ~ equal(relation_dom(skc8),relation_dom(skc8))
    | ~ in(skc10,relation_image(skc8,u))
    | ~ in(skf7(u,skc8,skc10),skc9) ),
    inference(res,[status(thm),theory(equality)],[885,887]),
    [iquote('1:Res:885.2,887.2')] ).

cnf(3194,plain,
    ( ~ in(skc10,relation_image(skc8,u))
    | ~ in(skf7(u,skc8,skc10),skc9) ),
    inference(obv,[status(thm),theory(equality)],[3191]),
    [iquote('1:Obv:3191.1')] ).

cnf(3304,plain,
    ( ~ in(skc10,relation_image(skc8,skc9))
    | equal(relation_image(skc8,skc9),empty_set) ),
    inference(res,[status(thm),theory(equality)],[1013,3194]),
    [iquote('1:Res:1013.1,3194.1')] ).

cnf(3310,plain,
    $false,
    inference(mrr,[status(thm)],[3304,51,171]),
    [iquote('1:MRR:3304.0,3304.1,51.0,171.0')] ).

cnf(3314,plain,
    ~ in(skc10,relation_image(skc8,skc9)),
    inference(spt,[spt(split,[position(sa)])],[3310,51]),
    [iquote('1:Spt:3310.0,22.1,51.0')] ).

cnf(3315,plain,
    in(skc11,skc9),
    inference(spt,[spt(split,[position(s2)])],[22]),
    [iquote('1:Spt:3310.0,22.0')] ).

cnf(3319,plain,
    in(ordered_pair(skc11,skc10),skc8),
    inference(mrr,[status(thm)],[28,3314]),
    [iquote('1:MRR:28.0,3314.0')] ).

cnf(3384,plain,
    ( ~ in(skc11,u)
    | in(skc10,relation_image(skc8,u)) ),
    inference(res,[status(thm),theory(equality)],[3319,1225]),
    [iquote('1:Res:3319.0,1225.1')] ).

cnf(3492,plain,
    ~ in(skc11,skc9),
    inference(res,[status(thm),theory(equality)],[3384,3314]),
    [iquote('1:Res:3384.1,3314.0')] ).

cnf(3497,plain,
    $false,
    inference(mrr,[status(thm)],[3492,3315]),
    [iquote('1:MRR:3492.0,3315.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU203+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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jun 18 21:09:49 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.01/1.18  
% 1.01/1.18  SPASS V 3.9 
% 1.01/1.18  SPASS beiseite: Proof found.
% 1.01/1.18  % SZS status Theorem
% 1.01/1.18  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.01/1.18  SPASS derived 2826 clauses, backtracked 87 clauses, performed 2 splits and kept 1247 clauses.
% 1.01/1.18  SPASS allocated 101021 KBytes.
% 1.01/1.18  SPASS spent	0:00:00.81 on the problem.
% 1.01/1.18  		0:00:00.04 for the input.
% 1.01/1.18  		0:00:00.07 for the FLOTTER CNF translation.
% 1.01/1.18  		0:00:00.04 for inferences.
% 1.01/1.18  		0:00:00.02 for the backtracking.
% 1.01/1.18  		0:00:00.61 for the reduction.
% 1.01/1.18  
% 1.01/1.18  
% 1.01/1.18  Here is a proof with depth 6, length 60 :
% 1.01/1.18  % SZS output start Refutation
% See solution above
% 1.01/1.18  Formulae used in the proof : t143_relat_1 fc4_relat_1 existence_m1_subset_1 cc1_relat_1 fc7_relat_1 t6_boole t7_boole t2_subset d4_relat_1 antisymmetry_r2_hidden d13_relat_1
% 1.01/1.18  
%------------------------------------------------------------------------------