TSTP Solution File: SEU075+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU075+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 14:33:50 EDT 2022

% Result   : Theorem 0.39s 0.58s
% Output   : Refutation 0.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   57 (  22 unt;   7 nHn;  57 RR)
%            Number of literals    :  183 (   0 equ; 120 neg)
%            Maximal clause size   :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    function(skc14),
    file('SEU075+1.p',unknown),
    [] ).

cnf(2,axiom,
    relation(skc14),
    file('SEU075+1.p',unknown),
    [] ).

cnf(3,axiom,
    function(skc13),
    file('SEU075+1.p',unknown),
    [] ).

cnf(4,axiom,
    relation(skc13),
    file('SEU075+1.p',unknown),
    [] ).

cnf(5,axiom,
    function(skc12),
    file('SEU075+1.p',unknown),
    [] ).

cnf(6,axiom,
    relation(skc12),
    file('SEU075+1.p',unknown),
    [] ).

cnf(31,axiom,
    equal(relation_rng(skc12),skc15),
    file('SEU075+1.p',unknown),
    [] ).

cnf(32,axiom,
    equal(relation_dom(skc13),skc15),
    file('SEU075+1.p',unknown),
    [] ).

cnf(33,axiom,
    equal(relation_dom(skc14),skc15),
    file('SEU075+1.p',unknown),
    [] ).

cnf(34,axiom,
    ~ equal(skc14,skc13),
    file('SEU075+1.p',unknown),
    [] ).

cnf(47,axiom,
    equal(relation_composition(skc12,skc14),relation_composition(skc12,skc13)),
    file('SEU075+1.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,w)
    | ~ equal(w,relation_rng(u))
    | in(skf7(u,x),relation_dom(u)) ),
    file('SEU075+1.p',unknown),
    [] ).

cnf(70,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(v,w)
    | ~ equal(w,relation_rng(u))
    | equal(apply(u,skf7(u,v)),v) ),
    file('SEU075+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ function(v)
    | ~ relation(v)
    | ~ equal(relation_dom(v),relation_dom(u))
    | equal(v,u)
    | in(skf14(v,w),relation_dom(v)) ),
    file('SEU075+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ relation(u)
    | ~ function(u)
    | ~ relation(v)
    | ~ function(v)
    | ~ in(w,relation_dom(u))
    | equal(apply(relation_composition(u,v),w),apply(v,apply(u,w))) ),
    file('SEU075+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ function(v)
    | ~ relation(v)
    | ~ equal(relation_dom(v),relation_dom(u))
    | ~ equal(apply(v,skf14(v,u)),apply(u,skf14(v,u)))
    | equal(v,u) ),
    file('SEU075+1.p',unknown),
    [] ).

cnf(82,plain,
    ( ~ function(skc12)
    | ~ in(u,v)
    | ~ equal(v,relation_rng(skc12))
    | equal(apply(skc12,skf7(skc12,u)),u) ),
    inference(res,[status(thm),theory(equality)],[6,70]),
    [iquote('0:Res:6.0,70.0')] ).

cnf(83,plain,
    ( ~ function(skc12)
    | ~ in(u,v)
    | ~ equal(v,relation_rng(skc12))
    | in(skf7(skc12,w),relation_dom(skc12)) ),
    inference(res,[status(thm),theory(equality)],[6,69]),
    [iquote('0:Res:6.0,69.0')] ).

cnf(133,plain,
    ( ~ relation(skc13)
    | ~ function(u)
    | ~ relation(u)
    | ~ in(v,relation_dom(u))
    | equal(apply(relation_composition(u,skc13),v),apply(skc13,apply(u,v))) ),
    inference(res,[status(thm),theory(equality)],[3,74]),
    [iquote('0:Res:3.0,74.0')] ).

cnf(134,plain,
    ( ~ relation(skc13)
    | ~ relation(u)
    | ~ function(u)
    | ~ equal(relation_dom(skc13),relation_dom(u))
    | in(skf14(skc13,v),relation_dom(skc13))
    | equal(skc13,u) ),
    inference(res,[status(thm),theory(equality)],[3,73]),
    [iquote('0:Res:3.0,73.1')] ).

cnf(147,plain,
    ( ~ function(skc14)
    | ~ relation(u)
    | ~ function(u)
    | ~ equal(relation_dom(skc14),relation_dom(u))
    | in(skf14(skc14,v),relation_dom(skc14))
    | equal(skc14,u) ),
    inference(res,[status(thm),theory(equality)],[2,73]),
    [iquote('0:Res:2.0,73.0')] ).

cnf(175,plain,
    ( ~ function(skc12)
    | ~ in(u,v)
    | ~ equal(v,skc15)
    | in(skf7(skc12,w),relation_dom(skc12)) ),
    inference(rew,[status(thm),theory(equality)],[31,83]),
    [iquote('0:Rew:31.0,83.2')] ).

cnf(176,plain,
    ( ~ in(u,v)
    | ~ equal(v,skc15)
    | in(skf7(skc12,w),relation_dom(skc12)) ),
    inference(mrr,[status(thm)],[175,5]),
    [iquote('0:MRR:175.0,5.0')] ).

cnf(191,plain,
    ( ~ function(skc12)
    | ~ in(u,v)
    | ~ equal(v,skc15)
    | equal(apply(skc12,skf7(skc12,u)),u) ),
    inference(rew,[status(thm),theory(equality)],[31,82]),
    [iquote('0:Rew:31.0,82.2')] ).

cnf(192,plain,
    ( ~ in(u,v)
    | ~ equal(v,skc15)
    | equal(apply(skc12,skf7(skc12,u)),u) ),
    inference(mrr,[status(thm)],[191,5]),
    [iquote('0:MRR:191.0,5.0')] ).

cnf(211,plain,
    ( ~ function(skc14)
    | ~ relation(u)
    | ~ function(u)
    | ~ equal(relation_dom(u),skc15)
    | in(skf14(skc14,v),skc15)
    | equal(skc14,u) ),
    inference(rew,[status(thm),theory(equality)],[33,147]),
    [iquote('0:Rew:33.0,147.4,33.0,147.3')] ).

cnf(212,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(relation_dom(u),skc15)
    | equal(skc14,u)
    | in(skf14(skc14,v),skc15) ),
    inference(mrr,[status(thm)],[211,1]),
    [iquote('0:MRR:211.0,1.0')] ).

cnf(215,plain,
    ( ~ relation(skc13)
    | ~ relation(u)
    | ~ function(u)
    | ~ equal(relation_dom(u),skc15)
    | in(skf14(skc13,v),skc15)
    | equal(skc13,u) ),
    inference(rew,[status(thm),theory(equality)],[32,134]),
    [iquote('0:Rew:32.0,134.4,32.0,134.3')] ).

cnf(216,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(relation_dom(u),skc15)
    | equal(skc13,u)
    | in(skf14(skc13,v),skc15) ),
    inference(mrr,[status(thm)],[215,4]),
    [iquote('0:MRR:215.0,4.0')] ).

cnf(226,plain,
    ( ~ relation(u)
    | ~ function(u)
    | ~ in(v,relation_dom(u))
    | equal(apply(relation_composition(u,skc13),v),apply(skc13,apply(u,v))) ),
    inference(mrr,[status(thm)],[133,4]),
    [iquote('0:MRR:133.0,4.0')] ).

cnf(242,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(relation_dom(u),skc15)
    | equal(skc14,u) ),
    inference(spt,[spt(split,[position(s1)])],[212]),
    [iquote('1:Spt:212.0,212.1,212.2,212.3')] ).

cnf(264,plain,
    ( ~ function(skc13)
    | ~ relation(skc13)
    | ~ equal(skc15,skc15)
    | equal(skc14,skc13) ),
    inference(spl,[status(thm),theory(equality)],[32,242]),
    [iquote('1:SpL:32.0,242.2')] ).

cnf(266,plain,
    ( ~ function(skc13)
    | ~ relation(skc13)
    | equal(skc14,skc13) ),
    inference(obv,[status(thm),theory(equality)],[264]),
    [iquote('1:Obv:264.2')] ).

cnf(267,plain,
    equal(skc14,skc13),
    inference(ssi,[status(thm)],[266,3,4]),
    [iquote('1:SSi:266.1,266.0,3.0,4.0,3.0,4.0')] ).

cnf(268,plain,
    $false,
    inference(mrr,[status(thm)],[267,34]),
    [iquote('1:MRR:267.0,34.0')] ).

cnf(270,plain,
    in(skf14(skc14,u),skc15),
    inference(spt,[spt(split,[position(s2)])],[212]),
    [iquote('1:Spt:268.0,212.4')] ).

cnf(271,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(relation_dom(u),skc15)
    | equal(skc13,u) ),
    inference(spt,[spt(split,[position(s2s1)])],[216]),
    [iquote('2:Spt:216.0,216.1,216.2,216.3')] ).

cnf(272,plain,
    ( ~ function(skc14)
    | ~ relation(skc14)
    | ~ equal(skc15,skc15)
    | equal(skc14,skc13) ),
    inference(spl,[status(thm),theory(equality)],[33,271]),
    [iquote('2:SpL:33.0,271.2')] ).

cnf(274,plain,
    ( ~ function(skc14)
    | ~ relation(skc14)
    | equal(skc14,skc13) ),
    inference(obv,[status(thm),theory(equality)],[272]),
    [iquote('2:Obv:272.2')] ).

cnf(275,plain,
    equal(skc14,skc13),
    inference(ssi,[status(thm)],[274,1,2]),
    [iquote('2:SSi:274.1,274.0,1.0,2.0,1.0,2.0')] ).

cnf(276,plain,
    $false,
    inference(mrr,[status(thm)],[275,34]),
    [iquote('2:MRR:275.0,34.0')] ).

cnf(277,plain,
    in(skf14(skc13,u),skc15),
    inference(spt,[spt(split,[position(s2s2)])],[216]),
    [iquote('2:Spt:276.0,216.4')] ).

cnf(841,plain,
    ( ~ relation(skc12)
    | ~ function(skc12)
    | ~ relation(skc14)
    | ~ function(skc14)
    | ~ in(u,relation_dom(skc12))
    | equal(apply(relation_composition(skc12,skc13),u),apply(skc14,apply(skc12,u))) ),
    inference(spr,[status(thm),theory(equality)],[47,74]),
    [iquote('0:SpR:47.0,74.5')] ).

cnf(850,plain,
    ( ~ relation(skc12)
    | ~ function(skc12)
    | ~ relation(skc14)
    | ~ function(skc14)
    | ~ in(u,relation_dom(skc12))
    | equal(apply(skc14,apply(skc12,u)),apply(skc13,apply(skc12,u))) ),
    inference(rew,[status(thm),theory(equality)],[226,841]),
    [iquote('0:Rew:226.3,841.5')] ).

cnf(851,plain,
    ( ~ in(u,relation_dom(skc12))
    | equal(apply(skc14,apply(skc12,u)),apply(skc13,apply(skc12,u))) ),
    inference(ssi,[status(thm)],[850,1,2,5,6]),
    [iquote('0:SSi:850.3,850.2,850.1,850.0,1.0,2.0,1.0,2.0,5.0,6.0,5.0,6.0')] ).

cnf(1151,plain,
    ( ~ equal(skc15,skc15)
    | in(skf7(skc12,u),relation_dom(skc12)) ),
    inference(res,[status(thm),theory(equality)],[277,176]),
    [iquote('2:Res:277.0,176.0')] ).

cnf(1161,plain,
    in(skf7(skc12,u),relation_dom(skc12)),
    inference(obv,[status(thm),theory(equality)],[1151]),
    [iquote('2:Obv:1151.0')] ).

cnf(1184,plain,
    ( ~ equal(skc15,skc15)
    | equal(apply(skc12,skf7(skc12,skf14(skc13,u))),skf14(skc13,u)) ),
    inference(res,[status(thm),theory(equality)],[277,192]),
    [iquote('2:Res:277.0,192.0')] ).

cnf(1194,plain,
    equal(apply(skc12,skf7(skc12,skf14(skc13,u))),skf14(skc13,u)),
    inference(obv,[status(thm),theory(equality)],[1184]),
    [iquote('2:Obv:1184.0')] ).

cnf(1224,plain,
    ( ~ in(skf7(skc12,skf14(skc13,u)),relation_dom(skc12))
    | equal(apply(skc14,skf14(skc13,u)),apply(skc13,skf14(skc13,u))) ),
    inference(spr,[status(thm),theory(equality)],[1194,851]),
    [iquote('2:SpR:1194.0,851.1')] ).

cnf(1227,plain,
    equal(apply(skc14,skf14(skc13,u)),apply(skc13,skf14(skc13,u))),
    inference(mrr,[status(thm)],[1224,1161]),
    [iquote('2:MRR:1224.0,1161.0')] ).

cnf(1288,plain,
    ( ~ function(skc14)
    | ~ relation(skc14)
    | ~ function(skc13)
    | ~ relation(skc13)
    | ~ equal(relation_dom(skc14),relation_dom(skc13))
    | ~ equal(apply(skc13,skf14(skc13,skc14)),apply(skc13,skf14(skc13,skc14)))
    | equal(skc14,skc13) ),
    inference(spl,[status(thm),theory(equality)],[1227,75]),
    [iquote('2:SpL:1227.0,75.5')] ).

cnf(1294,plain,
    ( ~ function(skc14)
    | ~ relation(skc14)
    | ~ function(skc13)
    | ~ relation(skc13)
    | ~ equal(relation_dom(skc14),relation_dom(skc13))
    | equal(skc14,skc13) ),
    inference(obv,[status(thm),theory(equality)],[1288]),
    [iquote('2:Obv:1288.5')] ).

cnf(1295,plain,
    ( ~ function(skc14)
    | ~ relation(skc14)
    | ~ function(skc13)
    | ~ relation(skc13)
    | ~ equal(skc15,skc15)
    | equal(skc14,skc13) ),
    inference(rew,[status(thm),theory(equality)],[33,1294,32]),
    [iquote('2:Rew:33.0,1294.4,32.0,1294.4')] ).

cnf(1296,plain,
    ( ~ function(skc14)
    | ~ relation(skc14)
    | ~ function(skc13)
    | ~ relation(skc13)
    | equal(skc14,skc13) ),
    inference(obv,[status(thm),theory(equality)],[1295]),
    [iquote('2:Obv:1295.4')] ).

cnf(1297,plain,
    equal(skc14,skc13),
    inference(ssi,[status(thm)],[1296,3,4,1,2]),
    [iquote('2:SSi:1296.3,1296.2,1296.1,1296.0,3.0,4.0,3.0,4.0,1.0,2.0,1.0,2.0')] ).

cnf(1298,plain,
    $false,
    inference(mrr,[status(thm)],[1297,34]),
    [iquote('2:MRR:1297.0,34.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU075+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n016.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 : Mon Jun 20 08:30:55 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.39/0.58  
% 0.39/0.58  SPASS V 3.9 
% 0.39/0.58  SPASS beiseite: Proof found.
% 0.39/0.58  % SZS status Theorem
% 0.39/0.58  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.39/0.58  SPASS derived 949 clauses, backtracked 64 clauses, performed 16 splits and kept 595 clauses.
% 0.39/0.58  SPASS allocated 98752 KBytes.
% 0.39/0.58  SPASS spent	0:00:00.23 on the problem.
% 0.39/0.58  		0:00:00.03 for the input.
% 0.39/0.58  		0:00:00.05 for the FLOTTER CNF translation.
% 0.39/0.58  		0:00:00.01 for inferences.
% 0.39/0.58  		0:00:00.00 for the backtracking.
% 0.39/0.58  		0:00:00.09 for the reduction.
% 0.39/0.58  
% 0.39/0.58  
% 0.39/0.58  Here is a proof with depth 5, length 57 :
% 0.39/0.58  % SZS output start Refutation
% See solution above
% 0.39/0.58  Formulae used in the proof : t156_funct_1 d5_funct_1 antisymmetry_r2_hidden t9_funct_1 t23_funct_1
% 0.39/0.58  
%------------------------------------------------------------------------------