TSTP Solution File: COM007+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COM007+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 : Fri Jul 15 01:44:14 EDT 2022

% Result   : Theorem 0.21s 0.45s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   43 (  21 unt;   8 nHn;  43 RR)
%            Number of literals    :   73 (   0 equ;  30 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   2 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ goal,
    file('COM007+1.p',unknown),
    [] ).

cnf(2,axiom,
    reflexive_rewrite(a,b),
    file('COM007+1.p',unknown),
    [] ).

cnf(3,axiom,
    reflexive_rewrite(a,c),
    file('COM007+1.p',unknown),
    [] ).

cnf(4,axiom,
    equalish(u,u),
    file('COM007+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ equalish(u,v)
    | equalish(v,u) ),
    file('COM007+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ equalish(u,v)
    | reflexive_rewrite(u,v) ),
    file('COM007+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ rewrite(u,v)
    | reflexive_rewrite(u,v) ),
    file('COM007+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ reflexive_rewrite(b,u)
    | ~ reflexive_rewrite(c,u)
    | goal ),
    file('COM007+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ rewrite(u,v)
    | rewrite(v,skf1(v,w)) ),
    file('COM007+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ reflexive_rewrite(u,v)
    | rewrite(u,v)
    | equalish(u,v) ),
    file('COM007+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ reflexive_rewrite(u,v)
    | ~ equalish(w,u)
    | reflexive_rewrite(w,v) ),
    file('COM007+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ rewrite(u,v)
    | ~ rewrite(u,w)
    | rewrite(w,skf1(v,w)) ),
    file('COM007+1.p',unknown),
    [] ).

cnf(13,plain,
    ( ~ reflexive_rewrite(c,u)
    | ~ reflexive_rewrite(b,u) ),
    inference(mrr,[status(thm)],[8,1]),
    [iquote('0:MRR:8.2,1.0')] ).

cnf(15,plain,
    reflexive_rewrite(u,u),
    inference(res,[status(thm),theory(equality)],[4,6]),
    [iquote('0:Res:4.0,6.0')] ).

cnf(16,plain,
    ~ reflexive_rewrite(c,b),
    inference(res,[status(thm),theory(equality)],[15,13]),
    [iquote('0:Res:15.0,13.1')] ).

cnf(17,plain,
    ( ~ reflexive_rewrite(u,v)
    | equalish(u,v)
    | rewrite(v,skf1(v,w)) ),
    inference(res,[status(thm),theory(equality)],[10,9]),
    [iquote('0:Res:10.1,9.0')] ).

cnf(19,plain,
    ( ~ equalish(u,a)
    | reflexive_rewrite(u,c) ),
    inference(res,[status(thm),theory(equality)],[3,11]),
    [iquote('0:Res:3.0,11.0')] ).

cnf(20,plain,
    ( ~ equalish(u,a)
    | reflexive_rewrite(u,b) ),
    inference(res,[status(thm),theory(equality)],[2,11]),
    [iquote('0:Res:2.0,11.0')] ).

cnf(23,plain,
    ( ~ reflexive_rewrite(u,v)
    | ~ rewrite(u,w)
    | equalish(u,v)
    | rewrite(w,skf1(v,w)) ),
    inference(res,[status(thm),theory(equality)],[10,12]),
    [iquote('0:Res:10.1,12.0')] ).

cnf(25,plain,
    ( equalish(a,c)
    | rewrite(c,skf1(c,u)) ),
    inference(res,[status(thm),theory(equality)],[3,17]),
    [iquote('0:Res:3.0,17.0')] ).

cnf(26,plain,
    ( equalish(a,b)
    | rewrite(b,skf1(b,u)) ),
    inference(res,[status(thm),theory(equality)],[2,17]),
    [iquote('0:Res:2.0,17.0')] ).

cnf(30,plain,
    ( equalish(a,c)
    | reflexive_rewrite(c,skf1(c,u)) ),
    inference(res,[status(thm),theory(equality)],[25,7]),
    [iquote('0:Res:25.1,7.0')] ).

cnf(33,plain,
    ( equalish(a,b)
    | reflexive_rewrite(b,skf1(b,u)) ),
    inference(res,[status(thm),theory(equality)],[26,7]),
    [iquote('0:Res:26.1,7.0')] ).

cnf(34,plain,
    ( ~ rewrite(a,u)
    | equalish(a,c)
    | rewrite(u,skf1(c,u)) ),
    inference(res,[status(thm),theory(equality)],[3,23]),
    [iquote('0:Res:3.0,23.0')] ).

cnf(37,plain,
    equalish(a,c),
    inference(spt,[spt(split,[position(s1)])],[30]),
    [iquote('1:Spt:30.0')] ).

cnf(39,plain,
    equalish(c,a),
    inference(res,[status(thm),theory(equality)],[37,5]),
    [iquote('1:Res:37.0,5.0')] ).

cnf(42,plain,
    reflexive_rewrite(c,b),
    inference(res,[status(thm),theory(equality)],[39,20]),
    [iquote('1:Res:39.0,20.0')] ).

cnf(44,plain,
    $false,
    inference(mrr,[status(thm)],[42,16]),
    [iquote('1:MRR:42.0,16.0')] ).

cnf(45,plain,
    ~ equalish(a,c),
    inference(spt,[spt(split,[position(sa)])],[44,37]),
    [iquote('1:Spt:44.0,30.0,37.0')] ).

cnf(46,plain,
    reflexive_rewrite(c,skf1(c,u)),
    inference(spt,[spt(split,[position(s2)])],[30]),
    [iquote('1:Spt:44.0,30.1')] ).

cnf(49,plain,
    ( ~ rewrite(a,u)
    | rewrite(u,skf1(c,u)) ),
    inference(mrr,[status(thm)],[34,45]),
    [iquote('1:MRR:34.1,45.0')] ).

cnf(59,plain,
    ( ~ rewrite(a,u)
    | reflexive_rewrite(u,skf1(c,u)) ),
    inference(res,[status(thm),theory(equality)],[49,7]),
    [iquote('1:Res:49.1,7.0')] ).

cnf(60,plain,
    equalish(a,b),
    inference(spt,[spt(split,[position(s2s1)])],[33]),
    [iquote('2:Spt:33.0')] ).

cnf(62,plain,
    equalish(b,a),
    inference(res,[status(thm),theory(equality)],[60,5]),
    [iquote('2:Res:60.0,5.0')] ).

cnf(66,plain,
    reflexive_rewrite(b,c),
    inference(res,[status(thm),theory(equality)],[62,19]),
    [iquote('2:Res:62.0,19.0')] ).

cnf(74,plain,
    ~ reflexive_rewrite(c,c),
    inference(res,[status(thm),theory(equality)],[66,13]),
    [iquote('2:Res:66.0,13.1')] ).

cnf(75,plain,
    $false,
    inference(mrr,[status(thm)],[74,15]),
    [iquote('2:MRR:74.0,15.0')] ).

cnf(76,plain,
    ~ equalish(a,b),
    inference(spt,[spt(split,[position(s2sa)])],[75,60]),
    [iquote('2:Spt:75.0,33.0,60.0')] ).

cnf(77,plain,
    reflexive_rewrite(b,skf1(b,u)),
    inference(spt,[spt(split,[position(s2s2)])],[33]),
    [iquote('2:Spt:75.0,33.1')] ).

cnf(103,plain,
    ( ~ rewrite(a,b)
    | ~ reflexive_rewrite(c,skf1(c,b)) ),
    inference(res,[status(thm),theory(equality)],[59,13]),
    [iquote('1:Res:59.1,13.1')] ).

cnf(104,plain,
    ~ rewrite(a,b),
    inference(mrr,[status(thm)],[103,46]),
    [iquote('1:MRR:103.1,46.0')] ).

cnf(105,plain,
    ( ~ reflexive_rewrite(a,b)
    | equalish(a,b) ),
    inference(res,[status(thm),theory(equality)],[10,104]),
    [iquote('1:Res:10.1,104.0')] ).

cnf(106,plain,
    $false,
    inference(mrr,[status(thm)],[105,2,76]),
    [iquote('2:MRR:105.0,105.1,2.0,76.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : COM007+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n027.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % 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 : Thu Jun 16 20:05:51 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.21/0.45  
% 0.21/0.45  SPASS V 3.9 
% 0.21/0.45  SPASS beiseite: Proof found.
% 0.21/0.45  % SZS status Theorem
% 0.21/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.45  SPASS derived 76 clauses, backtracked 12 clauses, performed 2 splits and kept 69 clauses.
% 0.21/0.45  SPASS allocated 85194 KBytes.
% 0.21/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.21/0.45  		0:00:00.03 for the input.
% 0.21/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.45  		0:00:00.00 for inferences.
% 0.21/0.45  		0:00:00.00 for the backtracking.
% 0.21/0.45  		0:00:00.00 for the reduction.
% 0.21/0.45  
% 0.21/0.45  
% 0.21/0.45  Here is a proof with depth 7, length 43 :
% 0.21/0.45  % SZS output start Refutation
% See solution above
% 0.21/0.45  Formulae used in the proof : goal_to_be_proved assumption reflexivity symmtery equalish_in_reflexive_rewrite rewrite_in_reflexive_rewrite goal_ax rewrite_diamond equalish_or_rewrite substitution
% 0.21/0.45  
%------------------------------------------------------------------------------