TSTP Solution File: COM007+2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COM007+2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   34 (  20 unt;   6 nHn;  34 RR)
%            Number of literals    :   55 (   0 equ;  25 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+2.p',unknown),
    [] ).

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

cnf(3,axiom,
    reflexive_rewrite(a,c),
    file('COM007+2.p',unknown),
    [] ).

cnf(4,axiom,
    reflexive_rewrite(u,u),
    file('COM007+2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ rewrite(u,v)
    | reflexive_rewrite(u,v) ),
    file('COM007+2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ reflexive_rewrite(b,u)
    | ~ reflexive_rewrite(c,u)
    | goal ),
    file('COM007+2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ rewrite(u,v)
    | rewrite(v,skf1(v,w)) ),
    file('COM007+2.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ reflexive_rewrite(u,v)
    | rewrite(u,v)
    | equal(u,v) ),
    file('COM007+2.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ rewrite(u,v)
    | ~ rewrite(u,w)
    | rewrite(w,skf1(v,w)) ),
    file('COM007+2.p',unknown),
    [] ).

cnf(10,plain,
    ( ~ reflexive_rewrite(c,u)
    | ~ reflexive_rewrite(b,u) ),
    inference(mrr,[status(thm)],[6,1]),
    [iquote('0:MRR:6.2,1.0')] ).

cnf(11,plain,
    ~ reflexive_rewrite(c,b),
    inference(res,[status(thm),theory(equality)],[4,10]),
    [iquote('0:Res:4.0,10.0')] ).

cnf(12,plain,
    ~ reflexive_rewrite(b,c),
    inference(res,[status(thm),theory(equality)],[4,10]),
    [iquote('0:Res:4.0,10.1')] ).

cnf(14,plain,
    ( ~ reflexive_rewrite(u,v)
    | equal(u,v)
    | rewrite(v,skf1(v,w)) ),
    inference(res,[status(thm),theory(equality)],[8,7]),
    [iquote('0:Res:8.1,7.0')] ).

cnf(16,plain,
    ( equal(c,a)
    | rewrite(c,skf1(c,u)) ),
    inference(res,[status(thm),theory(equality)],[3,14]),
    [iquote('0:Res:3.0,14.0')] ).

cnf(17,plain,
    ( equal(b,a)
    | rewrite(b,skf1(b,u)) ),
    inference(res,[status(thm),theory(equality)],[2,14]),
    [iquote('0:Res:2.0,14.0')] ).

cnf(19,plain,
    equal(c,a),
    inference(spt,[spt(split,[position(s1)])],[16]),
    [iquote('1:Spt:16.0')] ).

cnf(22,plain,
    ~ reflexive_rewrite(a,b),
    inference(rew,[status(thm),theory(equality)],[19,11]),
    [iquote('1:Rew:19.0,11.0')] ).

cnf(24,plain,
    $false,
    inference(mrr,[status(thm)],[22,2]),
    [iquote('1:MRR:22.0,2.0')] ).

cnf(25,plain,
    ~ equal(c,a),
    inference(spt,[spt(split,[position(sa)])],[24,19]),
    [iquote('1:Spt:24.0,16.0,19.0')] ).

cnf(26,plain,
    rewrite(c,skf1(c,u)),
    inference(spt,[spt(split,[position(s2)])],[16]),
    [iquote('1:Spt:24.0,16.1')] ).

cnf(28,plain,
    reflexive_rewrite(c,skf1(c,u)),
    inference(res,[status(thm),theory(equality)],[26,5]),
    [iquote('1:Res:26.0,5.0')] ).

cnf(31,plain,
    equal(b,a),
    inference(spt,[spt(split,[position(s2s1)])],[17]),
    [iquote('2:Spt:17.0')] ).

cnf(34,plain,
    ~ reflexive_rewrite(a,c),
    inference(rew,[status(thm),theory(equality)],[31,12]),
    [iquote('2:Rew:31.0,12.0')] ).

cnf(36,plain,
    $false,
    inference(mrr,[status(thm)],[34,3]),
    [iquote('2:MRR:34.0,3.0')] ).

cnf(37,plain,
    ~ equal(b,a),
    inference(spt,[spt(split,[position(s2sa)])],[36,31]),
    [iquote('2:Spt:36.0,17.0,31.0')] ).

cnf(38,plain,
    rewrite(b,skf1(b,u)),
    inference(spt,[spt(split,[position(s2s2)])],[17]),
    [iquote('2:Spt:36.0,17.1')] ).

cnf(44,plain,
    ~ reflexive_rewrite(b,skf1(c,u)),
    inference(res,[status(thm),theory(equality)],[28,10]),
    [iquote('1:Res:28.0,10.0')] ).

cnf(45,plain,
    ( ~ reflexive_rewrite(u,v)
    | ~ rewrite(u,w)
    | equal(u,v)
    | rewrite(w,skf1(v,w)) ),
    inference(res,[status(thm),theory(equality)],[8,9]),
    [iquote('0:Res:8.1,9.0')] ).

cnf(55,plain,
    ( ~ rewrite(a,u)
    | equal(c,a)
    | rewrite(u,skf1(c,u)) ),
    inference(res,[status(thm),theory(equality)],[3,45]),
    [iquote('0:Res:3.0,45.0')] ).

cnf(61,plain,
    ( ~ rewrite(a,u)
    | rewrite(u,skf1(c,u)) ),
    inference(mrr,[status(thm)],[55,25]),
    [iquote('1:MRR:55.1,25.0')] ).

cnf(67,plain,
    ( ~ rewrite(a,u)
    | reflexive_rewrite(u,skf1(c,u)) ),
    inference(res,[status(thm),theory(equality)],[61,5]),
    [iquote('1:Res:61.1,5.0')] ).

cnf(74,plain,
    ~ rewrite(a,b),
    inference(res,[status(thm),theory(equality)],[67,44]),
    [iquote('1:Res:67.1,44.0')] ).

cnf(79,plain,
    ( ~ reflexive_rewrite(a,b)
    | equal(b,a) ),
    inference(res,[status(thm),theory(equality)],[8,74]),
    [iquote('1:Res:8.1,74.0')] ).

cnf(80,plain,
    $false,
    inference(mrr,[status(thm)],[79,2,37]),
    [iquote('2:MRR:79.0,79.1,2.0,37.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : COM007+2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n019.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 : Thu Jun 16 18:16:39 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.44  
% 0.20/0.44  SPASS V 3.9 
% 0.20/0.44  SPASS beiseite: Proof found.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.44  SPASS derived 60 clauses, backtracked 12 clauses, performed 2 splits and kept 57 clauses.
% 0.20/0.44  SPASS allocated 85124 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.44  		0:00:00.04 for the input.
% 0.20/0.44  		0:00:00.02 for the FLOTTER CNF translation.
% 0.20/0.44  		0:00:00.00 for inferences.
% 0.20/0.44  		0:00:00.00 for the backtracking.
% 0.20/0.44  		0:00:00.00 for the reduction.
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Here is a proof with depth 7, length 34 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : goal_to_be_proved assumption equal_in_reflexive_rewrite rewrite_in_reflexive_rewrite goal_ax rewrite_diamond equal_or_rewrite
% 0.20/0.44  
%------------------------------------------------------------------------------