%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : CAT019-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 00:07:33 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   18 (  11 unt;   3 nHn;  18 RR)
%            Number of literals    :   28 (   0 equ;  12 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ there_exists(u)
    | ~ equal(a,u)
    | equal(b,u) ),
    file('CAT019-3.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ there_exists(u)
    | ~ equal(b,u)
    | equal(a,u) ),
    file('CAT019-3.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(b,a),
    file('CAT019-3.p',unknown),
    [] ).

cnf(18,axiom,
    ( there_exists(f1(u,v))
    | equal(u,v) ),
    file('CAT019-3.p',unknown),
    [] ).

cnf(19,axiom,
    ( equal(u,v)
    | equal(f1(u,v),v)
    | equal(f1(u,v),u) ),
    file('CAT019-3.p',unknown),
    [] ).

cnf(21,plain,
    ( ~ there_exists(a)
    | ~ equal(a,a) ),
    inference(res,[status(thm),theory(equality)],[1,3]),
    [iquote('0:Res:1.2,3.0')] ).

cnf(26,plain,
    ( ~ there_exists(b)
    | ~ equal(b,b) ),
    inference(res,[status(thm),theory(equality)],[2,3]),
    [iquote('0:Res:2.2,3.0')] ).

cnf(28,plain,
    ( equal(f1(a,b),b)
    | equal(f1(a,b),a) ),
    inference(res,[status(thm),theory(equality)],[19,3]),
    [iquote('0:Res:19.2,3.0')] ).

cnf(30,plain,
    there_exists(f1(a,b)),
    inference(res,[status(thm),theory(equality)],[18,3]),
    [iquote('0:Res:18.1,3.0')] ).

cnf(31,plain,
    ~ there_exists(a),
    inference(obv,[status(thm),theory(equality)],[21]),
    [iquote('0:Obv:21.1')] ).

cnf(32,plain,
    ~ there_exists(b),
    inference(obv,[status(thm),theory(equality)],[26]),
    [iquote('0:Obv:26.1')] ).

cnf(33,plain,
    equal(f1(a,b),b),
    inference(spt,[spt(split,[position(s1)])],[28]),
    [iquote('1:Spt:28.0')] ).

cnf(35,plain,
    there_exists(b),
    inference(rew,[status(thm),theory(equality)],[33,30]),
    [iquote('1:Rew:33.0,30.0')] ).

cnf(36,plain,
    $false,
    inference(mrr,[status(thm)],[35,32]),
    [iquote('1:MRR:35.0,32.0')] ).

cnf(37,plain,
    ~ equal(f1(a,b),b),
    inference(spt,[spt(split,[position(sa)])],[36,33]),
    [iquote('1:Spt:36.0,28.0,33.0')] ).

cnf(38,plain,
    equal(f1(a,b),a),
    inference(spt,[spt(split,[position(s2)])],[28]),
    [iquote('1:Spt:36.0,28.1')] ).

cnf(39,plain,
    there_exists(a),
    inference(rew,[status(thm),theory(equality)],[38,30]),
    [iquote('1:Rew:38.0,30.0')] ).

cnf(40,plain,
    $false,
    inference(mrr,[status(thm)],[39,31]),
    [iquote('1:MRR:39.0,31.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : CAT019-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n026.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun May 29 19:58:54 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 14 clauses, backtracked 4 clauses, performed 1 splits and kept 34 clauses.
% 0.19/0.42  SPASS allocated 75606 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.00 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 2, length 18 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : equality_of_a_and_b1 equality_of_a_and_b2 prove_a_equals_b indiscernibles1 indiscernibles2
% 0.19/0.42  
%------------------------------------------------------------------------------