%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP046-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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 : Sat Jul 16 11:44:59 EDT 2022

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (   8 unt;   0 nHn;  15 RR)
%            Number of literals    :   27 (   0 equ;  16 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equalish(a,b),
    file('GRP046-2.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equalish(multiply(a,c),multiply(b,c)),
    file('GRP046-2.p',unknown),
    [] ).

cnf(3,axiom,
    product(identity,u,u),
    file('GRP046-2.p',unknown),
    [] ).

cnf(5,axiom,
    product(u,v,multiply(u,v)),
    file('GRP046-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ product(u,v,w)
    | ~ product(u,v,x)
    | equalish(x,w) ),
    file('GRP046-2.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,y,v)
    | ~ product(u,x,z)
    | product(z,y,w) ),
    file('GRP046-2.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ equalish(u,v)
    | ~ product(w,x,u)
    | product(w,x,v) ),
    file('GRP046-2.p',unknown),
    [] ).

cnf(11,plain,
    ( ~ equalish(u,v)
    | product(identity,u,v) ),
    inference(res,[status(thm),theory(equality)],[3,9]),
    [iquote('0:Res:3.0,9.1')] ).

cnf(19,plain,
    ( ~ product(u,v,w)
    | equalish(w,multiply(u,v)) ),
    inference(res,[status(thm),theory(equality)],[5,6]),
    [iquote('0:Res:5.0,6.0')] ).

cnf(29,plain,
    ( ~ product(u,v,w)
    | ~ product(identity,u,x)
    | product(x,v,w) ),
    inference(res,[status(thm),theory(equality)],[3,8]),
    [iquote('0:Res:3.0,8.0')] ).

cnf(62,plain,
    ~ product(b,c,multiply(a,c)),
    inference(res,[status(thm),theory(equality)],[19,2]),
    [iquote('0:Res:19.1,2.0')] ).

cnf(88,plain,
    ( ~ product(identity,u,v)
    | product(v,w,multiply(u,w)) ),
    inference(res,[status(thm),theory(equality)],[5,29]),
    [iquote('0:Res:5.0,29.0')] ).

cnf(438,plain,
    ~ product(identity,a,b),
    inference(res,[status(thm),theory(equality)],[88,62]),
    [iquote('0:Res:88.1,62.0')] ).

cnf(440,plain,
    ~ equalish(a,b),
    inference(res,[status(thm),theory(equality)],[11,438]),
    [iquote('0:Res:11.1,438.0')] ).

cnf(441,plain,
    $false,
    inference(mrr,[status(thm)],[440,1]),
    [iquote('0:MRR:440.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP046-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n003.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
% 0.12/0.34  % DateTime : Tue Jun 14 11:49:40 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.48  
% 0.19/0.48  SPASS V 3.9 
% 0.19/0.48  SPASS beiseite: Proof found.
% 0.19/0.48  % SZS status Theorem
% 0.19/0.48  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.48  SPASS derived 431 clauses, backtracked 0 clauses, performed 0 splits and kept 333 clauses.
% 0.19/0.48  SPASS allocated 63437 KBytes.
% 0.19/0.48  SPASS spent	0:00:00.13 on the problem.
% 0.19/0.48  		0:00:00.03 for the input.
% 0.19/0.48  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48  		0:00:00.01 for inferences.
% 0.19/0.48  		0:00:00.00 for the backtracking.
% 0.19/0.48  		0:00:00.07 for the reduction.
% 0.19/0.48  
% 0.19/0.48  
% 0.19/0.48  Here is a proof with depth 4, length 15 :
% 0.19/0.48  % SZS output start Refutation
% See solution above
% 0.19/0.48  Formulae used in the proof : a_equals_b prove_multiply_substitution1 left_identity total_function1 total_function2 associativity2 product_substitution3
% 0.19/0.48  
%------------------------------------------------------------------------------