TSTP Solution File: GRP047-2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP047-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   33 (  13 unt;   0 nHn;  33 RR)
%            Number of literals    :   63 (   0 equ;  34 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equalish(a,b),
    file('GRP047-2.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equalish(multiply(c,a),multiply(c,b)),
    file('GRP047-2.p',unknown),
    [] ).

cnf(3,axiom,
    product(identity,u,u),
    file('GRP047-2.p',unknown),
    [] ).

cnf(4,axiom,
    product(inverse(u),u,identity),
    file('GRP047-2.p',unknown),
    [] ).

cnf(5,axiom,
    product(u,v,multiply(u,v)),
    file('GRP047-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ product(u,v,w)
    | ~ product(u,v,x)
    | equalish(x,w) ),
    file('GRP047-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,v,y)
    | ~ product(z,x,u)
    | product(z,y,w) ),
    file('GRP047-2.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,y,v)
    | ~ product(u,x,z)
    | product(z,y,w) ),
    file('GRP047-2.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ equalish(u,v)
    | ~ product(w,x,u)
    | product(w,x,v) ),
    file('GRP047-2.p',unknown),
    [] ).

cnf(10,plain,
    ( ~ product(u,v,multiply(c,b))
    | ~ product(u,v,multiply(c,a)) ),
    inference(res,[status(thm),theory(equality)],[6,2]),
    [iquote('0:Res:6.2,2.0')] ).

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(13,plain,
    ( ~ equalish(multiply(u,v),w)
    | product(u,v,w) ),
    inference(res,[status(thm),theory(equality)],[5,9]),
    [iquote('0:Res:5.0,9.1')] ).

cnf(14,plain,
    ( ~ equalish(u,v)
    | ~ equalish(v,w)
    | product(identity,u,w) ),
    inference(res,[status(thm),theory(equality)],[11,9]),
    [iquote('0:Res:11.1,9.1')] ).

cnf(16,plain,
    ( ~ product(identity,u,v)
    | equalish(v,u) ),
    inference(res,[status(thm),theory(equality)],[3,6]),
    [iquote('0:Res:3.0,6.0')] ).

cnf(22,plain,
    ( ~ equalish(u,v)
    | equalish(v,u) ),
    inference(res,[status(thm),theory(equality)],[11,16]),
    [iquote('0:Res:11.1,16.0')] ).

cnf(23,plain,
    equalish(multiply(identity,u),u),
    inference(res,[status(thm),theory(equality)],[5,16]),
    [iquote('0:Res:5.0,16.0')] ).

cnf(28,plain,
    equalish(u,multiply(identity,u)),
    inference(res,[status(thm),theory(equality)],[23,22]),
    [iquote('0:Res:23.0,22.0')] ).

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(43,plain,
    ( ~ product(u,v,w)
    | ~ product(x,u,identity)
    | product(x,w,v) ),
    inference(res,[status(thm),theory(equality)],[3,7]),
    [iquote('0:Res:3.0,7.0')] ).

cnf(46,plain,
    ( ~ product(u,v,w)
    | ~ product(x,u,y)
    | product(x,w,multiply(y,v)) ),
    inference(res,[status(thm),theory(equality)],[5,7]),
    [iquote('0:Res:5.0,7.0')] ).

cnf(87,plain,
    ( ~ product(identity,inverse(u),v)
    | product(v,u,identity) ),
    inference(res,[status(thm),theory(equality)],[4,29]),
    [iquote('0:Res:4.0,29.0')] ).

cnf(116,plain,
    ( ~ product(u,inverse(v),identity)
    | product(u,identity,v) ),
    inference(res,[status(thm),theory(equality)],[4,43]),
    [iquote('0:Res:4.0,43.0')] ).

cnf(254,plain,
    ( ~ product(u,identity,v)
    | product(u,w,multiply(v,w)) ),
    inference(res,[status(thm),theory(equality)],[3,46]),
    [iquote('0:Res:3.0,46.0')] ).

cnf(288,plain,
    product(multiply(identity,inverse(u)),u,identity),
    inference(res,[status(thm),theory(equality)],[5,87]),
    [iquote('0:Res:5.0,87.0')] ).

cnf(342,plain,
    product(multiply(identity,inverse(inverse(u))),identity,u),
    inference(res,[status(thm),theory(equality)],[288,116]),
    [iquote('0:Res:288.0,116.0')] ).

cnf(577,plain,
    ( ~ product(u,identity,c)
    | ~ product(u,a,multiply(c,b)) ),
    inference(res,[status(thm),theory(equality)],[254,10]),
    [iquote('0:Res:254.1,10.1')] ).

cnf(613,plain,
    ( ~ equalish(b,u)
    | product(identity,a,u) ),
    inference(res,[status(thm),theory(equality)],[1,14]),
    [iquote('0:Res:1.0,14.0')] ).

cnf(656,plain,
    ( ~ equalish(b,u)
    | equalish(u,a) ),
    inference(res,[status(thm),theory(equality)],[613,16]),
    [iquote('0:Res:613.1,16.0')] ).

cnf(668,plain,
    equalish(multiply(identity,b),a),
    inference(res,[status(thm),theory(equality)],[28,656]),
    [iquote('0:Res:28.0,656.0')] ).

cnf(700,plain,
    product(identity,b,a),
    inference(res,[status(thm),theory(equality)],[668,13]),
    [iquote('0:Res:668.0,13.0')] ).

cnf(705,plain,
    ( ~ product(u,identity,v)
    | product(u,a,multiply(v,b)) ),
    inference(res,[status(thm),theory(equality)],[700,46]),
    [iquote('0:Res:700.0,46.0')] ).

cnf(714,plain,
    ~ product(u,identity,c),
    inference(mrr,[status(thm)],[577,705]),
    [iquote('0:MRR:577.1,705.1')] ).

cnf(715,plain,
    $false,
    inference(unc,[status(thm)],[714,342]),
    [iquote('0:UnC:714.0,342.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP047-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n021.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 : Mon Jun 13 12:00:57 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.52  
% 0.19/0.52  SPASS V 3.9 
% 0.19/0.52  SPASS beiseite: Proof found.
% 0.19/0.52  % SZS status Theorem
% 0.19/0.52  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.52  SPASS derived 705 clauses, backtracked 0 clauses, performed 0 splits and kept 527 clauses.
% 0.19/0.52  SPASS allocated 63619 KBytes.
% 0.19/0.52  SPASS spent	0:00:00.17 on the problem.
% 0.19/0.52  		0:00:00.04 for the input.
% 0.19/0.52  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52  		0:00:00.01 for inferences.
% 0.19/0.52  		0:00:00.00 for the backtracking.
% 0.19/0.52  		0:00:00.10 for the reduction.
% 0.19/0.52  
% 0.19/0.52  
% 0.19/0.52  Here is a proof with depth 7, length 33 :
% 0.19/0.52  % SZS output start Refutation
% See solution above
% 0.19/0.52  Formulae used in the proof : a_equals_b prove_multiply_substitution2 left_identity left_inverse total_function1 total_function2 associativity1 associativity2 product_substitution3
% 0.19/0.52  
%------------------------------------------------------------------------------