TSTP Solution File: FLD050-4 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD050-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : Sat Jul 16 02:28:31 EDT 2022

% Result   : Unsatisfiable 3.23s 3.48s
% Output   : Refutation 3.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   36 (  16 unt;   6 nHn;  36 RR)
%            Number of literals    :   69 (   0 equ;  30 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;  14 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    defined(a),
    file('FLD050-4.p',unknown),
    [] ).

cnf(2,axiom,
    defined(b),
    file('FLD050-4.p',unknown),
    [] ).

cnf(3,axiom,
    defined(c),
    file('FLD050-4.p',unknown),
    [] ).

cnf(4,axiom,
    defined(d),
    file('FLD050-4.p',unknown),
    [] ).

cnf(7,axiom,
    ~ sum__dfg(additive_identity,b,additive_identity),
    file('FLD050-4.p',unknown),
    [] ).

cnf(8,axiom,
    ~ sum__dfg(additive_identity,d,additive_identity),
    file('FLD050-4.p',unknown),
    [] ).

cnf(9,axiom,
    product(a,multiplicative_inverse(b),s),
    file('FLD050-4.p',unknown),
    [] ).

cnf(10,axiom,
    product(a,d,k),
    file('FLD050-4.p',unknown),
    [] ).

cnf(11,axiom,
    product(b,c,k),
    file('FLD050-4.p',unknown),
    [] ).

cnf(12,axiom,
    ~ product(c,multiplicative_inverse(d),s),
    file('FLD050-4.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,v,y)
    | ~ product(z,x,u)
    | product(z,y,w) ),
    file('FLD050-4.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,y,v)
    | ~ product(u,x,z)
    | product(z,y,w) ),
    file('FLD050-4.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ defined(u)
    | product(multiplicative_identity,u,u) ),
    file('FLD050-4.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_identity,u,additive_identity)
    | product(multiplicative_inverse(u),u,multiplicative_identity) ),
    file('FLD050-4.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ product(u,v,w)
    | product(v,u,w) ),
    file('FLD050-4.p',unknown),
    [] ).

cnf(44,plain,
    ( ~ product(u,c,v)
    | ~ product(w,b,u)
    | product(w,k,v) ),
    inference(res,[status(thm),theory(equality)],[11,18]),
    [iquote('0:Res:11.0,18.1')] ).

cnf(54,plain,
    ( ~ product(a,u,v)
    | ~ product(d,w,u)
    | product(k,w,v) ),
    inference(res,[status(thm),theory(equality)],[10,19]),
    [iquote('0:Res:10.0,19.0')] ).

cnf(74,plain,
    ( ~ product(u,v,a)
    | ~ product(v,multiplicative_inverse(b),w)
    | product(u,w,s) ),
    inference(res,[status(thm),theory(equality)],[9,18]),
    [iquote('0:Res:9.0,18.2')] ).

cnf(99,plain,
    ( ~ defined(u)
    | product(u,multiplicative_identity,u) ),
    inference(res,[status(thm),theory(equality)],[20,22]),
    [iquote('0:Res:20.1,22.0')] ).

cnf(108,plain,
    ( ~ defined(u)
    | sum__dfg(additive_identity,u,additive_identity)
    | product(u,multiplicative_inverse(u),multiplicative_identity) ),
    inference(res,[status(thm),theory(equality)],[21,22]),
    [iquote('0:Res:21.2,22.0')] ).

cnf(124,plain,
    ( ~ defined(a)
    | ~ product(d,u,multiplicative_identity)
    | product(k,u,a) ),
    inference(res,[status(thm),theory(equality)],[99,54]),
    [iquote('0:Res:99.1,54.0')] ).

cnf(128,plain,
    ( ~ product(d,u,multiplicative_identity)
    | product(k,u,a) ),
    inference(ssi,[status(thm)],[124,1]),
    [iquote('0:SSi:124.0,1.0')] ).

cnf(144,plain,
    ( ~ defined(d)
    | sum__dfg(additive_identity,d,additive_identity)
    | product(k,multiplicative_inverse(d),a) ),
    inference(res,[status(thm),theory(equality)],[108,128]),
    [iquote('0:Res:108.2,128.0')] ).

cnf(145,plain,
    ( sum__dfg(additive_identity,d,additive_identity)
    | product(k,multiplicative_inverse(d),a) ),
    inference(ssi,[status(thm)],[144,4]),
    [iquote('0:SSi:144.0,4.0')] ).

cnf(146,plain,
    product(k,multiplicative_inverse(d),a),
    inference(mrr,[status(thm)],[145,8]),
    [iquote('0:MRR:145.0,8.0')] ).

cnf(147,plain,
    product(multiplicative_inverse(d),k,a),
    inference(res,[status(thm),theory(equality)],[146,22]),
    [iquote('0:Res:146.0,22.0')] ).

cnf(568,plain,
    ( ~ defined(c)
    | ~ product(u,b,multiplicative_identity)
    | product(u,k,c) ),
    inference(res,[status(thm),theory(equality)],[20,44]),
    [iquote('0:Res:20.1,44.0')] ).

cnf(578,plain,
    ( ~ product(u,b,multiplicative_identity)
    | product(u,k,c) ),
    inference(ssi,[status(thm)],[568,3]),
    [iquote('0:SSi:568.0,3.0')] ).

cnf(674,plain,
    ( ~ defined(b)
    | sum__dfg(additive_identity,b,additive_identity)
    | product(multiplicative_inverse(b),k,c) ),
    inference(res,[status(thm),theory(equality)],[21,578]),
    [iquote('0:Res:21.2,578.0')] ).

cnf(675,plain,
    ( sum__dfg(additive_identity,b,additive_identity)
    | product(multiplicative_inverse(b),k,c) ),
    inference(ssi,[status(thm)],[674,2]),
    [iquote('0:SSi:674.0,2.0')] ).

cnf(676,plain,
    product(multiplicative_inverse(b),k,c),
    inference(mrr,[status(thm)],[675,7]),
    [iquote('0:MRR:675.0,7.0')] ).

cnf(680,plain,
    product(k,multiplicative_inverse(b),c),
    inference(res,[status(thm),theory(equality)],[676,22]),
    [iquote('0:Res:676.0,22.0')] ).

cnf(925,plain,
    ( ~ product(u,k,a)
    | product(u,c,s) ),
    inference(res,[status(thm),theory(equality)],[680,74]),
    [iquote('0:Res:680.0,74.1')] ).

cnf(1670,plain,
    ( ~ product(u,k,a)
    | product(c,u,s) ),
    inference(res,[status(thm),theory(equality)],[925,22]),
    [iquote('0:Res:925.1,22.0')] ).

cnf(7381,plain,
    product(c,multiplicative_inverse(d),s),
    inference(res,[status(thm),theory(equality)],[147,1670]),
    [iquote('0:Res:147.0,1670.0')] ).

cnf(7383,plain,
    $false,
    inference(mrr,[status(thm)],[7381,12]),
    [iquote('0:MRR:7381.0,12.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06  % Problem  : FLD050-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.07  % Command  : run_spass %d %s
% 0.06/0.25  % Computer : n019.cluster.edu
% 0.06/0.25  % Model    : x86_64 x86_64
% 0.06/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25  % Memory   : 8042.1875MB
% 0.06/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25  % CPULimit : 300
% 0.06/0.25  % WCLimit  : 600
% 0.06/0.25  % DateTime : Tue Jun  7 04:21:55 EDT 2022
% 0.06/0.25  % CPUTime  : 
% 3.23/3.48  
% 3.23/3.48  SPASS V 3.9 
% 3.23/3.48  SPASS beiseite: Proof found.
% 3.23/3.48  % SZS status Theorem
% 3.23/3.48  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 3.23/3.48  SPASS derived 4964 clauses, backtracked 0 clauses, performed 2 splits and kept 4152 clauses.
% 3.23/3.48  SPASS allocated 81646 KBytes.
% 3.23/3.48  SPASS spent	0:00:03.18 on the problem.
% 3.23/3.48  		0:00:00.02 for the input.
% 3.23/3.48  		0:00:00.00 for the FLOTTER CNF translation.
% 3.23/3.48  		0:00:00.05 for inferences.
% 3.23/3.48  		0:00:00.03 for the backtracking.
% 3.23/3.48  		0:00:03.04 for the reduction.
% 3.23/3.48  
% 3.23/3.48  
% 3.23/3.48  Here is a proof with depth 7, length 36 :
% 3.23/3.48  % SZS output start Refutation
% See solution above
% 3.23/3.48  Formulae used in the proof : a_is_defined b_is_defined c_is_defined d_is_defined not_sum_7 not_sum_8 product_9 product_10 product_11 not_product_12 associativity_multiplication_1 associativity_multiplication_2 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication
% 3.23/3.48  
%------------------------------------------------------------------------------