TSTP Solution File: HEN005-4 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : HEN005-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n004.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 13:03:03 EDT 2022

% Result   : Unsatisfiable 0.51s 0.67s
% Output   : Refutation 0.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   19 (   9 unt;   0 nHn;  19 RR)
%            Number of literals    :   31 (   0 equ;  16 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    equal(divide(zero,u),zero),
    file('HEN005-4.p',unknown),
    [] ).

cnf(4,axiom,
    equal(divide(u,zero),u),
    file('HEN005-4.p',unknown),
    [] ).

cnf(5,axiom,
    less_equal(a,b),
    file('HEN005-4.p',unknown),
    [] ).

cnf(6,axiom,
    less_equal(b,c),
    file('HEN005-4.p',unknown),
    [] ).

cnf(7,axiom,
    ~ less_equal(a,c),
    file('HEN005-4.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ less_equal(u,v)
    | equal(divide(u,v),zero) ),
    file('HEN005-4.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ equal(divide(u,v),zero)
    | less_equal(u,v) ),
    file('HEN005-4.p',unknown),
    [] ).

cnf(11,axiom,
    less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
    file('HEN005-4.p',unknown),
    [] ).

cnf(15,plain,
    ~ equal(divide(a,c),zero),
    inference(res,[status(thm),theory(equality)],[9,7]),
    [iquote('0:Res:9.1,7.0')] ).

cnf(31,plain,
    ( ~ less_equal(u,zero)
    | equal(zero,u) ),
    inference(spr,[status(thm),theory(equality)],[8,4]),
    [iquote('0:SpR:8.1,4.0')] ).

cnf(61,plain,
    ( ~ less_equal(u,v)
    | less_equal(divide(divide(u,w),divide(v,w)),divide(zero,w)) ),
    inference(spr,[status(thm),theory(equality)],[8,11]),
    [iquote('0:SpR:8.1,11.0')] ).

cnf(91,plain,
    ( ~ less_equal(u,v)
    | less_equal(divide(divide(u,w),divide(v,w)),zero) ),
    inference(rew,[status(thm),theory(equality)],[2,61]),
    [iquote('0:Rew:2.0,61.1')] ).

cnf(431,plain,
    ( ~ less_equal(u,v)
    | equal(divide(divide(u,w),divide(v,w)),zero) ),
    inference(res,[status(thm),theory(equality)],[91,31]),
    [iquote('0:Res:91.1,31.0')] ).

cnf(1056,plain,
    ( ~ less_equal(u,v)
    | ~ less_equal(w,u)
    | equal(divide(divide(w,v),zero),zero) ),
    inference(spr,[status(thm),theory(equality)],[8,431]),
    [iquote('0:SpR:8.1,431.1')] ).

cnf(1090,plain,
    ( ~ less_equal(u,v)
    | ~ less_equal(w,u)
    | equal(divide(w,v),zero) ),
    inference(rew,[status(thm),theory(equality)],[4,1056]),
    [iquote('0:Rew:4.0,1056.2')] ).

cnf(3210,plain,
    ( ~ less_equal(u,b)
    | equal(divide(u,c),zero) ),
    inference(res,[status(thm),theory(equality)],[6,1090]),
    [iquote('0:Res:6.0,1090.0')] ).

cnf(3290,plain,
    ( ~ less_equal(a,b)
    | ~ equal(zero,zero) ),
    inference(spl,[status(thm),theory(equality)],[3210,15]),
    [iquote('0:SpL:3210.1,15.0')] ).

cnf(3294,plain,
    ~ less_equal(a,b),
    inference(obv,[status(thm),theory(equality)],[3290]),
    [iquote('0:Obv:3290.1')] ).

cnf(3295,plain,
    $false,
    inference(mrr,[status(thm)],[3294,5]),
    [iquote('0:MRR:3294.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : HEN005-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Fri Jul  1 13:26:23 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.51/0.67  
% 0.51/0.67  SPASS V 3.9 
% 0.51/0.67  SPASS beiseite: Proof found.
% 0.51/0.67  % SZS status Theorem
% 0.51/0.67  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.51/0.67  SPASS derived 2285 clauses, backtracked 0 clauses, performed 0 splits and kept 353 clauses.
% 0.51/0.67  SPASS allocated 65374 KBytes.
% 0.51/0.67  SPASS spent	0:00:00.29 on the problem.
% 0.51/0.67  		0:00:00.04 for the input.
% 0.51/0.67  		0:00:00.00 for the FLOTTER CNF translation.
% 0.51/0.67  		0:00:00.02 for inferences.
% 0.51/0.67  		0:00:00.00 for the backtracking.
% 0.51/0.67  		0:00:00.21 for the reduction.
% 0.51/0.67  
% 0.51/0.67  
% 0.51/0.67  Here is a proof with depth 5, length 19 :
% 0.51/0.67  % SZS output start Refutation
% See solution above
% 0.51/0.67  Formulae used in the proof : zero_divide_anything_is_zero x_divide_zero_is_x a_LE_b b_LE_c prove_a_LE_c quotient_less_equal1 quotient_less_equal2 quotient_property
% 0.51/0.67  
%------------------------------------------------------------------------------