TSTP Solution File: HEN004-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : HEN004-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 13:03:00 EDT 2022

% Result   : Unsatisfiable 0.17s 0.43s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   25 (  14 unt;   0 nHn;  25 RR)
%            Number of literals    :   38 (   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    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(divide(a,zero),a),
    file('HEN004-3.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ less_equal(u,v)
    | equal(divide(u,v),zero) ),
    file('HEN004-3.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ equal(divide(u,v),zero)
    | less_equal(u,v) ),
    file('HEN004-3.p',unknown),
    [] ).

cnf(4,axiom,
    less_equal(divide(u,v),u),
    file('HEN004-3.p',unknown),
    [] ).

cnf(5,axiom,
    less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
    file('HEN004-3.p',unknown),
    [] ).

cnf(6,axiom,
    less_equal(zero,u),
    file('HEN004-3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ less_equal(u,v)
    | ~ less_equal(v,u)
    | equal(v,u) ),
    file('HEN004-3.p',unknown),
    [] ).

cnf(9,plain,
    ( ~ less_equal(divide(a,zero),a)
    | ~ less_equal(a,divide(a,zero)) ),
    inference(res,[status(thm),theory(equality)],[7,1]),
    [iquote('0:Res:7.2,1.0')] ).

cnf(11,plain,
    ~ less_equal(a,divide(a,zero)),
    inference(mrr,[status(thm)],[9,4]),
    [iquote('0:MRR:9.0,4.0')] ).

cnf(18,plain,
    ( ~ less_equal(u,zero)
    | equal(u,zero) ),
    inference(res,[status(thm),theory(equality)],[6,7]),
    [iquote('0:Res:6.0,7.0')] ).

cnf(28,plain,
    equal(divide(zero,u),zero),
    inference(res,[status(thm),theory(equality)],[4,18]),
    [iquote('0:Res:4.0,18.0')] ).

cnf(35,plain,
    less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
    inference(spr,[status(thm),theory(equality)],[28,5]),
    [iquote('0:SpR:28.0,5.0')] ).

cnf(43,plain,
    ( ~ less_equal(divide(u,zero),v)
    | less_equal(divide(divide(u,v),zero),zero) ),
    inference(spr,[status(thm),theory(equality)],[2,35]),
    [iquote('0:SpR:2.1,35.0')] ).

cnf(206,plain,
    ( ~ less_equal(divide(u,zero),v)
    | equal(divide(divide(u,v),zero),zero) ),
    inference(res,[status(thm),theory(equality)],[43,18]),
    [iquote('0:Res:43.1,18.0')] ).

cnf(243,plain,
    ( ~ less_equal(divide(u,zero),v)
    | ~ equal(zero,zero)
    | less_equal(divide(u,v),zero) ),
    inference(spl,[status(thm),theory(equality)],[206,3]),
    [iquote('0:SpL:206.1,3.0')] ).

cnf(246,plain,
    ( ~ less_equal(divide(u,zero),v)
    | less_equal(divide(u,v),zero) ),
    inference(obv,[status(thm),theory(equality)],[243]),
    [iquote('0:Obv:243.1')] ).

cnf(256,plain,
    less_equal(divide(u,u),zero),
    inference(res,[status(thm),theory(equality)],[4,246]),
    [iquote('0:Res:4.0,246.0')] ).

cnf(327,plain,
    equal(divide(u,u),zero),
    inference(res,[status(thm),theory(equality)],[256,18]),
    [iquote('0:Res:256.0,18.0')] ).

cnf(349,plain,
    ( ~ equal(zero,zero)
    | less_equal(u,u) ),
    inference(spl,[status(thm),theory(equality)],[327,3]),
    [iquote('0:SpL:327.0,3.0')] ).

cnf(353,plain,
    less_equal(u,u),
    inference(obv,[status(thm),theory(equality)],[349]),
    [iquote('0:Obv:349.0')] ).

cnf(426,plain,
    less_equal(divide(u,divide(u,zero)),zero),
    inference(res,[status(thm),theory(equality)],[353,246]),
    [iquote('0:Res:353.0,246.0')] ).

cnf(437,plain,
    equal(divide(u,divide(u,zero)),zero),
    inference(res,[status(thm),theory(equality)],[426,18]),
    [iquote('0:Res:426.0,18.0')] ).

cnf(463,plain,
    ( ~ equal(zero,zero)
    | less_equal(u,divide(u,zero)) ),
    inference(spl,[status(thm),theory(equality)],[437,3]),
    [iquote('0:SpL:437.0,3.0')] ).

cnf(470,plain,
    less_equal(u,divide(u,zero)),
    inference(obv,[status(thm),theory(equality)],[463]),
    [iquote('0:Obv:463.0')] ).

cnf(471,plain,
    $false,
    inference(unc,[status(thm)],[470,11]),
    [iquote('0:UnC:470.0,11.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : HEN004-3 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12  % Command  : run_spass %d %s
% 0.13/0.32  % Computer : n025.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 600
% 0.13/0.32  % DateTime : Fri Jul  1 13:26:09 EDT 2022
% 0.13/0.32  % CPUTime  : 
% 0.17/0.43  
% 0.17/0.43  SPASS V 3.9 
% 0.17/0.43  SPASS beiseite: Proof found.
% 0.17/0.43  % SZS status Theorem
% 0.17/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.17/0.43  SPASS derived 347 clauses, backtracked 0 clauses, performed 0 splits and kept 94 clauses.
% 0.17/0.43  SPASS allocated 63446 KBytes.
% 0.17/0.43  SPASS spent	0:00:00.09 on the problem.
% 0.17/0.43  		0:00:00.04 for the input.
% 0.17/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.43  		0:00:00.01 for inferences.
% 0.17/0.43  		0:00:00.00 for the backtracking.
% 0.17/0.43  		0:00:00.03 for the reduction.
% 0.17/0.43  
% 0.17/0.43  
% 0.17/0.43  Here is a proof with depth 12, length 25 :
% 0.17/0.43  % SZS output start Refutation
% See solution above
% 0.17/0.43  Formulae used in the proof : prove_x_divide_zero_is_x quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.17/0.43  
%------------------------------------------------------------------------------