TSTP Solution File: KLE022+3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE022+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 : Sun Jul 17 02:28:05 EDT 2022

% Result   : Theorem 0.61s 0.83s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   23 (   9 unt;   0 nHn;  23 RR)
%            Number of literals    :   47 (   0 equ;  27 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    test__dfg(skc2),
    file('KLE022+3.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiplication(u,one),u),
    file('KLE022+3.p',unknown),
    [] ).

cnf(10,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE022+3.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ complement(u,v)
    | equal(multiplication(v,u),zero) ),
    file('KLE022+3.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ complement(u,v)
    | equal(multiplication(u,v),zero) ),
    file('KLE022+3.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ complement(u,v)
    | equal(addition(v,u),one) ),
    file('KLE022+3.p',unknown),
    [] ).

cnf(17,axiom,
    ~ equal(addition(multiplication(skc3,skc2),multiplication(skc3,c(skc2))),skc3),
    file('KLE022+3.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ test__dfg(u)
    | ~ equal(c(u),v)
    | complement(u,v) ),
    file('KLE022+3.p',unknown),
    [] ).

cnf(22,axiom,
    equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
    file('KLE022+3.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ equal(addition(u,v),one)
    | ~ equal(multiplication(v,u),zero)
    | ~ equal(multiplication(u,v),zero)
    | complement(v,u) ),
    file('KLE022+3.p',unknown),
    [] ).

cnf(29,plain,
    ( ~ equal(c(skc2),u)
    | complement(skc2,u) ),
    inference(res,[status(thm),theory(equality)],[1,20]),
    [iquote('0:Res:1.0,20.0')] ).

cnf(73,plain,
    ( ~ complement(u,v)
    | equal(addition(u,v),one) ),
    inference(spr,[status(thm),theory(equality)],[16,10]),
    [iquote('0:SpR:16.1,10.0')] ).

cnf(199,plain,
    complement(skc2,c(skc2)),
    inference(eqr,[status(thm),theory(equality)],[29]),
    [iquote('0:EqR:29.0')] ).

cnf(338,plain,
    ( ~ complement(u,v)
    | equal(multiplication(w,one),addition(multiplication(w,v),multiplication(w,u))) ),
    inference(spr,[status(thm),theory(equality)],[16,22]),
    [iquote('0:SpR:16.1,22.0')] ).

cnf(348,plain,
    ( ~ complement(u,v)
    | equal(addition(multiplication(w,v),multiplication(w,u)),w) ),
    inference(rew,[status(thm),theory(equality)],[4,338]),
    [iquote('0:Rew:4.0,338.1')] ).

cnf(516,plain,
    ( ~ complement(u,v)
    | ~ equal(one,one)
    | ~ equal(multiplication(v,u),zero)
    | ~ equal(multiplication(u,v),zero)
    | complement(v,u) ),
    inference(spl,[status(thm),theory(equality)],[73,26]),
    [iquote('0:SpL:73.1,26.0')] ).

cnf(530,plain,
    ( ~ complement(u,v)
    | ~ equal(multiplication(v,u),zero)
    | ~ equal(multiplication(u,v),zero)
    | complement(v,u) ),
    inference(obv,[status(thm),theory(equality)],[516]),
    [iquote('0:Obv:516.1')] ).

cnf(531,plain,
    ( ~ complement(u,v)
    | ~ equal(zero,zero)
    | ~ equal(zero,zero)
    | complement(v,u) ),
    inference(rew,[status(thm),theory(equality)],[15,530,14]),
    [iquote('0:Rew:15.1,530.2,14.1,530.1')] ).

cnf(532,plain,
    ( ~ complement(u,v)
    | complement(v,u) ),
    inference(obv,[status(thm),theory(equality)],[531]),
    [iquote('0:Obv:531.2')] ).

cnf(772,plain,
    complement(c(skc2),skc2),
    inference(res,[status(thm),theory(equality)],[199,532]),
    [iquote('0:Res:199.0,532.0')] ).

cnf(3896,plain,
    ( ~ complement(c(skc2),skc2)
    | ~ equal(skc3,skc3) ),
    inference(spl,[status(thm),theory(equality)],[348,17]),
    [iquote('0:SpL:348.1,17.0')] ).

cnf(3898,plain,
    ~ complement(c(skc2),skc2),
    inference(obv,[status(thm),theory(equality)],[3896]),
    [iquote('0:Obv:3896.1')] ).

cnf(3899,plain,
    $false,
    inference(mrr,[status(thm)],[3898,772]),
    [iquote('0:MRR:3898.0,772.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : KLE022+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n009.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 : Thu Jun 16 08:56:07 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.61/0.83  
% 0.61/0.83  SPASS V 3.9 
% 0.61/0.83  SPASS beiseite: Proof found.
% 0.61/0.83  % SZS status Theorem
% 0.61/0.83  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.61/0.83  SPASS derived 3052 clauses, backtracked 16 clauses, performed 1 splits and kept 1077 clauses.
% 0.61/0.83  SPASS allocated 100491 KBytes.
% 0.61/0.83  SPASS spent	0:00:00.47 on the problem.
% 0.61/0.83  		0:00:00.03 for the input.
% 0.61/0.83  		0:00:00.03 for the FLOTTER CNF translation.
% 0.61/0.83  		0:00:00.03 for inferences.
% 0.61/0.83  		0:00:00.00 for the backtracking.
% 0.61/0.83  		0:00:00.35 for the reduction.
% 0.61/0.83  
% 0.61/0.83  
% 0.61/0.83  Here is a proof with depth 3, length 23 :
% 0.61/0.83  % SZS output start Refutation
% See solution above
% 0.61/0.83  Formulae used in the proof : goals multiplicative_right_identity additive_commutativity test_2 test_3 right_distributivity
% 0.61/0.83  
%------------------------------------------------------------------------------