TSTP Solution File: NUM847+2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% 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 : Mon Jul 18 14:31:02 EDT 2022

% Result   : Theorem 1.16s 1.38s
% Output   : Refutation 1.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   13 (  13 unt;   0 nHn;  13 RR)
%            Number of literals    :   13 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    equal(vplus(u,v),vplus(v,u)),
    file('NUM847+2.p',unknown),
    [] ).

cnf(14,axiom,
    equal(vplus(vmul(u,v),u),vmul(u,vsucc(v))),
    file('NUM847+2.p',unknown),
    [] ).

cnf(15,axiom,
    equal(vplus(vplus(u,v),w),vplus(u,vplus(v,w))),
    file('NUM847+2.p',unknown),
    [] ).

cnf(17,axiom,
    equal(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vmul(vd436,vplus(vd437,vd439))),
    file('NUM847+2.p',unknown),
    [] ).

cnf(21,axiom,
    ~ equal(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))),
    file('NUM847+2.p',unknown),
    [] ).

cnf(24,plain,
    equal(vplus(u,vmul(u,v)),vmul(u,vsucc(v))),
    inference(rew,[status(thm),theory(equality)],[6,14]),
    [iquote('0:Rew:6.0,14.0')] ).

cnf(31,plain,
    ~ equal(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),vmul(vd436,vsucc(vplus(vd437,vd439)))),
    inference(rew,[status(thm),theory(equality)],[24,21,6,17]),
    [iquote('0:Rew:24.0,21.0,6.0,21.0,17.0,21.0,24.0,21.0,6.0,21.0')] ).

cnf(209,plain,
    equal(vplus(vplus(u,v),w),vplus(v,vplus(u,w))),
    inference(spr,[status(thm),theory(equality)],[6,15]),
    [iquote('0:SpR:6.0,15.0')] ).

cnf(222,plain,
    equal(vplus(u,vplus(v,w)),vplus(v,vplus(u,w))),
    inference(rew,[status(thm),theory(equality)],[15,209]),
    [iquote('0:Rew:15.0,209.0')] ).

cnf(566,plain,
    equal(vplus(u,vplus(v,vmul(u,w))),vplus(v,vmul(u,vsucc(w)))),
    inference(spr,[status(thm),theory(equality)],[24,222]),
    [iquote('0:SpR:24.0,222.0')] ).

cnf(6446,plain,
    equal(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),vplus(vd436,vmul(vd436,vplus(vd437,vd439)))),
    inference(spr,[status(thm),theory(equality)],[17,566]),
    [iquote('0:SpR:17.0,566.0')] ).

cnf(6482,plain,
    equal(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),vmul(vd436,vsucc(vplus(vd437,vd439)))),
    inference(rew,[status(thm),theory(equality)],[24,6446]),
    [iquote('0:Rew:24.0,6446.0')] ).

cnf(6483,plain,
    $false,
    inference(mrr,[status(thm)],[6482,31]),
    [iquote('0:MRR:6482.0,31.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jul  8 01:19:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.16/1.38  
% 1.16/1.38  SPASS V 3.9 
% 1.16/1.38  SPASS beiseite: Proof found.
% 1.16/1.38  % SZS status Theorem
% 1.16/1.38  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.16/1.38  SPASS derived 3694 clauses, backtracked 0 clauses, performed 0 splits and kept 702 clauses.
% 1.16/1.38  SPASS allocated 90318 KBytes.
% 1.16/1.38  SPASS spent	0:00:01.02 on the problem.
% 1.16/1.38  		0:00:00.03 for the input.
% 1.16/1.38  		0:00:00.02 for the FLOTTER CNF translation.
% 1.16/1.38  		0:00:00.04 for inferences.
% 1.16/1.38  		0:00:00.00 for the backtracking.
% 1.16/1.38  		0:00:00.90 for the reduction.
% 1.16/1.38  
% 1.16/1.38  
% 1.16/1.38  Here is a proof with depth 3, length 13 :
% 1.16/1.38  % SZS output start Refutation
% See solution above
% 1.16/1.38  Formulae used in the proof : ass_a40_cond_a40_61_a44__a32_0_a41__a44__a32_0_a41_ qu_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_32_a41__a44__a32_and_a40_holds_a40_definiens_a40_249_a41__a44__a32_399_a44__a32_0_a41__a44__a32_holds_a40_definiens_a40_249_a41__a44__a32_398_a44__a32_0_a41__a41__a41_ ass_a40_cond_a40_33_a44__a32_0_a41__a44__a32_0_a41_ holds_a40_285_a44__a32_440_a44__a32_0_a41_ holds_a40_286_a44__a32_441_a44__a32_3_a41_
% 1.16/1.38  
%------------------------------------------------------------------------------