TSTP Solution File: ALG245-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG245-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 : Thu Jul 14 18:03:11 EDT 2022

% Result   : Unsatisfiable 0.75s 0.94s
% Output   : Refutation 0.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   31 (  31 unt;   0 nHn;  31 RR)
%            Number of literals    :   31 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(mult(mult(u,v),mult(u,w)),mult(u,mult(v,w))),
    file('ALG245-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(mult(mult(u,v),mult(w,v)),mult(mult(u,w),v)),
    file('ALG245-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x)))),mult(mult(u,w),mult(v,x))),
    file('ALG245-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x))),
    file('ALG245-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(mult(u,u),u),
    file('ALG245-1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),
    file('ALG245-1.p',unknown),
    [] ).

cnf(9,plain,
    equal(mult(mult(u,mult(v,w)),mult(mult(x,v),w)),mult(mult(u,mult(x,w)),mult(v,w))),
    inference(spr,[status(thm),theory(equality)],[2]),
    [iquote('0:SpR:2.0,2.0')] ).

cnf(13,plain,
    equal(mult(mult(u,v),u),mult(u,mult(v,u))),
    inference(spr,[status(thm),theory(equality)],[5,2]),
    [iquote('0:SpR:5.0,2.0')] ).

cnf(15,plain,
    equal(mult(mult(u,v),mult(v,mult(w,v))),mult(mult(u,mult(v,w)),v)),
    inference(spr,[status(thm),theory(equality)],[13,2]),
    [iquote('0:SpR:13.0,2.0')] ).

cnf(16,plain,
    equal(mult(mult(u,mult(v,u)),mult(w,u)),mult(mult(mult(u,v),w),u)),
    inference(spr,[status(thm),theory(equality)],[13,2]),
    [iquote('0:SpR:13.0,2.0')] ).

cnf(49,plain,
    equal(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),y),mult(mult(u,v),mult(w,x))),mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(y,mult(mult(u,w),mult(v,x))))),
    inference(spr,[status(thm),theory(equality)],[4,1]),
    [iquote('0:SpR:4.0,1.0')] ).

cnf(51,plain,
    equal(mult(mult(u,mult(mult(mult(v,w),mult(x,y)),mult(mult(v,x),mult(w,y)))),mult(mult(v,x),mult(w,y))),mult(mult(u,mult(mult(v,x),mult(w,y))),mult(mult(v,w),mult(x,y)))),
    inference(spr,[status(thm),theory(equality)],[4,2]),
    [iquote('0:SpR:4.0,2.0')] ).

cnf(52,plain,
    equal(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),y),mult(mult(u,w),mult(v,x))),mult(mult(mult(u,v),mult(w,x)),mult(y,mult(mult(u,w),mult(v,x))))),
    inference(spr,[status(thm),theory(equality)],[4,2]),
    [iquote('0:SpR:4.0,2.0')] ).

cnf(53,plain,
    equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(mult(mult(u,w),mult(v,x)),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))))),mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))))),
    inference(spr,[status(thm),theory(equality)],[4,13]),
    [iquote('0:SpR:4.0,13.0')] ).

cnf(121,plain,
    equal(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),y),mult(mult(u,v),mult(w,x))),mult(mult(mult(mult(u,v),mult(w,x)),y),mult(mult(u,w),mult(v,x)))),
    inference(rew,[status(thm),theory(equality)],[2,49]),
    [iquote('0:Rew:2.0,49.0')] ).

cnf(122,plain,
    equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,v),mult(w,x)))),mult(mult(u,w),mult(v,x))),mult(mult(u,w),mult(v,x))),
    inference(rew,[status(thm),theory(equality)],[15,53,3]),
    [iquote('0:Rew:15.0,53.0,3.0,53.0')] ).

cnf(418,plain,
    equal(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(y,mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))))),mult(mult(u,w),mult(v,x))),mult(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),y),mult(mult(u,v),mult(w,x))),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))))),
    inference(spr,[status(thm),theory(equality)],[3,16]),
    [iquote('0:SpR:3.0,16.0')] ).

cnf(558,plain,
    equal(mult(mult(mult(mult(mult(u,v),mult(w,x)),y),mult(mult(u,w),mult(v,x))),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x)))),mult(mult(mult(u,v),mult(w,x)),mult(mult(y,mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x))))),
    inference(rew,[status(thm),theory(equality)],[51,418,52,121]),
    [iquote('0:Rew:51.0,418.0,52.0,418.0,121.0,418.0')] ).

cnf(559,plain,
    equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(y,mult(mult(u,v),mult(w,x)))),mult(mult(u,w),mult(v,x))),mult(mult(mult(u,v),mult(w,x)),mult(mult(y,mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x))))),
    inference(rew,[status(thm),theory(equality)],[13,558,2]),
    [iquote('0:Rew:13.0,558.0,2.0,558.0')] ).

cnf(560,plain,
    equal(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(mult(u,w),mult(v,x)),mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x)))),mult(mult(u,w),mult(v,x))),
    inference(rew,[status(thm),theory(equality)],[559,122]),
    [iquote('0:Rew:559.0,122.0')] ).

cnf(561,plain,
    equal(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,v),mult(w,x)))),mult(mult(u,w),mult(v,x))),
    inference(rew,[status(thm),theory(equality)],[5,560,1]),
    [iquote('0:Rew:5.0,560.0,1.0,560.0,1.0,560.0')] ).

cnf(591,plain,
    equal(mult(mult(mult(u,v),mult(u,w)),mult(v,w)),mult(mult(u,v),mult(mult(v,w),w))),
    inference(spr,[status(thm),theory(equality)],[9,1]),
    [iquote('0:SpR:9.0,1.0')] ).

cnf(653,plain,
    equal(mult(mult(u,mult(v,w)),mult(v,w)),mult(mult(u,v),mult(mult(v,w),w))),
    inference(rew,[status(thm),theory(equality)],[1,591]),
    [iquote('0:Rew:1.0,591.0')] ).

cnf(654,plain,
    equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(u,w)),mult(mult(mult(u,w),mult(v,x)),mult(v,x))),mult(mult(u,v),mult(w,x))),
    inference(rew,[status(thm),theory(equality)],[653,4]),
    [iquote('0:Rew:653.0,4.0')] ).

cnf(712,plain,
    equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(u,w)),mult(mult(mult(u,w),v),mult(mult(v,x),x))),mult(mult(u,v),mult(w,x))),
    inference(rew,[status(thm),theory(equality)],[653,654]),
    [iquote('0:Rew:653.0,654.0')] ).

cnf(818,plain,
    equal(mult(mult(u,v),mult(mult(v,u),u)),mult(mult(mult(u,v),v),u)),
    inference(spr,[status(thm),theory(equality)],[653,16]),
    [iquote('0:SpR:653.0,16.0')] ).

cnf(979,plain,
    equal(mult(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x))),mult(mult(u,v),mult(w,x))),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x)))),mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x))),mult(mult(mult(u,w),mult(v,x)),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x)))))),
    inference(spr,[status(thm),theory(equality)],[3,818]),
    [iquote('0:SpR:3.0,818.0')] ).

cnf(1049,plain,
    equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,v),mult(w,x)))),mult(mult(mult(u,w),mult(v,x)),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))))),mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(mult(mult(u,w),mult(v,x)),mult(u,v)),mult(mult(mult(u,v),w),mult(mult(w,x),x))),mult(mult(u,w),mult(v,x))))),
    inference(rew,[status(thm),theory(equality)],[1,979,653,13]),
    [iquote('0:Rew:1.0,979.0,653.0,979.0,653.0,979.0,13.0,979.0,13.0,979.0')] ).

cnf(1050,plain,
    equal(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,w),mult(v,x)))),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,v),mult(w,x)))),
    inference(rew,[status(thm),theory(equality)],[561,1049,712]),
    [iquote('0:Rew:561.0,1049.0,561.0,1049.0,712.0,1049.0')] ).

cnf(1051,plain,
    equal(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,v),mult(w,x)))),
    inference(rew,[status(thm),theory(equality)],[5,1050,1]),
    [iquote('0:Rew:5.0,1050.0,1.0,1050.0,1.0,1050.0')] ).

cnf(1052,plain,
    $false,
    inference(unc,[status(thm)],[1051,6]),
    [iquote('0:UnC:1051.0,6.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : ALG245-1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.11/0.33  % Computer : n027.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Wed Jun  8 09:02:56 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.75/0.94  
% 0.75/0.94  SPASS V 3.9 
% 0.75/0.94  SPASS beiseite: Proof found.
% 0.75/0.94  % SZS status Theorem
% 0.75/0.94  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.75/0.94  SPASS derived 628 clauses, backtracked 0 clauses, performed 0 splits and kept 375 clauses.
% 0.75/0.94  SPASS allocated 66797 KBytes.
% 0.75/0.94  SPASS spent	0:00:00.59 on the problem.
% 0.75/0.94  		0:00:00.04 for the input.
% 0.75/0.94  		0:00:00.00 for the FLOTTER CNF translation.
% 0.75/0.94  		0:00:00.01 for inferences.
% 0.75/0.94  		0:00:00.00 for the backtracking.
% 0.75/0.94  		0:00:00.52 for the reduction.
% 0.75/0.94  
% 0.75/0.94  
% 0.75/0.94  Here is a proof with depth 4, length 31 :
% 0.75/0.94  % SZS output start Refutation
% See solution above
% 0.75/0.94  Formulae used in the proof : c01 c02 c03 c04 c05 goals
% 0.75/0.94  
%------------------------------------------------------------------------------