TSTP Solution File: ALG236-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG236-1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Thu Jul 14 18:03:09 EDT 2022

% Result   : Unsatisfiable 1.53s 1.72s
% Output   : Refutation 1.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   35 (  35 unt;   0 nHn;  35 RR)
%            Number of literals    :   35 (   0 equ;   2 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    :   12 (  12 usr;  11 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(mult(u,mult(v,mult(u,v))),mult(u,v)),
    file('ALG236-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(mult(u,mult(v,mult(w,x))),mult(w,mult(v,mult(u,x)))),
    file('ALG236-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(mult(mult(u,mult(v,mult(w,v))),x),mult(u,mult(x,mult(mult(w,v),x)))),
    file('ALG236-1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(mult(mult(a,b),mult(c,mult(d,e))),mult(a,mult(c,mult(mult(d,b),e)))),
    file('ALG236-1.p',unknown),
    [] ).

cnf(5,plain,
    ~ equal(mult(d,mult(c,mult(mult(a,b),e))),mult(a,mult(c,mult(mult(d,b),e)))),
    inference(rew,[status(thm),theory(equality)],[2,4]),
    [iquote('0:Rew:2.0,4.0')] ).

cnf(11,plain,
    equal(mult(u,mult(v,mult(w,mult(x,y)))),mult(w,mult(x,mult(u,mult(v,y))))),
    inference(spr,[status(thm),theory(equality)],[2]),
    [iquote('0:SpR:2.0,2.0')] ).

cnf(26,plain,
    equal(mult(u,mult(v,mult(w,mult(x,mult(u,x))))),mult(w,mult(v,mult(u,x)))),
    inference(spr,[status(thm),theory(equality)],[1,2]),
    [iquote('0:SpR:1.0,2.0')] ).

cnf(27,plain,
    equal(mult(u,mult(v,mult(w,mult(v,u)))),mult(w,mult(v,u))),
    inference(spr,[status(thm),theory(equality)],[1,2]),
    [iquote('0:SpR:1.0,2.0')] ).

cnf(62,plain,
    equal(mult(u,mult(v,mult(w,mult(x,mult(u,v))))),mult(w,mult(x,mult(u,v)))),
    inference(spr,[status(thm),theory(equality)],[27,2]),
    [iquote('0:SpR:27.0,2.0')] ).

cnf(75,plain,
    equal(mult(mult(u,v),mult(v,mult(u,v))),mult(u,v)),
    inference(spr,[status(thm),theory(equality)],[1,27]),
    [iquote('0:SpR:1.0,27.0')] ).

cnf(83,plain,
    equal(mult(u,mult(v,mult(mult(u,v),v))),mult(u,v)),
    inference(rew,[status(thm),theory(equality)],[2,75]),
    [iquote('0:Rew:2.0,75.0')] ).

cnf(124,plain,
    equal(mult(mult(u,v),mult(w,mult(x,w))),mult(mult(x,mult(v,mult(u,v))),w)),
    inference(spr,[status(thm),theory(equality)],[3,2]),
    [iquote('0:SpR:3.0,2.0')] ).

cnf(142,plain,
    equal(mult(u,mult(v,mult(mult(u,w),v))),mult(mult(u,w),v)),
    inference(spr,[status(thm),theory(equality)],[1,3]),
    [iquote('0:SpR:1.0,3.0')] ).

cnf(143,plain,
    equal(mult(mult(u,mult(v,mult(w,v))),x),mult(w,mult(x,mult(mult(u,v),x)))),
    inference(spr,[status(thm),theory(equality)],[2,3]),
    [iquote('0:SpR:2.0,3.0')] ).

cnf(155,plain,
    equal(mult(mult(u,v),v),mult(u,v)),
    inference(rew,[status(thm),theory(equality)],[142,83]),
    [iquote('0:Rew:142.0,83.0')] ).

cnf(213,plain,
    equal(mult(mult(u,v),mult(w,mult(x,v))),mult(x,mult(w,mult(u,v)))),
    inference(spr,[status(thm),theory(equality)],[155,2]),
    [iquote('0:SpR:155.0,2.0')] ).

cnf(264,plain,
    equal(mult(u,mult(v,mult(mult(mult(u,w),x),v))),mult(mult(mult(u,w),x),v)),
    inference(spr,[status(thm),theory(equality)],[142]),
    [iquote('0:SpR:142.0,142.0')] ).

cnf(633,plain,
    equal(mult(u,mult(v,mult(w,mult(x,mult(y,z))))),mult(w,mult(x,mult(y,mult(v,mult(u,z)))))),
    inference(spr,[status(thm),theory(equality)],[2,11]),
    [iquote('0:SpR:2.0,11.0')] ).

cnf(788,plain,
    equal(mult(u,mult(v,mult(u,mult(w,mult(x,w))))),mult(x,mult(v,mult(u,w)))),
    inference(spr,[status(thm),theory(equality)],[2,26]),
    [iquote('0:SpR:2.0,26.0')] ).

cnf(1366,plain,
    equal(mult(mult(u,v),mult(w,mult(x,w))),mult(u,mult(w,mult(mult(x,v),w)))),
    inference(spr,[status(thm),theory(equality)],[143,124]),
    [iquote('0:SpR:143.0,124.0')] ).

cnf(1403,plain,
    equal(mult(u,mult(v,mult(mult(w,mult(x,mult(y,x))),z))),mult(y,mult(v,mult(u,mult(z,mult(mult(w,x),z)))))),
    inference(spr,[status(thm),theory(equality)],[143,2]),
    [iquote('0:SpR:143.0,2.0')] ).

cnf(1461,plain,
    equal(mult(mult(u,v),mult(w,mult(mult(u,x),w))),mult(mult(mult(u,v),x),w)),
    inference(spr,[status(thm),theory(equality)],[142,143]),
    [iquote('0:SpR:142.0,143.0')] ).

cnf(1552,plain,
    equal(mult(mult(mult(u,v),w),x),mult(mult(mult(u,w),v),x)),
    inference(rew,[status(thm),theory(equality)],[264,1461,1366]),
    [iquote('0:Rew:264.0,1461.0,1366.0,1461.0')] ).

cnf(1834,plain,
    equal(mult(mult(mult(u,v),w),v),mult(mult(u,w),v)),
    inference(spr,[status(thm),theory(equality)],[1552,155]),
    [iquote('0:SpR:1552.0,155.0')] ).

cnf(1903,plain,
    equal(mult(mult(mult(u,v),w),mult(x,mult(y,v))),mult(y,mult(x,mult(mult(u,w),v)))),
    inference(spr,[status(thm),theory(equality)],[1552,213]),
    [iquote('0:SpR:1552.0,213.0')] ).

cnf(1904,plain,
    equal(mult(mult(mult(u,v),mult(w,mult(x,w))),y),mult(x,mult(y,mult(mult(mult(u,w),v),y)))),
    inference(spr,[status(thm),theory(equality)],[1552,143]),
    [iquote('0:SpR:1552.0,143.0')] ).

cnf(2004,plain,
    equal(mult(mult(u,mult(v,mult(mult(w,x),v))),y),mult(w,mult(y,mult(mult(mult(u,v),x),y)))),
    inference(rew,[status(thm),theory(equality)],[1366,1904]),
    [iquote('0:Rew:1366.0,1904.0')] ).

cnf(2106,plain,
    equal(mult(mult(mult(u,v),w),mult(v,mult(x,mult(y,mult(mult(u,w),v))))),mult(x,mult(y,mult(mult(u,w),v)))),
    inference(spr,[status(thm),theory(equality)],[1834,62]),
    [iquote('0:SpR:1834.0,62.0')] ).

cnf(2186,plain,
    equal(mult(mult(mult(mult(u,v),w),x),v),mult(mult(mult(u,w),x),v)),
    inference(spr,[status(thm),theory(equality)],[1552,1834]),
    [iquote('0:SpR:1552.0,1834.0')] ).

cnf(2261,plain,
    equal(mult(mult(mult(u,v),v),mult(w,mult(x,y))),mult(u,mult(w,mult(mult(x,v),y)))),
    inference(rew,[status(thm),theory(equality)],[788,2106,2186,1366,2004,1403,633]),
    [iquote('0:Rew:788.0,2106.0,2186.0,2106.0,1366.0,2106.0,2004.0,2106.0,1366.0,2106.0,1403.0,2106.0,1366.0,2106.0,1366.0,2106.0,633.0,2106.0')] ).

cnf(2262,plain,
    equal(mult(mult(u,v),mult(w,mult(x,y))),mult(u,mult(w,mult(mult(x,v),y)))),
    inference(rew,[status(thm),theory(equality)],[155,2261]),
    [iquote('0:Rew:155.0,2261.0')] ).

cnf(2336,plain,
    equal(mult(mult(u,v),mult(w,mult(mult(x,y),v))),mult(x,mult(w,mult(mult(u,y),v)))),
    inference(rew,[status(thm),theory(equality)],[2262,1903]),
    [iquote('0:Rew:2262.0,1903.0')] ).

cnf(2351,plain,
    equal(mult(u,mult(v,mult(mult(mult(w,x),y),y))),mult(w,mult(v,mult(mult(u,x),y)))),
    inference(rew,[status(thm),theory(equality)],[2262,2336]),
    [iquote('0:Rew:2262.0,2336.0')] ).

cnf(2352,plain,
    equal(mult(u,mult(v,mult(mult(w,x),y))),mult(w,mult(v,mult(mult(u,x),y)))),
    inference(rew,[status(thm),theory(equality)],[155,2351]),
    [iquote('0:Rew:155.0,2351.0')] ).

cnf(2353,plain,
    $false,
    inference(unc,[status(thm)],[2352,5]),
    [iquote('0:UnC:2352.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : ALG236-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n021.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Wed Jun  8 15:06:52 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 1.53/1.72  
% 1.53/1.72  SPASS V 3.9 
% 1.53/1.72  SPASS beiseite: Proof found.
% 1.53/1.72  % SZS status Theorem
% 1.53/1.72  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.53/1.72  SPASS derived 1377 clauses, backtracked 0 clauses, performed 0 splits and kept 409 clauses.
% 1.53/1.72  SPASS allocated 67558 KBytes.
% 1.53/1.72  SPASS spent	0:00:01.35 on the problem.
% 1.53/1.72  		0:00:00.04 for the input.
% 1.53/1.72  		0:00:00.00 for the FLOTTER CNF translation.
% 1.53/1.72  		0:00:00.02 for inferences.
% 1.53/1.72  		0:00:00.00 for the backtracking.
% 1.53/1.72  		0:00:01.27 for the reduction.
% 1.53/1.72  
% 1.53/1.72  
% 1.53/1.72  Here is a proof with depth 4, length 35 :
% 1.53/1.72  % SZS output start Refutation
% See solution above
% 1.53/1.72  Formulae used in the proof : c01 c02 c03 goals
% 1.53/1.72  
%------------------------------------------------------------------------------