TSTP Solution File: GRP683-11 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP683-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 11:48:57 EDT 2022

% Result   : Unsatisfiable 0.81s 1.00s
% Output   : Refutation 0.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   54 (  54 unt;   0 nHn;  54 RR)
%            Number of literals    :   54 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 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,
    equal(ld(u,mult(u,u)),u),
    file('GRP683-11.p',unknown),
    [] ).

cnf(2,axiom,
    equal(rd(mult(u,u),u),u),
    file('GRP683-11.p',unknown),
    [] ).

cnf(3,axiom,
    equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
    file('GRP683-11.p',unknown),
    [] ).

cnf(4,axiom,
    equal(mult(rd(u,v),v),rd(mult(u,v),v)),
    file('GRP683-11.p',unknown),
    [] ).

cnf(5,axiom,
    equal(ld(ld(u,v),mult(ld(u,v),mult(w,x))),mult(ld(u,mult(u,w)),x)),
    file('GRP683-11.p',unknown),
    [] ).

cnf(6,axiom,
    equal(rd(mult(mult(u,v),rd(w,x)),rd(w,x)),mult(u,rd(mult(v,x),x))),
    file('GRP683-11.p',unknown),
    [] ).

cnf(7,axiom,
    equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
    file('GRP683-11.p',unknown),
    [] ).

cnf(8,axiom,
    ~ equal(mult(rd(mult(x3__dfg,x4__dfg),x4__dfg),x5__dfg),mult(x3__dfg,x5__dfg)),
    file('GRP683-11.p',unknown),
    [] ).

cnf(21,plain,
    equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(rd(u,u),v),v),v)),
    inference(spr,[status(thm),theory(equality)],[7,4]),
    [iquote('0:SpR:7.0,4.0')] ).

cnf(23,plain,
    equal(rd(rd(mult(u,u),u),u),ld(u,mult(u,ld(u,u)))),
    inference(spr,[status(thm),theory(equality)],[4,7]),
    [iquote('0:SpR:4.0,7.0')] ).

cnf(24,plain,
    equal(rd(u,u),ld(u,u)),
    inference(rew,[status(thm),theory(equality)],[2,23,1,3]),
    [iquote('0:Rew:2.0,23.0,1.0,23.0,3.0,23.0')] ).

cnf(25,plain,
    equal(rd(mult(ld(u,u),v),v),ld(u,mult(u,ld(v,v)))),
    inference(rew,[status(thm),theory(equality)],[24,7]),
    [iquote('0:Rew:24.0,7.0')] ).

cnf(27,plain,
    equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(ld(u,u),v),v),v)),
    inference(rew,[status(thm),theory(equality)],[24,21]),
    [iquote('0:Rew:24.0,21.0')] ).

cnf(29,plain,
    equal(mult(ld(u,u),u),rd(mult(u,u),u)),
    inference(spr,[status(thm),theory(equality)],[24,4]),
    [iquote('0:SpR:24.0,4.0')] ).

cnf(31,plain,
    equal(mult(ld(u,u),u),u),
    inference(rew,[status(thm),theory(equality)],[2,29]),
    [iquote('0:Rew:2.0,29.0')] ).

cnf(51,plain,
    equal(mult(u,rd(mult(v,w),w)),rd(mult(mult(u,v),w),w)),
    inference(spr,[status(thm),theory(equality)],[2,6]),
    [iquote('0:SpR:2.0,6.0')] ).

cnf(63,plain,
    equal(rd(mult(u,rd(v,w)),rd(v,w)),mult(ld(u,u),rd(mult(u,w),w))),
    inference(spr,[status(thm),theory(equality)],[31,6]),
    [iquote('0:SpR:31.0,6.0')] ).

cnf(70,plain,
    equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(mult(ld(u,u),u),w),w)),
    inference(rew,[status(thm),theory(equality)],[51,63]),
    [iquote('0:Rew:51.0,63.0')] ).

cnf(71,plain,
    equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(u,w),w)),
    inference(rew,[status(thm),theory(equality)],[31,70]),
    [iquote('0:Rew:31.0,70.0')] ).

cnf(102,plain,
    equal(rd(mult(mult(u,v),v),v),mult(u,v)),
    inference(spr,[status(thm),theory(equality)],[2,51]),
    [iquote('0:SpR:2.0,51.0')] ).

cnf(105,plain,
    equal(mult(u,ld(v,mult(v,ld(w,w)))),rd(mult(mult(u,ld(v,v)),w),w)),
    inference(spr,[status(thm),theory(equality)],[25,51]),
    [iquote('0:SpR:25.0,51.0')] ).

cnf(106,plain,
    equal(mult(ld(u,mult(u,ld(v,v))),v),mult(ld(u,u),v)),
    inference(rew,[status(thm),theory(equality)],[102,27]),
    [iquote('0:Rew:102.0,27.0')] ).

cnf(130,plain,
    equal(rd(mult(rd(u,v),v),v),rd(u,v)),
    inference(spr,[status(thm),theory(equality)],[71,2]),
    [iquote('0:SpR:71.0,2.0')] ).

cnf(135,plain,
    equal(rd(mult(mult(u,rd(v,w)),rd(v,w)),rd(v,w)),mult(rd(mult(u,w),w),rd(v,w))),
    inference(spr,[status(thm),theory(equality)],[71,4]),
    [iquote('0:SpR:71.0,4.0')] ).

cnf(139,plain,
    equal(rd(mult(u,mult(v,w)),mult(v,w)),rd(mult(u,w),w)),
    inference(spr,[status(thm),theory(equality)],[102,71]),
    [iquote('0:SpR:102.0,71.0')] ).

cnf(145,plain,
    equal(rd(rd(mult(mult(u,v),w),w),rd(mult(v,w),w)),rd(mult(u,w),w)),
    inference(spr,[status(thm),theory(equality)],[51,71]),
    [iquote('0:SpR:51.0,71.0')] ).

cnf(148,plain,
    equal(rd(rd(mult(u,v),v),v),rd(u,v)),
    inference(rew,[status(thm),theory(equality)],[4,130]),
    [iquote('0:Rew:4.0,130.0')] ).

cnf(165,plain,
    equal(mult(rd(mult(u,v),v),rd(w,v)),mult(u,rd(w,v))),
    inference(rew,[status(thm),theory(equality)],[102,135]),
    [iquote('0:Rew:102.0,135.0')] ).

cnf(178,plain,
    equal(mult(ld(u,mult(u,v)),w),ld(u,mult(u,mult(v,w)))),
    inference(spr,[status(thm),theory(equality)],[1,5]),
    [iquote('0:SpR:1.0,5.0')] ).

cnf(191,plain,
    equal(ld(u,mult(u,mult(ld(v,v),v))),mult(ld(u,u),v)),
    inference(rew,[status(thm),theory(equality)],[178,106]),
    [iquote('0:Rew:178.0,106.0')] ).

cnf(192,plain,
    equal(mult(ld(u,u),v),ld(u,mult(u,v))),
    inference(rew,[status(thm),theory(equality)],[31,191]),
    [iquote('0:Rew:31.0,191.0')] ).

cnf(227,plain,
    equal(rd(rd(mult(u,v),v),rd(w,v)),rd(u,rd(w,v))),
    inference(spr,[status(thm),theory(equality)],[71,148]),
    [iquote('0:SpR:71.0,148.0')] ).

cnf(232,plain,
    equal(rd(mult(u,v),rd(mult(v,w),w)),rd(mult(u,w),w)),
    inference(rew,[status(thm),theory(equality)],[227,145]),
    [iquote('0:Rew:227.0,145.0')] ).

cnf(398,plain,
    equal(rd(mult(u,ld(v,mult(v,w))),ld(v,mult(v,w))),rd(mult(u,w),w)),
    inference(spr,[status(thm),theory(equality)],[192,139]),
    [iquote('0:SpR:192.0,139.0')] ).

cnf(399,plain,
    equal(rd(mult(u,ld(v,mult(v,w))),ld(v,mult(v,w))),rd(mult(u,ld(v,w)),ld(v,w))),
    inference(spr,[status(thm),theory(equality)],[3,139]),
    [iquote('0:SpR:3.0,139.0')] ).

cnf(412,plain,
    equal(rd(mult(u,ld(v,w)),ld(v,w)),rd(mult(u,w),w)),
    inference(rew,[status(thm),theory(equality)],[398,399]),
    [iquote('0:Rew:398.0,399.0')] ).

cnf(470,plain,
    equal(ld(u,mult(u,mult(u,v))),mult(u,v)),
    inference(spr,[status(thm),theory(equality)],[1,178]),
    [iquote('0:SpR:1.0,178.0')] ).

cnf(1049,plain,
    equal(rd(mult(u,rd(v,w)),rd(mult(rd(v,w),x),x)),rd(mult(rd(mult(u,w),w),x),x)),
    inference(spr,[status(thm),theory(equality)],[165,232]),
    [iquote('0:SpR:165.0,232.0')] ).

cnf(1066,plain,
    equal(rd(mult(rd(mult(u,v),v),w),w),rd(mult(u,w),w)),
    inference(rew,[status(thm),theory(equality)],[232,1049]),
    [iquote('0:Rew:232.0,1049.0')] ).

cnf(1243,plain,
    equal(rd(rd(mult(u,v),v),ld(w,v)),rd(u,ld(w,v))),
    inference(spr,[status(thm),theory(equality)],[412,148]),
    [iquote('0:SpR:412.0,148.0')] ).

cnf(1454,plain,
    equal(rd(mult(mult(u,ld(u,u)),v),v),ld(u,mult(u,mult(u,ld(v,v))))),
    inference(spr,[status(thm),theory(equality)],[105,3]),
    [iquote('0:SpR:105.0,3.0')] ).

cnf(1486,plain,
    equal(mult(u,ld(v,v)),rd(mult(u,v),v)),
    inference(rew,[status(thm),theory(equality)],[1,1454,3,470]),
    [iquote('0:Rew:1.0,1454.0,3.0,1454.0,470.0,1454.0')] ).

cnf(1616,plain,
    equal(rd(rd(mult(u,v),v),ld(v,v)),rd(mult(u,v),v)),
    inference(spr,[status(thm),theory(equality)],[1486,412]),
    [iquote('0:SpR:1486.0,412.0')] ).

cnf(1644,plain,
    equal(rd(mult(u,v),v),rd(u,ld(v,v))),
    inference(rew,[status(thm),theory(equality)],[1243,1616]),
    [iquote('0:Rew:1243.0,1616.0')] ).

cnf(1653,plain,
    equal(rd(mult(u,v),ld(v,v)),mult(u,v)),
    inference(rew,[status(thm),theory(equality)],[1644,102]),
    [iquote('0:Rew:1644.0,102.0')] ).

cnf(1654,plain,
    ~ equal(mult(rd(x3__dfg,ld(x4__dfg,x4__dfg)),x5__dfg),mult(x3__dfg,x5__dfg)),
    inference(rew,[status(thm),theory(equality)],[1644,8]),
    [iquote('0:Rew:1644.0,8.0')] ).

cnf(1658,plain,
    equal(mult(rd(u,v),v),rd(u,ld(v,v))),
    inference(rew,[status(thm),theory(equality)],[1644,4]),
    [iquote('0:Rew:1644.0,4.0')] ).

cnf(1673,plain,
    equal(rd(rd(mult(u,v),v),ld(w,w)),rd(mult(u,w),w)),
    inference(rew,[status(thm),theory(equality)],[1644,1066]),
    [iquote('0:Rew:1644.0,1066.0')] ).

cnf(1783,plain,
    equal(rd(rd(u,ld(v,v)),ld(w,w)),rd(u,ld(w,w))),
    inference(rew,[status(thm),theory(equality)],[1644,1673]),
    [iquote('0:Rew:1644.0,1673.0,1644.0,1673.0')] ).

cnf(1894,plain,
    equal(mult(rd(u,ld(v,v)),v),rd(mult(u,v),ld(v,v))),
    inference(spr,[status(thm),theory(equality)],[1644,1658]),
    [iquote('0:SpR:1644.0,1658.0')] ).

cnf(1900,plain,
    equal(mult(rd(u,ld(v,v)),v),mult(u,v)),
    inference(rew,[status(thm),theory(equality)],[1653,1894]),
    [iquote('0:Rew:1653.0,1894.0')] ).

cnf(3449,plain,
    equal(mult(rd(u,ld(v,v)),v),mult(rd(u,ld(w,w)),v)),
    inference(spr,[status(thm),theory(equality)],[1783,1900]),
    [iquote('0:SpR:1783.0,1900.0')] ).

cnf(3495,plain,
    equal(mult(rd(u,ld(v,v)),w),mult(u,w)),
    inference(rew,[status(thm),theory(equality)],[1900,3449]),
    [iquote('0:Rew:1900.0,3449.0')] ).

cnf(3496,plain,
    $false,
    inference(unc,[status(thm)],[3495,1654]),
    [iquote('0:UnC:3495.0,1654.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GRP683-11 : TPTP v8.1.0. Released v8.1.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue Jun 14 00:49:51 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.81/1.00  
% 0.81/1.00  SPASS V 3.9 
% 0.81/1.00  SPASS beiseite: Proof found.
% 0.81/1.00  % SZS status Theorem
% 0.81/1.00  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.81/1.00  SPASS derived 2055 clauses, backtracked 0 clauses, performed 0 splits and kept 584 clauses.
% 0.81/1.00  SPASS allocated 68315 KBytes.
% 0.81/1.00  SPASS spent	0:00:00.61 on the problem.
% 0.81/1.00  		0:00:00.04 for the input.
% 0.81/1.00  		0:00:00.00 for the FLOTTER CNF translation.
% 0.81/1.00  		0:00:00.03 for inferences.
% 0.81/1.00  		0:00:00.00 for the backtracking.
% 0.81/1.00  		0:00:00.52 for the reduction.
% 0.81/1.00  
% 0.81/1.00  
% 0.81/1.00  Here is a proof with depth 8, length 54 :
% 0.81/1.00  % SZS output start Refutation
% See solution above
% 0.81/1.00  Formulae used in the proof : f01 f02 f03 f04 f05 f06 f07 goal
% 0.81/1.00  
%------------------------------------------------------------------------------