TSTP Solution File: LCL096-10 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 14:34:34 EDT 2022

% Result   : Unsatisfiable 34.24s 34.43s
% Output   : Refutation 34.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   23 (  23 unt;   0 nHn;  23 RR)
%            Number of literals    :   23 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;  10 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(ifeq(u,u,v,w),v),
    file('LCL096-10.p',unknown),
    [] ).

cnf(2,axiom,
    equal(ifeq(is_a_theorem(equivalent(u,v)),true__dfg,ifeq(is_a_theorem(u),true__dfg,is_a_theorem(v),true__dfg),true__dfg),true__dfg),
    file('LCL096-10.p',unknown),
    [] ).

cnf(3,axiom,
    equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x),x)),true__dfg),
    file('LCL096-10.p',unknown),
    [] ).

cnf(4,axiom,
    equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x)),y),y)),true__dfg),
    file('LCL096-10.p',unknown),
    [] ).

cnf(5,axiom,
    equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),w),x),equivalent(equivalent(equivalent(u,y),w),equivalent(equivalent(v,y),x)))),true__dfg),
    file('LCL096-10.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),true__dfg),
    file('LCL096-10.p',unknown),
    [] ).

cnf(12,plain,
    equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x),x),y)),true__dfg,ifeq(true__dfg,true__dfg,is_a_theorem(y),true__dfg),true__dfg),true__dfg),
    inference(spr,[status(thm),theory(equality)],[3,2]),
    [iquote('0:SpR:3.0,2.0')] ).

cnf(14,plain,
    equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x),x),y)),true__dfg,is_a_theorem(y),true__dfg),true__dfg),
    inference(rew,[status(thm),theory(equality)],[1,12]),
    [iquote('0:Rew:1.0,12.0')] ).

cnf(18,plain,
    equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x)),y),y),z)),true__dfg,ifeq(true__dfg,true__dfg,is_a_theorem(z),true__dfg),true__dfg),true__dfg),
    inference(spr,[status(thm),theory(equality)],[4,2]),
    [iquote('0:SpR:4.0,2.0')] ).

cnf(20,plain,
    equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x)),y),y),z)),true__dfg,is_a_theorem(z),true__dfg),true__dfg),
    inference(rew,[status(thm),theory(equality)],[1,18]),
    [iquote('0:Rew:1.0,18.0')] ).

cnf(28,plain,
    equal(ifeq(true__dfg,true__dfg,ifeq(is_a_theorem(equivalent(equivalent(equivalent(u,v),w),x)),true__dfg,is_a_theorem(equivalent(equivalent(equivalent(u,y),w),equivalent(equivalent(v,y),x))),true__dfg),true__dfg),true__dfg),
    inference(spr,[status(thm),theory(equality)],[5,2]),
    [iquote('0:SpR:5.0,2.0')] ).

cnf(33,plain,
    equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(u,v),w),x)),true__dfg,is_a_theorem(equivalent(equivalent(equivalent(u,y),w),equivalent(equivalent(v,y),x))),true__dfg),true__dfg),
    inference(rew,[status(thm),theory(equality)],[1,28]),
    [iquote('0:Rew:1.0,28.0')] ).

cnf(68,plain,
    equal(ifeq(true__dfg,true__dfg,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y),equivalent(equivalent(equivalent(v,w),x),y))),true__dfg),true__dfg),
    inference(spr,[status(thm),theory(equality)],[5,14]),
    [iquote('0:SpR:5.0,14.0')] ).

cnf(72,plain,
    equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y),equivalent(equivalent(equivalent(v,w),x),y))),true__dfg),
    inference(rew,[status(thm),theory(equality)],[1,68]),
    [iquote('0:Rew:1.0,68.0')] ).

cnf(250,plain,
    equal(ifeq(true__dfg,true__dfg,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y),z),equivalent(equivalent(equivalent(equivalent(v,w),x),y),z))),true__dfg),true__dfg),
    inference(spr,[status(thm),theory(equality)],[4,33]),
    [iquote('0:SpR:4.0,33.0')] ).

cnf(265,plain,
    equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y),z),equivalent(equivalent(equivalent(equivalent(v,w),x),y),z))),true__dfg),
    inference(rew,[status(thm),theory(equality)],[1,250]),
    [iquote('0:Rew:1.0,250.0')] ).

cnf(1683,plain,
    equal(ifeq(true__dfg,true__dfg,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y)),true__dfg,is_a_theorem(equivalent(equivalent(equivalent(v,w),x),y)),true__dfg),true__dfg),true__dfg),
    inference(spr,[status(thm),theory(equality)],[72,2]),
    [iquote('0:SpR:72.0,2.0')] ).

cnf(1727,plain,
    equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y)),true__dfg,is_a_theorem(equivalent(equivalent(equivalent(v,w),x),y)),true__dfg),true__dfg),
    inference(rew,[status(thm),theory(equality)],[1,1683]),
    [iquote('0:Rew:1.0,1683.0')] ).

cnf(3129,plain,
    equal(ifeq(true__dfg,true__dfg,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),equivalent(equivalent(u,x),w))),y),y)),true__dfg),true__dfg),
    inference(spr,[status(thm),theory(equality)],[265,20]),
    [iquote('0:SpR:265.0,20.0')] ).

cnf(3175,plain,
    equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),equivalent(equivalent(u,x),w))),y),y)),true__dfg),
    inference(rew,[status(thm),theory(equality)],[1,3129]),
    [iquote('0:Rew:1.0,3129.0')] ).

cnf(24317,plain,
    equal(ifeq(true__dfg,true__dfg,is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,v),u)),w),w)),true__dfg),true__dfg),
    inference(spr,[status(thm),theory(equality)],[3175,1727]),
    [iquote('0:SpR:3175.0,1727.0')] ).

cnf(24453,plain,
    equal(is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,v),u)),w),w)),true__dfg),
    inference(rew,[status(thm),theory(equality)],[1,24317]),
    [iquote('0:Rew:1.0,24317.0')] ).

cnf(24454,plain,
    $false,
    inference(unc,[status(thm)],[24453,6]),
    [iquote('0:UnC:24453.0,6.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jul  4 05:22:06 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 34.24/34.43  
% 34.24/34.43  SPASS V 3.9 
% 34.24/34.43  SPASS beiseite: Proof found.
% 34.24/34.43  % SZS status Theorem
% 34.24/34.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 34.24/34.43  SPASS derived 16079 clauses, backtracked 0 clauses, performed 0 splits and kept 5564 clauses.
% 34.24/34.43  SPASS allocated 99755 KBytes.
% 34.24/34.43  SPASS spent	0:0:32.94 on the problem.
% 34.24/34.43  		0:00:00.04 for the input.
% 34.24/34.43  		0:00:00.00 for the FLOTTER CNF translation.
% 34.24/34.43  		0:00:00.35 for inferences.
% 34.24/34.43  		0:00:00.00 for the backtracking.
% 34.24/34.43  		0:0:32.48 for the reduction.
% 34.24/34.43  
% 34.24/34.43  
% 34.24/34.43  Here is a proof with depth 4, length 23 :
% 34.24/34.43  % SZS output start Refutation
% See solution above
% 34.24/34.43  Formulae used in the proof : ifeq_axiom condensed_detachment lg_2 lg_3 lg_4 prove_lg_1
% 34.24/34.43  
%------------------------------------------------------------------------------