TSTP Solution File: LCL140-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL140-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 14:34:52 EDT 2022

% Result   : Unsatisfiable 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   32 (  32 unt;   0 nHn;  32 RR)
%            Number of literals    :   32 (   0 equ;   1 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    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(not__dfg(not__dfg(x__dfg)),x__dfg),
    file('LCL140-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(implies__dfg(truth,u),u),
    file('LCL140-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
    file('LCL140-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
    file('LCL140-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
    file('LCL140-1.p',unknown),
    [] ).

cnf(9,plain,
    equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(truth)),u),truth),
    inference(spr,[status(thm),theory(equality)],[2,5]),
    [iquote('0:SpR:2.0,5.0')] ).

cnf(18,plain,
    equal(implies__dfg(u,u),implies__dfg(implies__dfg(u,truth),truth)),
    inference(spr,[status(thm),theory(equality)],[2,4]),
    [iquote('0:SpR:2.0,4.0')] ).

cnf(80,plain,
    equal(implies__dfg(implies__dfg(truth,u),implies__dfg(implies__dfg(u,v),v)),truth),
    inference(spr,[status(thm),theory(equality)],[2,3]),
    [iquote('0:SpR:2.0,3.0')] ).

cnf(90,plain,
    equal(implies__dfg(implies__dfg(u,truth),implies__dfg(v,implies__dfg(u,v))),truth),
    inference(spr,[status(thm),theory(equality)],[2,3]),
    [iquote('0:SpR:2.0,3.0')] ).

cnf(117,plain,
    equal(implies__dfg(u,implies__dfg(implies__dfg(u,v),v)),truth),
    inference(rew,[status(thm),theory(equality)],[2,80]),
    [iquote('0:Rew:2.0,80.0')] ).

cnf(192,plain,
    equal(implies__dfg(implies__dfg(truth,u),u),truth),
    inference(spr,[status(thm),theory(equality)],[117,2]),
    [iquote('0:SpR:117.0,2.0')] ).

cnf(219,plain,
    equal(implies__dfg(u,implies__dfg(u,u)),truth),
    inference(spr,[status(thm),theory(equality)],[18,117]),
    [iquote('0:SpR:18.0,117.0')] ).

cnf(220,plain,
    equal(implies__dfg(u,u),truth),
    inference(rew,[status(thm),theory(equality)],[2,192]),
    [iquote('0:Rew:2.0,192.0')] ).

cnf(244,plain,
    equal(implies__dfg(u,truth),truth),
    inference(rew,[status(thm),theory(equality)],[220,219]),
    [iquote('0:Rew:220.0,219.0')] ).

cnf(251,plain,
    equal(implies__dfg(truth,implies__dfg(u,implies__dfg(v,u))),truth),
    inference(rew,[status(thm),theory(equality)],[244,90]),
    [iquote('0:Rew:244.0,90.0')] ).

cnf(262,plain,
    equal(implies__dfg(u,implies__dfg(v,u)),truth),
    inference(rew,[status(thm),theory(equality)],[2,251]),
    [iquote('0:Rew:2.0,251.0')] ).

cnf(350,plain,
    equal(implies__dfg(truth,implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),truth),
    inference(spr,[status(thm),theory(equality)],[262,3]),
    [iquote('0:SpR:262.0,3.0')] ).

cnf(365,plain,
    equal(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w)),truth),
    inference(rew,[status(thm),theory(equality)],[2,350]),
    [iquote('0:Rew:2.0,350.0')] ).

cnf(399,plain,
    equal(implies__dfg(truth,implies__dfg(not__dfg(truth),u)),truth),
    inference(spr,[status(thm),theory(equality)],[9,365]),
    [iquote('0:SpR:9.0,365.0')] ).

cnf(402,plain,
    equal(implies__dfg(truth,implies__dfg(not__dfg(u),implies__dfg(u,v))),truth),
    inference(spr,[status(thm),theory(equality)],[5,365]),
    [iquote('0:SpR:5.0,365.0')] ).

cnf(408,plain,
    equal(implies__dfg(not__dfg(truth),u),truth),
    inference(rew,[status(thm),theory(equality)],[2,399]),
    [iquote('0:Rew:2.0,399.0')] ).

cnf(414,plain,
    equal(implies__dfg(not__dfg(u),implies__dfg(u,v)),truth),
    inference(rew,[status(thm),theory(equality)],[2,402]),
    [iquote('0:Rew:2.0,402.0')] ).

cnf(502,plain,
    equal(implies__dfg(implies__dfg(u,not__dfg(truth)),not__dfg(truth)),implies__dfg(truth,u)),
    inference(spr,[status(thm),theory(equality)],[408,4]),
    [iquote('0:SpR:408.0,4.0')] ).

cnf(522,plain,
    equal(implies__dfg(implies__dfg(u,not__dfg(truth)),not__dfg(truth)),u),
    inference(rew,[status(thm),theory(equality)],[2,502]),
    [iquote('0:Rew:2.0,502.0')] ).

cnf(577,plain,
    equal(implies__dfg(not__dfg(implies__dfg(u,not__dfg(truth))),u),truth),
    inference(spr,[status(thm),theory(equality)],[522,414]),
    [iquote('0:SpR:522.0,414.0')] ).

cnf(712,plain,
    equal(implies__dfg(truth,implies__dfg(u,implies__dfg(not__dfg(u),not__dfg(truth)))),truth),
    inference(spr,[status(thm),theory(equality)],[577,5]),
    [iquote('0:SpR:577.0,5.0')] ).

cnf(738,plain,
    equal(implies__dfg(u,implies__dfg(not__dfg(u),not__dfg(truth))),truth),
    inference(rew,[status(thm),theory(equality)],[2,712]),
    [iquote('0:Rew:2.0,712.0')] ).

cnf(755,plain,
    equal(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),not__dfg(truth)),u),u),implies__dfg(truth,implies__dfg(not__dfg(u),not__dfg(truth)))),
    inference(spr,[status(thm),theory(equality)],[738,4]),
    [iquote('0:SpR:738.0,4.0')] ).

cnf(786,plain,
    equal(implies__dfg(not__dfg(u),not__dfg(truth)),u),
    inference(rew,[status(thm),theory(equality)],[2,755,9]),
    [iquote('0:Rew:2.0,755.0,9.0,755.0,2.0,755.0')] ).

cnf(827,plain,
    equal(implies__dfg(u,not__dfg(truth)),not__dfg(u)),
    inference(spr,[status(thm),theory(equality)],[786,522]),
    [iquote('0:SpR:786.0,522.0')] ).

cnf(832,plain,
    equal(not__dfg(not__dfg(u)),u),
    inference(rew,[status(thm),theory(equality)],[827,786]),
    [iquote('0:Rew:827.0,786.0')] ).

cnf(842,plain,
    $false,
    inference(unc,[status(thm)],[832,1]),
    [iquote('0:UnC:832.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : LCL140-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jul  3 16:42:26 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.49  
% 0.20/0.49  SPASS V 3.9 
% 0.20/0.49  SPASS beiseite: Proof found.
% 0.20/0.49  % SZS status Theorem
% 0.20/0.49  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.49  SPASS derived 561 clauses, backtracked 0 clauses, performed 0 splits and kept 155 clauses.
% 0.20/0.49  SPASS allocated 64128 KBytes.
% 0.20/0.49  SPASS spent	0:00:00.13 on the problem.
% 0.20/0.49  		0:00:00.03 for the input.
% 0.20/0.49  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49  		0:00:00.01 for inferences.
% 0.20/0.49  		0:00:00.00 for the backtracking.
% 0.20/0.49  		0:00:00.06 for the reduction.
% 0.20/0.49  
% 0.20/0.49  
% 0.20/0.49  Here is a proof with depth 8, length 32 :
% 0.20/0.49  % SZS output start Refutation
% See solution above
% 0.20/0.49  Formulae used in the proof : prove_wajsberg_lemma wajsberg_1 wajsberg_2 wajsberg_3 wajsberg_4
% 0.20/0.49  
%------------------------------------------------------------------------------