TSTP Solution File: LCL109-5 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 14:34:40 EDT 2022

% Result   : Unsatisfiable 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   33 (  19 unt;   0 nHn;  33 RR)
%            Number of literals    :   47 (   0 equ;  15 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ ordered(u,v)
    | ordered(implies__dfg(u,w),implies__dfg(v,w)) ),
    file('LCL109-5.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ ordered(u,implies__dfg(v,w))
    | ordered(v,implies__dfg(u,w)) ),
    file('LCL109-5.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(big_V(implies__dfg(x__dfg,y__dfg),implies__dfg(y__dfg,x__dfg)),truth),
    file('LCL109-5.p',unknown),
    [] ).

cnf(10,axiom,
    equal(implies__dfg(truth,u),u),
    file('LCL109-5.p',unknown),
    [] ).

cnf(12,axiom,
    equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
    file('LCL109-5.p',unknown),
    [] ).

cnf(13,axiom,
    equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
    file('LCL109-5.p',unknown),
    [] ).

cnf(14,axiom,
    equal(implies__dfg(implies__dfg(u,v),v),big_V(u,v)),
    file('LCL109-5.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ ordered(u,v)
    | equal(implies__dfg(u,v),truth) ),
    file('LCL109-5.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ equal(implies__dfg(u,v),truth)
    | ordered(u,v) ),
    file('LCL109-5.p',unknown),
    [] ).

cnf(20,plain,
    equal(big_V(u,v),big_V(v,u)),
    inference(rew,[status(thm),theory(equality)],[14,12]),
    [iquote('0:Rew:14.0,12.0,14.0,12.0')] ).

cnf(28,plain,
    ( ~ ordered(truth,u)
    | equal(truth,u) ),
    inference(spr,[status(thm),theory(equality)],[16,10]),
    [iquote('0:SpR:16.1,10.0')] ).

cnf(34,plain,
    ( ~ ordered(implies__dfg(u,v),v)
    | equal(big_V(u,v),truth) ),
    inference(spr,[status(thm),theory(equality)],[14,16]),
    [iquote('0:SpR:14.0,16.1')] ).

cnf(37,plain,
    equal(implies__dfg(u,u),big_V(truth,u)),
    inference(spr,[status(thm),theory(equality)],[10,14]),
    [iquote('0:SpR:10.0,14.0')] ).

cnf(46,plain,
    ( ~ ordered(u,u)
    | equal(big_V(truth,u),truth) ),
    inference(spr,[status(thm),theory(equality)],[37,16]),
    [iquote('0:SpR:37.0,16.1')] ).

cnf(48,plain,
    ( ~ equal(big_V(truth,u),truth)
    | ordered(u,u) ),
    inference(spl,[status(thm),theory(equality)],[37,17]),
    [iquote('0:SpL:37.0,17.0')] ).

cnf(57,plain,
    ( ~ ordered(u,u)
    | equal(big_V(u,truth),truth) ),
    inference(spr,[status(thm),theory(equality)],[46,20]),
    [iquote('0:SpR:46.1,20.0')] ).

cnf(96,plain,
    equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(truth)),u),truth),
    inference(spr,[status(thm),theory(equality)],[10,13]),
    [iquote('0:SpR:10.0,13.0')] ).

cnf(124,plain,
    ( ~ equal(truth,truth)
    | ordered(implies__dfg(not__dfg(u),not__dfg(truth)),u) ),
    inference(spl,[status(thm),theory(equality)],[96,17]),
    [iquote('0:SpL:96.0,17.0')] ).

cnf(129,plain,
    ordered(implies__dfg(not__dfg(u),not__dfg(truth)),u),
    inference(obv,[status(thm),theory(equality)],[124]),
    [iquote('0:Obv:124.0')] ).

cnf(160,plain,
    ( ~ ordered(u,truth)
    | ordered(implies__dfg(u,v),v) ),
    inference(spr,[status(thm),theory(equality)],[10,1]),
    [iquote('0:SpR:10.0,1.1')] ).

cnf(161,plain,
    ( ~ ordered(u,v)
    | ordered(implies__dfg(u,v),big_V(truth,v)) ),
    inference(spr,[status(thm),theory(equality)],[37,1]),
    [iquote('0:SpR:37.0,1.1')] ).

cnf(172,plain,
    ( ~ ordered(u,v)
    | ordered(truth,big_V(truth,v)) ),
    inference(rew,[status(thm),theory(equality)],[16,161]),
    [iquote('0:Rew:16.1,161.1')] ).

cnf(253,plain,
    ordered(truth,big_V(truth,u)),
    inference(res,[status(thm),theory(equality)],[129,172]),
    [iquote('0:Res:129.0,172.0')] ).

cnf(294,plain,
    equal(big_V(truth,u),truth),
    inference(res,[status(thm),theory(equality)],[253,28]),
    [iquote('0:Res:253.0,28.0')] ).

cnf(300,plain,
    ( ~ equal(truth,truth)
    | ordered(u,u) ),
    inference(rew,[status(thm),theory(equality)],[294,48]),
    [iquote('0:Rew:294.0,48.0')] ).

cnf(319,plain,
    ordered(u,u),
    inference(obv,[status(thm),theory(equality)],[300]),
    [iquote('0:Obv:300.0')] ).

cnf(320,plain,
    equal(big_V(u,truth),truth),
    inference(mrr,[status(thm)],[57,319]),
    [iquote('0:MRR:57.0,319.0')] ).

cnf(333,plain,
    ordered(u,implies__dfg(implies__dfg(u,v),v)),
    inference(res,[status(thm),theory(equality)],[319,4]),
    [iquote('0:Res:319.0,4.0')] ).

cnf(335,plain,
    ordered(u,big_V(u,v)),
    inference(rew,[status(thm),theory(equality)],[14,333]),
    [iquote('0:Rew:14.0,333.0')] ).

cnf(481,plain,
    ordered(u,truth),
    inference(spr,[status(thm),theory(equality)],[320,335]),
    [iquote('0:SpR:320.0,335.0')] ).

cnf(484,plain,
    ordered(implies__dfg(u,v),v),
    inference(mrr,[status(thm)],[160,481]),
    [iquote('0:MRR:160.0,481.0')] ).

cnf(490,plain,
    equal(big_V(u,v),truth),
    inference(mrr,[status(thm)],[34,484]),
    [iquote('0:MRR:34.0,484.0')] ).

cnf(491,plain,
    $false,
    inference(unc,[status(thm)],[490,9]),
    [iquote('0:UnC:490.0,9.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n011.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jul  2 09:44:04 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  
% 0.19/0.45  SPASS V 3.9 
% 0.19/0.45  SPASS beiseite: Proof found.
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.45  SPASS derived 354 clauses, backtracked 0 clauses, performed 0 splits and kept 192 clauses.
% 0.19/0.45  SPASS allocated 63645 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.10 on the problem.
% 0.19/0.45  		0:00:00.04 for the input.
% 0.19/0.45  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45  		0:00:00.00 for inferences.
% 0.19/0.45  		0:00:00.00 for the backtracking.
% 0.19/0.45  		0:00:00.04 for the reduction.
% 0.19/0.45  
% 0.19/0.45  
% 0.19/0.45  Here is a proof with depth 4, length 33 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : lemma_1 lemma_3_2 prove_mv_4 wajsberg_1 wajsberg_3 wajsberg_4 big_V_definition partial_order_definition1 partial_order_definition2
% 0.19/0.45  
%------------------------------------------------------------------------------