TSTP Solution File: SET909+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Jul 19 05:29:43 EDT 2022

% Result   : Theorem 0.20s 0.45s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   17 (  10 unt;   1 nHn;  17 RR)
%            Number of literals    :   27 (   0 equ;  15 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    equal(set_union2(unordered_pair(skc7,skc6),skc5),empty_set),
    file('SET909+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SET909+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(set_union2(u,v),set_union2(v,u)),
    file('SET909+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( equal(u,empty_set)
    | in(skf3(u),u) ),
    file('SET909+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ in(u,v)
    | ~ equal(v,empty_set) ),
    file('SET909+1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,unordered_pair(x,v))
    | in(u,w) ),
    file('SET909+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ in(u,v)
    | ~ equal(w,set_union2(x,v))
    | in(u,w) ),
    file('SET909+1.p',unknown),
    [] ).

cnf(25,plain,
    equal(set_union2(skc5,unordered_pair(skc6,skc7)),empty_set),
    inference(rew,[status(thm),theory(equality)],[7,5,6]),
    [iquote('0:Rew:7.0,5.0,6.0,5.0')] ).

cnf(26,plain,
    ~ in(u,set_union2(skc5,unordered_pair(skc6,skc7))),
    inference(res,[status(thm),theory(equality)],[25,12]),
    [iquote('0:Res:25.0,12.0')] ).

cnf(29,plain,
    ( ~ in(u,unordered_pair(skc6,skc7))
    | in(u,empty_set) ),
    inference(res,[status(thm),theory(equality)],[25,16]),
    [iquote('0:Res:25.0,16.1')] ).

cnf(34,plain,
    ~ in(u,empty_set),
    inference(rew,[status(thm),theory(equality)],[25,26]),
    [iquote('0:Rew:25.0,26.0')] ).

cnf(36,plain,
    ~ in(u,unordered_pair(skc6,skc7)),
    inference(mrr,[status(thm)],[29,34]),
    [iquote('0:MRR:29.1,34.0')] ).

cnf(43,plain,
    equal(unordered_pair(skc6,skc7),empty_set),
    inference(res,[status(thm),theory(equality)],[8,36]),
    [iquote('0:Res:8.1,36.0')] ).

cnf(72,plain,
    ( ~ equal(u,skc7)
    | ~ equal(v,empty_set)
    | in(u,v) ),
    inference(spl,[status(thm),theory(equality)],[43,14]),
    [iquote('0:SpL:43.0,14.1')] ).

cnf(75,plain,
    ( ~ equal(u,skc7)
    | ~ equal(v,empty_set) ),
    inference(mrr,[status(thm)],[72,12]),
    [iquote('0:MRR:72.2,12.0')] ).

cnf(93,plain,
    ~ equal(u,empty_set),
    inference(eqr,[status(thm),theory(equality)],[75]),
    [iquote('0:EqR:75.0')] ).

cnf(94,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[93]),
    [iquote('0:Obv:93.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 16:22:02 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.45  
% 0.20/0.45  SPASS V 3.9 
% 0.20/0.45  SPASS beiseite: Proof found.
% 0.20/0.45  % SZS status Theorem
% 0.20/0.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.45  SPASS derived 59 clauses, backtracked 0 clauses, performed 0 splits and kept 42 clauses.
% 0.20/0.45  SPASS allocated 85350 KBytes.
% 0.20/0.45  SPASS spent	0:00:00.10 on the problem.
% 0.20/0.45  		0:00:00.04 for the input.
% 0.20/0.45  		0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.45  		0:00:00.00 for inferences.
% 0.20/0.45  		0:00:00.00 for the backtracking.
% 0.20/0.45  		0:00:00.00 for the reduction.
% 0.20/0.45  
% 0.20/0.45  
% 0.20/0.45  Here is a proof with depth 4, length 17 :
% 0.20/0.45  % SZS output start Refutation
% See solution above
% 0.20/0.45  Formulae used in the proof : t50_zfmisc_1 commutativity_k2_tarski commutativity_k2_xboole_0 d1_xboole_0 d2_tarski idempotence_k2_xboole_0 d2_xboole_0
% 0.20/0.45  
%------------------------------------------------------------------------------