TSTP Solution File: SET906+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 05:29:42 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   16 (   9 unt;   0 nHn;  16 RR)
%            Number of literals    :   26 (   0 equ;  14 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    ~ in(skc5,skc6),
    file('SET906+1.p',unknown),
    [] ).

cnf(6,axiom,
    subset(set_union2(unordered_pair(skc5,skc7),skc6),skc6),
    file('SET906+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SET906+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(set_union2(u,v),set_union2(v,u)),
    file('SET906+1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ in(u,v)
    | ~ subset(v,w)
    | in(u,w) ),
    file('SET906+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,unordered_pair(x,v))
    | in(u,w) ),
    file('SET906+1.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ in(u,v)
    | ~ equal(w,set_union2(x,v))
    | in(u,w) ),
    file('SET906+1.p',unknown),
    [] ).

cnf(27,plain,
    subset(set_union2(skc6,unordered_pair(skc5,skc7)),skc6),
    inference(rew,[status(thm),theory(equality)],[8,6]),
    [iquote('0:Rew:8.0,6.0')] ).

cnf(35,plain,
    ( ~ in(u,set_union2(skc6,unordered_pair(skc5,skc7)))
    | in(u,skc6) ),
    inference(res,[status(thm),theory(equality)],[27,14]),
    [iquote('0:Res:27.0,14.0')] ).

cnf(38,plain,
    ~ in(skc5,set_union2(skc6,unordered_pair(skc5,skc7))),
    inference(res,[status(thm),theory(equality)],[35,4]),
    [iquote('0:Res:35.1,4.0')] ).

cnf(80,plain,
    ( ~ equal(u,v)
    | in(u,unordered_pair(w,v)) ),
    inference(eqr,[status(thm),theory(equality)],[16]),
    [iquote('0:EqR:16.1')] ).

cnf(83,plain,
    ( ~ equal(u,v)
    | in(u,unordered_pair(v,w)) ),
    inference(spr,[status(thm),theory(equality)],[7,80]),
    [iquote('0:SpR:7.0,80.1')] ).

cnf(121,plain,
    ( ~ in(u,v)
    | in(u,set_union2(w,v)) ),
    inference(eqr,[status(thm),theory(equality)],[18]),
    [iquote('0:EqR:18.1')] ).

cnf(132,plain,
    ~ in(skc5,unordered_pair(skc5,skc7)),
    inference(res,[status(thm),theory(equality)],[121,38]),
    [iquote('0:Res:121.1,38.0')] ).

cnf(141,plain,
    ~ equal(skc5,skc5),
    inference(res,[status(thm),theory(equality)],[83,132]),
    [iquote('0:Res:83.1,132.0')] ).

cnf(142,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[141]),
    [iquote('0:Obv:141.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n019.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 22:46:23 EDT 2022
% 0.12/0.34  % 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/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.45  SPASS derived 111 clauses, backtracked 0 clauses, performed 0 splits and kept 70 clauses.
% 0.19/0.45  SPASS allocated 85464 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.10 on the problem.
% 0.19/0.45  		0:00:00.03 for the input.
% 0.19/0.45  		0:00:00.04 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  		0:00:00.01 for the reduction.
% 0.19/0.45  
% 0.19/0.45  
% 0.19/0.45  Here is a proof with depth 4, length 16 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : t47_zfmisc_1 commutativity_k2_tarski commutativity_k2_xboole_0 d3_tarski d2_tarski idempotence_k2_xboole_0 d2_xboole_0
% 0.19/0.45  
%------------------------------------------------------------------------------