%------------------------------------------------------------------------------
% File : nanoCoP-M---2.0
% Problem : SYO886_5.311 : TPTP v9.0.0. Released v9.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_nanocopm %s %d
% Computer : n023.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 : 300s
% DateTime : Tue May 14 09:14:06 EDT 2024
% Result : Theorem 0.48s 1.56s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO886_5.311 : TPTP v9.0.0. Released v9.0.0.
% 0.07/0.13 % Command : run_nanocopm %s %d
% 0.13/0.34 % Computer : n023.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
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 13 15:27:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.48 % Logic is s5
% 0.20/0.48 % Designation is rigid
% 0.20/0.49 % Terms are local
% 0.20/0.49 % Domains are cumul
% 0.20/0.50 ------------ Start QMF file ---------------
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 % File : SYO886_5.311 : TPTP v9.0.0. Released v9.0.0.
% 0.20/0.50 % Domain : Syntactic
% 0.20/0.50 % Problem : Barcan scheme instance
% 0.20/0.50 % Version : Especial.
% 0.20/0.50 % English : If for all x necessarily f(x), then it is necessary that for
% 0.20/0.50 % all x f(x)
% 0.20/0.50 % Refs : [Bar46] Barcan (1946), A Functional Calculus of First Order Ba
% 0.20/0.50 % : [Sid10] Sider (2010), Logic for Philosophy
% 0.20/0.50 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.20/0.50 % Source : [TPTP]
% 0.20/0.50 % Names : SYM001+1 [QMLTP]
% 0.20/0.50 % Status : Theorem
% 0.20/0.50 % Rating : ? v9.0.0
% 0.20/0.50 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.20/0.50 % Number of atoms : 6 ( 0 equ)
% 0.20/0.50 % Maximal formula atoms : 4 ( 6 avg)
% 0.20/0.50 % Number of connectives : 3 ( 0 ~; 0 |; 0 &)
% 0.20/0.50 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.50 % ( 2 {}@; 0 {#}; 0 {.})
% 0.20/0.50 % Maximal formula depth : 4 ( 4 avg)
% 0.20/0.50 % Maximal term depth : 1 ( 1 avg)
% 0.20/0.50 % Number of FOOLs : 2 ( 2 fml; 0 var)
% 0.20/0.50 % Number of types : 2 ( 0 usr)
% 0.20/0.50 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.20/0.50 % Number of predicates : 2 ( 1 usr; 0 prp; 1-1 aty)
% 0.20/0.50 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.50 % Number of variables : 2 (; 2 !; 0 ?; 2 :)
% 0.20/0.50 % SPC : NX0_THM_NEQ_NAR
% 0.20/0.50 % Comments :
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 qmf(con,conjecture,(! [X] : ( #box : f(X) ) => ( #box : ! [X] : f(X) ) )).
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 ------------ End QMF file ---------------
% 0.48/1.56
% 0.48/1.56 % SZS status Theorem for $/export/starexec/sandbox2/tmp/tmp.Trz0SXdwsV/theBenchmark.p.qmf : (modal (s5/cumul))
% 0.48/1.56 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.Trz0SXdwsV/theBenchmark.p.qmf
% 0.48/1.56 ------------------------------------------------------
% 0.48/1.56 Explanations for the proof presented below:
% 0.48/1.56 - equality axioms are added if required
% 0.48/1.56 - terms and variables are represented by Prolog terms
% 0.48/1.56 and Prolog variables, negation is represented by -
% 0.48/1.56 - a prefix Pre is a list of variables and constants
% 0.48/1.56 and assigned to each literal Lit, i.e. Pre:Lit
% 0.48/1.56 - clauses and (sub-)matrices have a unique label I^K:
% 0.48/1.56 or I^K^[..]:, where I is a unique number/identifier
% 0.48/1.56 and K identifies the instance of clause/matrix I
% 0.48/1.56 - I:Lit refers to literal Lit in clause number I
% 0.48/1.56 - in the matrix, I^[t1,..,tn] may represent the atom
% 0.48/1.56 P_I(t1,..,tn) or the Skolem term f_I(t1,t2,..,tn)
% 0.48/1.56 - the substitution [[X1,..,Xn],[t1,..,tn]] represents
% 0.48/1.56 the assignments X1:=t1, .., Xn:=tn (for both term
% 0.48/1.56 and prefix variables)
% 0.48/1.56
% 0.48/1.56 Proof:
% 0.48/1.56 ------
% 0.48/1.56 Translation into a non-clausal matrix:
% 0.48/1.56 [(3 ^ _3669) ^ [_3784, _3786] ^ [_3786 : []] : [-(f(_3786)) : -([_3784])], (7 ^ _3669) ^ [] ^ [] : [f(5 ^ [] ^ [4 ^ []]) : [4 ^ []]]]
% 0.48/1.56
% 0.48/1.56 We prove that the given matrix is valid, i.e. for
% 0.48/1.56 a given substitution it evaluates to true for all
% 0.48/1.56 interpretations. A matrix is true iff at least one
% 0.48/1.56 of its clauses is true; a clause is true iff all of
% 0.48/1.56 its elements (literals and submatrices) are true.
% 0.48/1.56
% 0.48/1.56 The proof is by contradiction:
% 0.48/1.56 Assume there is an interpretation so that the given
% 0.48/1.56 matrix evaluates to false. Then in each clause there
% 0.48/1.56 has to be at least one element that is false.
% 0.48/1.56
% 0.48/1.56 Then clause (7 ^ 0) is false if at least one of the following is false:
% 0.48/1.56 [f(5 ^ [] ^ [4 ^ []]) : [4 ^ []]]
% 0.48/1.56 1 Assume f(5 ^ [] ^ [4 ^ []]) : [4 ^ []] is false.
% 0.48/1.56 Then clause (3 ^ 1) under the substitution [[_3784, _3786], [4 ^ [], 5 ^ [] ^ [4 ^ []]]]
% 0.48/1.56 is true.
% 0.48/1.56
% 0.48/1.56 Therefore there is no interpretation that makes the
% 0.48/1.56 given matrix false. Hence the given matrix is valid.
% 0.48/1.56 q.e.d.
% 0.48/1.56 ------------------------------------------------------
% 0.48/1.56 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.Trz0SXdwsV/theBenchmark.p.qmf
% 0.48/1.56 % nanoCoP-M exiting
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