%------------------------------------------------------------------------------
% File : nanoCoP-M---2.0
% Problem : DAT431_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_nanocopm %s %d
% Computer : n022.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 5 06:23:46 PM UTC 2026
% Result : Theorem 0.48s 1.56s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : DAT431_1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.13 % Command : run_nanocopm %s %d
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:51:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.31/0.47 % Logic is s5
% 0.31/0.47 % Designation is rigid
% 0.31/0.48 % Terms are local
% 0.31/0.48 % Domains are const
% 0.31/0.49 ------------ Start QMF file ---------------
% 0.31/0.49 %------------------------------------------------------------------------------
% 0.31/0.49 % File : DAT431_1 : TPTP v9.3.0. Released v9.3.0.
% 0.31/0.49 % Domain : Data Structures
% 0.31/0.49 % Problem : Database querying
% 0.31/0.49 % Version : Especial.
% 0.31/0.49 % English :
% 0.31/0.49 % Refs : [Rei92] Reiter (1992), What Should a Database Know?
% 0.31/0.49 % Source : [Rei92]
% 0.31/0.49 % Names :
% 0.31/0.49 % Status : Theorem
% 0.31/0.49 % Rating : ? v9.3.0
% 0.31/0.49 % Syntax : Number of formulae : 10 ( 0 unt; 7 typ; 0 def)
% 0.31/0.49 % Number of atoms : 13 ( 0 equ)
% 0.31/0.49 % Maximal formula atoms : 6 ( 4 avg)
% 0.31/0.49 % Number of connectives : 18 ( 3 ~; 0 |; 5 &)
% 0.31/0.49 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.31/0.49 % ( 5 {.}; 0 {#})
% 0.31/0.49 % Maximal formula depth : 5 ( 4 avg)
% 0.31/0.49 % Maximal term depth : 1 ( 1 avg)
% 0.31/0.49 % Number of FOOLs : 5 ( 5 fml; 0 var)
% 0.31/0.49 % Number of X terms : 5 ( 5 []; 0 ite; 0 let)
% 0.31/0.49 % Number of types : 2 ( 0 usr)
% 0.31/0.49 % Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% 0.31/0.49 % Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% 0.31/0.49 % Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% 0.31/0.49 % Number of variables : 2 ( 0 !; 2 ?; 2 :)
% 0.31/0.49 % SPC : NX0_THM_NEQ_NAR
% 0.31/0.49 % Comments :
% 0.31/0.49 %------------------------------------------------------------------------------
% 0.31/0.49 qmf(not_db,axiom,(~ ( #box : teach(john,cs) ) & ~ ( #box : teach(mary,cs) ) & ~ ( #box : teach(sue,cs) ) )).
% 0.31/0.49 qmf(db,axiom,(#box : ( teach(john,math) & ? [X] : teach(X,cs) & teach(mary,psych) & teach(sue,psych) ) )).
% 0.31/0.49 qmf(query,conjecture,(? [X] : ( #box : teach(john,X) ) )).
% 0.31/0.49 %------------------------------------------------------------------------------
% 0.31/0.49 ------------ End QMF file ---------------
% 0.48/1.56
% 0.48/1.56 % SZS status Theorem for $/export/starexec/sandbox2/tmp/tmp.8Mr6jYO7z0/theBenchmark.p.qmf : (modal (s5/const))
% 0.48/1.56 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.8Mr6jYO7z0/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 ^ _5925) ^ [] ^ [] : [teach(john, cs) : [1 ^ []]], (6 ^ _5925) ^ [] ^ [] : [teach(mary, cs) : [4 ^ []]], (9 ^ _5925) ^ [] ^ [] : [teach(sue, cs) : [7 ^ []]], (12 ^ _5925) ^ [_6354] ^ [] : [-(teach(john, math)) : -([_6354])], (15 ^ _5925) ^ [_6494] ^ [] : [-(teach(13 ^ [_6494] ^ [_6494], cs)) : -([_6494])], (17 ^ _5925) ^ [_6602] ^ [] : [-(teach(mary, psych)) : -([_6602])], (19 ^ _5925) ^ [_6674] ^ [] : [-(teach(sue, psych)) : -([_6674])], (22 ^ _5925) ^ [_6800] ^ [_6800 : []] : [teach(john, _6800) : [20 ^ [_6800]]]]
% 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 (22 ^ 0) under the substitution [[_6800], [math]]
% 0.48/1.56 is false if at least one of the following is false:
% 0.48/1.56 [teach(john, math) : [20 ^ [math]]]
% 0.48/1.56 1 Assume teach(john, math) : [20 ^ [math]] is false.
% 0.48/1.56 Then clause (12 ^ 1) under the substitution [[_6354], [20 ^ [math]]]
% 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.8Mr6jYO7z0/theBenchmark.p.qmf
% 0.48/1.56 % nanoCoP-M exiting
%------------------------------------------------------------------------------