%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT045+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:02:57 AM UTC 2026
% Result : Theorem 0.09s 0.75s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 36 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 31 ( 11 ~; 6 |; 8 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(assumption_6,axiom,
! [X,T0,T] :
( organization(X)
=> ( ( external_ties(X,T) = external_ties(X,T0)
=> position(X,T) = position(X,T0) )
& ( greater(external_ties(X,T),external_ties(X,T0))
=> greater(position(X,T),position(X,T0)) ) ) ),
file('theBenchmark.p',assumption_6) ).
fof(assumption_8,axiom,
! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& organization(X) )
=> greater(external_ties(X,T),external_ties(X,T0)) ),
file('theBenchmark.p',assumption_8) ).
fof(lemma_4,conjecture,
! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& organization(X) )
=> greater(position(X,T),position(X,T0)) ),
file('theBenchmark.p',lemma_4) ).
fof(lemma_4_neg,negated_conjecture,
~ ! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& organization(X) )
=> greater(position(X,T),position(X,T0)) ),
inference(assume_negation,[status(cth)],[lemma_4]) ).
cnf(c_19,plain,
( greater(external_ties(A,B),external_ties(A,C))
| ~ greater(age(A,B),age(A,C))
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_8]) ).
fof(nnf_9,plain,
? [X,T0,T] :
( ~ greater(position(X,T),position(X,T0))
& greater(age(X,T),age(X,T0))
& organization(X) ),
inference(fof_nnf,[status(thm)],[lemma_4_neg]) ).
fof(sk_lemma_4_neg,plain,
( ~ greater(position(sK0,sK1),position(sK0,sK2))
& greater(age(sK0,sK1),age(sK0,sK2))
& organization(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(T0,sK2),skolemize(T,sK1)],[nnf_9]) ).
cnf(c_20,negated_conjecture,
organization(sK0),
inference(split_conjunct,[status(thm)],[sk_lemma_4_neg]) ).
cnf(c_22,plain,
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_6]) ).
cnf(c_23,negated_conjecture,
( greater(position(sK0,A),position(sK0,B))
| ~ greater(external_ties(sK0,A),external_ties(sK0,B)) ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_25,negated_conjecture,
( greater(external_ties(sK0,A),external_ties(sK0,B))
| ~ greater(age(sK0,A),age(sK0,B)) ),
inference(resolve,[status(thm)],[c_19,c_20]) ).
cnf(c_29,negated_conjecture,
greater(age(sK0,sK1),age(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_lemma_4_neg]) ).
cnf(c_30,negated_conjecture,
~ greater(position(sK0,sK1),position(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_lemma_4_neg]) ).
cnf(c_43,plain,
greater(external_ties(sK0,sK1),external_ties(sK0,sK2)),
inference(resolve,[status(thm)],[c_29,c_25]) ).
cnf(c_46,negated_conjecture,
~ greater(external_ties(sK0,sK1),external_ties(sK0,sK2)),
inference(resolve,[status(thm)],[c_23,c_30]) ).
cnf(c_45,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_43,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT045+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.73 % Computer : n015.cluster.edu
% 0.09/0.73 % Model : x86_64 x86_64
% 0.09/0.73 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.73 % Memory : 8046.5625MB
% 0.09/0.73 % OS : Linux 6.8.0-71-generic
% 0.09/0.73 % CPULimit : 300
% 0.09/0.73 % WCLimit : 300
% 0.09/0.73 % DateTime : Sat Sep 26 00:12:44 UTC 2026
% 0.09/0.74 % CPUTime :
% 0.09/0.74 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.74 % Process 2611503 was started by sandbox2 on n015,
% 0.09/0.74 % Sat Sep 26 00:12:44 2026
% 0.09/0.74 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.74
% 0.09/0.74 % From the command line: assign(max_seconds, 300).
% 0.09/0.75
% 0.09/0.75 % SZS status Theorem for theBenchmark
% 0.09/0.75
% 0.09/0.75 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.75 % Length of proof is 12.
% 0.09/0.75 % Level of proof is 4.
% 0.09/0.75 % Maximum clause weight is 14.000.
% 0.09/0.75 % Given clauses 8.
% 0.09/0.75
% 0.09/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------