%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT044+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 8 unt; 0 def)
% Number of atoms : 59 ( 8 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 52 ( 17 ~; 14 |; 12 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 7 sgn 17 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(definition_smaller_or_equal,axiom,
! [X,Y] :
( smaller_or_equal(X,Y)
<=> ( X = Y
| smaller(X,Y) ) ),
file('theBenchmark.p',definition_smaller_or_equal) ).
fof(assumption_5,axiom,
! [X,T0,T] :
( organization(X)
=> ( ( ( internal_friction(X,T) = internal_friction(X,T0)
& stock_of_knowledge(X,T) = stock_of_knowledge(X,T0) )
=> capability(X,T) = capability(X,T0) )
& ( ( greater(internal_friction(X,T),internal_friction(X,T0))
& smaller_or_equal(stock_of_knowledge(X,T),stock_of_knowledge(X,T0)) )
=> smaller(capability(X,T),capability(X,T0)) )
& ( ( smaller_or_equal(internal_friction(X,T),internal_friction(X,T0))
& greater(stock_of_knowledge(X,T),stock_of_knowledge(X,T0)) )
=> greater(capability(X,T),capability(X,T0)) ) ) ),
file('theBenchmark.p',assumption_5) ).
fof(assumption_7,axiom,
! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& organization(X) )
=> greater(stock_of_knowledge(X,T),stock_of_knowledge(X,T0)) ),
file('theBenchmark.p',assumption_7) ).
fof(assumption_9,axiom,
! [X,T0,T] :
( organization(X)
=> internal_friction(X,T) = internal_friction(X,T0) ),
file('theBenchmark.p',assumption_9) ).
fof(lemma_3,conjecture,
! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& organization(X) )
=> greater(capability(X,T),capability(X,T0)) ),
file('theBenchmark.p',lemma_3) ).
fof(lemma_3_neg,negated_conjecture,
~ ! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& organization(X) )
=> greater(capability(X,T),capability(X,T0)) ),
inference(assume_negation,[status(cth)],[lemma_3]) ).
fof(nnf_10,plain,
? [X,T0,T] :
( ~ greater(capability(X,T),capability(X,T0))
& greater(age(X,T),age(X,T0))
& organization(X) ),
inference(fof_nnf,[status(thm)],[lemma_3_neg]) ).
fof(sk_lemma_3_neg,plain,
( ~ greater(capability(sK0,sK1),capability(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_10]) ).
cnf(c_20,negated_conjecture,
organization(sK0),
inference(split_conjunct,[status(thm)],[sk_lemma_3_neg]) ).
cnf(c_21,plain,
( internal_friction(A,B) = internal_friction(A,C)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_9]) ).
cnf(c_22,plain,
( greater(stock_of_knowledge(A,B),stock_of_knowledge(A,C))
| ~ greater(age(A,B),age(A,C))
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_7]) ).
cnf(c_24,plain,
( greater(capability(A,B),capability(A,C))
| ~ smaller_or_equal(internal_friction(A,B),internal_friction(A,C))
| ~ greater(stock_of_knowledge(A,B),stock_of_knowledge(A,C))
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_5]) ).
cnf(c_29,negated_conjecture,
( greater(capability(sK0,A),capability(sK0,B))
| ~ smaller_or_equal(internal_friction(sK0,A),internal_friction(sK0,B))
| ~ greater(stock_of_knowledge(sK0,A),stock_of_knowledge(sK0,B)) ),
inference(resolve,[status(thm)],[c_20,c_24]) ).
cnf(c_31,negated_conjecture,
( greater(stock_of_knowledge(sK0,A),stock_of_knowledge(sK0,B))
| ~ greater(age(sK0,A),age(sK0,B)) ),
inference(resolve,[status(thm)],[c_20,c_22]) ).
cnf(c_32,negated_conjecture,
internal_friction(sK0,A) = internal_friction(sK0,B),
inference(resolve,[status(thm)],[c_20,c_21]) ).
cnf(c_37,negated_conjecture,
~ greater(capability(sK0,sK1),capability(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_lemma_3_neg]) ).
cnf(c_38,negated_conjecture,
greater(age(sK0,sK1),age(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_lemma_3_neg]) ).
cnf(c_41,plain,
( B != A
| smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
cnf(c_45,plain,
( greater(capability(sK0,A),capability(sK0,B))
| ~ smaller_or_equal(internal_friction(sK0,A),internal_friction(sK0,C))
| ~ greater(stock_of_knowledge(sK0,A),stock_of_knowledge(sK0,B)) ),
inference(paramod,[status(thm)],[c_32,c_29]) ).
cnf(c_53,plain,
greater(stock_of_knowledge(sK0,sK1),stock_of_knowledge(sK0,sK2)),
inference(resolve,[status(thm)],[c_38,c_31]) ).
cnf(c_61,plain,
smaller_or_equal(internal_friction(sK0,A),internal_friction(sK0,B)),
inference(resolve,[status(thm)],[c_41,c_32]) ).
cnf(c_63,plain,
( greater(capability(sK0,A),capability(sK0,B))
| ~ greater(stock_of_knowledge(sK0,A),stock_of_knowledge(sK0,B)) ),
inference(resolve,[status(thm)],[c_61,c_45]) ).
cnf(c_119,plain,
greater(capability(sK0,sK1),capability(sK0,sK2)),
inference(resolve,[status(thm)],[c_63,c_53]) ).
cnf(c_118,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_37,c_119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT044+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 00:08:29 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2892900 was started by sandbox on n009,
% 0.10/0.37 % Sat Sep 26 00:08:29 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.10/0.40 % Length of proof is 20.
% 0.10/0.40 % Level of proof is 5.
% 0.10/0.40 % Maximum clause weight is 21.000.
% 0.10/0.40 % Given clauses 41.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------