%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT002+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 08:02:02 AM UTC 2026
% Result : Theorem 0.10s 0.63s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 14 unt; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 189 ( 76 ~; 71 |; 35 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 92 ( 2 sgn 32 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp3,axiom,
! [X,T] :
( organization(X,T)
=> ? [Rp] : reproducibility(X,Rp,T) ),
file('theBenchmark.p',mp3) ).
fof(mp4,axiom,
! [X,T1,T2] :
( reorganization_free(X,T1,T2)
=> ( reorganization_free(X,T2,T2)
& reorganization_free(X,T1,T1) ) ),
file('theBenchmark.p',mp4) ).
fof(a3_FOL,axiom,
! [X,Y,T1,T2,Rp1,Rp2,I1,I2] :
( ( inertia(Y,I2,T2)
& inertia(X,I1,T1)
& reproducibility(Y,Rp2,T2)
& reproducibility(X,Rp1,T1)
& reorganization_free(Y,T2,T2)
& reorganization_free(X,T1,T1)
& organization(Y,T2)
& organization(X,T1) )
=> ( greater(Rp2,Rp1)
<=> greater(I2,I1) ) ),
file('theBenchmark.p',a3_FOL) ).
fof(a4_FOL,axiom,
! [X,Rp1,Rp2,T1,T2] :
( ( greater(T2,T1)
& reproducibility(X,Rp2,T2)
& reproducibility(X,Rp1,T1)
& reorganization_free(X,T1,T2)
& organization(X,T2)
& organization(X,T1) )
=> greater(Rp2,Rp1) ),
file('theBenchmark.p',a4_FOL) ).
fof(t2_FOL,conjecture,
! [X,I1,I2,T1,T2] :
( ( greater(T2,T1)
& inertia(X,I2,T2)
& inertia(X,I1,T1)
& reorganization_free(X,T1,T2)
& organization(X,T2)
& organization(X,T1) )
=> greater(I2,I1) ),
file('theBenchmark.p',t2_FOL) ).
fof(t2_FOL_neg,negated_conjecture,
~ ! [X,I1,I2,T1,T2] :
( ( greater(T2,T1)
& inertia(X,I2,T2)
& inertia(X,I1,T1)
& reorganization_free(X,T1,T2)
& organization(X,T2)
& organization(X,T1) )
=> greater(I2,I1) ),
inference(assume_negation,[status(cth)],[t2_FOL]) ).
fof(nnf_1,plain,
! [X,T] :
( ? [Rp] : reproducibility(X,Rp,T)
| ~ organization(X,T) ),
inference(fof_nnf,[status(thm)],[mp3]) ).
fof(sk_mp3,plain,
! [X,T] :
( reproducibility(X,sK0(X,T),T)
| ~ organization(X,T) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Rp,sK0(X,T))],[nnf_1]) ).
cnf(c_6,plain,
( reproducibility(A,sK0(A,B),B)
| ~ organization(A,B) ),
inference(split_conjunct,[status(thm)],[sk_mp3]) ).
cnf(c_7,plain,
( reorganization_free(A,B,B)
| ~ reorganization_free(A,B,C) ),
inference(clausify,[status(thm)],[mp4]) ).
cnf(c_8,plain,
( reorganization_free(A,C,C)
| ~ reorganization_free(A,B,C) ),
inference(clausify,[status(thm)],[mp4]) ).
cnf(c_9,plain,
( greater(V7,V6)
| ~ greater(F,E)
| ~ inertia(C,V7,D)
| ~ inertia(A,V6,B)
| ~ reproducibility(C,F,D)
| ~ reproducibility(A,E,B)
| ~ reorganization_free(C,D,D)
| ~ reorganization_free(A,B,B)
| ~ organization(C,D)
| ~ organization(A,B) ),
inference(clausify,[status(thm)],[a3_FOL]) ).
cnf(c_11,plain,
( greater(E,D)
| ~ greater(C,B)
| ~ reproducibility(A,E,C)
| ~ reproducibility(A,D,B)
| ~ reorganization_free(A,B,C)
| ~ organization(A,C)
| ~ organization(A,B) ),
inference(clausify,[status(thm)],[a4_FOL]) ).
fof(nnf_5,plain,
? [X,I1,I2,T1,T2] :
( ~ greater(I2,I1)
& greater(T2,T1)
& inertia(X,I2,T2)
& inertia(X,I1,T1)
& reorganization_free(X,T1,T2)
& organization(X,T2)
& organization(X,T1) ),
inference(fof_nnf,[status(thm)],[t2_FOL_neg]) ).
fof(sk_t2_FOL_neg,plain,
( ~ greater(sK5,sK4)
& greater(sK3,sK2)
& inertia(sK1,sK5,sK3)
& inertia(sK1,sK4,sK2)
& reorganization_free(sK1,sK2,sK3)
& organization(sK1,sK3)
& organization(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5]),skolemize(X,sK1),skolemize(I1,sK4),skolemize(I2,sK5),skolemize(T1,sK2),skolemize(T2,sK3)],[nnf_5]) ).
cnf(c_12,negated_conjecture,
organization(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t2_FOL_neg]) ).
cnf(c_13,negated_conjecture,
organization(sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_t2_FOL_neg]) ).
cnf(c_14,negated_conjecture,
reorganization_free(sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t2_FOL_neg]) ).
cnf(c_15,negated_conjecture,
inertia(sK1,sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_t2_FOL_neg]) ).
cnf(c_16,negated_conjecture,
inertia(sK1,sK5,sK3),
inference(split_conjunct,[status(thm)],[sk_t2_FOL_neg]) ).
cnf(c_17,negated_conjecture,
greater(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_t2_FOL_neg]) ).
cnf(c_18,negated_conjecture,
~ greater(sK5,sK4),
inference(split_conjunct,[status(thm)],[sk_t2_FOL_neg]) ).
cnf(c_19,plain,
reproducibility(sK1,sK0(sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_12,c_6]) ).
cnf(c_20,plain,
reproducibility(sK1,sK0(sK1,sK3),sK3),
inference(resolve,[status(thm)],[c_13,c_6]) ).
cnf(c_21,plain,
reorganization_free(sK1,sK3,sK3),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_22,plain,
reorganization_free(sK1,sK2,sK2),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_60,negated_conjecture,
( greater(C,B)
| ~ greater(A,sK2)
| ~ reproducibility(sK1,C,A)
| ~ reproducibility(sK1,B,sK2)
| ~ reorganization_free(sK1,sK2,A)
| ~ organization(sK1,A) ),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_61,negated_conjecture,
( greater(B,A)
| ~ greater(sK3,sK2)
| ~ reproducibility(sK1,B,sK3)
| ~ reproducibility(sK1,A,sK2)
| ~ reorganization_free(sK1,sK2,sK3) ),
inference(resolve,[status(thm)],[c_60,c_13]) ).
cnf(c_62,negated_conjecture,
( greater(B,A)
| ~ greater(sK3,sK2)
| ~ reproducibility(sK1,B,sK3)
| ~ reproducibility(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_61,c_14]) ).
cnf(c_63,negated_conjecture,
( greater(A,sK0(sK1,sK2))
| ~ greater(sK3,sK2)
| ~ reproducibility(sK1,A,sK3) ),
inference(resolve,[status(thm)],[c_62,c_19]) ).
cnf(c_64,negated_conjecture,
( greater(sK0(sK1,sK3),sK0(sK1,sK2))
| ~ greater(sK3,sK2) ),
inference(resolve,[status(thm)],[c_63,c_20]) ).
cnf(c_58,negated_conjecture,
greater(sK0(sK1,sK3),sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_64,c_17]) ).
cnf(c_65,negated_conjecture,
( greater(F,E)
| ~ greater(D,C)
| ~ inertia(A,F,B)
| ~ inertia(sK1,E,sK2)
| ~ reproducibility(A,D,B)
| ~ reproducibility(sK1,C,sK2)
| ~ reorganization_free(A,B,B)
| ~ reorganization_free(sK1,sK2,sK2)
| ~ organization(A,B) ),
inference(resolve,[status(thm)],[c_9,c_12]) ).
cnf(c_66,negated_conjecture,
( greater(D,C)
| ~ greater(B,A)
| ~ inertia(sK1,D,sK3)
| ~ inertia(sK1,C,sK2)
| ~ reproducibility(sK1,B,sK3)
| ~ reproducibility(sK1,A,sK2)
| ~ reorganization_free(sK1,sK3,sK3)
| ~ reorganization_free(sK1,sK2,sK2) ),
inference(resolve,[status(thm)],[c_65,c_13]) ).
cnf(c_67,negated_conjecture,
( greater(D,C)
| ~ greater(B,A)
| ~ inertia(sK1,D,sK3)
| ~ inertia(sK1,C,sK2)
| ~ reproducibility(sK1,B,sK3)
| ~ reproducibility(sK1,A,sK2)
| ~ reorganization_free(sK1,sK3,sK3) ),
inference(resolve,[status(thm)],[c_66,c_22]) ).
cnf(c_68,negated_conjecture,
( greater(D,C)
| ~ greater(B,A)
| ~ inertia(sK1,D,sK3)
| ~ inertia(sK1,C,sK2)
| ~ reproducibility(sK1,B,sK3)
| ~ reproducibility(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_67,c_21]) ).
cnf(c_69,negated_conjecture,
( greater(C,B)
| ~ greater(A,sK0(sK1,sK2))
| ~ inertia(sK1,C,sK3)
| ~ inertia(sK1,B,sK2)
| ~ reproducibility(sK1,A,sK3) ),
inference(resolve,[status(thm)],[c_68,c_19]) ).
cnf(c_70,negated_conjecture,
( greater(B,A)
| ~ greater(sK0(sK1,sK3),sK0(sK1,sK2))
| ~ inertia(sK1,B,sK3)
| ~ inertia(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_69,c_20]) ).
cnf(c_71,negated_conjecture,
( greater(A,sK4)
| ~ greater(sK0(sK1,sK3),sK0(sK1,sK2))
| ~ inertia(sK1,A,sK3) ),
inference(resolve,[status(thm)],[c_70,c_15]) ).
cnf(c_72,negated_conjecture,
( greater(sK5,sK4)
| ~ greater(sK0(sK1,sK3),sK0(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_71,c_16]) ).
cnf(c_73,negated_conjecture,
~ greater(sK0(sK1,sK3),sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_72,c_18]) ).
cnf(c_59,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_58,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT002+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.58 % Computer : n004.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Sat Sep 26 00:02:22 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.58 % Process 293856 was started by sandbox on n004,
% 0.10/0.58 % Sat Sep 26 00:02:22 2026
% 0.10/0.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.59
% 0.10/0.59 % From the command line: assign(max_seconds, 300).
% 0.10/0.63
% 0.10/0.63 % SZS status Theorem for theBenchmark
% 0.10/0.63
% 0.10/0.63 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.10/0.63 % Length of proof is 23.
% 0.10/0.63 % Level of proof is 4.
% 0.10/0.63 % Maximum clause weight is 41.000.
% 0.10/0.63 % Given clauses 21.
% 0.10/0.63
% 0.10/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------