%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT008+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 : n001.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 08:02:04 AM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 17 unt; 0 def)
% Number of atoms : 201 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 254 ( 98 ~; 93 |; 58 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 41 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp5,axiom,
! [X,T] :
( organization(X,T)
=> ? [I] : inertia(X,I,T) ),
file('theBenchmark.p',mp5) ).
fof(a5_FOL,axiom,
! [X,Y,C,S1,S2,I1,I2,T1,T2] :
( ( greater(S2,S1)
& inertia(Y,I2,T2)
& inertia(X,I1,T1)
& size(Y,S2,T2)
& size(X,S1,T1)
& class(Y,C,T2)
& class(X,C,T1)
& organization(Y,T2)
& organization(X,T1) )
=> greater(I2,I1) ),
file('theBenchmark.p',a5_FOL) ).
fof(t1_FOL,axiom,
! [X,Y,T1,T2,I1,I2,P1,P2] :
( ( greater(I2,I1)
& survival_chance(Y,P2,T2)
& survival_chance(X,P1,T1)
& inertia(Y,I2,T2)
& inertia(X,I1,T1)
& reorganization_free(Y,T2,T2)
& reorganization_free(X,T1,T1)
& organization(Y,T2)
& organization(X,T1) )
=> greater(P2,P1) ),
file('theBenchmark.p',t1_FOL) ).
fof(t8_FOL,conjecture,
! [X,Y,C,P1,P2,S1,S2,T1,T2] :
( ( greater(S2,S1)
& size(Y,S2,T2)
& size(X,S1,T1)
& survival_chance(Y,P2,T2)
& survival_chance(X,P1,T1)
& class(Y,C,T2)
& class(X,C,T1)
& reorganization_free(Y,T2,T2)
& reorganization_free(X,T1,T1)
& organization(Y,T2)
& organization(X,T1) )
=> greater(P2,P1) ),
file('theBenchmark.p',t8_FOL) ).
fof(t8_FOL_neg,negated_conjecture,
~ ! [X,Y,C,P1,P2,S1,S2,T1,T2] :
( ( greater(S2,S1)
& size(Y,S2,T2)
& size(X,S1,T1)
& survival_chance(Y,P2,T2)
& survival_chance(X,P1,T1)
& class(Y,C,T2)
& class(X,C,T1)
& reorganization_free(Y,T2,T2)
& reorganization_free(X,T1,T1)
& organization(Y,T2)
& organization(X,T1) )
=> greater(P2,P1) ),
inference(assume_negation,[status(cth)],[t8_FOL]) ).
fof(nnf_1,plain,
! [X,T] :
( ? [I] : inertia(X,I,T)
| ~ organization(X,T) ),
inference(fof_nnf,[status(thm)],[mp5]) ).
fof(sk_mp5,plain,
! [X,T] :
( inertia(X,sK0(X,T),T)
| ~ organization(X,T) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(I,sK0(X,T))],[nnf_1]) ).
cnf(c_5,plain,
( inertia(A,sK0(A,B),B)
| ~ organization(A,B) ),
inference(split_conjunct,[status(thm)],[sk_mp5]) ).
cnf(c_6,plain,
( greater(V8,V7)
| ~ greater(V6,F)
| ~ inertia(C,V8,D)
| ~ inertia(A,V7,B)
| ~ size(C,V6,D)
| ~ size(A,F,B)
| ~ class(C,E,D)
| ~ class(A,E,B)
| ~ organization(C,D)
| ~ organization(A,B) ),
inference(clausify,[status(thm)],[a5_FOL]) ).
cnf(c_7,plain,
( greater(V7,V6)
| ~ greater(F,E)
| ~ survival_chance(C,V7,D)
| ~ survival_chance(A,V6,B)
| ~ inertia(C,F,D)
| ~ inertia(A,E,B)
| ~ reorganization_free(C,D,D)
| ~ reorganization_free(A,B,B)
| ~ organization(C,D)
| ~ organization(A,B) ),
inference(clausify,[status(thm)],[t1_FOL]) ).
fof(nnf_4,plain,
? [X,Y,C,P1,P2,S1,S2,T1,T2] :
( ~ greater(P2,P1)
& greater(S2,S1)
& size(Y,S2,T2)
& size(X,S1,T1)
& survival_chance(Y,P2,T2)
& survival_chance(X,P1,T1)
& class(Y,C,T2)
& class(X,C,T1)
& reorganization_free(Y,T2,T2)
& reorganization_free(X,T1,T1)
& organization(Y,T2)
& organization(X,T1) ),
inference(fof_nnf,[status(thm)],[t8_FOL_neg]) ).
fof(sk_t8_FOL_neg,plain,
( ~ greater(sK7,sK6)
& greater(sK9,sK8)
& size(sK3,sK9,sK4)
& size(sK1,sK8,sK2)
& survival_chance(sK3,sK7,sK4)
& survival_chance(sK1,sK6,sK2)
& class(sK3,sK5,sK4)
& class(sK1,sK5,sK2)
& reorganization_free(sK3,sK4,sK4)
& reorganization_free(sK1,sK2,sK2)
& organization(sK3,sK4)
& organization(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9]),skolemize(X,sK1),skolemize(Y,sK3),skolemize(C,sK5),skolemize(P1,sK6),skolemize(P2,sK7),skolemize(S1,sK8),skolemize(S2,sK9),skolemize(T1,sK2),skolemize(T2,sK4)],[nnf_4]) ).
cnf(c_8,negated_conjecture,
organization(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_9,negated_conjecture,
organization(sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_10,negated_conjecture,
reorganization_free(sK1,sK2,sK2),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_11,negated_conjecture,
reorganization_free(sK3,sK4,sK4),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_12,negated_conjecture,
class(sK1,sK5,sK2),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_13,negated_conjecture,
class(sK3,sK5,sK4),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_14,negated_conjecture,
survival_chance(sK1,sK6,sK2),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_15,negated_conjecture,
survival_chance(sK3,sK7,sK4),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_16,negated_conjecture,
size(sK1,sK8,sK2),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_17,negated_conjecture,
size(sK3,sK9,sK4),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_18,negated_conjecture,
greater(sK9,sK8),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_19,negated_conjecture,
~ greater(sK7,sK6),
inference(split_conjunct,[status(thm)],[sk_t8_FOL_neg]) ).
cnf(c_20,negated_conjecture,
inertia(sK1,sK0(sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_5,c_8]) ).
cnf(c_21,negated_conjecture,
inertia(sK3,sK0(sK3,sK4),sK4),
inference(resolve,[status(thm)],[c_5,c_9]) ).
cnf(c_27,negated_conjecture,
( greater(V6,F)
| ~ greater(E,D)
| ~ inertia(A,V6,B)
| ~ inertia(sK1,F,sK2)
| ~ size(A,E,B)
| ~ size(sK1,D,sK2)
| ~ class(A,C,B)
| ~ class(sK1,C,sK2)
| ~ organization(A,B) ),
inference(resolve,[status(thm)],[c_6,c_8]) ).
cnf(c_28,negated_conjecture,
( greater(E,D)
| ~ greater(C,B)
| ~ inertia(sK3,E,sK4)
| ~ inertia(sK1,D,sK2)
| ~ size(sK3,C,sK4)
| ~ size(sK1,B,sK2)
| ~ class(sK3,A,sK4)
| ~ class(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_27,c_9]) ).
cnf(c_29,negated_conjecture,
( greater(D,C)
| ~ greater(B,A)
| ~ inertia(sK3,D,sK4)
| ~ inertia(sK1,C,sK2)
| ~ size(sK3,B,sK4)
| ~ size(sK1,A,sK2)
| ~ class(sK3,sK5,sK4) ),
inference(resolve,[status(thm)],[c_28,c_12]) ).
cnf(c_30,negated_conjecture,
( greater(D,C)
| ~ greater(B,A)
| ~ inertia(sK3,D,sK4)
| ~ inertia(sK1,C,sK2)
| ~ size(sK3,B,sK4)
| ~ size(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_29,c_13]) ).
cnf(c_31,negated_conjecture,
( greater(C,B)
| ~ greater(A,sK8)
| ~ inertia(sK3,C,sK4)
| ~ inertia(sK1,B,sK2)
| ~ size(sK3,A,sK4) ),
inference(resolve,[status(thm)],[c_30,c_16]) ).
cnf(c_32,negated_conjecture,
( greater(B,A)
| ~ greater(sK9,sK8)
| ~ inertia(sK3,B,sK4)
| ~ inertia(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_31,c_17]) ).
cnf(c_33,negated_conjecture,
( greater(A,sK0(sK1,sK2))
| ~ greater(sK9,sK8)
| ~ inertia(sK3,A,sK4) ),
inference(resolve,[status(thm)],[c_32,c_20]) ).
cnf(c_34,negated_conjecture,
( greater(sK0(sK3,sK4),sK0(sK1,sK2))
| ~ greater(sK9,sK8) ),
inference(resolve,[status(thm)],[c_33,c_21]) ).
cnf(c_24,negated_conjecture,
greater(sK0(sK3,sK4),sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_34,c_18]) ).
cnf(c_35,negated_conjecture,
( greater(F,E)
| ~ greater(D,C)
| ~ survival_chance(A,F,B)
| ~ survival_chance(sK1,E,sK2)
| ~ inertia(A,D,B)
| ~ inertia(sK1,C,sK2)
| ~ reorganization_free(A,B,B)
| ~ reorganization_free(sK1,sK2,sK2)
| ~ organization(A,B) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_36,negated_conjecture,
( greater(D,C)
| ~ greater(B,A)
| ~ survival_chance(sK3,D,sK4)
| ~ survival_chance(sK1,C,sK2)
| ~ inertia(sK3,B,sK4)
| ~ inertia(sK1,A,sK2)
| ~ reorganization_free(sK3,sK4,sK4)
| ~ reorganization_free(sK1,sK2,sK2) ),
inference(resolve,[status(thm)],[c_35,c_9]) ).
cnf(c_37,negated_conjecture,
( greater(D,C)
| ~ greater(B,A)
| ~ survival_chance(sK3,D,sK4)
| ~ survival_chance(sK1,C,sK2)
| ~ inertia(sK3,B,sK4)
| ~ inertia(sK1,A,sK2)
| ~ reorganization_free(sK3,sK4,sK4) ),
inference(resolve,[status(thm)],[c_36,c_10]) ).
cnf(c_38,negated_conjecture,
( greater(D,C)
| ~ greater(B,A)
| ~ survival_chance(sK3,D,sK4)
| ~ survival_chance(sK1,C,sK2)
| ~ inertia(sK3,B,sK4)
| ~ inertia(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_37,c_11]) ).
cnf(c_39,negated_conjecture,
( greater(C,B)
| ~ greater(A,sK0(sK1,sK2))
| ~ survival_chance(sK3,C,sK4)
| ~ survival_chance(sK1,B,sK2)
| ~ inertia(sK3,A,sK4) ),
inference(resolve,[status(thm)],[c_38,c_20]) ).
cnf(c_40,negated_conjecture,
( greater(B,A)
| ~ greater(sK0(sK3,sK4),sK0(sK1,sK2))
| ~ survival_chance(sK3,B,sK4)
| ~ survival_chance(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_39,c_21]) ).
cnf(c_41,negated_conjecture,
( greater(A,sK6)
| ~ greater(sK0(sK3,sK4),sK0(sK1,sK2))
| ~ survival_chance(sK3,A,sK4) ),
inference(resolve,[status(thm)],[c_40,c_14]) ).
cnf(c_42,negated_conjecture,
( greater(sK7,sK6)
| ~ greater(sK0(sK3,sK4),sK0(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_41,c_15]) ).
cnf(c_25,negated_conjecture,
~ greater(sK0(sK3,sK4),sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_42,c_19]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT008+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 00:08:41 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 387194 was started by sandbox on n001,
% 0.12/0.36 % Sat Sep 26 00:08:41 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.38 % Length of proof is 24.
% 0.12/0.38 % Level of proof is 4.
% 0.12/0.38 % Maximum clause weight is 41.000.
% 0.12/0.38 % Given clauses 17.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------