%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT018+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 : 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 08:02:07 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 18 unt; 0 def)
% Number of atoms : 245 ( 0 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 330 ( 134 ~; 126 |; 65 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 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 : 136 ( 0 sgn 42 !; 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(a14_FOL,axiom,
! [X,Y,Rt,C,I1,I2,Ta,Tb,Tc] :
( ( greater(I2,I1)
& inertia(Y,I2,Ta)
& inertia(X,I1,Ta)
& reorganization_type(Y,Rt,Ta)
& reorganization_type(X,Rt,Ta)
& reorganization(Y,Ta,Tc)
& reorganization(X,Ta,Tb)
& class(Y,C,Ta)
& class(X,C,Ta)
& ~ organization(Y,Tc)
& organization(Y,Ta)
& organization(X,Ta) )
=> greater(Tb,Tc) ),
file('theBenchmark.p',a14_FOL) ).
fof(t18_FOL,conjecture,
! [X,Y,Rt,C,S1,S2,Ta,Tb,Tc] :
( ( greater(S2,S1)
& size(Y,S2,Ta)
& size(X,S1,Ta)
& reorganization_type(Y,Rt,Ta)
& reorganization_type(X,Rt,Ta)
& reorganization(Y,Ta,Tc)
& reorganization(X,Ta,Tb)
& class(Y,C,Ta)
& class(X,C,Ta)
& ~ organization(Y,Tc)
& organization(Y,Ta)
& organization(X,Ta) )
=> greater(Tb,Tc) ),
file('theBenchmark.p',t18_FOL) ).
fof(t18_FOL_neg,negated_conjecture,
~ ! [X,Y,Rt,C,S1,S2,Ta,Tb,Tc] :
( ( greater(S2,S1)
& size(Y,S2,Ta)
& size(X,S1,Ta)
& reorganization_type(Y,Rt,Ta)
& reorganization_type(X,Rt,Ta)
& reorganization(Y,Ta,Tc)
& reorganization(X,Ta,Tb)
& class(Y,C,Ta)
& class(X,C,Ta)
& ~ organization(Y,Tc)
& organization(Y,Ta)
& organization(X,Ta) )
=> greater(Tb,Tc) ),
inference(assume_negation,[status(cth)],[t18_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(F,D)
| ~ greater(V8,V7)
| ~ inertia(C,V8,B)
| ~ inertia(A,V7,B)
| ~ reorganization_type(C,V6,B)
| ~ reorganization_type(A,V6,B)
| ~ reorganization(C,B,D)
| ~ reorganization(A,B,F)
| ~ class(C,E,B)
| ~ class(A,E,B)
| organization(C,D)
| ~ organization(C,B)
| ~ organization(A,B) ),
inference(clausify,[status(thm)],[a14_FOL]) ).
fof(nnf_4,plain,
? [X,Y,Rt,C,S1,S2,Ta,Tb,Tc] :
( ~ greater(Tb,Tc)
& greater(S2,S1)
& size(Y,S2,Ta)
& size(X,S1,Ta)
& reorganization_type(Y,Rt,Ta)
& reorganization_type(X,Rt,Ta)
& reorganization(Y,Ta,Tc)
& reorganization(X,Ta,Tb)
& class(Y,C,Ta)
& class(X,C,Ta)
& ~ organization(Y,Tc)
& organization(Y,Ta)
& organization(X,Ta) ),
inference(fof_nnf,[status(thm)],[t18_FOL_neg]) ).
fof(sk_t18_FOL_neg,plain,
( ~ greater(sK6,sK4)
& greater(sK9,sK8)
& size(sK3,sK9,sK2)
& size(sK1,sK8,sK2)
& reorganization_type(sK3,sK7,sK2)
& reorganization_type(sK1,sK7,sK2)
& reorganization(sK3,sK2,sK4)
& reorganization(sK1,sK2,sK6)
& class(sK3,sK5,sK2)
& class(sK1,sK5,sK2)
& ~ organization(sK3,sK4)
& organization(sK3,sK2)
& 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(Rt,sK7),skolemize(C,sK5),skolemize(S1,sK8),skolemize(S2,sK9),skolemize(Ta,sK2),skolemize(Tb,sK6),skolemize(Tc,sK4)],[nnf_4]) ).
cnf(c_8,negated_conjecture,
organization(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_9,negated_conjecture,
organization(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_10,negated_conjecture,
~ organization(sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_11,negated_conjecture,
class(sK1,sK5,sK2),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_12,negated_conjecture,
class(sK3,sK5,sK2),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_13,negated_conjecture,
reorganization(sK1,sK2,sK6),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_14,negated_conjecture,
reorganization(sK3,sK2,sK4),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_15,negated_conjecture,
reorganization_type(sK1,sK7,sK2),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_16,negated_conjecture,
reorganization_type(sK3,sK7,sK2),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_17,negated_conjecture,
size(sK1,sK8,sK2),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_18,negated_conjecture,
size(sK3,sK9,sK2),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_19,negated_conjecture,
greater(sK9,sK8),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_20,negated_conjecture,
~ greater(sK6,sK4),
inference(split_conjunct,[status(thm)],[sk_t18_FOL_neg]) ).
cnf(c_29,plain,
inertia(sK1,sK0(sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_30,plain,
inertia(sK3,sK0(sK3,sK2),sK2),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_61,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_62,negated_conjecture,
( greater(E,D)
| ~ greater(C,B)
| ~ inertia(sK3,E,sK2)
| ~ inertia(sK1,D,sK2)
| ~ size(sK3,C,sK2)
| ~ size(sK1,B,sK2)
| ~ class(sK3,A,sK2)
| ~ class(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_61,c_9]) ).
cnf(c_63,negated_conjecture,
( greater(D,C)
| ~ greater(B,A)
| ~ inertia(sK3,D,sK2)
| ~ inertia(sK1,C,sK2)
| ~ size(sK3,B,sK2)
| ~ size(sK1,A,sK2)
| ~ class(sK3,sK5,sK2) ),
inference(resolve,[status(thm)],[c_62,c_11]) ).
cnf(c_64,negated_conjecture,
( greater(D,C)
| ~ greater(B,A)
| ~ inertia(sK3,D,sK2)
| ~ inertia(sK1,C,sK2)
| ~ size(sK3,B,sK2)
| ~ size(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_63,c_12]) ).
cnf(c_65,negated_conjecture,
( greater(C,B)
| ~ greater(A,sK8)
| ~ inertia(sK3,C,sK2)
| ~ inertia(sK1,B,sK2)
| ~ size(sK3,A,sK2) ),
inference(resolve,[status(thm)],[c_64,c_17]) ).
cnf(c_66,negated_conjecture,
( greater(B,A)
| ~ greater(sK9,sK8)
| ~ inertia(sK3,B,sK2)
| ~ inertia(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_65,c_18]) ).
cnf(c_67,negated_conjecture,
( greater(A,sK0(sK1,sK2))
| ~ greater(sK9,sK8)
| ~ inertia(sK3,A,sK2) ),
inference(resolve,[status(thm)],[c_66,c_29]) ).
cnf(c_68,negated_conjecture,
( greater(sK0(sK3,sK2),sK0(sK1,sK2))
| ~ greater(sK9,sK8) ),
inference(resolve,[status(thm)],[c_67,c_30]) ).
cnf(c_59,negated_conjecture,
greater(sK0(sK3,sK2),sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_68,c_19]) ).
cnf(c_69,negated_conjecture,
( greater(D,B)
| ~ greater(V6,F)
| ~ inertia(A,V6,sK2)
| ~ inertia(sK1,F,sK2)
| ~ reorganization_type(A,E,sK2)
| ~ reorganization_type(sK1,E,sK2)
| ~ reorganization(A,sK2,B)
| ~ reorganization(sK1,sK2,D)
| ~ class(A,C,sK2)
| ~ class(sK1,C,sK2)
| organization(A,B)
| ~ organization(A,sK2) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_70,negated_conjecture,
( greater(C,A)
| ~ greater(F,E)
| ~ inertia(sK3,F,sK2)
| ~ inertia(sK1,E,sK2)
| ~ reorganization_type(sK3,D,sK2)
| ~ reorganization_type(sK1,D,sK2)
| ~ reorganization(sK3,sK2,A)
| ~ reorganization(sK1,sK2,C)
| ~ class(sK3,B,sK2)
| ~ class(sK1,B,sK2)
| organization(sK3,A) ),
inference(resolve,[status(thm)],[c_69,c_9]) ).
cnf(c_71,negated_conjecture,
( greater(B,sK4)
| ~ greater(E,D)
| ~ inertia(sK3,E,sK2)
| ~ inertia(sK1,D,sK2)
| ~ reorganization_type(sK3,C,sK2)
| ~ reorganization_type(sK1,C,sK2)
| ~ reorganization(sK3,sK2,sK4)
| ~ reorganization(sK1,sK2,B)
| ~ class(sK3,A,sK2)
| ~ class(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_70,c_10]) ).
cnf(c_72,negated_conjecture,
( greater(A,sK4)
| ~ greater(D,C)
| ~ inertia(sK3,D,sK2)
| ~ inertia(sK1,C,sK2)
| ~ reorganization_type(sK3,B,sK2)
| ~ reorganization_type(sK1,B,sK2)
| ~ reorganization(sK3,sK2,sK4)
| ~ reorganization(sK1,sK2,A)
| ~ class(sK3,sK5,sK2) ),
inference(resolve,[status(thm)],[c_71,c_11]) ).
cnf(c_73,negated_conjecture,
( greater(A,sK4)
| ~ greater(D,C)
| ~ inertia(sK3,D,sK2)
| ~ inertia(sK1,C,sK2)
| ~ reorganization_type(sK3,B,sK2)
| ~ reorganization_type(sK1,B,sK2)
| ~ reorganization(sK3,sK2,sK4)
| ~ reorganization(sK1,sK2,A) ),
inference(resolve,[status(thm)],[c_72,c_12]) ).
cnf(c_74,negated_conjecture,
( greater(sK6,sK4)
| ~ greater(C,B)
| ~ inertia(sK3,C,sK2)
| ~ inertia(sK1,B,sK2)
| ~ reorganization_type(sK3,A,sK2)
| ~ reorganization_type(sK1,A,sK2)
| ~ reorganization(sK3,sK2,sK4) ),
inference(resolve,[status(thm)],[c_73,c_13]) ).
cnf(c_75,negated_conjecture,
( greater(sK6,sK4)
| ~ greater(C,B)
| ~ inertia(sK3,C,sK2)
| ~ inertia(sK1,B,sK2)
| ~ reorganization_type(sK3,A,sK2)
| ~ reorganization_type(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_74,c_14]) ).
cnf(c_76,negated_conjecture,
( greater(sK6,sK4)
| ~ greater(B,A)
| ~ inertia(sK3,B,sK2)
| ~ inertia(sK1,A,sK2)
| ~ reorganization_type(sK3,sK7,sK2) ),
inference(resolve,[status(thm)],[c_75,c_15]) ).
cnf(c_77,negated_conjecture,
( greater(sK6,sK4)
| ~ greater(B,A)
| ~ inertia(sK3,B,sK2)
| ~ inertia(sK1,A,sK2) ),
inference(resolve,[status(thm)],[c_76,c_16]) ).
cnf(c_78,negated_conjecture,
( greater(sK6,sK4)
| ~ greater(A,sK0(sK1,sK2))
| ~ inertia(sK3,A,sK2) ),
inference(resolve,[status(thm)],[c_77,c_29]) ).
cnf(c_79,negated_conjecture,
( greater(sK6,sK4)
| ~ greater(sK0(sK3,sK2),sK0(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_78,c_30]) ).
cnf(c_80,negated_conjecture,
~ greater(sK0(sK3,sK2),sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_79,c_20]) ).
cnf(c_60,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_59,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MGT018+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n009.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 00:03:44 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 2886091 was started by sandbox on n009,
% 0.17/0.45 % Sat Sep 26 00:03:44 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48
% 0.17/0.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.48 % Length of proof is 24.
% 0.17/0.48 % Level of proof is 4.
% 0.17/0.48 % Maximum clause weight is 52.000.
% 0.17/0.48 % Given clauses 26.
% 0.17/0.48
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------