%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PHI011+1 : TPTP v9.3.1. Released v7.2.0.
% 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 08:19:49 AM UTC 2026
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 66 ( 6 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 73 ( 25 ~; 21 |; 16 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 30 ( 6 sgn 9 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(description_is_property_and_described_is_object,axiom,
! [X,F] :
( is_the(X,F)
=> ( object(X)
& property(F) ) ),
file('theBenchmark.p',description_is_property_and_described_is_object) ).
fof(lemma_1,axiom,
! [X,F,Y] :
( ( object(Y)
& property(F)
& object(X) )
=> ( ( X = Y
& is_the(X,F) )
=> exemplifies_property(F,Y) ) ),
file('theBenchmark.p',lemma_1) ).
fof(description_theorem_2,conjecture,
! [F] :
( property(F)
=> ( ? [Y] :
( is_the(Y,F)
& object(Y) )
=> ! [Z] :
( object(Z)
=> ( is_the(Z,F)
=> exemplifies_property(F,Z) ) ) ) ),
file('theBenchmark.p',description_theorem_2) ).
fof(description_theorem_2_neg,negated_conjecture,
~ ! [F] :
( property(F)
=> ( ? [Y] :
( is_the(Y,F)
& object(Y) )
=> ! [Z] :
( object(Z)
=> ( is_the(Z,F)
=> exemplifies_property(F,Z) ) ) ) ),
inference(assume_negation,[status(cth)],[description_theorem_2]) ).
cnf(c_8,plain,
( property(B)
| ~ is_the(A,B) ),
inference(clausify,[status(thm)],[description_is_property_and_described_is_object]) ).
cnf(c_9,plain,
( exemplifies_property(B,C)
| C != A
| ~ is_the(A,B)
| ~ object(C)
| ~ property(B)
| ~ object(A) ),
inference(clausify,[status(thm)],[lemma_1]) ).
cnf(c_12,plain,
( ~ is_the(D,C)
| exemplifies_property(C,B)
| B != A
| ~ is_the(A,C)
| ~ object(B)
| ~ object(A) ),
inference(resolve,[status(thm)],[c_9,c_8]) ).
fof(nnf_5,plain,
? [F] :
( ? [Z] :
( ~ exemplifies_property(F,Z)
& is_the(Z,F)
& object(Z) )
& ? [Y] :
( is_the(Y,F)
& object(Y) )
& property(F) ),
inference(fof_nnf,[status(thm)],[description_theorem_2_neg]) ).
fof(sk_description_theorem_2_neg,plain,
( ~ exemplifies_property(sK0,sK1)
& is_the(sK1,sK0)
& object(sK1)
& is_the(sK2,sK0)
& object(sK2)
& property(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(F,sK0),skolemize(Y,sK2),skolemize(Z,sK1)],[nnf_5]) ).
cnf(c_15,negated_conjecture,
~ exemplifies_property(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_description_theorem_2_neg]) ).
cnf(c_16,negated_conjecture,
is_the(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_description_theorem_2_neg]) ).
cnf(c_17,negated_conjecture,
object(sK1),
inference(split_conjunct,[status(thm)],[sk_description_theorem_2_neg]) ).
cnf(c_26,negated_conjecture,
( ~ is_the(C,B)
| exemplifies_property(B,A)
| A != sK1
| ~ is_the(sK1,B)
| ~ object(A) ),
inference(resolve,[status(thm)],[c_12,c_17]) ).
cnf(c_27,negated_conjecture,
( ~ is_the(B,A)
| exemplifies_property(A,sK1)
| sK1 != sK1
| ~ is_the(sK1,A) ),
inference(resolve,[status(thm)],[c_26,c_17]) ).
cnf(c_28,negated_conjecture,
( ~ is_the(A,sK0)
| exemplifies_property(sK0,sK1)
| sK1 != sK1 ),
inference(resolve,[status(thm)],[c_27,c_16]) ).
cnf(c_29,plain,
( ~ is_the(A,sK0)
| exemplifies_property(sK0,sK1) ),
inference(xxres,[status(thm)],[c_28]) ).
cnf(c_30,negated_conjecture,
exemplifies_property(sK0,sK1),
inference(resolve,[status(thm)],[c_29,c_16]) ).
cnf(c_25,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_15,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI011+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n001.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 04:44:57 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 928152 was started by sandbox on n001,
% 0.07/0.35 % Sat Sep 26 04:44:57 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.36
% 0.12/0.36 % SZS status Theorem for theBenchmark
% 0.12/0.36
% 0.12/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.36 % Length of proof is 10.
% 0.12/0.36 % Level of proof is 3.
% 0.12/0.36 % Maximum clause weight is 16.000.
% 0.12/0.36 % Given clauses 7.
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------