%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PHI009+1 : TPTP v9.3.1. Released v7.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 : Fri Sep 25 02:30:17 PM UTC 2026
% Result : Theorem 2.59s 0.78s
% Output : Proof 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 40 ( 6 unt; 0 def)
% Number of atoms : 207 ( 20 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 274 ( 107 ~; 121 |; 34 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 66 ( 0 sgn 22 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [F,G,X] :
( ( object(X)
& property(G)
& property(F) )
=> ( ( exemplifies_property(G,X)
& is_the(X,F) )
<=> ? [Y] :
( exemplifies_property(G,Y)
& ! [Z] :
( object(Z)
=> ( exemplifies_property(F,Z)
=> Z = Y ) )
& exemplifies_property(F,Y)
& object(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',description_axiom_schema_instance) ).
fof(f0_nnf,plain,
! [F,G,X] :
( ( ( ! [Y] :
( ~ exemplifies_property(G,Y)
| ? [Z] :
( Z != Y
& exemplifies_property(F,Z)
& object(Z) )
| ~ exemplifies_property(F,Y)
| ~ object(Y) )
| ( exemplifies_property(G,X)
& is_the(X,F) ) )
& ( ? [Y] :
( exemplifies_property(G,Y)
& ! [Z] :
( Z = Y
| ~ exemplifies_property(F,Z)
| ~ object(Z) )
& exemplifies_property(F,Y)
& object(Y) )
| ~ exemplifies_property(G,X)
| ~ is_the(X,F) ) )
| ~ object(X)
| ~ property(G)
| ~ property(F) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [F,G,X,Z,Y] :
( ( ( ~ exemplifies_property(G,Y)
| ( sk1(F,G,X,Y) != Y
& exemplifies_property(F,sk1(F,G,X,Y))
& object(sk1(F,G,X,Y)) )
| ~ exemplifies_property(F,Y)
| ~ object(Y)
| ( exemplifies_property(G,X)
& is_the(X,F) ) )
& ( ( exemplifies_property(G,sk0(F,G,X))
& ( Z = sk0(F,G,X)
| ~ exemplifies_property(F,Z)
| ~ object(Z) )
& exemplifies_property(F,sk0(F,G,X))
& object(sk0(F,G,X)) )
| ~ exemplifies_property(G,X)
| ~ is_the(X,F) ) )
| ~ object(X)
| ~ property(G)
| ~ property(F) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c6,plain,
( ~ exemplifies_property(X1,X3)
| sk1(X0,X1,X2,X3) != X3
| ~ exemplifies_property(X0,X3)
| ~ object(X3)
| is_the(X2,X0)
| ~ object(X2)
| ~ property(X1)
| ~ property(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,conjecture,
! [F] :
( property(F)
=> ( ? [Y] :
( ! [Z] :
( object(Z)
=> ( exemplifies_property(F,Z)
=> Z = Y ) )
& exemplifies_property(F,Y)
& object(Y) )
=> ? [U] :
( is_the(U,F)
& object(U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',description_theorem_1) ).
fof(f1_neg,negated_conjecture,
~ ! [F] :
( property(F)
=> ( ? [Y] :
( ! [Z] :
( object(Z)
=> ( exemplifies_property(F,Z)
=> Z = Y ) )
& exemplifies_property(F,Y)
& object(Y) )
=> ? [U] :
( is_the(U,F)
& object(U) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f1_nnf,plain,
? [F] :
( ! [U] :
( ~ is_the(U,F)
| ~ object(U) )
& ? [Y] :
( ! [Z] :
( Z = Y
| ~ exemplifies_property(F,Z)
| ~ object(Z) )
& exemplifies_property(F,Y)
& object(Y) )
& property(F) ),
inference(nnf_transformation,[status(thm)],[f1_neg]) ).
fof(f1_sk,plain,
! [Z,U] :
( ( ~ is_the(U,sk2)
| ~ object(U) )
& ( Z = sk3
| ~ exemplifies_property(sk2,Z)
| ~ object(Z) )
& exemplifies_property(sk2,sk3)
& object(sk3)
& property(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f1_nnf]) ).
cnf(c10,plain,
property(sk2),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p46,plain,
( ~ exemplifies_property(X0,X2)
| sk1(sk2,X0,X1,X2) != X2
| ~ exemplifies_property(sk2,X2)
| ~ object(X2)
| is_the(X1,sk2)
| ~ object(X1)
| ~ property(X0) ),
inference(resolution,[status(thm)],[c6,c10]) ).
cnf(p98,plain,
( sk1(sk2,sk2,X0,X1) != X1
| ~ exemplifies_property(sk2,X1)
| ~ object(X1)
| is_the(X0,sk2)
| ~ object(X0)
| ~ property(sk2) ),
inference(factoring,[status(thm)],[p46]) ).
cnf(p100,plain,
( sk1(sk2,sk2,X0,X0) != X0
| ~ exemplifies_property(sk2,X0)
| is_the(X0,sk2)
| ~ object(X0)
| ~ property(sk2) ),
inference(factoring,[status(thm)],[p98]) ).
cnf(p102,plain,
( sk1(sk2,sk2,X0,X0) != X0
| ~ exemplifies_property(sk2,X0)
| is_the(X0,sk2)
| ~ object(X0) ),
inference(resolution,[status(thm)],[p100,c10]) ).
cnf(c11,plain,
object(sk3),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p104,plain,
( sk1(sk2,sk2,sk3,sk3) != sk3
| ~ exemplifies_property(sk2,sk3)
| is_the(sk3,sk2) ),
inference(resolution,[status(thm)],[p102,c11]) ).
cnf(c12,plain,
exemplifies_property(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p107,plain,
( sk1(sk2,sk2,sk3,sk3) != sk3
| is_the(sk3,sk2) ),
inference(resolution,[status(thm)],[p104,c12]) ).
cnf(c5,plain,
( ~ exemplifies_property(X1,X3)
| exemplifies_property(X0,sk1(X0,X1,X2,X3))
| ~ exemplifies_property(X0,X3)
| ~ object(X3)
| is_the(X2,X0)
| ~ object(X2)
| ~ property(X1)
| ~ property(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p38,plain,
( ~ exemplifies_property(X0,X2)
| exemplifies_property(sk2,sk1(sk2,X0,X1,X2))
| ~ exemplifies_property(sk2,X2)
| ~ object(X2)
| is_the(X1,sk2)
| ~ object(X1)
| ~ property(X0) ),
inference(resolution,[status(thm)],[c5,c10]) ).
cnf(p62,plain,
( exemplifies_property(sk2,sk1(sk2,sk2,X0,X1))
| ~ exemplifies_property(sk2,X1)
| ~ object(X1)
| is_the(X0,sk2)
| ~ object(X0)
| ~ property(sk2) ),
inference(factoring,[status(thm)],[p38]) ).
cnf(p64,plain,
( exemplifies_property(sk2,sk1(sk2,sk2,X0,X0))
| ~ exemplifies_property(sk2,X0)
| is_the(X0,sk2)
| ~ object(X0)
| ~ property(sk2) ),
inference(factoring,[status(thm)],[p62]) ).
cnf(p66,plain,
( exemplifies_property(sk2,sk1(sk2,sk2,X0,X0))
| ~ exemplifies_property(sk2,X0)
| is_the(X0,sk2)
| ~ object(X0) ),
inference(resolution,[status(thm)],[p64,c10]) ).
cnf(p67,plain,
( exemplifies_property(sk2,sk1(sk2,sk2,sk3,sk3))
| ~ exemplifies_property(sk2,sk3)
| is_the(sk3,sk2) ),
inference(resolution,[status(thm)],[p66,c11]) ).
cnf(p72,plain,
( exemplifies_property(sk2,sk1(sk2,sk2,sk3,sk3))
| is_the(sk3,sk2) ),
inference(resolution,[status(thm)],[p67,c12]) ).
cnf(c4,plain,
( ~ exemplifies_property(X1,X3)
| object(sk1(X0,X1,X2,X3))
| ~ exemplifies_property(X0,X3)
| ~ object(X3)
| is_the(X2,X0)
| ~ object(X2)
| ~ property(X1)
| ~ property(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p27,plain,
( ~ exemplifies_property(X0,X2)
| object(sk1(sk2,X0,X1,X2))
| ~ exemplifies_property(sk2,X2)
| ~ object(X2)
| is_the(X1,sk2)
| ~ object(X1)
| ~ property(X0) ),
inference(resolution,[status(thm)],[c4,c10]) ).
cnf(p29,plain,
( object(sk1(sk2,sk2,X0,X1))
| ~ exemplifies_property(sk2,X1)
| ~ object(X1)
| is_the(X0,sk2)
| ~ object(X0)
| ~ property(sk2) ),
inference(factoring,[status(thm)],[p27]) ).
cnf(p31,plain,
( object(sk1(sk2,sk2,X0,X0))
| ~ exemplifies_property(sk2,X0)
| is_the(X0,sk2)
| ~ object(X0)
| ~ property(sk2) ),
inference(factoring,[status(thm)],[p29]) ).
cnf(p33,plain,
( object(sk1(sk2,sk2,X0,X0))
| ~ exemplifies_property(sk2,X0)
| is_the(X0,sk2)
| ~ object(X0) ),
inference(resolution,[status(thm)],[p31,c10]) ).
cnf(p34,plain,
( object(sk1(sk2,sk2,sk3,sk3))
| ~ exemplifies_property(sk2,sk3)
| is_the(sk3,sk2) ),
inference(resolution,[status(thm)],[p33,c11]) ).
cnf(p39,plain,
( object(sk1(sk2,sk2,sk3,sk3))
| is_the(sk3,sk2) ),
inference(resolution,[status(thm)],[p34,c12]) ).
cnf(c13,plain,
( X2 = sk3
| ~ exemplifies_property(sk2,X2)
| ~ object(X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p41,plain,
( sk1(sk2,sk2,sk3,sk3) = sk3
| ~ exemplifies_property(sk2,sk1(sk2,sk2,sk3,sk3))
| is_the(sk3,sk2) ),
inference(resolution,[status(thm)],[p39,c13]) ).
cnf(p73,plain,
( sk1(sk2,sk2,sk3,sk3) = sk3
| is_the(sk3,sk2)
| is_the(sk3,sk2) ),
inference(resolution,[status(thm)],[p72,p41]) ).
cnf(p75,plain,
( sk1(sk2,sk2,sk3,sk3) = sk3
| is_the(sk3,sk2) ),
inference(factoring,[status(thm)],[p73]) ).
cnf(p108,plain,
( is_the(sk3,sk2)
| is_the(sk3,sk2) ),
inference(resolution,[status(thm)],[p107,p75]) ).
cnf(p109,plain,
is_the(sk3,sk2),
inference(factoring,[status(thm)],[p108]) ).
cnf(c14,plain,
( ~ is_the(X3,sk2)
| ~ object(X3) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p15,plain,
~ is_the(sk3,sk2),
inference(resolution,[status(thm)],[c14,c11]) ).
cnf(p112,plain,
$false,
inference(resolution,[status(thm)],[p109,p15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI009+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.35 % Computer : n013.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 06:05:21 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.59/0.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.59/0.78 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------