%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PHI009+1 : TPTP v9.3.1. Released v7.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 : Thu Sep 24 01:58:03 PM UTC 2026
% Result : Theorem 0.10s 0.59s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 8 unt; 7 def)
% Number of atoms : 293 ( 21 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 420 ( 180 ~; 182 |; 38 &)
% ( 9 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 86 ( 76 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox/benchmark/theBenchmark.p') ).
fof(f2,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/sandbox/benchmark/theBenchmark.p') ).
fof(f3,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)],[f2]) ).
fof(f4,plain,
! [F,G,X] :
( ( ( 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) ) )
| ~ object(X)
| ~ property(G)
| ~ property(F) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f5,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)],[f4]) ).
fof(f6,plain,
! [F,G,X] :
( ( ( ! [Y] :
( ~ exemplifies_property(G,Y)
| ( sK1_skl(Y,X,G,F) != Y
& exemplifies_property(F,sK1_skl(Y,X,G,F))
& object(sK1_skl(Y,X,G,F)) )
| ~ exemplifies_property(F,Y)
| ~ object(Y) )
| ( exemplifies_property(G,X)
& is_the(X,F) ) )
& ( ( exemplifies_property(G,sK0_skl(X,G,F))
& ! [Z] :
( Z = sK0_skl(X,G,F)
| ~ exemplifies_property(F,Z)
| ~ object(Z) )
& exemplifies_property(F,sK0_skl(X,G,F))
& object(sK0_skl(X,G,F)) )
| ~ exemplifies_property(G,X)
| ~ is_the(X,F) ) )
| ~ object(X)
| ~ property(G)
| ~ property(F) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl(X,G,F)),skolemize(Z,sK1_skl(Y,X,G,F))],[f5]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( ~ exemplifies_property(X1,X3)
| object(sK1_skl(X3,X2,X1,X0))
| ~ exemplifies_property(X0,X3)
| ~ object(X3)
| is_the(X2,X0)
| ~ object(X2)
| ~ property(X1)
| ~ property(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( ~ exemplifies_property(X1,X3)
| exemplifies_property(X0,sK1_skl(X3,X2,X1,X0))
| ~ exemplifies_property(X0,X3)
| ~ object(X3)
| is_the(X2,X0)
| ~ object(X2)
| ~ property(X1)
| ~ property(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( ~ exemplifies_property(X1,X3)
| sK1_skl(X3,X2,X1,X0) != X3
| ~ exemplifies_property(X0,X3)
| ~ object(X3)
| is_the(X2,X0)
| ~ object(X2)
| ~ property(X1)
| ~ property(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,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(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
( ! [U] :
( ~ is_the(U,sK2_skl)
| ~ object(U) )
& ! [Z] :
( Z = sK3_skl
| ~ exemplifies_property(sK2_skl,Z)
| ~ object(Z) )
& exemplifies_property(sK2_skl,sK3_skl)
& object(sK3_skl)
& property(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(F,sK2_skl),skolemize(Y,sK3_skl)],[f17]) ).
fof(f19,plain,
property(sK2_skl),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
object(sK3_skl),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
exemplifies_property(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,plain,
! [X0] :
( X0 = sK3_skl
| ~ exemplifies_property(sK2_skl,X0)
| ~ object(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f23,plain,
! [X0] :
( ~ is_the(X0,sK2_skl)
| ~ object(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f25,definition,
( sQ0_spl
<=> object(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( sQ0_spl
| ~ object(sK3_skl) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f32,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f20]) ).
fof(f33,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f32]) ).
fof(f35,definition,
( sQ2_spl
<=> property(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( sQ2_spl
| ~ property(sK2_skl) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f42,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f19]) ).
fof(f43,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f42]) ).
fof(f59,plain,
! [X0,X1,X2] :
( sK1_skl(X2,X1,X0,sK2_skl) = sK3_skl
| ~ object(sK1_skl(X2,X1,X0,sK2_skl))
| ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| is_the(X1,sK2_skl)
| ~ object(X1)
| ~ property(X0)
| ~ property(sK2_skl) ),
inference(resolution,[status(thm)],[f12,f22]) ).
fof(f60,definition,
! [X0,X1,X2] :
( sQ6_spl
<=> ( sK1_skl(X2,X1,X0,sK2_skl) = sK3_skl
| ~ object(sK1_skl(X2,X1,X0,sK2_skl))
| ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| is_the(X1,sK2_skl)
| ~ object(X1)
| ~ property(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| sK1_skl(X2,X1,X0,sK2_skl) = sK3_skl
| ~ object(sK1_skl(X2,X1,X0,sK2_skl))
| ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| is_the(X1,sK2_skl)
| ~ object(X1)
| ~ property(X0) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f59,f35,f60]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| sK1_skl(X2,X1,X0,sK2_skl) = sK3_skl
| ~ object(sK1_skl(X2,X1,X0,sK2_skl))
| ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| ~ object(X1)
| ~ property(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f23]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| is_the(X1,sK2_skl)
| ~ object(X1)
| ~ property(X0)
| ~ property(sK2_skl)
| sK1_skl(X2,X1,X0,sK2_skl) = sK3_skl
| ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| ~ object(X1)
| ~ property(X0) ),
inference(resolution,[status(thm)],[f64,f11]) ).
fof(f71,definition,
! [X0,X1,X2] :
( sQ8_spl
<=> ( ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| is_the(X1,sK2_skl)
| ~ object(X1)
| ~ property(X0)
| sK1_skl(X2,X1,X0,sK2_skl) = sK3_skl
| ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| ~ object(X1)
| ~ property(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| is_the(X1,sK2_skl)
| ~ object(X1)
| ~ property(X0)
| sK1_skl(X2,X1,X0,sK2_skl) = sK3_skl
| ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| ~ object(X1)
| ~ property(X0) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f66,f71,f35,f60]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| is_the(X1,sK2_skl)
| sK1_skl(X2,X1,X0,sK2_skl) = sK3_skl
| ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| ~ object(X1)
| ~ property(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f72]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| sK1_skl(X2,X1,X0,sK2_skl) = sK3_skl
| ~ exemplifies_property(X0,X2)
| ~ exemplifies_property(sK2_skl,X2)
| ~ object(X2)
| ~ object(X1)
| ~ property(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f23]) ).
fof(f79,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ exemplifies_property(X0,sK3_skl)
| ~ exemplifies_property(sK2_skl,sK3_skl)
| ~ object(sK3_skl)
| is_the(X1,sK2_skl)
| ~ object(X1)
| ~ property(X0)
| ~ property(sK2_skl)
| ~ exemplifies_property(X0,sK3_skl)
| ~ exemplifies_property(sK2_skl,sK3_skl)
| ~ object(sK3_skl)
| ~ object(X1)
| ~ property(X0) ),
inference(resolution,[status(thm)],[f77,f13]) ).
fof(f83,definition,
( sQ10_spl
<=> exemplifies_property(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( sQ10_spl
| ~ exemplifies_property(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f87,definition,
! [X0] :
( sQ11_spl
<=> ( ~ exemplifies_property(X0,sK3_skl)
| ~ property(X0)
| ~ exemplifies_property(X0,sK3_skl)
| ~ property(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f88,plain,
! [X0] :
( ~ sQ11_spl
| ~ exemplifies_property(X0,sK3_skl)
| ~ property(X0)
| ~ exemplifies_property(X0,sK3_skl)
| ~ property(X0) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,definition,
! [X1] :
( sQ12_spl
<=> ( is_the(X1,sK2_skl)
| ~ object(X1)
| ~ object(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f91,plain,
! [X0] :
( ~ sQ12_spl
| is_the(X0,sK2_skl)
| ~ object(X0)
| ~ object(X0) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f87,f90,f25,f83,f35,f71]) ).
fof(f94,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f21]) ).
fof(f95,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f97,plain,
! [X0] :
( ~ sQ11_spl
| ~ exemplifies_property(X0,sK3_skl)
| ~ property(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f88]) ).
fof(f98,plain,
( ~ sQ11_spl
| ~ property(sK2_skl) ),
inference(resolution,[status(thm)],[f97,f21]) ).
fof(f99,plain,
( ~ sQ11_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f98,f35,f87]) ).
fof(f100,plain,
! [X0] :
( ~ sQ12_spl
| is_the(X0,sK2_skl)
| ~ object(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f91]) ).
fof(f101,plain,
! [X0] :
( ~ sQ12_spl
| ~ object(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f23]) ).
fof(f107,plain,
( ~ sQ12_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f20,f101]) ).
fof(f108,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f107]) ).
fof(f109,plain,
$false,
inference(sat_refutation,[status(thm)],[f33,f43,f63,f74,f93,f95,f99,f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI009+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n016.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Mon Sep 21 03:34:40 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.58 % Drodi V4.1.1
% 0.10/0.59 % Refutation found
% 0.10/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.61 % Elapsed time: 0.040906 seconds
% 0.10/0.61 % CPU time: 0.111229 seconds
% 0.10/0.61 % Total memory used: 52.877 MB
% 0.10/0.61 % Net memory used: 52.605 MB
%------------------------------------------------------------------------------