%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL672+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 : Thu Sep 24 01:08:30 PM UTC 2026
% Result : Theorem 0.22s 5.51s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 13 unt; 6 def)
% Number of atoms : 443 ( 0 equ)
% Maximal formula atoms : 49 ( 8 avg)
% Number of connectives : 704 ( 315 ~; 292 |; 90 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 233 ( 198 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : r1(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] :
( ( r1(Y,Z)
& r1(X,Y) )
=> r1(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
~ ? [X] :
~ ( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( p1(X)
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
| ( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ! [X] :
( $false
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
| ( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ( ~ ! [X] :
( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ! [Y] :
( ~ ! [X] :
( p1(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
| ( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& ~ ! [Y] :
( ! [X] :
( ~ ( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ! [X] :
( p1(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
| ( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ( p1(Y)
& ~ ! [X] :
( ~ ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( p1(X)
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
| ( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ! [X] :
( $false
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
| ( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ( ~ ! [X] :
( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ! [Y] :
( ~ ! [X] :
( p1(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
| ( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& ~ ! [Y] :
( ! [X] :
( ~ ( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ! [X] :
( p1(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
| ( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ( p1(Y)
& ~ ! [X] :
( ~ ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X,Y,Z] :
( r1(X,Z)
| ~ r1(Y,Z)
| ~ r1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X,Z] :
( r1(X,Z)
| ! [Y] :
( ~ r1(Y,Z)
| ~ r1(X,Y) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( r1(X0,X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
? [X] :
( ? [Y] :
( ~ p1(Y)
& r1(X,Y) )
& ? [Y] :
( ? [X] :
( ~ p1(X)
& r1(Y,X) )
& ? [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& ? [Y] :
( ~ p2(Y)
& r1(X,Y) )
& ( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ? [X] :
( $true
& r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ? [Y] :
( ~ p1(Y)
& r1(X,Y) )
| ~ r1(Y,X) )
| ! [X] :
( ? [Y] :
( ! [X] :
( p1(X)
| ~ r1(Y,X) )
& r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ? [X] :
( ~ p1(X)
& r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ~ p1(Y)
| ! [X] :
( ? [Y] :
( p1(Y)
& r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
? [X] :
( ? [Y] :
( ~ p1(Y)
& r1(X,Y) )
& ? [Y] :
( ? [X] :
( ~ p1(X)
& r1(Y,X) )
& ? [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& ? [Y] :
( ~ p2(Y)
& r1(X,Y) )
& ( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ( $true
& ? [X] : r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ? [Y] :
( ~ p1(Y)
& r1(X,Y) )
| ~ r1(Y,X) )
| ! [X] :
( ? [Y] :
( ! [X] :
( p1(X)
| ~ r1(Y,X) )
& r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ? [X] :
( ~ p1(X)
& r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ~ p1(Y)
| ! [X] :
( ? [Y] :
( p1(Y)
& r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f11,plain,
( ~ p1(sK10_skl)
& r1(sK0_skl,sK10_skl)
& ~ p1(sK9_skl)
& r1(sK7_skl,sK9_skl)
& ! [Y] :
( p1(Y)
| ~ r1(sK8_skl,Y) )
& r1(sK7_skl,sK8_skl)
& r1(sK0_skl,sK7_skl)
& ~ p2(sK6_skl)
& r1(sK0_skl,sK6_skl)
& ( ! [Y] :
( p1(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( ( $true
& r1(Y,sK5_skl(Y)) )
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( ! [X] :
( ( ~ p1(sK4_skl(X,Y))
& r1(X,sK4_skl(X,Y)) )
| ~ r1(Y,X) )
| ! [X] :
( ( ! [X] :
( p1(X)
| ~ r1(sK3_skl(X,Y),X) )
& r1(X,sK3_skl(X,Y)) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ( ~ p1(sK2_skl(Y,X,Y))
& r1(Y,sK2_skl(Y,X,Y)) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( ~ p1(Y)
| ! [X] :
( ( p1(sK1_skl(X,Y))
& r1(X,sK1_skl(X,Y)) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(sK0_skl,Y) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl,sK9_skl,sK10_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl(X,Y)),skolemize(X,sK2_skl(Y,X,Y)),skolemize(Y,sK3_skl(X,Y)),skolemize(Y,sK4_skl(X,Y)),skolemize(X,sK5_skl(Y)),skolemize(Y,sK6_skl),skolemize(Y,sK7_skl),skolemize(X,sK8_skl),skolemize(X,sK9_skl),skolemize(Y,sK10_skl)],[f10]) ).
fof(f12,plain,
? [X] :
( ? [Y] :
( ~ p1(sK10_skl)
& r1(sK0_skl,sK10_skl) )
& ? [Y] :
( ? [X] :
( ~ p1(sK9_skl)
& r1(sK7_skl,sK9_skl) )
& ? [X] :
( ! [Y] :
( p1(Y)
| ~ r1(sK8_skl,Y) )
& r1(sK7_skl,sK8_skl) )
& r1(sK0_skl,sK7_skl) )
& ? [Y] :
( ~ p2(sK6_skl)
& r1(sK0_skl,sK6_skl) )
& ( ! [Y] :
( p1(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( ? [X] : r1(Y,sK5_skl(Y))
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( ! [X] :
( ? [Y] :
( ~ p1(sK4_skl(X,Y))
& r1(X,sK4_skl(X,Y)) )
| ~ r1(Y,X) )
| ! [X] :
( ? [Y] :
( ! [X] :
( p1(X)
| ~ r1(sK3_skl(X,Y),X) )
& r1(X,sK3_skl(X,Y)) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ? [X] :
( ~ p1(sK2_skl(Y,X,Y))
& r1(Y,sK2_skl(Y,X,Y)) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ! [Y] :
( p1(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( ~ p1(Y)
| ! [X] :
( ? [Y] :
( p1(sK1_skl(X,Y))
& r1(X,sK1_skl(X,Y)) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(sK0_skl,Y) ) ) ),
inference(true_and_false_simplification,[status(thm)],[f11]) ).
fof(f15,plain,
! [X0,X1,X2,X3,X4,X5] :
( p1(X5)
| ~ r1(sK0_skl,X5)
| p1(X4)
| ~ r1(X2,X4)
| r1(X3,sK2_skl(X3,X2,X1))
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(sK0_skl,X1)
| p2(X0)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,plain,
! [X0,X1,X2,X3,X4,X5] :
( p1(X5)
| ~ r1(sK0_skl,X5)
| p1(X4)
| ~ r1(X2,X4)
| ~ p1(sK2_skl(X3,X2,X1))
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(sK0_skl,X1)
| p2(X0)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f22,plain,
r1(sK0_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f23,plain,
~ p2(sK6_skl),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f24,plain,
r1(sK0_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f25,plain,
r1(sK7_skl,sK8_skl),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f26,plain,
! [X0] :
( p1(X0)
| ~ r1(sK8_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
r1(sK0_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
~ p1(sK10_skl),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f31,definition,
! [X0] :
( sQ0_spl
<=> ( p2(X0)
| ~ r1(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f32,plain,
! [X0] :
( ~ sQ0_spl
| p2(X0)
| ~ r1(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f37,definition,
! [X3] :
( sQ2_spl
<=> ( p1(X3)
| ~ r1(sK0_skl,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f38,plain,
! [X0] :
( ~ sQ2_spl
| p1(X0)
| ~ r1(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f45,definition,
! [X1,X2,X3,X4] :
( sQ4_spl
<=> ( p1(X4)
| ~ r1(X2,X4)
| r1(X3,sK2_skl(X3,X2,X1))
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(sK0_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| p1(X3)
| ~ r1(X1,X3)
| r1(X2,sK2_skl(X2,X1,X0))
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( sQ2_spl
| sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f15,f31,f45,f37]) ).
fof(f49,definition,
! [X1,X2,X3,X4] :
( sQ5_spl
<=> ( p1(X4)
| ~ r1(X2,X4)
| ~ p1(sK2_skl(X3,X2,X1))
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(sK0_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ~ sQ5_spl
| p1(X3)
| ~ r1(X1,X3)
| ~ p1(sK2_skl(X2,X1,X0))
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( sQ2_spl
| sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f31,f49,f37]) ).
fof(f74,plain,
( ~ sQ2_spl
| ~ r1(sK0_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f38,f30]) ).
fof(f76,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f29]) ).
fof(f77,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f78,plain,
( ~ sQ0_spl
| ~ r1(sK0_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f32,f23]) ).
fof(f79,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f22]) ).
fof(f80,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f82,definition,
( sQ11_spl
<=> r1(sK0_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ11_spl
| r1(sK0_skl,sK8_skl) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f84,plain,
( sQ11_spl
| ~ r1(sK0_skl,sK8_skl) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f89,plain,
! [X0] :
( sQ11_spl
| ~ r1(X0,sK8_skl)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f8,f84]) ).
fof(f91,plain,
( sQ11_spl
| ~ r1(sK0_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f89,f25]) ).
fof(f94,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f24]) ).
fof(f95,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| p1(sK2_skl(sK8_skl,X1,X0))
| p1(X2)
| ~ r1(X1,X2)
| ~ r1(X1,sK8_skl)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f46,f26]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ sQ5_spl
| p1(X2)
| ~ r1(X1,X2)
| ~ r1(X1,sK8_skl)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f50]) ).
fof(f148,plain,
! [X0,X1] :
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ5_spl
| p1(X1)
| ~ r1(sK0_skl,X1)
| ~ r1(X0,sK0_skl)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f142,f83]) ).
fof(f158,definition,
! [X0] :
( sQ15_spl
<=> ( ~ r1(X0,sK0_skl)
| ~ r1(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f159,plain,
! [X0] :
( ~ sQ15_spl
| ~ r1(X0,sK0_skl)
| ~ r1(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f148,f158,f37,f49,f45,f82]) ).
fof(f170,plain,
( ~ sQ15_spl
| ~ r1(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f159,f5]) ).
fof(f171,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f5]) ).
fof(f172,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f173,plain,
$false,
inference(sat_refutation,[status(thm)],[f48,f52,f77,f80,f95,f161,f172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL672+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.46 % Computer : n001.cluster.edu
% 0.17/5.46 % Model : x86_64 x86_64
% 0.17/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.46 % Memory : 8046.5625MB
% 0.17/5.46 % OS : Linux 6.8.0-71-generic
% 0.17/5.46 % CPULimit : 300
% 0.17/5.46 % WCLimit : 300
% 0.17/5.46 % DateTime : Mon Sep 21 00:58:33 UTC 2026
% 0.17/5.47 % CPUTime :
% 0.17/5.48 % Drodi V4.1.1
% 0.22/5.51 % Refutation found
% 0.22/5.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/5.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/5.55 % Elapsed time: 0.060553 seconds
% 0.22/5.55 % CPU time: 0.212944 seconds
% 0.22/5.55 % Total memory used: 18.157 MB
% 0.22/5.55 % Net memory used: 17.786 MB
%------------------------------------------------------------------------------