%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG224+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 11:49:01 AM UTC 2026
% Result : Theorem 0.12s 0.50s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of formulae : 52 ( 10 unt; 0 def)
% Number of atoms : 240 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 357 ( 169 ~; 148 |; 24 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-5 aty)
% Number of variables : 112 ( 104 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k1_closure2(A,B)))
=> ( ( r2_closure3(A,B,D,E)
& r2_closure3(A,B,C,D) )
=> r2_closure3(A,B,C,E) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k1_closure2(A,B)))
=> ( ( r2_closure3(A,B,D,E)
& r2_closure3(A,B,C,D) )
=> r2_closure3(A,B,C,E) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B)))
=> ( r2_closure3(A,B,C,D)
<=> ! [E] :
~ ( ! [F] :
~ ( r1_tarski(F,E)
& r2_hidden(F,D) )
& r2_hidden(E,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B,C] :
( ( r1_tarski(B,C)
& r1_tarski(A,B) )
=> r1_tarski(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,plain,
? [A,B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ r2_closure3(A,B,C,E)
& r2_closure3(A,B,D,E)
& r2_closure3(A,B,C,D)
& m1_subset_1(E,k1_zfmisc_1(k1_closure2(A,B))) )
& m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) )
& m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
& m1_pboole(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f45,plain,
( ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,sK4_skl)
& r2_closure3(sK0_skl,sK1_skl,sK3_skl,sK4_skl)
& r2_closure3(sK0_skl,sK1_skl,sK2_skl,sK3_skl)
& m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
& m1_subset_1(sK3_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
& m1_subset_1(sK2_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
& m1_pboole(sK1_skl,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(D,sK3_skl),skolemize(E,sK4_skl)],[f44]) ).
fof(f46,plain,
m1_pboole(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
m1_subset_1(sK2_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
m1_subset_1(sK3_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,plain,
m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f50,plain,
r2_closure3(sK0_skl,sK1_skl,sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f51,plain,
r2_closure3(sK0_skl,sK1_skl,sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f52,plain,
~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f67,plain,
! [A,B] :
( ! [C] :
( ! [D] :
( ( r2_closure3(A,B,C,D)
<=> ! [E] :
( ? [F] :
( r1_tarski(F,E)
& r2_hidden(F,D) )
| ~ r2_hidden(E,C) ) )
| ~ m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) )
| ~ m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
| ~ m1_pboole(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f68,plain,
! [A,B] :
( ! [C] :
( ! [D] :
( ( ( ? [E] :
( ! [F] :
( ~ r1_tarski(F,E)
| ~ r2_hidden(F,D) )
& r2_hidden(E,C) )
| r2_closure3(A,B,C,D) )
& ( ! [E] :
( ? [F] :
( r1_tarski(F,E)
& r2_hidden(F,D) )
| ~ r2_hidden(E,C) )
| ~ r2_closure3(A,B,C,D) ) )
| ~ m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) )
| ~ m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
| ~ m1_pboole(B,A) ),
inference(NNF_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [A,B] :
( ! [C] :
( ! [D] :
( ( ( ( ! [F] :
( ~ r1_tarski(F,sK6_skl(D,C,B,A))
| ~ r2_hidden(F,D) )
& r2_hidden(sK6_skl(D,C,B,A),C) )
| r2_closure3(A,B,C,D) )
& ( ! [E] :
( ( r1_tarski(sK5_skl(E,D,C,B,A),E)
& r2_hidden(sK5_skl(E,D,C,B,A),D) )
| ~ r2_hidden(E,C) )
| ~ r2_closure3(A,B,C,D) ) )
| ~ m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) )
| ~ m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
| ~ m1_pboole(B,A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(F,sK5_skl(E,D,C,B,A)),skolemize(E,sK6_skl(D,C,B,A))],[f68]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4] :
( r2_hidden(sK5_skl(X4,X3,X2,X0,X1),X3)
| ~ r2_hidden(X4,X2)
| ~ r2_closure3(X1,X0,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X1,X0)))
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( r1_tarski(sK5_skl(X4,X3,X2,X0,X1),X4)
| ~ r2_hidden(X4,X2)
| ~ r2_closure3(X1,X0,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X1,X0)))
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( r2_hidden(sK6_skl(X3,X2,X0,X1),X2)
| r2_closure3(X1,X0,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X1,X0)))
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4] :
( ~ r1_tarski(X4,sK6_skl(X3,X2,X0,X1))
| ~ r2_hidden(X4,X3)
| r2_closure3(X1,X0,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X1,X0)))
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f152,plain,
! [A,B,C] :
( r1_tarski(A,C)
| ~ r1_tarski(B,C)
| ~ r1_tarski(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f153,plain,
! [A,C] :
( r1_tarski(A,C)
| ! [B] :
( ~ r1_tarski(B,C)
| ~ r1_tarski(A,B) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,plain,
! [X0,X1,X2] :
( r1_tarski(X0,X2)
| ~ r1_tarski(X1,X2)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f190,plain,
! [X0,X1] :
( r2_hidden(sK6_skl(X1,X0,sK1_skl,sK0_skl),X0)
| r2_closure3(sK0_skl,sK1_skl,X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f72,f46]) ).
fof(f191,plain,
! [X0,X1,X2] :
( ~ r1_tarski(X2,sK6_skl(X1,X0,sK1_skl,sK0_skl))
| ~ r2_hidden(X2,X1)
| r2_closure3(sK0_skl,sK1_skl,X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f73,f46]) ).
fof(f192,plain,
( r2_hidden(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),sK2_skl)
| ~ m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f190,f52]) ).
fof(f193,plain,
( r2_hidden(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),sK2_skl)
| ~ m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f47]) ).
fof(f194,plain,
r2_hidden(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f193,f49]) ).
fof(f195,plain,
! [X0,X1,X2] :
( r2_hidden(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X2,sK2_skl,X0,X1),X2)
| ~ r2_closure3(X1,X0,sK2_skl,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X1,X0)))
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(k1_closure2(X1,X0)))
| ~ m1_pboole(X0,X1) ),
inference(resolution,[status(thm)],[f194,f70]) ).
fof(f198,plain,
! [X0] :
( ~ r1_tarski(X0,sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl))
| ~ r2_hidden(X0,sK4_skl)
| ~ m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f191,f52]) ).
fof(f199,plain,
! [X0] :
( ~ r1_tarski(X0,sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl))
| ~ r2_hidden(X0,sK4_skl)
| ~ m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f47]) ).
fof(f200,plain,
! [X0] :
( ~ r1_tarski(X0,sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl))
| ~ r2_hidden(X0,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f199,f49]) ).
fof(f203,plain,
! [X0] :
( r2_hidden(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),X0)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f195,f46]) ).
fof(f204,plain,
! [X0] :
( r2_hidden(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),X0)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f47]) ).
fof(f207,plain,
! [X0,X1,X2,X3] :
( r2_hidden(sK5_skl(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),X3,X0,X1,X2),X3)
| ~ r2_closure3(X2,X1,X0,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X2,X1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(X2,X1)))
| ~ m1_pboole(X1,X2)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f204,f70]) ).
fof(f209,plain,
! [X0,X1] :
( r2_hidden(sK5_skl(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),X1,X0,sK1_skl,sK0_skl),X1)
| ~ r2_closure3(sK0_skl,sK1_skl,X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f207,f46]) ).
fof(f210,plain,
! [X0,X1] :
( r2_hidden(sK5_skl(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),X1,X0,sK1_skl,sK0_skl),X1)
| ~ r2_closure3(sK0_skl,sK1_skl,X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f209]) ).
fof(f212,plain,
! [X0] :
( ~ r1_tarski(sK5_skl(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),sK4_skl,X0,sK1_skl,sK0_skl),sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl))
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f210,f200]) ).
fof(f215,plain,
! [X0] :
( ~ r1_tarski(sK5_skl(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),sK4_skl,X0,sK1_skl,sK0_skl),sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl))
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f212,f49]) ).
fof(f216,plain,
! [X0,X1] :
( ~ r1_tarski(X1,sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl))
| ~ r1_tarski(sK5_skl(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),sK4_skl,X0,sK1_skl,sK0_skl),X1)
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f215,f154]) ).
fof(f221,plain,
! [X0,X1,X2,X3,X4] :
( ~ r2_hidden(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X2)
| ~ r2_closure3(X4,X3,X2,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_closure2(X4,X3)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X4,X3)))
| ~ m1_pboole(X3,X4)
| ~ r1_tarski(sK5_skl(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),sK4_skl,X0,sK1_skl,sK0_skl),sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X1,X2,X3,X4))
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f216,f71]) ).
fof(f229,plain,
! [X0,X1,X2] :
( ~ r2_hidden(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X2)
| ~ r2_closure3(sK0_skl,sK1_skl,X2,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ r1_tarski(sK5_skl(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),sK4_skl,X0,sK1_skl,sK0_skl),sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X1,X2,sK1_skl,sK0_skl))
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f221,f46]) ).
fof(f307,plain,
! [X0] :
( ~ r2_hidden(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),X0)
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_pboole(sK1_skl,sK0_skl)
| ~ r2_hidden(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),sK2_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f229,f71]) ).
fof(f309,plain,
! [X0] :
( ~ r2_hidden(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),X0)
| ~ m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_pboole(sK1_skl,sK0_skl)
| ~ r2_hidden(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),sK2_skl)
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f307]) ).
fof(f310,plain,
! [X0] :
( ~ r2_hidden(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),X0)
| ~ m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_pboole(sK1_skl,sK0_skl)
| ~ r2_hidden(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),sK2_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f309,f47]) ).
fof(f311,plain,
! [X0] :
( ~ r2_hidden(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),X0)
| ~ m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ m1_pboole(sK1_skl,sK0_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f194]) ).
fof(f312,plain,
! [X0] :
( ~ r2_hidden(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),X0)
| ~ m1_subset_1(sK4_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl)))
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f311,f46]) ).
fof(f313,plain,
! [X0] :
( ~ r2_hidden(sK5_skl(sK6_skl(sK4_skl,sK2_skl,sK1_skl,sK0_skl),X0,sK2_skl,sK1_skl,sK0_skl),X0)
| ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f49]) ).
fof(f317,plain,
! [X0] :
( ~ r2_closure3(sK0_skl,sK1_skl,X0,sK4_skl)
| ~ r2_closure3(sK0_skl,sK1_skl,sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f204]) ).
fof(f318,plain,
( ~ r2_closure3(sK0_skl,sK1_skl,sK3_skl,sK4_skl)
| ~ m1_subset_1(sK3_skl,k1_zfmisc_1(k1_closure2(sK0_skl,sK1_skl))) ),
inference(resolution,[status(thm)],[f317,f50]) ).
fof(f322,plain,
~ r2_closure3(sK0_skl,sK1_skl,sK3_skl,sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f318,f48]) ).
fof(f328,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f322,f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG224+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 13:05:20 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.50 % Refutation found
% 0.12/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.53 % Elapsed time: 0.151379 seconds
% 0.12/0.53 % CPU time: 0.960253 seconds
% 0.12/0.53 % Total memory used: 103.705 MB
% 0.12/0.53 % Net memory used: 101.259 MB
%------------------------------------------------------------------------------