%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM403+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 01:40:26 PM UTC 2026
% Result : Theorem 90.69s 16.98s
% Output : CNFRefutation 65.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 5 unt; 0 def)
% Number of atoms : 210 ( 8 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 253 ( 97 ~; 100 |; 37 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 120 ( 109 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,succ(B))
<=> ordinal_subset(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A] :
( ! [B] :
( in(B,A)
=> ordinal(B) )
=> ordinal(union(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
! [A] :
~ ( ! [B] :
( ordinal(B)
=> ~ subset(A,B) )
& ! [B] :
( in(B,A)
=> ordinal(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
~ ! [A] :
~ ( ! [B] :
( ordinal(B)
=> ~ subset(A,B) )
& ! [B] :
( in(B,A)
=> ordinal(B) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f78,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f79,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f79]) ).
fof(f81,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f80]) ).
fof(f83,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f84,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f85,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ( ! [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f86,plain,
( ! [A,B] :
( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(miniscoping,[status(thm)],[f85]) ).
fof(f87,plain,
( ! [A,B] :
( ( ( ( in(sK3_skl(B,A),A)
& in(sK2_skl(B,A),sK3_skl(B,A)) )
| in(sK2_skl(B,A),B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(sK2_skl(B,A),D) )
| ~ in(sK2_skl(B,A),B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ( in(sK1_skl(C,B,A),A)
& in(C,sK1_skl(C,B,A)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f86]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| ~ in(X2,X3)
| in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f114,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f118,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f179,plain,
! [A,B] :
( ( ordinal_subset(A,B)
<=> subset(A,B) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f180,plain,
! [A,B] :
( ( ( ~ subset(A,B)
| ordinal_subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f179]) ).
fof(f182,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f195,plain,
! [A] :
( ! [B] :
( ( in(A,succ(B))
<=> ordinal_subset(A,B) )
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f196,plain,
! [A] :
( ! [B] :
( ( ( ~ ordinal_subset(A,B)
| in(A,succ(B)) )
& ( ordinal_subset(A,B)
| ~ in(A,succ(B)) ) )
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f195]) ).
fof(f198,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| in(X0,succ(X1))
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f199,plain,
! [A] :
( ordinal(union(A))
| ? [B] :
( ~ ordinal(B)
& in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f200,plain,
! [A] :
( ordinal(union(A))
| ( ~ ordinal(sK18_skl(A))
& in(sK18_skl(A),A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(B,sK18_skl(A))],[f199]) ).
fof(f201,plain,
! [X0] :
( ordinal(union(X0))
| in(sK18_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f202,plain,
! [X0] :
( ordinal(union(X0))
| ~ ordinal(sK18_skl(X0)) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f203,plain,
? [A] :
( ! [B] :
( ~ subset(A,B)
| ~ ordinal(B) )
& ! [B] :
( ordinal(B)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f204,plain,
( ! [B] :
( ~ subset(sK19_skl,B)
| ~ ordinal(B) )
& ! [B] :
( ordinal(B)
| ~ in(B,sK19_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(A,sK19_skl)],[f203]) ).
fof(f205,plain,
! [X0] :
( ordinal(X0)
| ~ in(X0,sK19_skl) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f206,plain,
! [X0] :
( ~ subset(sK19_skl,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f228,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(X0,X2)
| in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f90]) ).
fof(f298,plain,
! [X0] :
( ordinal(sK0_skl(X0,sK19_skl))
| subset(sK19_skl,X0) ),
inference(resolution,[status(thm)],[f83,f205]) ).
fof(f369,plain,
( ordinal(sK18_skl(sK19_skl))
| ordinal(union(sK19_skl)) ),
inference(resolution,[status(thm)],[f201,f205]) ).
fof(f372,plain,
ordinal(union(sK19_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f369,f202]) ).
fof(f382,plain,
! [X0,X1,X2] :
( subset(X1,X2)
| ~ in(X0,sK0_skl(X2,X1))
| in(X0,union(X1)) ),
inference(resolution,[status(thm)],[f228,f83]) ).
fof(f813,plain,
! [X0,X1] :
( subset(X1,succ(X0))
| ~ ordinal_subset(sK0_skl(succ(X0),X1),X0)
| ~ ordinal(X0)
| ~ ordinal(sK0_skl(succ(X0),X1)) ),
inference(resolution,[status(thm)],[f198,f84]) ).
fof(f1082,plain,
! [X0,X1,X2] :
( subset(sK0_skl(X1,X2),X0)
| subset(X2,X1)
| in(sK0_skl(X0,sK0_skl(X1,X2)),union(X2)) ),
inference(resolution,[status(thm)],[f382,f83]) ).
fof(f4921,plain,
! [X0] :
( subset(sK19_skl,succ(X0))
| subset(sK19_skl,succ(X0))
| ~ ordinal_subset(sK0_skl(succ(X0),sK19_skl),X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f813,f298]) ).
fof(f4924,plain,
! [X0] :
( subset(sK19_skl,succ(X0))
| ~ ordinal_subset(sK0_skl(succ(X0),sK19_skl),X0)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4921]) ).
fof(f4930,plain,
! [X0] :
( ~ subset(sK0_skl(succ(X0),sK19_skl),X0)
| ~ ordinal(X0)
| ~ ordinal(sK0_skl(succ(X0),sK19_skl))
| subset(sK19_skl,succ(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f4924,f182]) ).
fof(f4940,plain,
! [X0] :
( ~ subset(sK0_skl(succ(X0),sK19_skl),X0)
| ~ ordinal(sK0_skl(succ(X0),sK19_skl))
| subset(sK19_skl,succ(X0))
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4930]) ).
fof(f4941,plain,
! [X0] :
( ~ subset(sK0_skl(succ(X0),sK19_skl),X0)
| subset(sK19_skl,succ(X0))
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4940,f298]) ).
fof(f8556,plain,
! [X0,X1] :
( subset(sK0_skl(X1,X0),union(X0))
| subset(sK0_skl(X1,X0),union(X0))
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f1082,f84]) ).
fof(f8578,plain,
! [X0,X1] :
( subset(sK0_skl(X1,X0),union(X0))
| subset(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f8556]) ).
fof(f9059,plain,
( subset(sK19_skl,succ(union(sK19_skl)))
| ~ ordinal(union(sK19_skl))
| subset(sK19_skl,succ(union(sK19_skl))) ),
inference(resolution,[status(thm)],[f8578,f4941]) ).
fof(f9089,plain,
( ~ ordinal(union(sK19_skl))
| subset(sK19_skl,succ(union(sK19_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f9059]) ).
fof(f9090,plain,
subset(sK19_skl,succ(union(sK19_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f9089,f372]) ).
fof(f9092,plain,
~ ordinal(succ(union(sK19_skl))),
inference(resolution,[status(thm)],[f9090,f206]) ).
fof(f9111,plain,
~ ordinal(union(sK19_skl)),
inference(resolution,[status(thm)],[f9092,f118]) ).
fof(f9112,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f9111,f372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM403+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.39 % Computer : n008.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Mon Sep 21 02:27:59 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.17/5.41 % Drodi V4.1.1
% 90.69/16.98 % Refutation found
% 90.69/16.98 % SZS status Theorem for theBenchmark: Theorem is valid
% 90.69/16.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 65.38/17.06 % Elapsed time: 11.648695 seconds
% 65.38/17.06 % CPU time: 91.838899 seconds
% 65.38/17.06 % Total memory used: 431.953 MB
% 65.38/17.06 % Net memory used: 362.335 MB
%------------------------------------------------------------------------------