%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET697+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:10:28 PM UTC 2026
% Result : Theorem 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 7 unt; 0 def)
% Number of atoms : 180 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 204 ( 82 ~; 80 |; 31 &)
% ( 7 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 113 ( 105 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,E] :
( ( subset(B,E)
& subset(A,E) )
=> ( subset(A,B)
<=> equal_set(intersection(A,difference(E,B)),empty_set) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,E] :
( ( subset(B,E)
& subset(A,E) )
=> ( subset(A,B)
<=> equal_set(intersection(A,difference(E,B)),empty_set) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f30,plain,
! [X,A,B] :
( ( ~ member(X,B)
| ~ member(X,A)
| member(X,intersection(A,B)) )
& ( ( member(X,B)
& member(X,A) )
| ~ member(X,intersection(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
( ! [X,A,B] :
( ~ member(X,B)
| ~ member(X,A)
| member(X,intersection(A,B)) )
& ! [X,A,B] :
( ( member(X,B)
& member(X,A) )
| ~ member(X,intersection(A,B)) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
! [B,A,E] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( ! [B,A,E] :
( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ! [B,A,E] :
( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f68,plain,
? [A,B,E] :
( ( subset(A,B)
<~> equal_set(intersection(A,difference(E,B)),empty_set) )
& subset(B,E)
& subset(A,E) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
? [A,B,E] :
( ( ~ equal_set(intersection(A,difference(E,B)),empty_set)
| ~ subset(A,B) )
& ( equal_set(intersection(A,difference(E,B)),empty_set)
| subset(A,B) )
& subset(B,E)
& subset(A,E) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
( ( ~ equal_set(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),empty_set)
| ~ subset(sK3_skl,sK4_skl) )
& ( equal_set(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),empty_set)
| subset(sK3_skl,sK4_skl) )
& subset(sK4_skl,sK5_skl)
& subset(sK3_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(E,sK5_skl)],[f69]) ).
fof(f71,plain,
subset(sK3_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
( equal_set(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),empty_set)
| subset(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f74,plain,
( ~ equal_set(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),empty_set)
| ~ subset(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f79,plain,
! [X0] :
( member(X0,sK5_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f18,f71]) ).
fof(f84,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,intersection(X0,X1)),X1)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f85,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,intersection(X0,X1)),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f32]) ).
fof(f91,plain,
( subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),empty_set)
| subset(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f73,f23]) ).
fof(f93,plain,
( ~ subset(empty_set,intersection(sK3_skl,difference(sK5_skl,sK4_skl)))
| ~ subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),empty_set)
| ~ subset(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f74,f25]) ).
fof(f94,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f40,f19]) ).
fof(f95,plain,
( ~ subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),empty_set)
| ~ subset(sK3_skl,sK4_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f93,f94]) ).
fof(f109,plain,
! [X0] :
( member(X0,empty_set)
| ~ member(X0,intersection(sK3_skl,difference(sK5_skl,sK4_skl)))
| subset(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f91,f18]) ).
fof(f110,plain,
! [X0] :
( ~ member(X0,intersection(sK3_skl,difference(sK5_skl,sK4_skl)))
| subset(sK3_skl,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f40]) ).
fof(f112,plain,
! [X0,X1] :
( member(X1,sK4_skl)
| ~ member(X1,sK3_skl)
| ~ member(X0,intersection(sK3_skl,difference(sK5_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f110,f18]) ).
fof(f114,plain,
! [X0,X1] :
( ~ member(X1,difference(sK5_skl,sK4_skl))
| ~ member(X1,sK3_skl)
| member(X0,sK4_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f112,f34]) ).
fof(f115,plain,
( ~ subset(sK3_skl,sK4_skl)
| member(sK0_skl(empty_set,intersection(sK3_skl,difference(sK5_skl,sK4_skl))),difference(sK5_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f84,f95]) ).
fof(f117,plain,
( ~ subset(sK3_skl,sK4_skl)
| member(sK0_skl(empty_set,intersection(sK3_skl,difference(sK5_skl,sK4_skl))),sK3_skl) ),
inference(resolution,[status(thm)],[f85,f95]) ).
fof(f121,plain,
( ~ member(sK0_skl(empty_set,intersection(sK3_skl,difference(sK5_skl,sK4_skl))),sK4_skl)
| ~ subset(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f115,f44]) ).
fof(f144,plain,
! [X0,X1] :
( member(X1,sK4_skl)
| ~ member(X1,sK5_skl)
| ~ member(X1,sK3_skl)
| member(X0,sK4_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f114,f45]) ).
fof(f145,plain,
! [X0,X1] :
( member(X1,sK4_skl)
| ~ member(X1,sK3_skl)
| member(X0,sK4_skl)
| ~ member(X0,sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f79]) ).
fof(f162,plain,
( ~ subset(sK3_skl,sK4_skl)
| ~ member(sK0_skl(empty_set,intersection(sK3_skl,difference(sK5_skl,sK4_skl))),sK3_skl)
| ~ member(sK0_skl(empty_set,intersection(sK3_skl,difference(sK5_skl,sK4_skl))),sK3_skl) ),
inference(resolution,[status(thm)],[f145,f121]) ).
fof(f164,plain,
! [X0] :
( subset(X0,sK4_skl)
| ~ member(sK0_skl(sK4_skl,X0),sK3_skl)
| ~ member(sK0_skl(sK4_skl,X0),sK3_skl) ),
inference(resolution,[status(thm)],[f145,f20]) ).
fof(f173,plain,
( ~ subset(sK3_skl,sK4_skl)
| ~ member(sK0_skl(empty_set,intersection(sK3_skl,difference(sK5_skl,sK4_skl))),sK3_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f162]) ).
fof(f177,plain,
~ subset(sK3_skl,sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f173,f117]) ).
fof(f178,plain,
! [X0] :
( subset(X0,sK4_skl)
| ~ member(sK0_skl(sK4_skl,X0),sK3_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f164]) ).
fof(f193,plain,
( subset(sK3_skl,sK4_skl)
| subset(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f178,f19]) ).
fof(f194,plain,
subset(sK3_skl,sK4_skl),
inference(duplicate_literals_removal,[status(thm)],[f193]) ).
fof(f195,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f194,f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET697+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:35:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.14/0.47 % Refutation found
% 0.14/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.49 % Elapsed time: 0.108419 seconds
% 0.14/0.49 % CPU time: 0.615855 seconds
% 0.14/0.49 % Total memory used: 87.649 MB
% 0.14/0.49 % Net memory used: 86.797 MB
%------------------------------------------------------------------------------