%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET690+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 : n018.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 02:10:27 PM UTC 2026
% Result : Theorem 44.79s 6.33s
% Output : CNFRefutation 44.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 67 ( 3 unt; 0 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 233 ( 101 ~; 101 |; 22 &)
% ( 7 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 117 ( 109 !; 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(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,C] :
( equal_set(union(intersection(A,B),C),intersection(A,union(B,C)))
<=> subset(C,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,C] :
( equal_set(union(intersection(A,B),C),intersection(A,union(B,C)))
<=> subset(C,A) ),
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(f35,plain,
! [X,A,B] :
( ( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
( ! [X,A,B] :
( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ! [X,A,B] :
( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f68,plain,
? [A,B,C] :
( equal_set(union(intersection(A,B),C),intersection(A,union(B,C)))
<~> subset(C,A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
? [A,B,C] :
( ( ~ subset(C,A)
| ~ equal_set(union(intersection(A,B),C),intersection(A,union(B,C))) )
& ( subset(C,A)
| equal_set(union(intersection(A,B),C),intersection(A,union(B,C))) ) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
( ( ~ subset(sK5_skl,sK3_skl)
| ~ equal_set(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))) )
& ( subset(sK5_skl,sK3_skl)
| equal_set(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_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(C,sK5_skl)],[f69]) ).
fof(f71,plain,
( subset(sK5_skl,sK3_skl)
| equal_set(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
( ~ subset(sK5_skl,sK3_skl)
| ~ equal_set(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f77,plain,
( subset(sK5_skl,sK3_skl)
| subset(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f23,f71]) ).
fof(f79,plain,
( ~ subset(sK5_skl,sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl))
| ~ subset(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f25,f72]) ).
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(f87,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(intersection(X1,X2),X0),X2)
| ~ member(sK0_skl(intersection(X1,X2),X0),X1)
| subset(X0,intersection(X1,X2)) ),
inference(resolution,[status(thm)],[f20,f34]) ).
fof(f90,plain,
! [X0] :
( member(X0,intersection(sK3_skl,union(sK4_skl,sK5_skl)))
| ~ member(X0,union(intersection(sK3_skl,sK4_skl),sK5_skl))
| subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f77,f18]) ).
fof(f92,plain,
! [X0,X1,X2] :
( subset(union(X1,X2),X0)
| member(sK0_skl(X0,union(X1,X2)),X2)
| member(sK0_skl(X0,union(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f37,f19]) ).
fof(f93,plain,
! [X0,X1,X2] :
( subset(X2,union(X0,X1))
| ~ member(sK0_skl(union(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f38,f20]) ).
fof(f95,plain,
! [X0,X1,X2] :
( subset(X2,union(X0,X1))
| ~ member(sK0_skl(union(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f39,f20]) ).
fof(f116,plain,
( ~ subset(sK5_skl,sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl))
| ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),union(sK4_skl,sK5_skl))
| ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f87,f79]) ).
fof(f119,plain,
( ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),sK5_skl)
| ~ subset(sK5_skl,sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl))
| ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f116,f39]) ).
fof(f120,plain,
( ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),sK4_skl)
| ~ subset(sK5_skl,sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl))
| ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f116,f38]) ).
fof(f121,plain,
( ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),sK5_skl)
| ~ subset(sK5_skl,sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f18]) ).
fof(f133,plain,
( ~ subset(sK5_skl,sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl))
| member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),sK5_skl)
| member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f92,f79]) ).
fof(f135,plain,
( ~ subset(sK5_skl,sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl))
| member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),intersection(sK3_skl,sK4_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f121]) ).
fof(f138,plain,
( member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),sK4_skl)
| ~ subset(sK5_skl,sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)) ),
inference(resolution,[status(thm)],[f135,f33]) ).
fof(f139,plain,
( member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),sK3_skl)
| ~ subset(sK5_skl,sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)) ),
inference(resolution,[status(thm)],[f135,f32]) ).
fof(f140,plain,
( ~ subset(sK5_skl,sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl))
| ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)),sK3_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f120,f138]) ).
fof(f142,plain,
( ~ subset(sK5_skl,sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),sK5_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f139]) ).
fof(f144,plain,
( member(sK0_skl(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK3_skl)
| ~ subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f142,f85]) ).
fof(f145,plain,
( member(sK0_skl(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))),union(sK4_skl,sK5_skl))
| ~ subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f142,f84]) ).
fof(f146,plain,
( ~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK5_skl)
| ~ subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f142,f95]) ).
fof(f147,plain,
( ~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))),intersection(sK3_skl,sK4_skl))
| ~ subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f142,f93]) ).
fof(f151,plain,
( member(sK0_skl(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK5_skl)
| member(sK0_skl(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK4_skl)
| ~ subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f145,f37]) ).
fof(f152,plain,
( member(sK0_skl(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK4_skl)
| ~ subset(sK5_skl,sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f146]) ).
fof(f156,plain,
( ~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK4_skl)
| ~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK3_skl)
| ~ subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f147,f34]) ).
fof(f157,plain,
~ subset(sK5_skl,sK3_skl),
inference(backward_subsumption_resolution,[status(thm)],[f152,f158]) ).
fof(f158,plain,
( ~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),sK5_skl),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK4_skl)
| ~ subset(sK5_skl,sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f144]) ).
fof(f163,plain,
! [X0] :
( member(X0,intersection(sK3_skl,union(sK4_skl,sK5_skl)))
| ~ member(X0,union(intersection(sK3_skl,sK4_skl),sK5_skl)) ),
inference(backward_subsumption_resolution,[status(thm)],[f90,f157]) ).
fof(f175,plain,
! [X0] :
( ~ member(X0,sK5_skl)
| member(X0,intersection(sK3_skl,union(sK4_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f163,f39]) ).
fof(f186,plain,
! [X0] :
( member(X0,sK3_skl)
| ~ member(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f175,f32]) ).
fof(f212,plain,
! [X0] :
( subset(sK5_skl,X0)
| member(sK0_skl(X0,sK5_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f186,f19]) ).
fof(f663,plain,
( subset(sK5_skl,sK3_skl)
| subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f212,f20]) ).
fof(f664,plain,
subset(sK5_skl,sK3_skl),
inference(duplicate_literals_removal,[status(thm)],[f663]) ).
fof(f665,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f664,f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET690+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n018.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:34:44 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 44.79/6.33 % Refutation found
% 44.79/6.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 44.79/6.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 44.79/6.41 % Elapsed time: 5.953870 seconds
% 44.79/6.41 % CPU time: 46.539653 seconds
% 44.79/6.41 % Total memory used: 281.345 MB
% 44.79/6.41 % Net memory used: 245.505 MB
%------------------------------------------------------------------------------