%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET169+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 02:09:33 PM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 14 unt; 0 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 166 ( 72 ~; 68 |; 20 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 2 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 : 104 ( 99 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,C] : equal_set(intersection(A,union(B,C)),union(intersection(A,B),intersection(A,C))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,C] : equal_set(intersection(A,union(B,C)),union(intersection(A,B),intersection(A,C))),
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(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(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(intersection(A,union(B,C)),union(intersection(A,B),intersection(A,C))),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
~ equal_set(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(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(C,sK5_skl)],[f68]) ).
fof(f70,plain,
~ equal_set(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f74,plain,
( ~ subset(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl)))
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f25,f70]) ).
fof(f79,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,union(X0,X1)),X1)
| member(sK0_skl(X2,union(X0,X1)),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f37]) ).
fof(f80,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,intersection(X0,X1)),X1)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f81,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,intersection(X0,X1)),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f32]) ).
fof(f83,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(f86,plain,
! [X0,X1,X2] :
( subset(X2,union(X0,X1))
| ~ member(sK0_skl(union(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f38,f20]) ).
fof(f88,plain,
! [X0,X1,X2] :
( subset(X2,union(X0,X1))
| ~ member(sK0_skl(union(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f39,f20]) ).
fof(f90,plain,
( ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)))
| member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),intersection(sK3_skl,sK5_skl))
| member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f79,f74]) ).
fof(f103,plain,
( member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),sK5_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)))
| member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f90,f33]) ).
fof(f104,plain,
( member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)))
| member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f90,f32]) ).
fof(f105,plain,
( member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),sK3_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f104,f32]) ).
fof(f106,plain,
( member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),sK4_skl)
| member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),sK5_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f103,f33]) ).
fof(f108,plain,
( ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)))
| ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_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),intersection(sK3_skl,sK5_skl))),sK3_skl) ),
inference(resolution,[status(thm)],[f83,f74]) ).
fof(f110,plain,
( ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)))
| ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),union(sK4_skl,sK5_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f105]) ).
fof(f113,plain,
( ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),sK5_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f110,f39]) ).
fof(f114,plain,
( ~ member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),sK4_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f110,f38]) ).
fof(f116,plain,
( member(sK0_skl(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),sK4_skl)
| ~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))) ),
inference(backward_subsumption_resolution,[status(thm)],[f106,f113]) ).
fof(f117,plain,
~ subset(intersection(sK3_skl,union(sK4_skl,sK5_skl)),union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f116,f114]) ).
fof(f118,plain,
member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK3_skl),
inference(resolution,[status(thm)],[f117,f81]) ).
fof(f119,plain,
member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),union(sK4_skl,sK5_skl)),
inference(resolution,[status(thm)],[f117,f80]) ).
fof(f120,plain,
~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),intersection(sK3_skl,sK5_skl)),
inference(resolution,[status(thm)],[f117,f88]) ).
fof(f121,plain,
~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),intersection(sK3_skl,sK4_skl)),
inference(resolution,[status(thm)],[f117,f86]) ).
fof(f125,plain,
( member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK5_skl)
| member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK4_skl) ),
inference(resolution,[status(thm)],[f119,f37]) ).
fof(f126,plain,
( ~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK5_skl)
| ~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK3_skl) ),
inference(resolution,[status(thm)],[f120,f34]) ).
fof(f127,plain,
member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK4_skl),
inference(backward_subsumption_resolution,[status(thm)],[f125,f128]) ).
fof(f128,plain,
~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK5_skl),
inference(forward_subsumption_resolution,[status(thm)],[f126,f118]) ).
fof(f129,plain,
( ~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK4_skl)
| ~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK3_skl) ),
inference(resolution,[status(thm)],[f121,f34]) ).
fof(f131,plain,
~ member(sK0_skl(union(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),intersection(sK3_skl,union(sK4_skl,sK5_skl))),sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f129,f118]) ).
fof(f132,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f127,f131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET169+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:00:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.42 % Refutation found
% 0.09/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.075960 seconds
% 0.09/0.44 % CPU time: 0.293423 seconds
% 0.09/0.44 % Total memory used: 84.478 MB
% 0.09/0.44 % Net memory used: 83.853 MB
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