%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET607+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 02:10:13 PM UTC 2026
% Result : Theorem 130.98s 17.00s
% Output : CNFRefutation 69.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 12 unt; 0 def)
% Number of atoms : 134 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 134 ( 48 ~; 60 |; 20 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 135 ( 131 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [B,C] : union(B,difference(C,B)) = union(B,C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [B,C] : union(B,difference(C,B)) = union(B,C),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [B,C,D] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
( ! [B,C,D] :
( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ! [B,C,D] :
( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f15,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
( ! [B,C,D] :
( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ! [B,C,D] :
( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
( ! [B,C] :
( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f24,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f25,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
( ! [B,C] :
( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
( ! [B,C] :
( ( ~ member(sK0_skl(C,B),C)
& member(sK0_skl(C,B),B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f28]) ).
fof(f31,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f41,plain,
? [B,C] : union(B,difference(C,B)) != union(B,C),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
union(sK2_skl,difference(sK3_skl,sK2_skl)) != union(sK2_skl,sK3_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl)],[f41]) ).
fof(f43,plain,
union(sK2_skl,difference(sK3_skl,sK2_skl)) != union(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f63,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)],[f31,f12]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(union(X1,X2),X0),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[f32,f14]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(union(X1,X2),X0),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[f32,f13]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( member(sK0_skl(X3,union(X0,difference(X1,X2))),X1)
| member(sK0_skl(X3,union(X0,difference(X1,X2))),X0)
| subset(union(X0,difference(X1,X2)),X3) ),
inference(resolution,[status(thm)],[f63,f17]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( member(sK0_skl(union(X1,difference(X2,X3)),X0),X3)
| ~ member(sK0_skl(union(X1,difference(X2,X3)),X0),X2)
| subset(X0,union(X1,difference(X2,X3))) ),
inference(resolution,[status(thm)],[f68,f19]) ).
fof(f166,plain,
! [X0,X1,X2] :
( member(sK0_skl(union(X1,X2),union(X0,X1)),X0)
| subset(union(X0,X1),union(X1,X2))
| subset(union(X0,X1),union(X1,X2)) ),
inference(resolution,[status(thm)],[f69,f63]) ).
fof(f174,plain,
! [X0,X1,X2] :
( member(sK0_skl(union(X1,X2),union(X0,X1)),X0)
| subset(union(X0,X1),union(X1,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f166]) ).
fof(f889,plain,
! [X0,X1,X2,X3] :
( subset(union(X0,difference(X1,X2)),union(X1,X3))
| member(sK0_skl(union(X1,X3),union(X0,difference(X1,X2))),X0)
| subset(union(X0,difference(X1,X2)),union(X1,X3)) ),
inference(resolution,[status(thm)],[f96,f69]) ).
fof(f910,plain,
! [X0,X1,X2,X3] :
( member(sK0_skl(union(X1,X3),union(X0,difference(X1,X2))),X0)
| subset(union(X0,difference(X1,X2)),union(X1,X3)) ),
inference(duplicate_literals_removal,[status(thm)],[f889]) ).
fof(f2109,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,difference(X2,X1)))
| ~ member(sK0_skl(union(X1,difference(X2,X1)),X0),X2)
| subset(X0,union(X1,difference(X2,X1))) ),
inference(resolution,[status(thm)],[f158,f69]) ).
fof(f2143,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(union(X1,difference(X2,X1)),X0),X2)
| subset(X0,union(X1,difference(X2,X1))) ),
inference(duplicate_literals_removal,[status(thm)],[f2109]) ).
fof(f30536,plain,
! [X0,X1,X2] :
( subset(union(X0,difference(X1,X2)),union(X1,X0))
| subset(union(X0,difference(X1,X2)),union(X1,X0)) ),
inference(resolution,[status(thm)],[f910,f68]) ).
fof(f30619,plain,
! [X0,X1,X2] : subset(union(X0,difference(X1,X2)),union(X1,X0)),
inference(duplicate_literals_removal,[status(thm)],[f30536]) ).
fof(f59119,plain,
! [X0,X1] :
( subset(union(X0,X1),union(X1,difference(X0,X1)))
| subset(union(X0,X1),union(X1,difference(X0,X1))) ),
inference(resolution,[status(thm)],[f2143,f174]) ).
fof(f59271,plain,
! [X0,X1] : subset(union(X0,X1),union(X1,difference(X0,X1))),
inference(duplicate_literals_removal,[status(thm)],[f59119]) ).
fof(f74157,plain,
! [X0,X1] :
( ~ subset(union(X0,difference(X1,X0)),union(X1,X0))
| union(X0,difference(X1,X0)) = union(X1,X0) ),
inference(resolution,[status(thm)],[f59271,f24]) ).
fof(f74215,plain,
! [X0,X1] : union(X0,difference(X1,X0)) = union(X1,X0),
inference(forward_subsumption_resolution,[status(thm)],[f74157,f30619]) ).
fof(f74280,plain,
union(sK3_skl,sK2_skl) != union(sK2_skl,sK3_skl),
inference(backward_demodulation,[status(thm)],[f74215,f43]) ).
fof(f74761,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f74280,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET607+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.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 05:31:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 130.98/17.00 % Refutation found
% 130.98/17.00 % SZS status Theorem for theBenchmark: Theorem is valid
% 130.98/17.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 69.91/17.08 % Elapsed time: 16.702255 seconds
% 69.91/17.08 % CPU time: 132.096913 seconds
% 69.91/17.08 % Total memory used: 587.113 MB
% 69.91/17.08 % Net memory used: 546.448 MB
%------------------------------------------------------------------------------