%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:10:07 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 5 unt; 0 def)
% Number of atoms : 143 ( 14 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 155 ( 56 ~; 60 |; 29 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 87 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( ~ member(E,D)
& member(E,C) ) )
=> B = difference(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( ~ member(E,D)
& member(E,C) ) )
=> B = difference(C,D) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,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)],[f1]) ).
fof(f8,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)],[f7]) ).
fof(f9,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f12,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f13,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)],[f12]) ).
fof(f16,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f18,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)],[f17]) ).
fof(f19,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)],[f18]) ).
fof(f20,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))],[f19]) ).
fof(f22,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f25,plain,
? [B,C,D] :
( B != difference(C,D)
& ! [E] :
( member(E,B)
<=> ( ~ member(E,D)
& member(E,C) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f26,plain,
? [B,C,D] :
( B != difference(C,D)
& ! [E] :
( ( member(E,D)
| ~ member(E,C)
| member(E,B) )
& ( ( ~ member(E,D)
& member(E,C) )
| ~ member(E,B) ) ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
? [B,C,D] :
( B != difference(C,D)
& ! [E] :
( member(E,D)
| ~ member(E,C)
| member(E,B) )
& ! [E] :
( ( ~ member(E,D)
& member(E,C) )
| ~ member(E,B) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
( sK1_skl != difference(sK2_skl,sK3_skl)
& ! [E] :
( member(E,sK3_skl)
| ~ member(E,sK2_skl)
| member(E,sK1_skl) )
& ! [E] :
( ( ~ member(E,sK3_skl)
& member(E,sK2_skl) )
| ~ member(E,sK1_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(D,sK3_skl)],[f27]) ).
fof(f29,plain,
! [X0] :
( member(X0,sK2_skl)
| ~ member(X0,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0] :
( ~ member(X0,sK3_skl)
| ~ member(X0,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,plain,
! [X0] :
( member(X0,sK3_skl)
| ~ member(X0,sK2_skl)
| member(X0,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f32,plain,
sK1_skl != difference(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(X2,difference(X0,X1)),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[f22,f10]) ).
fof(f37,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,difference(X0,X1)),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[f22,f9]) ).
fof(f39,plain,
! [X0] :
( ~ member(sK0_skl(X0,sK1_skl),sK3_skl)
| subset(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f22,f30]) ).
fof(f40,plain,
! [X0] :
( member(sK0_skl(X0,sK1_skl),sK2_skl)
| subset(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f22,f29]) ).
fof(f43,plain,
! [X0,X1] :
( member(sK0_skl(X0,sK1_skl),X1)
| member(sK0_skl(X0,sK1_skl),difference(sK2_skl,X1))
| subset(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f40,f11]) ).
fof(f47,plain,
! [X0,X1] :
( member(sK0_skl(X1,difference(sK2_skl,X0)),sK3_skl)
| member(sK0_skl(X1,difference(sK2_skl,X0)),sK1_skl)
| subset(difference(sK2_skl,X0),X1) ),
inference(resolution,[status(thm)],[f37,f31]) ).
fof(f193,plain,
! [X0] :
( subset(sK1_skl,difference(sK2_skl,X0))
| member(sK0_skl(difference(sK2_skl,X0),sK1_skl),X0)
| subset(sK1_skl,difference(sK2_skl,X0)) ),
inference(resolution,[status(thm)],[f43,f23]) ).
fof(f200,plain,
! [X0] :
( member(sK0_skl(difference(sK2_skl,X0),sK1_skl),X0)
| subset(sK1_skl,difference(sK2_skl,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f193]) ).
fof(f270,plain,
! [X0] :
( subset(difference(sK2_skl,X0),sK1_skl)
| member(sK0_skl(sK1_skl,difference(sK2_skl,X0)),sK3_skl)
| subset(difference(sK2_skl,X0),sK1_skl) ),
inference(resolution,[status(thm)],[f47,f23]) ).
fof(f277,plain,
! [X0] :
( member(sK0_skl(sK1_skl,difference(sK2_skl,X0)),sK3_skl)
| subset(difference(sK2_skl,X0),sK1_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f270]) ).
fof(f1051,plain,
( subset(sK1_skl,difference(sK2_skl,sK3_skl))
| subset(sK1_skl,difference(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f200,f39]) ).
fof(f1066,plain,
subset(sK1_skl,difference(sK2_skl,sK3_skl)),
inference(duplicate_literals_removal,[status(thm)],[f1051]) ).
fof(f1074,plain,
( ~ subset(difference(sK2_skl,sK3_skl),sK1_skl)
| sK1_skl = difference(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f1066,f16]) ).
fof(f1075,plain,
~ subset(difference(sK2_skl,sK3_skl),sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1074,f32]) ).
fof(f1473,plain,
( subset(difference(sK2_skl,sK3_skl),sK1_skl)
| subset(difference(sK2_skl,sK3_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f277,f36]) ).
fof(f1480,plain,
subset(difference(sK2_skl,sK3_skl),sK1_skl),
inference(duplicate_literals_removal,[status(thm)],[f1473]) ).
fof(f1481,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1480,f1075]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.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 05:27:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.46 % Refutation found
% 0.10/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.52 % Elapsed time: 0.139416 seconds
% 0.17/0.52 % CPU time: 0.671225 seconds
% 0.17/0.52 % Total memory used: 86.137 MB
% 0.17/0.52 % Net memory used: 84.703 MB
%------------------------------------------------------------------------------