%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET616+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 : 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 02:10:15 PM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 7 unt; 0 def)
% Number of atoms : 102 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 42 ~; 40 |; 18 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 69 ( 65 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(f5,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C] :
( difference(B,C) = difference(C,B)
=> B = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C] :
( difference(B,C) = difference(C,B)
=> B = C ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f14,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(f15,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)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,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(f20,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)],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f31,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f32,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)],[f31]) ).
fof(f33,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)],[f32]) ).
fof(f34,plain,
( ! [B,C] :
( ( ~ member(sK2_skl(C,B),C)
& member(sK2_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,[sK2_skl]),skolemize(D,sK2_skl(C,B))],[f33]) ).
fof(f36,plain,
! [X0,X1] :
( member(sK2_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( ~ member(sK2_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f39,plain,
? [B,C] :
( B != C
& difference(B,C) = difference(C,B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f40,plain,
( sK3_skl != sK4_skl
& difference(sK3_skl,sK4_skl) = difference(sK4_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f39]) ).
fof(f41,plain,
difference(sK3_skl,sK4_skl) = difference(sK4_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
sK3_skl != sK4_skl,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
! [X0] :
( member(X0,sK4_skl)
| ~ member(X0,difference(sK3_skl,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f41,f16]) ).
fof(f46,plain,
! [X0] : ~ member(X0,difference(sK3_skl,sK4_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f45,f17]) ).
fof(f49,plain,
! [X0] :
( member(X0,sK4_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f18,f46]) ).
fof(f52,plain,
! [X0] :
( member(X0,sK3_skl)
| ~ member(X0,sK4_skl)
| member(X0,difference(sK3_skl,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f41,f18]) ).
fof(f53,plain,
! [X0] :
( member(X0,sK3_skl)
| ~ member(X0,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f52,f46]) ).
fof(f65,plain,
! [X0] :
( member(sK2_skl(X0,sK4_skl),sK3_skl)
| subset(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f36,f53]) ).
fof(f71,plain,
! [X0] :
( ~ member(sK2_skl(sK4_skl,X0),sK3_skl)
| subset(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f37,f49]) ).
fof(f76,plain,
( subset(sK4_skl,sK3_skl)
| subset(sK4_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f65,f37]) ).
fof(f77,plain,
subset(sK4_skl,sK3_skl),
inference(duplicate_literals_removal,[status(thm)],[f76]) ).
fof(f89,plain,
( ~ subset(sK3_skl,sK4_skl)
| sK3_skl = sK4_skl ),
inference(resolution,[status(thm)],[f77,f23]) ).
fof(f90,plain,
~ subset(sK3_skl,sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f89,f42]) ).
fof(f92,plain,
( subset(sK3_skl,sK4_skl)
| subset(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f71,f36]) ).
fof(f94,plain,
subset(sK3_skl,sK4_skl),
inference(duplicate_literals_removal,[status(thm)],[f92]) ).
fof(f95,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f94,f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET616+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n002.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 05:32:02 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 0.19/0.48 % Refutation found
% 0.19/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.51 % Elapsed time: 0.060972 seconds
% 0.19/0.51 % CPU time: 0.165729 seconds
% 0.19/0.51 % Total memory used: 66.699 MB
% 0.19/0.51 % Net memory used: 66.443 MB
%------------------------------------------------------------------------------