%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET603+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 : n012.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 02:10:12 PM UTC 2026
% Result : Theorem 0.07s 0.33s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 92 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 37 ~; 37 |; 16 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 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 : 76 ( 73 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B] : difference(B,empty_set) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B] : difference(B,empty_set) = B,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f16,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(f17,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)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f23,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)],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f34,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f35,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)],[f34]) ).
fof(f36,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)],[f35]) ).
fof(f37,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))],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( member(sK2_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,plain,
! [X0,X1] :
( ~ member(sK2_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f47,plain,
? [B] : difference(B,empty_set) != B,
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f48,plain,
difference(sK4_skl,empty_set) != sK4_skl,
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(B,sK4_skl)],[f47]) ).
fof(f49,plain,
difference(sK4_skl,empty_set) != sK4_skl,
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f280,plain,
! [X0,X1,X2] :
( member(sK2_skl(X2,difference(X0,X1)),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[f39,f18]) ).
fof(f293,plain,
! [X0,X1,X2] :
( member(sK2_skl(difference(X1,X2),X0),X2)
| ~ member(sK2_skl(difference(X1,X2),X0),X1)
| subset(X0,difference(X1,X2)) ),
inference(resolution,[status(thm)],[f40,f20]) ).
fof(f550,plain,
! [X0,X1] :
( subset(difference(X0,X1),X0)
| subset(difference(X0,X1),X0) ),
inference(resolution,[status(thm)],[f280,f40]) ).
fof(f563,plain,
! [X0,X1] : subset(difference(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f550]) ).
fof(f572,plain,
! [X0,X1] :
( ~ subset(X0,difference(X0,X1))
| X0 = difference(X0,X1) ),
inference(resolution,[status(thm)],[f563,f26]) ).
fof(f666,plain,
! [X0,X1] :
( subset(X0,difference(X0,X1))
| member(sK2_skl(difference(X0,X1),X0),X1)
| subset(X0,difference(X0,X1)) ),
inference(resolution,[status(thm)],[f293,f39]) ).
fof(f673,plain,
! [X0,X1] :
( member(sK2_skl(difference(X0,X1),X0),X1)
| subset(X0,difference(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f666]) ).
fof(f765,plain,
! [X0] : subset(X0,difference(X0,empty_set)),
inference(resolution,[status(thm)],[f673,f21]) ).
fof(f781,plain,
! [X0] : X0 = difference(X0,empty_set),
inference(resolution,[status(thm)],[f765,f572]) ).
fof(f793,plain,
sK4_skl != sK4_skl,
inference(backward_demodulation,[status(thm)],[f781,f49]) ).
fof(f856,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET603+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Mon Sep 21 05:28:21 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 0.07/0.33 % Refutation found
% 0.07/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.34 % Elapsed time: 0.042139 seconds
% 0.07/0.34 % CPU time: 0.129786 seconds
% 0.07/0.34 % Total memory used: 82.575 MB
% 0.07/0.34 % Net memory used: 81.887 MB
%------------------------------------------------------------------------------