%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET587+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 : n010.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 02:10:09 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 7 unt; 0 def)
% Number of atoms : 149 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 153 ( 57 ~; 66 |; 21 &)
% ( 7 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 92 !; 8 ?)
% 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] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
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(f19,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ 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(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f23,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)],[f22]) ).
fof(f24,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)],[f23]) ).
fof(f25,plain,
( ! [B,C] :
( ( ~ member(sK1_skl(C,B),C)
& member(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f30,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)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f42,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( ! [B] :
( ? [C] : member(C,B)
| empty(B) )
& ! [B] :
( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
( ! [B] :
( member(sK3_skl(B),B)
| empty(B) )
& ! [B] :
( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(C,sK3_skl(B))],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0] :
( member(sK3_skl(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,plain,
? [B,C] :
( difference(B,C) = empty_set
<~> subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f48,plain,
? [B,C] :
( ( ~ subset(B,C)
| difference(B,C) != empty_set )
& ( subset(B,C)
| difference(B,C) = empty_set ) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
( ( ~ subset(sK4_skl,sK5_skl)
| difference(sK4_skl,sK5_skl) != empty_set )
& ( subset(sK4_skl,sK5_skl)
| difference(sK4_skl,sK5_skl) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(B,sK4_skl),skolemize(C,sK5_skl)],[f48]) ).
fof(f50,plain,
( subset(sK4_skl,sK5_skl)
| difference(sK4_skl,sK5_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
( ~ subset(sK4_skl,sK5_skl)
| difference(sK4_skl,sK5_skl) != empty_set ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f57,plain,
! [X0] :
( difference(sK4_skl,sK5_skl) = empty_set
| member(X0,sK5_skl)
| ~ member(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f26,f50]) ).
fof(f60,plain,
! [X0,X1] :
( ~ member(sK3_skl(difference(X0,X1)),X1)
| empty(difference(X0,X1)) ),
inference(resolution,[status(thm)],[f46,f19]) ).
fof(f61,plain,
! [X0,X1] :
( member(sK3_skl(difference(X0,X1)),X0)
| empty(difference(X0,X1)) ),
inference(resolution,[status(thm)],[f46,f18]) ).
fof(f66,plain,
! [X0] :
( difference(sK4_skl,sK5_skl) = empty_set
| member(sK3_skl(difference(sK4_skl,X0)),sK5_skl)
| empty(difference(sK4_skl,X0)) ),
inference(resolution,[status(thm)],[f61,f57]) ).
fof(f87,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f27,f21]) ).
fof(f88,plain,
! [X0,X1] :
( ~ empty(X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f27,f45]) ).
fof(f89,plain,
! [X0,X1,X2] :
( member(sK1_skl(X1,X0),X2)
| member(sK1_skl(X1,X0),difference(X0,X2))
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f27,f20]) ).
fof(f91,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[status(thm)],[f87,f33]) ).
fof(f171,plain,
( empty(difference(sK4_skl,sK5_skl))
| difference(sK4_skl,sK5_skl) = empty_set
| empty(difference(sK4_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f66,f60]) ).
fof(f175,plain,
( difference(sK4_skl,sK5_skl) = empty_set
| empty(difference(sK4_skl,sK5_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f171]) ).
fof(f177,plain,
! [X0] :
( subset(difference(sK4_skl,sK5_skl),X0)
| difference(sK4_skl,sK5_skl) = empty_set ),
inference(resolution,[status(thm)],[f175,f88]) ).
fof(f179,plain,
( empty_set = difference(sK4_skl,sK5_skl)
| difference(sK4_skl,sK5_skl) = empty_set ),
inference(resolution,[status(thm)],[f177,f91]) ).
fof(f182,plain,
difference(sK4_skl,sK5_skl) = empty_set,
inference(duplicate_literals_removal,[status(thm)],[f179]) ).
fof(f205,plain,
( ~ subset(sK4_skl,sK5_skl)
| empty_set != empty_set ),
inference(backward_demodulation,[status(thm)],[f182,f51]) ).
fof(f212,plain,
~ subset(sK4_skl,sK5_skl),
inference(trivial_equality_resolution,[status(thm)],[f205]) ).
fof(f370,plain,
! [X0] :
( member(sK1_skl(X0,sK4_skl),sK5_skl)
| member(sK1_skl(X0,sK4_skl),empty_set)
| subset(sK4_skl,X0) ),
inference(paramodulation,[status(thm)],[f182,f89]) ).
fof(f374,plain,
! [X0] :
( member(sK1_skl(X0,sK4_skl),sK5_skl)
| subset(sK4_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f370,f21]) ).
fof(f443,plain,
( subset(sK4_skl,sK5_skl)
| subset(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f374,f28]) ).
fof(f446,plain,
subset(sK4_skl,sK5_skl),
inference(duplicate_literals_removal,[status(thm)],[f443]) ).
fof(f447,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f446,f212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET587+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % 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 05:27:57 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.055728 seconds
% 0.10/0.42 % CPU time: 0.219306 seconds
% 0.10/0.42 % Total memory used: 58.150 MB
% 0.10/0.42 % Net memory used: 57.638 MB
%------------------------------------------------------------------------------