%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET146+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 : 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 02:09:29 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 99 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 44 ~; 38 |; 19 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 72 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B] : intersection(B,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B] : intersection(B,empty_set) = empty_set,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
( ! [B,C,D] :
( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ! [B,C,D] :
( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,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(f18,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)],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f23,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f24,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)],[f23]) ).
fof(f25,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)],[f24]) ).
fof(f26,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))],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f31,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
( ! [B] :
( ? [C] : member(C,B)
| empty(B) )
& ! [B] :
( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
( ! [B] :
( member(sK1_skl(B),B)
| empty(B) )
& ! [B] :
( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B))],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0] :
( member(sK1_skl(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f43,plain,
? [B] : intersection(B,empty_set) != empty_set,
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f44,plain,
intersection(sK3_skl,empty_set) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl)],[f43]) ).
fof(f45,plain,
intersection(sK3_skl,empty_set) != empty_set,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f63,plain,
! [X0,X1] :
( member(sK1_skl(intersection(X0,X1)),X1)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[f35,f14]) ).
fof(f70,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f28,f16]) ).
fof(f71,plain,
! [X0,X1] :
( ~ empty(X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f28,f34]) ).
fof(f72,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f70,f21]) ).
fof(f75,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f72,f71]) ).
fof(f89,plain,
! [X0] : empty(intersection(X0,empty_set)),
inference(resolution,[status(thm)],[f63,f16]) ).
fof(f100,plain,
! [X0] : intersection(X0,empty_set) = empty_set,
inference(resolution,[status(thm)],[f89,f75]) ).
fof(f107,plain,
empty_set != empty_set,
inference(backward_demodulation,[status(thm)],[f100,f45]) ).
fof(f120,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET146+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 04:59:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % 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
% 0.10/0.43 % Elapsed time: 0.054820 seconds
% 0.10/0.43 % CPU time: 0.156944 seconds
% 0.10/0.43 % Total memory used: 101.688 MB
% 0.10/0.43 % Net memory used: 101.266 MB
%------------------------------------------------------------------------------