%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU122+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 02:19:16 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 62 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 28 ~; 20 |; 9 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 41 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ! [A] : subset(empty_set,A),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f20,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
( ! [A] :
( in(sK0_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f32,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [A,B] :
( ( ~ in(sK1_skl(B,A),B)
& in(sK1_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f33]) ).
fof(f36,plain,
! [X0,X1] :
( in(sK1_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f54,plain,
empty(sK3_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f11]) ).
fof(f55,plain,
empty(sK3_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f65,plain,
? [A] : ~ subset(empty_set,A),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f66,plain,
~ subset(empty_set,sK5_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f65]) ).
fof(f67,plain,
~ subset(empty_set,sK5_skl),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f79,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f80,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f87,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f29]) ).
fof(f94,plain,
sK3_skl = empty_set,
inference(resolution,[status(thm)],[f55,f80]) ).
fof(f98,plain,
! [X0] : ~ in(X0,sK3_skl),
inference(backward_demodulation,[status(thm)],[f94,f87]) ).
fof(f100,plain,
~ subset(sK3_skl,sK5_skl),
inference(backward_demodulation,[status(thm)],[f94,f67]) ).
fof(f134,plain,
! [X0] : subset(sK3_skl,X0),
inference(resolution,[status(thm)],[f36,f98]) ).
fof(f151,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f100,f134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU122+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n003.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 05:53:00 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 0.16/0.47 % Refutation found
% 0.16/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.56 % Elapsed time: 0.121713 seconds
% 0.16/0.56 % CPU time: 0.103261 seconds
% 0.16/0.56 % Total memory used: 3.235 MB
% 0.16/0.56 % Net memory used: 3.227 MB
%------------------------------------------------------------------------------