%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU160+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 : n013.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 02:19:27 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 99 ( 54 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 99 ( 38 ~; 42 |; 13 &)
% ( 4 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 38 ( 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f70]) ).
fof(f83,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f100,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f226,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(NNF_transformation,[status(thm)],[f44]) ).
fof(f227,plain,
( ! [A,B] :
( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ! [A,B] :
( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(miniscoping,[status(thm)],[f226]) ).
fof(f228,plain,
! [X0,X1] :
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f238,plain,
empty(sK16_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(A,sK16_skl)],[f47]) ).
fof(f239,plain,
empty(sK16_skl),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f270,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f292,plain,
? [A,B] :
( subset(A,singleton(B))
<~> ( A = singleton(B)
| A = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f71]) ).
fof(f293,plain,
? [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| ~ subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| subset(A,singleton(B)) ) ),
inference(NNF_transformation,[status(thm)],[f292]) ).
fof(f294,plain,
( ( ( sK19_skl != singleton(sK20_skl)
& sK19_skl != empty_set )
| ~ subset(sK19_skl,singleton(sK20_skl)) )
& ( sK19_skl = singleton(sK20_skl)
| sK19_skl = empty_set
| subset(sK19_skl,singleton(sK20_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(A,sK19_skl),skolemize(B,sK20_skl)],[f293]) ).
fof(f295,plain,
( sK19_skl = singleton(sK20_skl)
| sK19_skl = empty_set
| subset(sK19_skl,singleton(sK20_skl)) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f296,plain,
( sK19_skl != empty_set
| ~ subset(sK19_skl,singleton(sK20_skl)) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f297,plain,
( sK19_skl != singleton(sK20_skl)
| ~ subset(sK19_skl,singleton(sK20_skl)) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f323,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f324,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f323]) ).
fof(f352,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f101]) ).
fof(f396,plain,
sK16_skl = empty_set,
inference(resolution,[status(thm)],[f324,f239]) ).
fof(f401,plain,
! [X0] : subset(sK16_skl,X0),
inference(backward_demodulation,[status(thm)],[f396,f270]) ).
fof(f406,plain,
( sK19_skl = singleton(sK20_skl)
| sK19_skl = sK16_skl
| subset(sK19_skl,singleton(sK20_skl)) ),
inference(backward_demodulation,[status(thm)],[f396,f295]) ).
fof(f407,plain,
( sK19_skl != sK16_skl
| ~ subset(sK19_skl,singleton(sK20_skl)) ),
inference(backward_demodulation,[status(thm)],[f396,f296]) ).
fof(f426,plain,
( sK19_skl = singleton(sK20_skl)
| sK19_skl = sK16_skl ),
inference(backward_subsumption_resolution,[status(thm)],[f406,f427]) ).
fof(f427,plain,
! [X0,X1] :
( X0 = singleton(X1)
| X0 = sK16_skl
| ~ subset(X0,singleton(X1)) ),
inference(forward_demodulation,[status(thm)],[f396,f228]) ).
fof(f461,plain,
( sK19_skl = singleton(sK20_skl)
| sK19_skl != sK16_skl
| ~ subset(sK16_skl,singleton(sK20_skl)) ),
inference(paramodulation,[status(thm)],[f426,f407]) ).
fof(f464,plain,
( sK19_skl = singleton(sK20_skl)
| sK19_skl != sK16_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f461,f401]) ).
fof(f467,plain,
( sK19_skl != sK19_skl
| ~ subset(sK19_skl,singleton(sK20_skl)) ),
inference(backward_demodulation,[status(thm)],[f468,f297]) ).
fof(f468,plain,
sK19_skl = singleton(sK20_skl),
inference(forward_subsumption_resolution,[status(thm)],[f464,f426]) ).
fof(f476,plain,
( sK19_skl != sK19_skl
| ~ subset(sK19_skl,sK19_skl) ),
inference(forward_demodulation,[status(thm)],[f468,f467]) ).
fof(f477,plain,
~ subset(sK19_skl,sK19_skl),
inference(trivial_equality_resolution,[status(thm)],[f476]) ).
fof(f478,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f477,f352]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU160+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n013.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 05:53:06 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.052661 seconds
% 0.13/0.40 % CPU time: 0.140030 seconds
% 0.13/0.40 % Total memory used: 86.794 MB
% 0.13/0.40 % Net memory used: 86.706 MB
%------------------------------------------------------------------------------