%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET917+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:10:58 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 29 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 7 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 24 ( 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B] :
( set_intersection2(singleton(A),B) = singleton(A)
| disjoint(singleton(A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B] :
( set_intersection2(singleton(A),B) = singleton(A)
| disjoint(singleton(A),B) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [A,B] :
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
! [X0,X1] :
( set_intersection2(X1,singleton(X0)) = singleton(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f26,plain,
? [A,B] :
( set_intersection2(singleton(A),B) != singleton(A)
& ~ disjoint(singleton(A),B) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
( set_intersection2(singleton(sK2_skl),sK3_skl) != singleton(sK2_skl)
& ~ disjoint(singleton(sK2_skl),sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f26]) ).
fof(f28,plain,
~ disjoint(singleton(sK2_skl),sK3_skl),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
set_intersection2(singleton(sK2_skl),sK3_skl) != singleton(sK2_skl),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
set_intersection2(sK3_skl,singleton(sK2_skl)) != singleton(sK2_skl),
inference(backward_demodulation,[status(thm)],[f13,f29]) ).
fof(f42,plain,
! [X0,X1] :
( disjoint(singleton(X1),X0)
| set_intersection2(X0,singleton(X1)) = singleton(X1) ),
inference(resolution,[status(thm)],[f19,f17]) ).
fof(f43,plain,
set_intersection2(sK3_skl,singleton(sK2_skl)) = singleton(sK2_skl),
inference(resolution,[status(thm)],[f42,f28]) ).
fof(f45,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f43,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET917+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 05:45:15 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.054560 seconds
% 0.13/0.42 % CPU time: 0.150372 seconds
% 0.13/0.42 % Total memory used: 101.164 MB
% 0.13/0.42 % Net memory used: 100.710 MB
%------------------------------------------------------------------------------