%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET987+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 : n009.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 02:11:06 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 27 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 5 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [A,B] :
( ~ in(A,B)
=> set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,plain,
? [A,B] :
( set_difference(set_union2(B,singleton(A)),singleton(A)) != B
& ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
( set_difference(set_union2(sK3_skl,singleton(sK2_skl)),singleton(sK2_skl)) != sK3_skl
& ~ in(sK2_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f27]) ).
fof(f29,plain,
~ in(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
set_difference(set_union2(sK3_skl,singleton(sK2_skl)),singleton(sK2_skl)) != sK3_skl,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,plain,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
! [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) = A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f33,plain,
( ! [A,B] :
( in(B,A)
| set_difference(A,singleton(B)) = A )
& ! [A,B] :
( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f35,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f40,plain,
set_difference(sK3_skl,singleton(sK2_skl)) != sK3_skl,
inference(backward_demodulation,[status(thm)],[f31,f30]) ).
fof(f45,plain,
in(sK2_skl,sK3_skl),
inference(resolution,[status(thm)],[f35,f40]) ).
fof(f51,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f45,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET987+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:46:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.059548 seconds
% 0.08/0.42 % CPU time: 0.161657 seconds
% 0.08/0.42 % Total memory used: 69.627 MB
% 0.08/0.42 % Net memory used: 69.337 MB
%------------------------------------------------------------------------------