%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET873+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 : n026.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 02:10:52 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 66 ( 36 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 67 ( 26 ~; 25 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 43 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B] :
( set_union2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B] :
( set_union2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f15,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f31,plain,
! [A,B] :
( in(A,B)
| ~ subset(set_union2(singleton(A),B),B) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(set_union2(singleton(X0),X1),X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f37,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f38,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
? [A,B] :
( A != B
& set_union2(singleton(A),singleton(B)) = singleton(A) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
( sK3_skl != sK4_skl
& set_union2(singleton(sK3_skl),singleton(sK4_skl)) = singleton(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f39]) ).
fof(f41,plain,
set_union2(singleton(sK3_skl),singleton(sK4_skl)) = singleton(sK3_skl),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
sK3_skl != sK4_skl,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f60,plain,
! [X0,X1] :
( in(X1,X0)
| ~ subset(set_union2(X0,singleton(X1)),X0) ),
inference(paramodulation,[status(thm)],[f15,f32]) ).
fof(f63,plain,
( in(sK4_skl,singleton(sK3_skl))
| ~ subset(singleton(sK3_skl),singleton(sK3_skl)) ),
inference(paramodulation,[status(thm)],[f41,f60]) ).
fof(f67,plain,
in(sK4_skl,singleton(sK3_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f63,f38]) ).
fof(f68,plain,
sK4_skl = sK3_skl,
inference(resolution,[status(thm)],[f67,f43]) ).
fof(f70,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f68,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:45:22 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.051837 seconds
% 0.12/0.41 % CPU time: 0.149405 seconds
% 0.12/0.41 % Total memory used: 101.543 MB
% 0.12/0.41 % Net memory used: 101.163 MB
%------------------------------------------------------------------------------