%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET890+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 : n006.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 02:10:55 PM UTC 2026
% Result : Theorem 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 137 ( 56 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 163 ( 59 ~; 75 |; 25 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 84 ( 74 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [A] : union(singleton(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A] : union(singleton(A)) = A,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f19,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(f20,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)],[f19]) ).
fof(f21,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))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f33,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ( ! [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
( ! [A,B] :
( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
( ! [A,B] :
( ( ( ( in(sK4_skl(B,A),A)
& in(sK3_skl(B,A),sK4_skl(B,A)) )
| in(sK3_skl(B,A),B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(sK3_skl(B,A),D) )
| ~ in(sK3_skl(B,A),B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ( in(sK2_skl(C,B,A),A)
& in(C,sK2_skl(C,B,A)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(D,sK2_skl(C,B,A)),skolemize(C,sK3_skl(B,A)),skolemize(D,sK4_skl(B,A))],[f34]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(sK3_skl(X0,X1),X2)
| ~ in(sK3_skl(X0,X1),X0)
| X0 = union(X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f40,plain,
! [X0,X1] :
( in(sK3_skl(X0,X1),sK4_skl(X0,X1))
| in(sK3_skl(X0,X1),X0)
| X0 = union(X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f41,plain,
! [X0,X1] :
( in(sK4_skl(X0,X1),X1)
| in(sK3_skl(X0,X1),X0)
| X0 = union(X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f50,plain,
? [A] : union(singleton(A)) != A,
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f51,plain,
union(singleton(sK7_skl)) != sK7_skl,
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f50]) ).
fof(f52,plain,
union(singleton(sK7_skl)) != sK7_skl,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f22]) ).
fof(f56,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f23]) ).
fof(f220,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(sK3_skl(X0,X1),X0)
| X0 = union(X1)
| in(sK4_skl(X0,X1),X1)
| X0 = union(X1) ),
inference(resolution,[status(thm)],[f41,f39]) ).
fof(f245,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(sK3_skl(X0,X1),X0)
| in(sK4_skl(X0,X1),X1)
| X0 = union(X1) ),
inference(duplicate_literals_removal,[status(thm)],[f220]) ).
fof(f246,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(sK4_skl(X0,X1),X1)
| X0 = union(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f245,f41]) ).
fof(f334,plain,
! [X0] :
( in(sK4_skl(X0,singleton(X0)),singleton(X0))
| X0 = union(singleton(X0)) ),
inference(resolution,[status(thm)],[f246,f56]) ).
fof(f481,plain,
! [X0] :
( sK4_skl(X0,singleton(X0)) = X0
| X0 = union(singleton(X0)) ),
inference(resolution,[status(thm)],[f334,f55]) ).
fof(f495,plain,
! [X0] :
( X0 = union(singleton(X0))
| in(sK3_skl(X0,singleton(X0)),X0)
| in(sK3_skl(X0,singleton(X0)),X0)
| X0 = union(singleton(X0)) ),
inference(paramodulation,[status(thm)],[f481,f40]) ).
fof(f502,plain,
! [X0] :
( in(sK3_skl(X0,singleton(X0)),X0)
| X0 = union(singleton(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f495]) ).
fof(f503,plain,
! [X0] :
( ~ in(X0,singleton(X0))
| ~ in(sK3_skl(X0,singleton(X0)),X0)
| X0 = union(singleton(X0))
| X0 = union(singleton(X0)) ),
inference(resolution,[status(thm)],[f502,f39]) ).
fof(f520,plain,
! [X0] :
( ~ in(X0,singleton(X0))
| ~ in(sK3_skl(X0,singleton(X0)),X0)
| X0 = union(singleton(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f503]) ).
fof(f521,plain,
! [X0] :
( ~ in(X0,singleton(X0))
| X0 = union(singleton(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f520,f502]) ).
fof(f532,plain,
sK7_skl != sK7_skl,
inference(backward_demodulation,[status(thm)],[f547,f52]) ).
fof(f547,plain,
! [X0] : X0 = union(singleton(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f521,f56]) ).
fof(f574,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.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 05:42:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.47 % Refutation found
% 0.13/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.49 % Elapsed time: 0.138866 seconds
% 0.13/0.49 % CPU time: 0.814745 seconds
% 0.13/0.49 % Total memory used: 93.499 MB
% 0.13/0.49 % Net memory used: 90.716 MB
%------------------------------------------------------------------------------