%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU230+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:19:48 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 99 ( 32 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 123 ( 46 ~; 49 |; 24 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 65 ( 60 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A] : in(A,succ(A)),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f51,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f52,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)],[f7]) ).
fof(f53,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)],[f52]) ).
fof(f54,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))],[f53]) ).
fof(f56,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f59,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f60,plain,
( ! [A,B,C] :
( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
( ! [A,B,C] :
( ( ( in(sK1_skl(C,B,A),B)
| in(sK1_skl(C,B,A),A)
| in(sK1_skl(C,B,A),C) )
& ( ( ~ in(sK1_skl(C,B,A),B)
& ~ in(sK1_skl(C,B,A),A) )
| ~ in(sK1_skl(C,B,A),C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f60]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f115,plain,
? [A] : ~ in(A,succ(A)),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f116,plain,
~ in(sK12_skl,succ(sK12_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(A,sK12_skl)],[f115]) ).
fof(f117,plain,
~ in(sK12_skl,succ(sK12_skl)),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f132,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f56]) ).
fof(f135,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f64]) ).
fof(f262,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| in(X0,succ(X1)) ),
inference(paramodulation,[status(thm)],[f51,f135]) ).
fof(f327,plain,
! [X0] : in(X0,succ(X0)),
inference(resolution,[status(thm)],[f262,f132]) ).
fof(f329,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f117,f327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU230+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n009.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 06:00:57 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.052914 seconds
% 0.12/0.41 % CPU time: 0.160388 seconds
% 0.12/0.41 % Total memory used: 99.738 MB
% 0.12/0.41 % Net memory used: 99.672 MB
%------------------------------------------------------------------------------