%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.22s 0.71s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 101 ( 34 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 121 ( 45 ~; 48 |; 24 &)
% ( 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 : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 71 ( 66 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f143,conjecture,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,negated_conjecture,
~ ! [A] : in(A,succ(A)),
inference(negated_conjecture,[status(cth)],[f143]) ).
fof(f270,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f357,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f377,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)],[f21]) ).
fof(f378,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)],[f377]) ).
fof(f379,plain,
( ! [A,B] :
( ( ( sK23_skl(B,A) = A
| in(sK23_skl(B,A),B) )
& ( sK23_skl(B,A) != A
| ~ in(sK23_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,[sK23_skl]),skolemize(C,sK23_skl(B,A))],[f378]) ).
fof(f381,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f420,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)],[f27]) ).
fof(f421,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)],[f420]) ).
fof(f422,plain,
( ! [A,B,C] :
( ( ( in(sK29_skl(C,B,A),B)
| in(sK29_skl(C,B,A),A)
| in(sK29_skl(C,B,A),C) )
& ( ( ~ in(sK29_skl(C,B,A),B)
& ~ in(sK29_skl(C,B,A),A) )
| ~ in(sK29_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,[sK29_skl]),skolemize(D,sK29_skl(C,B,A))],[f421]) ).
fof(f424,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f422]) ).
fof(f752,plain,
? [A] : ~ in(A,succ(A)),
inference(pre_NNF_transformation,[status(thm)],[f144]) ).
fof(f753,plain,
~ in(sK74_skl,succ(sK74_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74_skl]),skolemize(A,sK74_skl)],[f752]) ).
fof(f754,plain,
~ in(sK74_skl,succ(sK74_skl)),
inference(cnf_transformation,[status(thm)],[f753]) ).
fof(f1168,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f381]) ).
fof(f1176,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f424]) ).
fof(f1258,plain,
! [X0,X1] : in(X0,set_union2(singleton(X0),X1)),
inference(resolution,[status(thm)],[f1176,f1168]) ).
fof(f1267,plain,
! [X0,X1] : in(X0,set_union2(X1,singleton(X0))),
inference(paramodulation,[status(thm)],[f270,f1258]) ).
fof(f1281,plain,
! [X0] : in(X0,succ(X0)),
inference(paramodulation,[status(thm)],[f357,f1267]) ).
fof(f1286,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f754,f1281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 % Computer : n002.cluster.edu
% 0.17/0.47 % Model : x86_64 x86_64
% 0.17/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.47 % Memory : 8046.5625MB
% 0.17/0.47 % OS : Linux 6.8.0-71-generic
% 0.17/0.48 % CPULimit : 300
% 0.17/0.48 % WCLimit : 300
% 0.17/0.48 % DateTime : Mon Sep 21 06:03:31 UTC 2026
% 0.17/0.48 % CPUTime :
% 0.17/0.50 % Drodi V4.1.1
% 0.22/0.71 % Refutation found
% 0.22/0.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.77 % Elapsed time: 0.269924 seconds
% 0.22/0.77 % CPU time: 1.646051 seconds
% 0.22/0.77 % Total memory used: 136.513 MB
% 0.22/0.77 % Net memory used: 133.911 MB
%------------------------------------------------------------------------------