%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:10:40 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 55 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 56 ( 22 ~; 19 |; 10 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 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 : 42 ( 41 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,X] :
( member(X,suc(A))
<=> member(X,union(A,singleton(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
! [A] :
( member(A,on)
=> member(A,suc(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [A] :
( member(A,on)
=> member(A,suc(A)) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f43,plain,
! [X,A,B] :
( ( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f44,plain,
( ! [X,A,B] :
( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ! [X,A,B] :
( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f54,plain,
! [X,A] :
( ( X != A
| member(X,singleton(A)) )
& ( X = A
| ~ member(X,singleton(A)) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f55,plain,
( ! [X,A] :
( X != A
| member(X,singleton(A)) )
& ! [X,A] :
( X = A
| ~ member(X,singleton(A)) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f57,plain,
! [X0,X1] :
( X0 != X1
| member(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f128,plain,
! [A,X] :
( ( ~ member(X,union(A,singleton(A)))
| member(X,suc(A)) )
& ( member(X,union(A,singleton(A)))
| ~ member(X,suc(A)) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f129,plain,
( ! [A,X] :
( ~ member(X,union(A,singleton(A)))
| member(X,suc(A)) )
& ! [A,X] :
( member(X,union(A,singleton(A)))
| ~ member(X,suc(A)) ) ),
inference(miniscoping,[status(thm)],[f128]) ).
fof(f131,plain,
! [X0,X1] :
( ~ member(X0,union(X1,singleton(X1)))
| member(X0,suc(X1)) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
? [A] :
( ~ member(A,suc(A))
& member(A,on) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f133,plain,
( ~ member(sK13_skl,suc(sK13_skl))
& member(sK13_skl,on) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f132]) ).
fof(f135,plain,
~ member(sK13_skl,suc(sK13_skl)),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f143,plain,
! [X0] : member(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f57]) ).
fof(f164,plain,
! [X0,X1] :
( member(X0,suc(X1))
| ~ member(X0,singleton(X1)) ),
inference(resolution,[status(thm)],[f47,f131]) ).
fof(f175,plain,
! [X0] : member(X0,suc(X0)),
inference(resolution,[status(thm)],[f164,f143]) ).
fof(f177,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f135,f175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n026.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:41:53 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.17/0.48 % Refutation found
% 0.17/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.56 % Elapsed time: 0.104942 seconds
% 0.17/0.56 % CPU time: 0.110845 seconds
% 0.17/0.56 % Total memory used: 5.188 MB
% 0.17/0.56 % Net memory used: 5.180 MB
%------------------------------------------------------------------------------