%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV041+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 02:46:30 PM UTC 2026
% Result : Theorem 0.21s 0.55s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 15 unt; 0 def)
% Number of atoms : 72 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 59 ( 17 ~; 12 |; 21 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-3 aty)
% Number of variables : 31 ( 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] :
( leq(X,Y)
=> leq(X,succ(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X] : minus(X,n1) = pred(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [X] : succ(pred(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( geq(minus(n410,n1),n0)
& geq(minus(n330,n1),n0) )
=> ! [A] :
( ( leq(A,n2)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,minus(n0,n1))
& leq(n0,B) )
=> a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),B,A) = init ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( geq(minus(n410,n1),n0)
& geq(minus(n330,n1),n0) )
=> ! [A] :
( ( leq(A,n2)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,minus(n0,n1))
& leq(n0,B) )
=> a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),B,A) = init ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f93,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f106,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f123,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f124,plain,
( ! [X,Y] :
( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ! [X,Y] :
( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(miniscoping,[status(thm)],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f128,plain,
! [X,Y] :
( leq(X,succ(Y))
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f129,plain,
! [X0,X1] :
( leq(X0,succ(X1))
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f225,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f227,plain,
! [X0] : succ(pred(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f259,plain,
( ? [A] :
( ? [B] :
( a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),B,A) != init
& leq(B,minus(n0,n1))
& leq(n0,B) )
& leq(A,n2)
& leq(n0,A) )
& geq(minus(n410,n1),n0)
& geq(minus(n330,n1),n0) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f260,plain,
( a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),sK24_skl,sK23_skl) != init
& leq(sK24_skl,minus(n0,n1))
& leq(n0,sK24_skl)
& leq(sK23_skl,n2)
& leq(n0,sK23_skl)
& geq(minus(n410,n1),n0)
& geq(minus(n330,n1),n0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl]),skolemize(A,sK23_skl),skolemize(B,sK24_skl)],[f259]) ).
fof(f265,plain,
leq(n0,sK24_skl),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f266,plain,
leq(sK24_skl,minus(n0,n1)),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f308,plain,
! [X] :
( X = n0
| ~ leq(X,n0)
| ~ leq(n0,X) ),
inference(pre_NNF_transformation,[status(thm)],[f93]) ).
fof(f309,plain,
! [X0] :
( X0 = n0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f450,plain,
leq(sK24_skl,pred(n0)),
inference(backward_demodulation,[status(thm)],[f225,f266]) ).
fof(f505,plain,
gt(n0,sK24_skl),
inference(resolution,[status(thm)],[f450,f125]) ).
fof(f506,plain,
leq(sK24_skl,succ(pred(n0))),
inference(resolution,[status(thm)],[f450,f129]) ).
fof(f511,plain,
leq(sK24_skl,n0),
inference(forward_demodulation,[status(thm)],[f227,f506]) ).
fof(f600,plain,
( sK24_skl = n0
| ~ leq(sK24_skl,n0) ),
inference(resolution,[status(thm)],[f309,f265]) ).
fof(f603,plain,
sK24_skl = n0,
inference(forward_subsumption_resolution,[status(thm)],[f600,f511]) ).
fof(f612,plain,
gt(sK24_skl,sK24_skl),
inference(backward_demodulation,[status(thm)],[f603,f505]) ).
fof(f634,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f612,f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV041+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.46 % Computer : n019.cluster.edu
% 0.15/0.46 % Model : x86_64 x86_64
% 0.15/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.46 % Memory : 8046.5625MB
% 0.15/0.46 % OS : Linux 6.8.0-71-generic
% 0.15/0.46 % CPULimit : 300
% 0.15/0.46 % WCLimit : 300
% 0.15/0.46 % DateTime : Mon Sep 21 08:28:20 UTC 2026
% 0.15/0.47 % CPUTime :
% 0.15/0.49 % Drodi V4.1.1
% 0.21/0.55 % Refutation found
% 0.21/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.58 % Elapsed time: 0.107592 seconds
% 0.21/0.58 % CPU time: 0.406578 seconds
% 0.21/0.58 % Total memory used: 81.079 MB
% 0.21/0.58 % Net memory used: 80.536 MB
%------------------------------------------------------------------------------