%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV167+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 02:46:47 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 202 ( 54 equ)
% Maximal formula atoms : 36 ( 6 avg)
% Number of connectives : 244 ( 73 ~; 66 |; 74 &)
% ( 1 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-3 aty)
% Number of variables : 74 ( 73 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X] : leq(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( ( X != Y
& leq(X,Y) )
=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( ( gt(loopcounter,n1)
=> ! [I] :
( ( leq(I,n4)
& leq(n0,I) )
=> a_select2(sigmaold_init,I) = init ) )
& ( gt(loopcounter,n1)
=> ! [H] :
( ( leq(H,n4)
& leq(n0,H) )
=> a_select2(rhoold_init,H) = init ) )
& ( gt(loopcounter,n1)
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(muold_init,G) = init ) )
& ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select3(center_init,F,n0) = init )
& ! [E] :
( ( leq(E,pred(pv40))
& leq(n0,E) )
=> a_select2(sigma_init,E) = init )
& ! [D] :
( ( leq(D,pred(pv40))
& leq(n0,D) )
=> a_select2(mu_init,D) = init )
& ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select2(rho_init,C) = init )
& ! [A] :
( ( leq(A,n135299)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init )
=> ! [J] :
( ( leq(J,pv40)
& leq(n0,J) )
=> a_select2(mu_init,J) = init ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ( gt(loopcounter,n1)
=> ! [I] :
( ( leq(I,n4)
& leq(n0,I) )
=> a_select2(sigmaold_init,I) = init ) )
& ( gt(loopcounter,n1)
=> ! [H] :
( ( leq(H,n4)
& leq(n0,H) )
=> a_select2(rhoold_init,H) = init ) )
& ( gt(loopcounter,n1)
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(muold_init,G) = init ) )
& ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select3(center_init,F,n0) = init )
& ! [E] :
( ( leq(E,pred(pv40))
& leq(n0,E) )
=> a_select2(sigma_init,E) = init )
& ! [D] :
( ( leq(D,pred(pv40))
& leq(n0,D) )
=> a_select2(mu_init,D) = init )
& ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select2(rho_init,C) = init )
& ! [A] :
( ( leq(A,n135299)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init )
=> ! [J] :
( ( leq(J,pv40)
& leq(n0,J) )
=> a_select2(mu_init,J) = init ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f99,plain,
! [X0] : leq(X0,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f100,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f101,plain,
! [X,Z] :
( leq(X,Z)
| ! [Y] :
( ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f113,plain,
! [X,Y] :
( gt(Y,X)
| X = Y
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f114,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f116,plain,
( ! [X,Y] :
( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ! [X,Y] :
( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,pred(X1)) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f251,plain,
( ? [J] :
( a_select2(mu_init,J) != init
& leq(J,pv40)
& leq(n0,J) )
& ( ! [I] :
( a_select2(sigmaold_init,I) = init
| ~ leq(I,n4)
| ~ leq(n0,I) )
| ~ gt(loopcounter,n1) )
& ( ! [H] :
( a_select2(rhoold_init,H) = init
| ~ leq(H,n4)
| ~ leq(n0,H) )
| ~ gt(loopcounter,n1) )
& ( ! [G] :
( a_select2(muold_init,G) = init
| ~ leq(G,n4)
| ~ leq(n0,G) )
| ~ gt(loopcounter,n1) )
& ! [F] :
( a_select3(center_init,F,n0) = init
| ~ leq(F,n4)
| ~ leq(n0,F) )
& ! [E] :
( a_select2(sigma_init,E) = init
| ~ leq(E,pred(pv40))
| ~ leq(n0,E) )
& ! [D] :
( a_select2(mu_init,D) = init
| ~ leq(D,pred(pv40))
| ~ leq(n0,D) )
& ! [C] :
( a_select2(rho_init,C) = init
| ~ leq(C,n4)
| ~ leq(n0,C) )
& ! [A] :
( ! [B] :
( a_select3(q_init,A,B) = init
| ~ leq(B,n4)
| ~ leq(n0,B) )
| ~ leq(A,n135299)
| ~ leq(n0,A) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f252,plain,
( a_select2(mu_init,sK23_skl) != init
& leq(sK23_skl,pv40)
& leq(n0,sK23_skl)
& ( ! [I] :
( a_select2(sigmaold_init,I) = init
| ~ leq(I,n4)
| ~ leq(n0,I) )
| ~ gt(loopcounter,n1) )
& ( ! [H] :
( a_select2(rhoold_init,H) = init
| ~ leq(H,n4)
| ~ leq(n0,H) )
| ~ gt(loopcounter,n1) )
& ( ! [G] :
( a_select2(muold_init,G) = init
| ~ leq(G,n4)
| ~ leq(n0,G) )
| ~ gt(loopcounter,n1) )
& ! [F] :
( a_select3(center_init,F,n0) = init
| ~ leq(F,n4)
| ~ leq(n0,F) )
& ! [E] :
( a_select2(sigma_init,E) = init
| ~ leq(E,pred(pv40))
| ~ leq(n0,E) )
& ! [D] :
( a_select2(mu_init,D) = init
| ~ leq(D,pred(pv40))
| ~ leq(n0,D) )
& ! [C] :
( a_select2(rho_init,C) = init
| ~ leq(C,n4)
| ~ leq(n0,C) )
& ! [A] :
( ! [B] :
( a_select3(q_init,A,B) = init
| ~ leq(B,n4)
| ~ leq(n0,B) )
| ~ leq(A,n135299)
| ~ leq(n0,A) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(J,sK23_skl)],[f251]) ).
fof(f253,plain,
a_select2(mu_init,pv40) = init,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f259,plain,
! [X0] :
( a_select2(mu_init,X0) = init
| ~ leq(X0,pred(pv40))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f265,plain,
leq(n0,sK23_skl),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f266,plain,
leq(sK23_skl,pv40),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f267,plain,
a_select2(mu_init,sK23_skl) != init,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f363,plain,
! [X0,X1] :
( ~ leq(X1,pred(pv40))
| ~ leq(X0,X1)
| a_select2(mu_init,X0) = init
| ~ leq(n0,X0) ),
inference(resolution,[status(thm)],[f259,f102]) ).
fof(f656,plain,
! [X0] :
( ~ leq(X0,pred(pv40))
| ~ leq(sK23_skl,X0)
| ~ leq(n0,sK23_skl) ),
inference(resolution,[status(thm)],[f363,f267]) ).
fof(f658,plain,
! [X0] :
( ~ leq(X0,pred(pv40))
| ~ leq(sK23_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f656,f265]) ).
fof(f693,plain,
~ leq(sK23_skl,pred(pv40)),
inference(resolution,[status(thm)],[f658,f99]) ).
fof(f694,plain,
~ gt(pv40,sK23_skl),
inference(resolution,[status(thm)],[f693,f118]) ).
fof(f772,plain,
( sK23_skl = pv40
| ~ leq(sK23_skl,pv40) ),
inference(resolution,[status(thm)],[f694,f114]) ).
fof(f775,plain,
sK23_skl = pv40,
inference(forward_subsumption_resolution,[status(thm)],[f772,f266]) ).
fof(f794,plain,
a_select2(mu_init,sK23_skl) = init,
inference(backward_demodulation,[status(thm)],[f775,f253]) ).
fof(f800,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f794,f267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV167+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 08:33:33 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.071697 seconds
% 0.14/0.42 % CPU time: 0.269620 seconds
% 0.14/0.42 % Total memory used: 111.543 MB
% 0.14/0.42 % Net memory used: 111.044 MB
%------------------------------------------------------------------------------