%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG088+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 02:04:55 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 62 ( 2 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 66 ( 24 ~; 16 |; 20 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,hypothesis,
( aIdeal0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) )
& ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f116,plain,
( aIdeal0(xJ)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xJ)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xJ)
| ~ aElementOf0(W1,xJ) ) )
| ~ aElementOf0(W0,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f118,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f122,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f135,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f136,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f138,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f139,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f141,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f142,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f172,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(xn,xJ)
| ~ aElementOf0(xl,xJ) ),
inference(resolution,[status(thm)],[f122,f142]) ).
fof(f175,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(xn,xJ) ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f136]) ).
fof(f190,plain,
~ aElementOf0(sdtpldt0(xk,xm),xI),
inference(forward_subsumption_resolution,[status(thm)],[f175,f139]) ).
fof(f191,plain,
( ~ aElementOf0(xm,xI)
| ~ aElementOf0(xk,xI) ),
inference(resolution,[status(thm)],[f190,f118]) ).
fof(f192,plain,
~ aElementOf0(xm,xI),
inference(forward_subsumption_resolution,[status(thm)],[f191,f135]) ).
fof(f193,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f192,f138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG088+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:19:25 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.059891 seconds
% 0.12/0.42 % CPU time: 0.165686 seconds
% 0.12/0.42 % Total memory used: 104.425 MB
% 0.12/0.42 % Net memory used: 104.327 MB
%------------------------------------------------------------------------------