%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG089+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.13s 5.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 76 ( 5 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 80 ( 24 ~; 16 |; 34 &)
% ( 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 : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 20 ( 16 !; 4 ?)
% 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xy
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xx
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f117,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(f120,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f124,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f126,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& sdtpldt0(sK13_skl,sK14_skl) = xy
& aElementOf0(sK14_skl,xJ)
& aElementOf0(sK13_skl,xI)
& aElementOf0(xx,sdtpldt1(xI,xJ))
& sdtpldt0(sK11_skl,sK12_skl) = xx
& aElementOf0(sK12_skl,xJ)
& aElementOf0(sK11_skl,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(W0,sK11_skl),skolemize(W1,sK12_skl),skolemize(W0,sK13_skl),skolemize(W1,sK14_skl)],[f26]) ).
fof(f135,plain,
aElement0(xz),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f136,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f137,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f144,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f145,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f165,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElement0(xz)
| ~ aElementOf0(xl,xJ) ),
inference(resolution,[status(thm)],[f124,f145]) ).
fof(f166,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElement0(xz) ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f137]) ).
fof(f169,plain,
~ aElementOf0(sdtasdt0(xz,xk),xI),
inference(forward_subsumption_resolution,[status(thm)],[f166,f135]) ).
fof(f170,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xk,xI) ),
inference(resolution,[status(thm)],[f169,f120]) ).
fof(f171,plain,
~ aElement0(xz),
inference(forward_subsumption_resolution,[status(thm)],[f170,f136]) ).
fof(f172,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f171,f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG089+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n003.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 04:20:51 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.13/5.41 % Refutation found
% 0.13/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.43 % Elapsed time: 0.049326 seconds
% 0.13/5.43 % CPU time: 0.137817 seconds
% 0.13/5.43 % Total memory used: 81.531 MB
% 0.13/5.43 % Net memory used: 81.456 MB
%------------------------------------------------------------------------------