%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG099+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 : 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 02:04:57 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 17 unt; 1 def)
% Number of atoms : 141 ( 3 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 158 ( 65 ~; 53 |; 30 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 46 ( 44 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,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(f30,hypothesis,
( aElement0(xy)
& aElement0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,hypothesis,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
? [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,xy,xJ)
| aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(W0,xx,xI)
| aElementOf0(sdtpldt0(W0,smndt0(xx)),xI) )
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ? [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,xy,xJ)
| aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(W0,xx,xI)
| aElementOf0(sdtpldt0(W0,smndt0(xx)),xI) )
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f44,plain,
! [W0,W1] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f45,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f80,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f81,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f130,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)],[f28]) ).
fof(f131,plain,
aSet0(xI),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f133,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f135,plain,
aSet0(xJ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f137,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f145,plain,
aElement0(xx),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f146,plain,
aElement0(xy),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f147,plain,
aElementOf0(xa,xI),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f148,plain,
aElementOf0(xb,xJ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f150,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f151,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f152,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f153,plain,
! [W0] :
( ( ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ)
& ~ aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ) )
| ( ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
& ~ aElementOf0(sdtpldt0(W0,smndt0(xx)),xI) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f154,definition,
! [W0] :
( sP2_prd(W0)
<=> ( ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
& ~ aElementOf0(sdtpldt0(W0,smndt0(xx)),xI) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f155,plain,
! [W0] :
( ( ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ)
& ~ aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ) )
| sP2_prd(W0)
| ~ aElement0(W0) ),
inference(formula_renaming,[status(thm)],[f153,f154]) ).
fof(f156,plain,
! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| sP2_prd(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f169,plain,
! [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,xx,xI)
| aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sP2_prd(W0) )
& ( ( ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
& ~ aElementOf0(sdtpldt0(W0,smndt0(xx)),xI) )
| ~ sP2_prd(W0) ) ),
inference(NNF_transformation,[status(thm)],[f154]) ).
fof(f170,plain,
( ! [W0] :
( sdteqdtlpzmzozddtrp0(W0,xx,xI)
| aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sP2_prd(W0) )
& ! [W0] :
( ( ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
& ~ aElementOf0(sdtpldt0(W0,smndt0(xx)),xI) )
| ~ sP2_prd(W0) ) ),
inference(miniscoping,[status(thm)],[f169]) ).
fof(f171,plain,
! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f204,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElementOf0(X1,xJ)
| aElement0(sdtasdt0(X0,X1))
| ~ aSet0(xJ) ),
inference(resolution,[status(thm)],[f81,f137]) ).
fof(f205,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElementOf0(X1,xI)
| aElement0(sdtasdt0(X0,X1))
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f81,f133]) ).
fof(f212,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElementOf0(X1,xJ)
| aElement0(sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f135]) ).
fof(f213,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElementOf0(X1,xI)
| aElement0(sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f131]) ).
fof(f243,plain,
~ sP2_prd(xw),
inference(resolution,[status(thm)],[f151,f171]) ).
fof(f252,plain,
( sP2_prd(xw)
| ~ aElement0(xw) ),
inference(resolution,[status(thm)],[f152,f156]) ).
fof(f255,plain,
~ aElement0(xw),
inference(forward_subsumption_resolution,[status(thm)],[f252,f243]) ).
fof(f267,plain,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(paramodulation,[status(thm)],[f150,f45]) ).
fof(f270,plain,
( ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f255]) ).
fof(f277,plain,
( ~ aElement0(xy)
| ~ aElementOf0(xa,xI)
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(resolution,[status(thm)],[f270,f213]) ).
fof(f280,plain,
( ~ aElement0(xy)
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(forward_subsumption_resolution,[status(thm)],[f277,f147]) ).
fof(f283,plain,
~ aElement0(sdtasdt0(xx,xb)),
inference(forward_subsumption_resolution,[status(thm)],[f280,f146]) ).
fof(f285,plain,
( ~ aElement0(xx)
| ~ aElementOf0(xb,xJ) ),
inference(resolution,[status(thm)],[f283,f212]) ).
fof(f288,plain,
~ aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[f285,f148]) ).
fof(f290,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f288,f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG099+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.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 04:19:33 UTC 2026
% 0.12/0.36 % 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
% 0.12/0.43 % Elapsed time: 0.056897 seconds
% 0.12/0.43 % CPU time: 0.179735 seconds
% 0.12/0.43 % Total memory used: 105.981 MB
% 0.12/0.43 % Net memory used: 105.798 MB
%------------------------------------------------------------------------------