%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM538+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 : 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 01:40:55 PM UTC 2026
% Result : Theorem 1.96s 0.79s
% Output : CNFRefutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 12 unt; 0 def)
% Number of atoms : 119 ( 27 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 128 ( 48 ~; 43 |; 23 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isFinite0(W1)
& aSet0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [W0] :
( ( isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( aElementOf0(xx,xS)
& isFinite0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
~ ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f54,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f55,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f112,plain,
! [W0] :
( ! [W1] :
( sdtpldt0(sdtmndt0(W0,W1),W1) = W0
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f113,plain,
! [X0,X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f122,plain,
! [W0] :
( ! [W1] :
( isFinite0(sdtmndt0(W1,W0))
| ~ isFinite0(W1)
| ~ aSet0(W1) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f123,plain,
! [X0,X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f172,plain,
! [W0] :
( ! [W1] :
( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0))
| aElementOf0(W1,W0)
| ~ aElement0(W1) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f173,plain,
! [X0,X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f174,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f175,plain,
isFinite0(xS),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f176,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f177,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS)
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f178,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS)
& ! [W0] :
( ( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx)) ),
inference(NNF_transformation,[status(thm)],[f177]) ).
fof(f179,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS)
& ! [W0] :
( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ! [W0] :
( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) ),
inference(miniscoping,[status(thm)],[f178]) ).
fof(f180,plain,
aSet0(sdtmndt0(xS,xx)),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f183,plain,
! [X0] :
( X0 != xx
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f185,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f196,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f176,f55]) ).
fof(f197,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[f196,f174]) ).
fof(f302,plain,
! [X0] :
( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),X0)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f173,f180]) ).
fof(f2559,plain,
( sdtpldt0(sdtmndt0(xS,xx),xx) = xS
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f113,f176]) ).
fof(f2572,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) = xS,
inference(forward_subsumption_resolution,[status(thm)],[f2559,f174]) ).
fof(f4094,plain,
! [X0] :
( isFinite0(sdtmndt0(X0,xx))
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f123,f197]) ).
fof(f4974,plain,
( isFinite0(sdtmndt0(xS,xx))
| ~ isFinite0(xS) ),
inference(resolution,[status(thm)],[f4094,f174]) ).
fof(f5011,plain,
isFinite0(sdtmndt0(xS,xx)),
inference(forward_subsumption_resolution,[status(thm)],[f4974,f175]) ).
fof(f5014,plain,
! [X0] :
( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),X0)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f302,f5011]) ).
fof(f5091,plain,
( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))
| aElementOf0(xx,sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f5014,f197]) ).
fof(f5092,plain,
( sbrdtbr0(xS) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))
| aElementOf0(xx,sdtmndt0(xS,xx)) ),
inference(forward_demodulation,[status(thm)],[f2572,f5091]) ).
fof(f5093,plain,
aElementOf0(xx,sdtmndt0(xS,xx)),
inference(forward_subsumption_resolution,[status(thm)],[f5092,f185]) ).
fof(f5113,plain,
xx != xx,
inference(resolution,[status(thm)],[f5093,f183]) ).
fof(f5118,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f5113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM538+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:40:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 1.96/0.79 % Refutation found
% 1.96/0.79 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.96/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.96/0.83 % Elapsed time: 0.459047 seconds
% 1.96/0.83 % CPU time: 3.239956 seconds
% 1.96/0.83 % Total memory used: 122.219 MB
% 1.96/0.83 % Net memory used: 118.834 MB
%------------------------------------------------------------------------------