%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM623+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 01:41:14 PM UTC 2026
% Result : Theorem 6.70s 1.52s
% Output : CNFRefutation 6.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 100 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 29 ~; 24 |; 30 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 13 con; 0-2 aty)
% Number of variables : 23 ( 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,hypothesis,
( aSubsetOf0(xO,xS)
& ! [W0] :
( aElementOf0(W0,xO)
=> aElementOf0(W0,xS) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f99,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,hypothesis,
( xp = szmzizndt0(xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& aElementOf0(xp,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,hypothesis,
( aElementOf0(xx,xP)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xQ)
& aElement0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,hypothesis,
( ? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& aElementOf0(xx,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,hypothesis,
! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f119,hypothesis,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f120,conjecture,
xp = xx,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f121,negated_conjecture,
xp != xx,
inference(negated_conjecture,[status(cth)],[f120]) ).
fof(f226,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f227,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f381,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,xS) )
& aSet0(xS) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f383,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f606,plain,
( aSubsetOf0(xO,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xO) ) ),
inference(pre_NNF_transformation,[status(thm)],[f98]) ).
fof(f607,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[status(thm)],[f606]) ).
fof(f609,plain,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [W0] :
( aElementOf0(W0,xO)
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f99]) ).
fof(f611,plain,
! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[status(thm)],[f609]) ).
fof(f629,plain,
( xp = szmzizndt0(xQ)
& ! [W0] :
( sdtlseqdt0(xp,W0)
| ~ aElementOf0(W0,xQ) )
& aElementOf0(xp,xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f103]) ).
fof(f630,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[status(thm)],[f629]) ).
fof(f631,plain,
! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[status(thm)],[f629]) ).
fof(f662,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f665,plain,
( sdtlpdtrp0(xe,sK38_skl) = xx
& aElementOf0(sK38_skl,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xx,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl]),skolemize(W0,sK38_skl)],[f114]) ).
fof(f666,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f665]) ).
fof(f671,plain,
! [W0] :
( sdtlseqdt0(xx,W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(pre_NNF_transformation,[status(thm)],[f116]) ).
fof(f672,plain,
! [X0] :
( sdtlseqdt0(xx,X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(cnf_transformation,[status(thm)],[f671]) ).
fof(f681,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f683,plain,
xp != xx,
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f880,plain,
sdtlseqdt0(xx,xp),
inference(resolution,[status(thm)],[f672,f681]) ).
fof(f1183,plain,
aElementOf0(xp,xO),
inference(resolution,[status(thm)],[f611,f630]) ).
fof(f1212,plain,
aElementOf0(xp,xS),
inference(resolution,[status(thm)],[f1183,f607]) ).
fof(f1219,plain,
aElementOf0(xp,szNzAzT0),
inference(resolution,[status(thm)],[f1212,f383]) ).
fof(f1754,plain,
! [X0] :
( X0 = xx
| ~ sdtlseqdt0(xx,X0)
| ~ sdtlseqdt0(X0,xx)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f227,f666]) ).
fof(f2052,plain,
( xp = xx
| ~ sdtlseqdt0(xp,xx)
| ~ aElementOf0(xp,szNzAzT0) ),
inference(resolution,[status(thm)],[f1754,f880]) ).
fof(f2062,plain,
( xp = xx
| ~ sdtlseqdt0(xp,xx) ),
inference(forward_subsumption_resolution,[status(thm)],[f2052,f1219]) ).
fof(f2086,plain,
~ sdtlseqdt0(xp,xx),
inference(forward_subsumption_resolution,[status(thm)],[f2062,f683]) ).
fof(f2087,plain,
~ aElementOf0(xx,xQ),
inference(resolution,[status(thm)],[f2086,f631]) ).
fof(f2089,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2087,f662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM623+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n001.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 02:50:58 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.53 % Drodi V4.1.1
% 6.70/1.52 % Refutation found
% 6.70/1.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.70/1.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.70/1.54 % Elapsed time: 1.087430 seconds
% 6.70/1.54 % CPU time: 7.606189 seconds
% 6.70/1.54 % Total memory used: 180.015 MB
% 6.70/1.54 % Net memory used: 175.184 MB
%------------------------------------------------------------------------------