%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM633+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 01:41:16 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 7 unt; 3 def)
% Number of atoms : 91 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 100 ( 38 ~; 29 |; 24 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 22 ( 17 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,hypothesis,
( isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(szDzizrdt0(xd),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,hypothesis,
( isCountable0(xO)
& aSet0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,hypothesis,
aSubsetOf0(xO,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,conjecture,
( ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xO,xK))
=> ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xc))
& aSubsetOf0(W0,szNzAzT0)
& W0 != slcrc0 ) )
=> ? [W0] :
( ? [W1] :
( ! [W2] :
( aElementOf0(W2,slbdtsldtrb0(W1,xK))
=> sdtlpdtrp0(xc,W2) = W0 )
& isCountable0(W1)
& aSubsetOf0(W1,xS) )
& aElementOf0(W0,xT) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,negated_conjecture,
~ ( ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xO,xK))
=> ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xc))
& aSubsetOf0(W0,szNzAzT0)
& W0 != slcrc0 ) )
=> ? [W0] :
( ? [W1] :
( ! [W2] :
( aElementOf0(W2,slbdtsldtrb0(W1,xK))
=> sdtlpdtrp0(xc,W2) = W0 )
& isCountable0(W1)
& aSubsetOf0(W1,xS) )
& aElementOf0(W0,xT) ) ),
inference(negated_conjecture,[status(cth)],[f99]) ).
fof(f419,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f424,plain,
isCountable0(xO),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f430,plain,
aSubsetOf0(xO,xS),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f431,plain,
( ! [W0] :
( ! [W1] :
( ? [W2] :
( sdtlpdtrp0(xc,W2) != W0
& aElementOf0(W2,slbdtsldtrb0(W1,xK)) )
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS) )
| ~ aElementOf0(W0,xT) )
& ! [W0] :
( ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xc))
& aSubsetOf0(W0,szNzAzT0)
& W0 != slcrc0 )
| ~ aElementOf0(W0,slbdtsldtrb0(xO,xK)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f100]) ).
fof(f432,plain,
( ! [W0] :
( ! [W1] :
( ( sdtlpdtrp0(xc,sK25_skl(W1,W0)) != W0
& aElementOf0(sK25_skl(W1,W0),slbdtsldtrb0(W1,xK)) )
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS) )
| ~ aElementOf0(W0,xT) )
& ! [W0] :
( ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xc))
& aSubsetOf0(W0,szNzAzT0)
& W0 != slcrc0 )
| ~ aElementOf0(W0,slbdtsldtrb0(xO,xK)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(W2,sK25_skl(W1,W0))],[f431]) ).
fof(f436,plain,
! [X0] :
( sdtlpdtrp0(xc,X0) = szDzizrdt0(xd)
| ~ aElementOf0(X0,slbdtsldtrb0(xO,xK)) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f437,plain,
! [X0,X1] :
( aElementOf0(sK25_skl(X1,X0),slbdtsldtrb0(X1,xK))
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f438,plain,
! [X0,X1] :
( sdtlpdtrp0(xc,sK25_skl(X1,X0)) != X0
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f593,plain,
! [X0] :
( aElementOf0(sK25_skl(X0,szDzizrdt0(xd)),slbdtsldtrb0(X0,xK))
| ~ isCountable0(X0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f419,f437]) ).
fof(f594,plain,
! [X0] :
( sdtlpdtrp0(xc,sK25_skl(X0,szDzizrdt0(xd))) != szDzizrdt0(xd)
| ~ isCountable0(X0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f419,f438]) ).
fof(f684,plain,
( sdtlpdtrp0(xc,sK25_skl(xO,szDzizrdt0(xd))) = szDzizrdt0(xd)
| ~ isCountable0(xO)
| ~ aSubsetOf0(xO,xS) ),
inference(resolution,[status(thm)],[f593,f436]) ).
fof(f687,definition,
( sQ30_spl
<=> aSubsetOf0(xO,xS) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( sQ30_spl
| ~ aSubsetOf0(xO,xS) ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f690,definition,
( sQ31_spl
<=> isCountable0(xO) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f692,plain,
( sQ31_spl
| ~ isCountable0(xO) ),
inference(component_clause,[status(thm)],[f690]) ).
fof(f693,definition,
( sQ32_spl
<=> sdtlpdtrp0(xc,sK25_skl(xO,szDzizrdt0(xd))) = szDzizrdt0(xd) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f696,plain,
( sQ32_spl
| ~ sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f684,f687,f690,f693]) ).
fof(f705,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f692,f424]) ).
fof(f706,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f705]) ).
fof(f707,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f689,f430]) ).
fof(f708,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f707]) ).
fof(f736,plain,
( sdtlpdtrp0(xc,sK25_skl(xO,szDzizrdt0(xd))) != szDzizrdt0(xd)
| ~ aSubsetOf0(xO,xS) ),
inference(resolution,[status(thm)],[f594,f424]) ).
fof(f739,plain,
( ~ sQ32_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f736,f687,f693]) ).
fof(f751,plain,
$false,
inference(sat_refutation,[status(thm)],[f696,f706,f708,f739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM633+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n017.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 02:41:27 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.48 % Refutation found
% 0.17/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.51 % Elapsed time: 0.069568 seconds
% 0.17/0.51 % CPU time: 0.180912 seconds
% 0.17/0.51 % Total memory used: 62.662 MB
% 0.17/0.51 % Net memory used: 62.572 MB
%------------------------------------------------------------------------------