%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM552+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 : n016.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 01:40:58 PM UTC 2026
% Result : Theorem 0.18s 0.63s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 11 unt; 2 def)
% Number of atoms : 174 ( 26 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 222 ( 88 ~; 85 |; 38 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 66 ( 62 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,definition,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,hypothesis,
( slbdtsldtrb0(xS,xk) != slcrc0
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,conjecture,
( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,negated_conjecture,
~ ( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) ),
inference(negated_conjecture,[status(cth)],[f68]) ).
fof(f94,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f95,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f95]) ).
fof(f97,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f96]) ).
fof(f99,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f251,plain,
! [W0,W1] :
( ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f252,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| aElementOf0(W3,W2) )
& ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ( ( ! [W3] :
( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f251]) ).
fof(f253,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| aElementOf0(W3,W2) )
& ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f252]) ).
fof(f254,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( sbrdtbr0(sK10_skl(W2,W1,W0)) = W1
& aSubsetOf0(sK10_skl(W2,W1,W0),W0) )
| aElementOf0(sK10_skl(W2,W1,W0),W2) )
& ( sbrdtbr0(sK10_skl(W2,W1,W0)) != W1
| ~ aSubsetOf0(sK10_skl(W2,W1,W0),W0)
| ~ aElementOf0(sK10_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(W3,sK10_skl(W2,W1,W0))],[f253]) ).
fof(f255,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f256,plain,
! [X0,X1,X2,X3] :
( aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f268,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f270,plain,
aSet0(xT),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f272,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f275,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f281,plain,
( ~ aElementOf0(xx,xT)
& aElementOf0(xx,xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f282,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f283,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f313,plain,
! [X0,X1] :
( aSet0(slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f255]) ).
fof(f314,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X0)
| ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f256]) ).
fof(f337,plain,
! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(resolution,[status(thm)],[f99,f272]) ).
fof(f1230,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk))
| aSubsetOf0(X0,xT)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f314,f337]) ).
fof(f1235,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk))
| aSubsetOf0(X0,xT)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1230,f270]) ).
fof(f1922,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk))
| aSubsetOf0(X0,xT) ),
inference(forward_subsumption_resolution,[status(thm)],[f1235,f268]) ).
fof(f1928,plain,
( ~ aSet0(slbdtsldtrb0(xT,xk))
| aSubsetOf0(xQ,xT) ),
inference(resolution,[status(thm)],[f1922,f275]) ).
fof(f1950,plain,
( ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT)
| aSubsetOf0(xQ,xT) ),
inference(resolution,[status(thm)],[f1928,f313]) ).
fof(f1951,plain,
( ~ aElementOf0(xk,szNzAzT0)
| aSubsetOf0(xQ,xT) ),
inference(forward_subsumption_resolution,[status(thm)],[f1950,f270]) ).
fof(f1952,plain,
aSubsetOf0(xQ,xT),
inference(forward_subsumption_resolution,[status(thm)],[f1951,f268]) ).
fof(f1962,plain,
! [X0] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,xQ)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f1952,f99]) ).
fof(f1970,plain,
! [X0] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,xQ) ),
inference(forward_subsumption_resolution,[status(thm)],[f1962,f270]) ).
fof(f1980,plain,
~ aElementOf0(xx,xQ),
inference(resolution,[status(thm)],[f1970,f283]) ).
fof(f1985,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1980,f282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM552+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n016.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 02:44:24 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.18/0.63 % Refutation found
% 0.18/0.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.29/0.70 % Elapsed time: 0.240497 seconds
% 0.29/0.70 % CPU time: 1.264395 seconds
% 0.29/0.70 % Total memory used: 120.931 MB
% 0.29/0.70 % Net memory used: 119.612 MB
%------------------------------------------------------------------------------