%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM606+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 : n013.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 01:41:10 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 12 unt; 1 def)
% Number of atoms : 103 ( 1 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 120 ( 50 ~; 47 |; 17 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 43 !; 2 ?)
% 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(f14,axiom,
! [W0,W1,W2] :
( ( aSet0(W2)
& aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W2)
& aSubsetOf0(W0,W1) )
=> aSubsetOf0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,hypothesis,
aSubsetOf0(xO,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f101,conjecture,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f102,negated_conjecture,
~ aSubsetOf0(xQ,szNzAzT0),
inference(negated_conjecture,[status(cth)],[f101]) ).
fof(f127,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(f128,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)],[f127]) ).
fof(f129,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)],[f128]) ).
fof(f130,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))],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f141,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f142,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f179,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f362,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f432,plain,
aSubsetOf0(xO,xS),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f434,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f436,plain,
~ aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f485,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f131]) ).
fof(f504,plain,
! [X0,X1] :
( aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f179,f485]) ).
fof(f507,plain,
! [X0] :
( aSet0(X0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f179,f131]) ).
fof(f522,plain,
! [X0,X1] :
( aSubsetOf0(X0,szNzAzT0)
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f507]) ).
fof(f560,plain,
! [X0] :
( aSubsetOf0(X0,szNzAzT0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f362,f522]) ).
fof(f561,plain,
aSet0(xS),
inference(resolution,[status(thm)],[f362,f507]) ).
fof(f562,plain,
! [X0,X1] :
( aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f561,f485]) ).
fof(f565,plain,
! [X0] :
( aSet0(X0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f561,f131]) ).
fof(f646,plain,
! [X0,X1] :
( aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f562,f565]) ).
fof(f649,plain,
! [X0] :
( aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X0,xO) ),
inference(resolution,[status(thm)],[f432,f646]) ).
fof(f712,plain,
aSubsetOf0(xQ,xS),
inference(resolution,[status(thm)],[f649,f434]) ).
fof(f715,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(resolution,[status(thm)],[f712,f560]) ).
fof(f724,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f715,f436]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM606+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:43:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.066305 seconds
% 0.14/0.44 % CPU time: 0.186772 seconds
% 0.14/0.44 % Total memory used: 111.327 MB
% 0.14/0.44 % Net memory used: 111.103 MB
%------------------------------------------------------------------------------