%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM607+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 : n006.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 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 6 unt; 1 def)
% Number of atoms : 134 ( 2 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 163 ( 58 ~; 50 |; 42 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 48 ( 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/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/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(f102,conjecture,
( aElementOf0(xQ,szDzozmdt0(xc))
| aSubsetOf0(xQ,xS)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
| aSubsetOf0(xQ,xS)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,negated_conjecture,
~ ( aElementOf0(xQ,szDzozmdt0(xc))
| aSubsetOf0(xQ,xS)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
| aSubsetOf0(xQ,xS)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) ) ),
inference(negated_conjecture,[status(cth)],[f102]) ).
fof(f128,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(f129,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)],[f128]) ).
fof(f130,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)],[f129]) ).
fof(f131,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))],[f130]) ).
fof(f132,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f142,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(f143,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f363,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,xS) )
& aSet0(xS) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f364,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f363]) ).
fof(f588,plain,
( aSubsetOf0(xO,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xO) ) ),
inference(pre_NNF_transformation,[status(thm)],[f98]) ).
fof(f590,plain,
aSubsetOf0(xO,xS),
inference(cnf_transformation,[status(thm)],[f588]) ).
fof(f591,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(f594,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[status(thm)],[f591]) ).
fof(f605,plain,
( ~ aElementOf0(xQ,szDzozmdt0(xc))
& ~ aSubsetOf0(xQ,xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,xQ) )
& ~ aSubsetOf0(xQ,xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,xQ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f103]) ).
fof(f606,plain,
( ~ aElementOf0(xQ,szDzozmdt0(xc))
& ~ aSubsetOf0(xQ,xS)
& ~ aElementOf0(sK38_skl,xS)
& aElementOf0(sK38_skl,xQ)
& ~ aSubsetOf0(xQ,xS)
& ~ aElementOf0(sK37_skl,xS)
& aElementOf0(sK37_skl,xQ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37_skl,sK38_skl]),skolemize(W0,sK37_skl),skolemize(W0,sK38_skl)],[f605]) ).
fof(f609,plain,
~ aSubsetOf0(xQ,xS),
inference(cnf_transformation,[status(thm)],[f606]) ).
fof(f883,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f132]) ).
fof(f884,plain,
! [X0] :
( ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(xQ,X0)
| ~ aSet0(xS)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f883,f609]) ).
fof(f888,plain,
! [X0] :
( ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(xQ,X0)
| ~ aSet0(xS) ),
inference(forward_subsumption_resolution,[status(thm)],[f884,f132]) ).
fof(f911,plain,
! [X0] :
( ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(xQ,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f888,f364]) ).
fof(f913,plain,
~ aSubsetOf0(xO,xS),
inference(resolution,[status(thm)],[f911,f594]) ).
fof(f989,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f590,f913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM607+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:44:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.40 % Drodi V4.1.1
% 0.11/0.43 % Refutation found
% 0.11/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.46 % Elapsed time: 0.083851 seconds
% 0.11/0.46 % CPU time: 0.230204 seconds
% 0.11/0.46 % Total memory used: 125.878 MB
% 0.11/0.46 % Net memory used: 125.488 MB
%------------------------------------------------------------------------------