%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM533+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 : n015.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 01:40:53 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 11 unt; 1 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 100 ( 39 ~; 38 |; 17 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 29 !; 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,hypothesis,
( aSet0(xC)
& aSet0(xB)
& aSet0(xA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
( ( aSubsetOf0(xB,xC)
& aSubsetOf0(xA,xB) )
=> aSubsetOf0(xA,xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ( ( aSubsetOf0(xB,xC)
& aSubsetOf0(xA,xB) )
=> aSubsetOf0(xA,xC) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f43,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)],[f42]) ).
fof(f44,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))],[f43]) ).
fof(f46,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f55,plain,
aSet0(xA),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f56,plain,
aSet0(xB),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f57,plain,
aSet0(xC),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f58,plain,
( ~ aSubsetOf0(xA,xC)
& aSubsetOf0(xB,xC)
& aSubsetOf0(xA,xB) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f59,plain,
aSubsetOf0(xA,xB),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
aSubsetOf0(xB,xC),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f61,plain,
~ aSubsetOf0(xA,xC),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f112,plain,
! [X0] :
( aElementOf0(X0,xC)
| ~ aElementOf0(X0,xB)
| ~ aSet0(xC) ),
inference(resolution,[status(thm)],[f46,f60]) ).
fof(f114,plain,
! [X0] :
( aElementOf0(X0,xB)
| ~ aElementOf0(X0,xA)
| ~ aSet0(xB) ),
inference(resolution,[status(thm)],[f46,f59]) ).
fof(f115,plain,
! [X0] :
( aElementOf0(X0,xC)
| ~ aElementOf0(X0,xB) ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f57]) ).
fof(f116,plain,
! [X0] :
( aElementOf0(X0,xB)
| ~ aElementOf0(X0,xA) ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f56]) ).
fof(f120,plain,
! [X0] :
( aElementOf0(sK1_skl(X0,xC),X0)
| ~ aSet0(X0)
| aSubsetOf0(X0,xC) ),
inference(resolution,[status(thm)],[f47,f57]) ).
fof(f126,plain,
( aElementOf0(sK1_skl(xA,xC),xA)
| aSubsetOf0(xA,xC) ),
inference(resolution,[status(thm)],[f120,f55]) ).
fof(f127,plain,
aElementOf0(sK1_skl(xA,xC),xA),
inference(forward_subsumption_resolution,[status(thm)],[f126,f61]) ).
fof(f128,plain,
aElementOf0(sK1_skl(xA,xC),xB),
inference(resolution,[status(thm)],[f127,f116]) ).
fof(f156,plain,
aElementOf0(sK1_skl(xA,xC),xC),
inference(resolution,[status(thm)],[f128,f115]) ).
fof(f159,plain,
( ~ aSet0(xA)
| aSubsetOf0(xA,xC)
| ~ aSet0(xC) ),
inference(resolution,[status(thm)],[f156,f48]) ).
fof(f162,plain,
( ~ aSet0(xA)
| aSubsetOf0(xA,xC) ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f57]) ).
fof(f164,plain,
~ aSet0(xA),
inference(forward_subsumption_resolution,[status(thm)],[f162,f61]) ).
fof(f165,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f55,f164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM533+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:41:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.062271 seconds
% 0.09/0.43 % CPU time: 0.186337 seconds
% 0.09/0.43 % Total memory used: 80.443 MB
% 0.09/0.43 % Net memory used: 80.112 MB
%------------------------------------------------------------------------------