%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM617+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 01:41:13 PM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 9 unt; 3 def)
% Number of atoms : 81 ( 1 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 85 ( 32 ~; 29 |; 17 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 23 !; 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(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f101,hypothesis,
( aSubsetOf0(xQ,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,hypothesis,
( aElementOf0(xx,xP)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xQ)
& aElement0(xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,conjecture,
aElementOf0(xx,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,negated_conjecture,
~ aElementOf0(xx,szNzAzT0),
inference(negated_conjecture,[status(cth)],[f114]) ).
fof(f140,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(f141,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)],[f140]) ).
fof(f142,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)],[f141]) ).
fof(f143,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))],[f142]) ).
fof(f145,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f192,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f614,plain,
( aSubsetOf0(xQ,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,xQ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f101]) ).
fof(f616,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f614]) ).
fof(f656,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f659,plain,
~ aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f921,definition,
( sQ3_spl
<=> aSet0(szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f923,plain,
( sQ3_spl
| ~ aSet0(szNzAzT0) ),
inference(component_clause,[status(thm)],[f921]) ).
fof(f928,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f923,f192]) ).
fof(f929,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f928]) ).
fof(f1030,plain,
! [X0] :
( aElementOf0(xx,X0)
| ~ aSubsetOf0(xQ,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f145,f656]) ).
fof(f1081,plain,
( aElementOf0(xx,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f1030,f616]) ).
fof(f1087,definition,
( sQ30_spl
<=> aElementOf0(xx,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1088,plain,
( ~ sQ30_spl
| aElementOf0(xx,szNzAzT0) ),
inference(component_clause,[status(thm)],[f1087]) ).
fof(f1090,plain,
( sQ30_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1081,f921,f1087]) ).
fof(f1095,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1088,f659]) ).
fof(f1096,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f1095]) ).
fof(f1097,plain,
$false,
inference(sat_refutation,[status(thm)],[f929,f1090,f1096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM617+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:47:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.40 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.060519 seconds
% 0.10/0.44 % CPU time: 0.131458 seconds
% 0.10/0.44 % Total memory used: 31.929 MB
% 0.10/0.44 % Net memory used: 31.821 MB
%------------------------------------------------------------------------------