%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM617+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 : n004.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 01:41:12 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 50 ( 17 unt; 7 def)
% Number of atoms : 118 ( 1 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 115 ( 47 ~; 44 |; 14 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 26 ( 24 !; 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(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,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f107,hypothesis,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,hypothesis,
aElementOf0(xx,xP),
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(f144,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
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(f375,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f445,plain,
aSubsetOf0(xO,xS),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f447,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f449,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f456,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f464,plain,
aElementOf0(xx,xP),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f465,plain,
~ aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f534,definition,
( sQ4_spl
<=> aSet0(szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ4_spl
| ~ aSet0(szNzAzT0) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f541,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f192]) ).
fof(f542,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f596,plain,
! [X0] :
( aElementOf0(xx,X0)
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f145,f464]) ).
fof(f598,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f375,f144]) ).
fof(f599,definition,
( sQ17_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( sQ17_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f598,f534,f599]) ).
fof(f632,plain,
( aSet0(xO)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f445,f144]) ).
fof(f633,definition,
( sQ22_spl
<=> aSet0(xO) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( sQ22_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f632,f599,f633]) ).
fof(f637,plain,
( aSet0(xQ)
| ~ aSet0(xO) ),
inference(resolution,[status(thm)],[f447,f144]) ).
fof(f638,definition,
( sQ23_spl
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f641,plain,
( sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f637,f633,f638]) ).
fof(f661,plain,
( aElementOf0(xx,xQ)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f456,f596]) ).
fof(f663,definition,
( sQ27_spl
<=> aElementOf0(xx,xQ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f664,plain,
( ~ sQ27_spl
| aElementOf0(xx,xQ) ),
inference(component_clause,[status(thm)],[f663]) ).
fof(f666,plain,
( sQ27_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f661,f638,f663]) ).
fof(f750,plain,
! [X0] :
( ~ sQ27_spl
| aElementOf0(xx,X0)
| ~ aSubsetOf0(xQ,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f664,f145]) ).
fof(f756,plain,
( ~ sQ27_spl
| aElementOf0(xx,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f750,f449]) ).
fof(f759,definition,
( sQ43_spl
<=> aElementOf0(xx,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f760,plain,
( ~ sQ43_spl
| aElementOf0(xx,szNzAzT0) ),
inference(component_clause,[status(thm)],[f759]) ).
fof(f762,plain,
( ~ sQ27_spl
| sQ43_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f756,f534,f759,f663]) ).
fof(f765,plain,
( ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f760,f465]) ).
fof(f766,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f765]) ).
fof(f767,plain,
$false,
inference(sat_refutation,[status(thm)],[f542,f602,f636,f641,f666,f762,f766]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM617+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:44:50 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.47 % Elapsed time: 0.102411 seconds
% 0.12/0.47 % CPU time: 0.128242 seconds
% 0.12/0.47 % Total memory used: 7.072 MB
% 0.12/0.47 % Net memory used: 7.058 MB
%------------------------------------------------------------------------------