%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM602+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 : n017.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 01:41:09 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 6 unt; 4 def)
% Number of atoms : 107 ( 9 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 112 ( 43 ~; 40 |; 20 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 31 !; 6 ?)
% 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(f12,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,hypothesis,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,hypothesis,
! [W0] :
( aElementOf0(W0,xO)
=> ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(W1,szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,hypothesis,
aElementOf0(xx,xO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,conjecture,
? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,negated_conjecture,
~ ? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f99]) ).
fof(f125,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(f126,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)],[f125]) ).
fof(f127,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)],[f126]) ).
fof(f128,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))],[f127]) ).
fof(f130,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f135,plain,
! [W0] :
( aSubsetOf0(W0,W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f136,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f421,plain,
aSet0(xO),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f425,plain,
! [W0] :
( ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(W0,xO) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f426,plain,
! [W0] :
( ( sdtlpdtrp0(xe,sK24_skl(W0)) = W0
& aElementOf0(sK24_skl(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(sK24_skl(W0),szNzAzT0) )
| ~ aElementOf0(W0,xO) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl]),skolemize(W1,sK24_skl(W0))],[f425]) ).
fof(f427,plain,
! [X0] :
( aElementOf0(sK24_skl(X0),szNzAzT0)
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[status(thm)],[f426]) ).
fof(f429,plain,
! [X0] :
( sdtlpdtrp0(xe,sK24_skl(X0)) = X0
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[status(thm)],[f426]) ).
fof(f430,plain,
aElementOf0(xx,xO),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f431,plain,
! [W0] :
( sdtlpdtrp0(xe,W0) != xx
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f100]) ).
fof(f432,plain,
! [X0] :
( sdtlpdtrp0(xe,X0) != xx
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f481,definition,
( sQ0_spl
<=> aSet0(xO) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ0_spl
| ~ aSet0(xO) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f488,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f421,f483]) ).
fof(f489,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f488]) ).
fof(f577,plain,
! [X0] :
( aElementOf0(xx,X0)
| ~ aSubsetOf0(xO,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f130,f430]) ).
fof(f579,plain,
( ~ aSet0(xO)
| aElementOf0(xx,xO)
| ~ aSet0(xO) ),
inference(resolution,[status(thm)],[f577,f136]) ).
fof(f580,definition,
( sQ19_spl
<=> aElementOf0(xx,xO) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f583,plain,
( sQ19_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f579,f481,f580]) ).
fof(f1306,plain,
( ~ aElementOf0(sK24_skl(xx),szNzAzT0)
| ~ aElementOf0(xx,xO) ),
inference(resolution,[status(thm)],[f429,f432]) ).
fof(f1307,definition,
( sQ105_spl
<=> aElementOf0(sK24_skl(xx),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1309,plain,
( sQ105_spl
| ~ aElementOf0(sK24_skl(xx),szNzAzT0) ),
inference(component_clause,[status(thm)],[f1307]) ).
fof(f1310,plain,
( ~ sQ105_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1306,f580,f1307]) ).
fof(f1311,plain,
( sQ105_spl
| ~ aElementOf0(xx,xO) ),
inference(resolution,[status(thm)],[f1309,f427]) ).
fof(f1312,plain,
( sQ105_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1311,f430]) ).
fof(f1313,plain,
sQ105_spl,
inference(contradiction_clause,[status(thm)],[f1312]) ).
fof(f1314,plain,
$false,
inference(sat_refutation,[status(thm)],[f489,f583,f1310,f1313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM602+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 : n017.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 02:39:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.065935 seconds
% 0.14/0.43 % CPU time: 0.198664 seconds
% 0.14/0.43 % Total memory used: 87.674 MB
% 0.14/0.43 % Net memory used: 87.523 MB
%------------------------------------------------------------------------------