%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM610+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 : 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 01:41:11 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 6 unt; 1 def)
% Number of atoms : 162 ( 20 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 200 ( 69 ~; 61 |; 58 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 61 ( 55 !; 6 ?)
% 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(f95,hypothesis,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( aElementOf0(W0,xO)
<=> ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( sdtlpdtrp0(xd,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xd)) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
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(f107,hypothesis,
( aSubsetOf0(xP,xQ)
& ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f108,conjecture,
( aSubsetOf0(xP,xO)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xO) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,negated_conjecture,
~ ( aSubsetOf0(xP,xO)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xO) ) ),
inference(negated_conjecture,[status(cth)],[f108]) ).
fof(f134,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(f135,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)],[f134]) ).
fof(f136,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)],[f135]) ).
fof(f137,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))],[f136]) ).
fof(f138,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f148,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(f149,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f572,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( ( ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(W0,xO) )
& ( ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ aElementOf0(W0,xO) ) )
& ! [W0] :
( ( sdtlpdtrp0(xd,W0) != szDzizrdt0(xd)
| ~ aElementOf0(W0,szDzozmdt0(xd))
| aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( ( sdtlpdtrp0(xd,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xd)) )
| ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(NNF_transformation,[status(thm)],[f95]) ).
fof(f573,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(W0,xO) )
& ! [W0] :
( ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ aElementOf0(W0,xO) )
& ! [W0] :
( sdtlpdtrp0(xd,W0) != szDzizrdt0(xd)
| ~ aElementOf0(W0,szDzozmdt0(xd))
| aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ! [W0] :
( ( sdtlpdtrp0(xd,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xd)) )
| ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(miniscoping,[status(thm)],[f572]) ).
fof(f574,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(W0,xO) )
& ! [W0] :
( ( sdtlpdtrp0(xe,sK34_skl(W0)) = W0
& aElementOf0(sK34_skl(W0),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| ~ aElementOf0(W0,xO) )
& ! [W0] :
( sdtlpdtrp0(xd,W0) != szDzizrdt0(xd)
| ~ aElementOf0(W0,szDzozmdt0(xd))
| aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ! [W0] :
( ( sdtlpdtrp0(xd,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xd)) )
| ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl]),skolemize(W1,sK34_skl(W0))],[f573]) ).
fof(f575,plain,
aSet0(xO),
inference(cnf_transformation,[status(thm)],[f574]) ).
fof(f597,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(f600,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[status(thm)],[f597]) ).
fof(f635,plain,
( aSubsetOf0(xP,xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
| ~ aElementOf0(W0,xP) ) ),
inference(pre_NNF_transformation,[status(thm)],[f107]) ).
fof(f637,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[status(thm)],[f635]) ).
fof(f638,plain,
( ~ aSubsetOf0(xP,xO)
& ? [W0] :
( ~ aElementOf0(W0,xO)
& aElementOf0(W0,xP) ) ),
inference(pre_NNF_transformation,[status(thm)],[f109]) ).
fof(f639,plain,
( ~ aSubsetOf0(xP,xO)
& ~ aElementOf0(sK38_skl,xO)
& aElementOf0(sK38_skl,xP) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl]),skolemize(W0,sK38_skl)],[f638]) ).
fof(f642,plain,
~ aSubsetOf0(xP,xO),
inference(cnf_transformation,[status(thm)],[f639]) ).
fof(f902,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f138]) ).
fof(f903,plain,
! [X0] :
( ~ aSubsetOf0(X0,xO)
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(xO)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f902,f642]) ).
fof(f906,plain,
! [X0] :
( ~ aSubsetOf0(X0,xO)
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(xO) ),
inference(forward_subsumption_resolution,[status(thm)],[f903,f138]) ).
fof(f918,plain,
! [X0] :
( ~ aSubsetOf0(X0,xO)
| ~ aSubsetOf0(xP,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f906,f575]) ).
fof(f919,plain,
~ aSubsetOf0(xQ,xO),
inference(resolution,[status(thm)],[f918,f637]) ).
fof(f922,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f919,f600]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM610+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.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 02:47:01 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.079041 seconds
% 0.13/0.44 % CPU time: 0.188733 seconds
% 0.13/0.44 % Total memory used: 86.802 MB
% 0.13/0.44 % Net memory used: 86.512 MB
%------------------------------------------------------------------------------