%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM606+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 : n007.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 01:41:10 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 12 unt; 1 def)
% Number of atoms : 164 ( 20 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 187 ( 62 ~; 52 |; 62 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 54 ( 48 !; 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(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSet0(xS) ),
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(f98,hypothesis,
( aSubsetOf0(xO,xS)
& ! [W0] :
( aElementOf0(W0,xO)
=> aElementOf0(W0,xS) ) ),
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(f101,conjecture,
( aSubsetOf0(xQ,szNzAzT0)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f102,negated_conjecture,
~ ( aSubsetOf0(xQ,szNzAzT0)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) ) ),
inference(negated_conjecture,[status(cth)],[f101]) ).
fof(f127,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(f128,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)],[f127]) ).
fof(f129,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)],[f128]) ).
fof(f130,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))],[f129]) ).
fof(f132,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f179,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f362,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,xS) )
& aSet0(xS) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f363,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f362]) ).
fof(f365,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f362]) ).
fof(f565,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(f566,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)],[f565]) ).
fof(f567,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))],[f566]) ).
fof(f568,plain,
aSet0(xO),
inference(cnf_transformation,[status(thm)],[f567]) ).
fof(f587,plain,
( aSubsetOf0(xO,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xO) ) ),
inference(pre_NNF_transformation,[status(thm)],[f98]) ).
fof(f589,plain,
aSubsetOf0(xO,xS),
inference(cnf_transformation,[status(thm)],[f587]) ).
fof(f590,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(f593,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[status(thm)],[f590]) ).
fof(f601,plain,
( ~ aSubsetOf0(xQ,szNzAzT0)
& ? [W0] :
( ~ aElementOf0(W0,szNzAzT0)
& aElementOf0(W0,xQ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f102]) ).
fof(f602,plain,
( ~ aSubsetOf0(xQ,szNzAzT0)
& ~ aElementOf0(sK37_skl,szNzAzT0)
& aElementOf0(sK37_skl,xQ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37_skl]),skolemize(W0,sK37_skl)],[f601]) ).
fof(f603,plain,
aElementOf0(sK37_skl,xQ),
inference(cnf_transformation,[status(thm)],[f602]) ).
fof(f604,plain,
~ aElementOf0(sK37_skl,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f602]) ).
fof(f852,plain,
! [X0] :
( aElementOf0(sK37_skl,X0)
| ~ aSubsetOf0(xQ,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f132,f603]) ).
fof(f854,plain,
! [X0] :
( ~ aElementOf0(sK37_skl,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f132,f604]) ).
fof(f863,plain,
( aElementOf0(sK37_skl,xO)
| ~ aSet0(xO) ),
inference(resolution,[status(thm)],[f852,f593]) ).
fof(f866,plain,
! [X0] :
( ~ aElementOf0(sK37_skl,X0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f854,f179]) ).
fof(f905,plain,
aElementOf0(sK37_skl,xO),
inference(backward_subsumption_resolution,[status(thm)],[f863,f568]) ).
fof(f966,plain,
~ aElementOf0(sK37_skl,xS),
inference(resolution,[status(thm)],[f365,f866]) ).
fof(f980,plain,
! [X0] :
( ~ aElementOf0(sK37_skl,X0)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f966,f132]) ).
fof(f981,plain,
! [X0] :
( ~ aElementOf0(sK37_skl,X0)
| ~ aSubsetOf0(X0,xS) ),
inference(forward_subsumption_resolution,[status(thm)],[f980,f363]) ).
fof(f1021,plain,
~ aElementOf0(sK37_skl,xO),
inference(resolution,[status(thm)],[f589,f981]) ).
fof(f1028,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1021,f905]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM606+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:42:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.059716 seconds
% 0.13/0.43 % CPU time: 0.230068 seconds
% 0.13/0.43 % Total memory used: 122.127 MB
% 0.13/0.43 % Net memory used: 121.711 MB
%------------------------------------------------------------------------------