%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM618+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 : 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 01:41:13 PM UTC 2026
% Result : Theorem 0.14s 0.91s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 5 unt; 1 def)
% Number of atoms : 94 ( 26 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 100 ( 32 ~; 28 |; 37 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 32 ( 24 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f97,hypothesis,
! [W0] :
( ( aElementOf0(W0,xO)
| ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
=> ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,W1) = szDzizrdt0(xd)
& aElementOf0(W1,szNzAzT0) ) ),
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(f113,hypothesis,
( aElementOf0(xx,xP)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xQ)
& aElement0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,conjecture,
? [W0] :
( xx = sdtlpdtrp0(xe,W0)
& aElementOf0(W0,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,negated_conjecture,
~ ? [W0] :
( xx = sdtlpdtrp0(xe,W0)
& aElementOf0(W0,szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f115]) ).
fof(f593,plain,
! [W0] :
( ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,W1) = szDzizrdt0(xd)
& aElementOf0(W1,szNzAzT0) )
| ( ~ aElementOf0(W0,xO)
& ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f594,definition,
! [W0] :
( sP9_prd(W0)
<=> ( ~ aElementOf0(W0,xO)
& ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f595,plain,
! [W0] :
( ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,W1) = szDzizrdt0(xd)
& aElementOf0(W1,szNzAzT0) )
| sP9_prd(W0) ),
inference(formula_renaming,[status(thm)],[f593,f594]) ).
fof(f596,plain,
! [W0] :
( ( sdtlpdtrp0(xe,sK35_skl(W0)) = W0
& aElementOf0(sK35_skl(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,sK35_skl(W0)) = szDzizrdt0(xd)
& aElementOf0(sK35_skl(W0),szNzAzT0) )
| sP9_prd(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl]),skolemize(W1,sK35_skl(W0))],[f595]) ).
fof(f597,plain,
! [X0] :
( aElementOf0(sK35_skl(X0),szNzAzT0)
| sP9_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f596]) ).
fof(f600,plain,
! [X0] :
( sdtlpdtrp0(xe,sK35_skl(X0)) = X0
| sP9_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f596]) ).
fof(f604,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(f606,plain,
! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[status(thm)],[f604]) ).
fof(f657,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f664,plain,
! [W0] :
( xx != sdtlpdtrp0(xe,W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f116]) ).
fof(f665,plain,
! [X0] :
( xx != sdtlpdtrp0(xe,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f664]) ).
fof(f787,plain,
! [W0] :
( ( aElementOf0(W0,xO)
| ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| sP9_prd(W0) )
& ( ( ~ aElementOf0(W0,xO)
& ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ~ sP9_prd(W0) ) ),
inference(NNF_transformation,[status(thm)],[f594]) ).
fof(f788,plain,
( ! [W0] :
( aElementOf0(W0,xO)
| ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| sP9_prd(W0) )
& ! [W0] :
( ( ~ aElementOf0(W0,xO)
& ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ~ sP9_prd(W0) ) ),
inference(miniscoping,[status(thm)],[f787]) ).
fof(f789,plain,
( ! [W0] :
( aElementOf0(W0,xO)
| ( sdtlpdtrp0(xe,sK61_skl(W0)) = W0
& aElementOf0(sK61_skl(W0),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| sP9_prd(W0) )
& ! [W0] :
( ( ~ aElementOf0(W0,xO)
& ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ~ sP9_prd(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61_skl]),skolemize(W1,sK61_skl(W0))],[f788]) ).
fof(f791,plain,
! [X0] :
( ~ aElementOf0(X0,xO)
| ~ sP9_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f789]) ).
fof(f1548,plain,
aElementOf0(xx,xO),
inference(resolution,[status(thm)],[f606,f657]) ).
fof(f1559,plain,
~ sP9_prd(xx),
inference(resolution,[status(thm)],[f1548,f791]) ).
fof(f2064,plain,
! [X0] :
( sP9_prd(X0)
| xx != X0
| ~ aElementOf0(sK35_skl(X0),szNzAzT0) ),
inference(paramodulation,[status(thm)],[f600,f665]) ).
fof(f2091,plain,
( sP9_prd(xx)
| ~ aElementOf0(sK35_skl(xx),szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f2064]) ).
fof(f2092,plain,
sP9_prd(xx),
inference(forward_subsumption_resolution,[status(thm)],[f2091,f597]) ).
fof(f2106,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2092,f1559]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM618+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n004.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 21 02:44:50 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.14/0.60 % Drodi V4.1.1
% 0.14/0.91 % Refutation found
% 0.14/0.91 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.92 % Elapsed time: 0.340339 seconds
% 0.14/0.92 % CPU time: 2.396863 seconds
% 0.14/0.92 % Total memory used: 154.037 MB
% 0.14/0.92 % Net memory used: 151.137 MB
%------------------------------------------------------------------------------