%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM600+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 : n026.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 0.21s 0.73s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 8 unt; 2 def)
% Number of atoms : 116 ( 40 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 125 ( 41 ~; 35 |; 41 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 26 ( 19 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f92,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) )
& aSet0(W1) )
=> sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,hypothesis,
( ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( sdtlpdtrp0(xd,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xd)) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(szDzizrdt0(xd),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,conjecture,
! [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(f98,negated_conjecture,
~ ! [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) ) ),
inference(negated_conjecture,[status(cth)],[f97]) ).
fof(f536,plain,
( ! [W0] :
( ! [W1] :
( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ? [W2] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aElementOf0(W2,W1) ) ) ) )
| ~ aSet0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(pre_NNF_transformation,[status(thm)],[f92]) ).
fof(f537,plain,
( ! [W0] :
( ! [W1] :
( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ aElementOf0(sK32_skl(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aElementOf0(sK32_skl(W1,W0),W1) ) ) )
| ~ aSet0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(W2,sK32_skl(W1,W0))],[f536]) ).
fof(f539,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(cnf_transformation,[status(thm)],[f537]) ).
fof(f554,plain,
( ! [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)))
& aElementOf0(szDzizrdt0(xd),xT) ),
inference(NNF_transformation,[status(thm)],[f94]) ).
fof(f555,plain,
( ! [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)))
& aElementOf0(szDzizrdt0(xd),xT) ),
inference(miniscoping,[status(thm)],[f554]) ).
fof(f558,plain,
! [X0] :
( aElementOf0(X0,szDzozmdt0(xd))
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(cnf_transformation,[status(thm)],[f555]) ).
fof(f559,plain,
! [X0] :
( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(cnf_transformation,[status(thm)],[f555]) ).
fof(f575,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)],[f98]) ).
fof(f576,plain,
( ! [W1] :
( sdtlpdtrp0(xe,W1) != sK35_skl
| ( ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,W1) != szDzizrdt0(xd) )
| ~ aElementOf0(W1,szNzAzT0) )
& aElementOf0(sK35_skl,xO)
& sdtlpdtrp0(xe,sK36_skl) = sK35_skl
& aElementOf0(sK36_skl,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl,sK36_skl]),skolemize(W0,sK35_skl),skolemize(W1,sK36_skl)],[f575]) ).
fof(f577,plain,
aElementOf0(sK36_skl,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[status(thm)],[f576]) ).
fof(f578,plain,
sdtlpdtrp0(xe,sK36_skl) = sK35_skl,
inference(cnf_transformation,[status(thm)],[f576]) ).
fof(f580,plain,
! [X0] :
( sdtlpdtrp0(xe,X0) != sK35_skl
| sdtlpdtrp0(xd,X0) != szDzizrdt0(xd)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f576]) ).
fof(f1090,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(forward_demodulation,[status(thm)],[f539,f558]) ).
fof(f1091,plain,
aElementOf0(sK36_skl,szNzAzT0),
inference(resolution,[status(thm)],[f1090,f577]) ).
fof(f1096,plain,
sdtlpdtrp0(xd,sK36_skl) = szDzizrdt0(xd),
inference(resolution,[status(thm)],[f559,f577]) ).
fof(f1099,plain,
( sdtlpdtrp0(xe,sK36_skl) != sK35_skl
| sdtlpdtrp0(xd,sK36_skl) != szDzizrdt0(xd) ),
inference(resolution,[status(thm)],[f1091,f580]) ).
fof(f1100,definition,
( sQ51_spl
<=> sdtlpdtrp0(xd,sK36_skl) = szDzizrdt0(xd) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1102,plain,
( sQ51_spl
| sdtlpdtrp0(xd,sK36_skl) != szDzizrdt0(xd) ),
inference(component_clause,[status(thm)],[f1100]) ).
fof(f1103,definition,
( sQ52_spl
<=> sdtlpdtrp0(xe,sK36_skl) = sK35_skl ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1105,plain,
( sQ52_spl
| sdtlpdtrp0(xe,sK36_skl) != sK35_skl ),
inference(component_clause,[status(thm)],[f1103]) ).
fof(f1106,plain,
( ~ sQ52_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f1099,f1100,f1103]) ).
fof(f1201,plain,
( sQ51_spl
| szDzizrdt0(xd) != szDzizrdt0(xd) ),
inference(forward_demodulation,[status(thm)],[f1096,f1102]) ).
fof(f1202,plain,
( sQ51_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1201]) ).
fof(f1203,plain,
sQ51_spl,
inference(contradiction_clause,[status(thm)],[f1202]) ).
fof(f1204,plain,
( sQ52_spl
| sK35_skl != sK35_skl ),
inference(forward_demodulation,[status(thm)],[f578,f1105]) ).
fof(f1205,plain,
( sQ52_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1204]) ).
fof(f1206,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f1205]) ).
fof(f1207,plain,
$false,
inference(sat_refutation,[status(thm)],[f1106,f1203,f1206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM600+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.67 % Computer : n026.cluster.edu
% 0.18/0.67 % Model : x86_64 x86_64
% 0.18/0.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.67 % Memory : 8046.5625MB
% 0.18/0.67 % OS : Linux 6.8.0-71-generic
% 0.18/0.67 % CPULimit : 300
% 0.18/0.67 % WCLimit : 300
% 0.18/0.67 % DateTime : Mon Sep 21 02:46:08 UTC 2026
% 0.18/0.68 % CPUTime :
% 0.21/0.72 % Drodi V4.1.1
% 0.21/0.73 % Refutation found
% 0.21/0.73 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.81 % Elapsed time: 0.122705 seconds
% 0.21/0.81 % CPU time: 0.187108 seconds
% 0.21/0.81 % Total memory used: 35.362 MB
% 0.21/0.81 % Net memory used: 35.264 MB
%------------------------------------------------------------------------------