%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG119+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:05:02 PM UTC 2026
% Result : Theorem 0.12s 0.62s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 71 ( 15 unt; 10 def)
% Number of atoms : 230 ( 33 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 261 ( 102 ~; 95 |; 42 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 9 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 68 ( 59 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,definition,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,definition,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( sdtasdt0(W0,W2) = W1
& aElement0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( ! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
~ doDivides0(xu,xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,conjecture,
xr != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
~ ( xr != sz00 ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f62,plain,
! [W0,W1] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f63,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f68,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f69,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f74,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f75,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f96,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f97,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f126,plain,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f127,plain,
! [W0] :
( ( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(NNF_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
( ! [W0] :
( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ! [W0] :
( ( ( ( ~ aElementOf0(sdtasdt0(sK10_skl(W0),sK8_skl(W0)),W0)
& aElement0(sK10_skl(W0)) )
| ( ~ aElementOf0(sdtpldt0(sK8_skl(W0),sK9_skl(W0)),W0)
& aElementOf0(sK9_skl(W0),W0) ) )
& aElementOf0(sK8_skl(W0),W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl]),skolemize(W1,sK8_skl(W0)),skolemize(W2,sK9_skl(W0)),skolemize(W2,sK10_skl(W0))],[f128]) ).
fof(f130,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f166,plain,
! [W0,W1] :
( ( doDivides0(W0,W1)
<=> ? [W2] :
( sdtasdt0(W0,W2) = W1
& aElement0(W2) ) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f167,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtasdt0(W0,W2) != W1
| ~ aElement0(W2) )
| doDivides0(W0,W1) )
& ( ? [W2] :
( sdtasdt0(W0,W2) = W1
& aElement0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(NNF_transformation,[status(thm)],[f166]) ).
fof(f168,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtasdt0(W0,W2) != W1
| ~ aElement0(W2) )
| doDivides0(W0,W1) )
& ( ( sdtasdt0(W0,sK15_skl(W1,W0)) = W1
& aElement0(sK15_skl(W1,W0)) )
| ~ doDivides0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(W2,sK15_skl(W1,W0))],[f167]) ).
fof(f171,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2)
| doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f209,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f218,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ~ aElementOf0(W0,xI) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f219,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f229,plain,
~ doDivides0(xu,xb),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f230,plain,
aElement0(xq),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f232,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f234,plain,
xr = sz00,
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f295,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f130,f209]) ).
fof(f298,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f97,f219]) ).
fof(f299,definition,
( sQ11_spl
<=> aSet0(xI) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( sQ11_spl
| ~ aSet0(xI) ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,definition,
( sQ12_spl
<=> aElement0(xu) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f298,f299,f302]) ).
fof(f306,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f301,f295]) ).
fof(f307,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f334,definition,
( sQ16_spl
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f424,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),sz00),
inference(forward_demodulation,[status(thm)],[f234,f232]) ).
fof(f425,plain,
( xb = sdtasdt0(xq,xu)
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(paramodulation,[status(thm)],[f424,f69]) ).
fof(f431,definition,
( sQ21_spl
<=> aElement0(sdtasdt0(xq,xu)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( sQ21_spl
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f434,definition,
( sQ22_spl
<=> xb = sdtasdt0(xq,xu) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ22_spl
| xb = sdtasdt0(xq,xu) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,plain,
( sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f425,f431,f434]) ).
fof(f448,plain,
( sQ21_spl
| ~ aElement0(xu)
| ~ aElement0(xq) ),
inference(resolution,[status(thm)],[f433,f63]) ).
fof(f449,definition,
( sQ25_spl
<=> aElement0(xq) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( sQ25_spl
| ~ aElement0(xq) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( sQ21_spl
| ~ sQ12_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f448,f449,f302,f431]) ).
fof(f453,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f451,f230]) ).
fof(f454,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f453]) ).
fof(f464,plain,
( ~ sQ22_spl
| sdtasdt0(xu,xq) = xb
| ~ aElement0(xq)
| ~ aElement0(xu) ),
inference(paramodulation,[status(thm)],[f435,f75]) ).
fof(f492,definition,
( sQ32_spl
<=> sdtasdt0(xu,xq) = xb ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( ~ sQ32_spl
| sdtasdt0(xu,xq) = xb ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( ~ sQ22_spl
| sQ32_spl
| ~ sQ25_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f464,f302,f449,f492,f434]) ).
fof(f553,plain,
( ~ sQ32_spl
| aElement0(xb)
| ~ aElement0(xq)
| ~ aElement0(xu) ),
inference(paramodulation,[status(thm)],[f493,f63]) ).
fof(f579,plain,
( ~ sQ32_spl
| sQ16_spl
| ~ sQ25_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f553,f302,f449,f334,f492]) ).
fof(f653,plain,
( ~ sQ32_spl
| ~ aElement0(xq)
| doDivides0(xu,xb)
| ~ aElement0(xb)
| ~ aElement0(xu) ),
inference(resolution,[status(thm)],[f171,f493]) ).
fof(f677,definition,
( sQ51_spl
<=> doDivides0(xu,xb) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f678,plain,
( ~ sQ51_spl
| doDivides0(xu,xb) ),
inference(component_clause,[status(thm)],[f677]) ).
fof(f680,plain,
( ~ sQ32_spl
| ~ sQ25_spl
| sQ51_spl
| ~ sQ16_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f653,f302,f334,f677,f449,f492]) ).
fof(f744,plain,
( ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f678,f229]) ).
fof(f745,plain,
~ sQ51_spl,
inference(contradiction_clause,[status(thm)],[f744]) ).
fof(f746,plain,
$false,
inference(sat_refutation,[status(thm)],[f305,f307,f437,f452,f454,f495,f579,f680,f745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG119+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.55 % Computer : n003.cluster.edu
% 0.08/0.55 % Model : x86_64 x86_64
% 0.08/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.55 % Memory : 8046.5625MB
% 0.08/0.55 % OS : Linux 6.8.0-71-generic
% 0.08/0.55 % CPULimit : 300
% 0.08/0.55 % WCLimit : 300
% 0.08/0.55 % DateTime : Mon Sep 21 04:23:01 UTC 2026
% 0.12/0.55 % CPUTime :
% 0.12/0.57 % Drodi V4.1.1
% 0.12/0.62 % Refutation found
% 0.12/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.66 % Elapsed time: 0.085577 seconds
% 0.13/0.66 % CPU time: 0.375302 seconds
% 0.13/0.66 % Total memory used: 111.274 MB
% 0.13/0.66 % Net memory used: 110.738 MB
%------------------------------------------------------------------------------