%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM478+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 01:40:40 PM UTC 2026
% Result : Theorem 32.51s 4.64s
% Output : CNFRefutation 32.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 24 unt; 4 def)
% Number of atoms : 216 ( 84 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 236 ( 96 ~; 95 |; 31 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 73 ( 69 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
( doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& xl != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aNaturalNumber0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,conjecture,
( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl)
| sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
~ ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl)
| sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f49,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f50,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f58,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f59,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f61,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f122,plain,
! [W0,W1] :
( ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f123,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ( W1 = sdtasdt0(W0,sK1_skl(W1,W0))
& aNaturalNumber0(sK1_skl(W1,W0)) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f123]) ).
fof(f127,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f128,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f129,plain,
! [W0,W1] :
( ! [W2] :
( ( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [W0,W1] :
( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ! [W2] :
( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(miniscoping,[status(thm)],[f129]) ).
fof(f133,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f142,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f143,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f144,plain,
( doDivides0(xl,xm)
& xm = sdtasdt0(xl,sK2_skl)
& aNaturalNumber0(sK2_skl)
& xl != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W0,sK2_skl)],[f37]) ).
fof(f145,plain,
xl != sz00,
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f146,plain,
aNaturalNumber0(sK2_skl),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f147,plain,
xm = sdtasdt0(xl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f149,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f150,plain,
( sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl)
& sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f151,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f153,plain,
sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f163,plain,
! [X0,X2] :
( ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f127]) ).
fof(f164,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f50]) ).
fof(f167,plain,
! [X0,X2] :
( ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(sdtasdt0(X0,X2),X0)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| X0 = sz00
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f133]) ).
fof(f168,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| X1 = sdtsldt0(sdtasdt0(X0,X1),X0)
| ~ doDivides0(X0,sdtasdt0(X0,X1))
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f50]) ).
fof(f194,plain,
! [X0] :
( sdtasdt0(X0,xn) = sdtasdt0(xn,X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f59,f149]) ).
fof(f196,plain,
! [X0] :
( sdtasdt0(X0,xl) = sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f59,f142]) ).
fof(f197,plain,
! [X0] :
( sdtasdt0(X0,sdtsldt0(xm,xl)) = sdtasdt0(sdtsldt0(xm,xl),X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f59,f151]) ).
fof(f238,plain,
! [X0,X1] :
( sdtasdt0(sdtasdt0(X0,sK2_skl),X1) = sdtasdt0(X0,sdtasdt0(sK2_skl,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f146,f61]) ).
fof(f242,plain,
! [X0] :
( aNaturalNumber0(sdtasdt0(sK2_skl,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f146,f50]) ).
fof(f433,plain,
sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtasdt0(sdtsldt0(xm,xl),xn),
inference(resolution,[status(thm)],[f197,f149]) ).
fof(f569,plain,
! [X0] :
( doDivides0(X0,sdtasdt0(X0,sK2_skl))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f164,f146]) ).
fof(f711,plain,
aNaturalNumber0(sdtasdt0(sK2_skl,xn)),
inference(resolution,[status(thm)],[f242,f149]) ).
fof(f1152,plain,
sdtasdt0(xm,xn) = sdtasdt0(xn,xm),
inference(resolution,[status(thm)],[f194,f143]) ).
fof(f1185,plain,
sdtasdt0(xm,xn) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(backward_demodulation,[status(thm)],[f1152,f153]) ).
fof(f1430,plain,
! [X0] :
( sK2_skl = sdtsldt0(sdtasdt0(X0,sK2_skl),X0)
| ~ doDivides0(X0,sdtasdt0(X0,sK2_skl))
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f168,f146]) ).
fof(f1454,plain,
! [X0] :
( sK2_skl = sdtsldt0(sdtasdt0(X0,sK2_skl),X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1430,f569]) ).
fof(f1478,plain,
sdtasdt0(sK2_skl,xl) = sdtasdt0(xl,sK2_skl),
inference(resolution,[status(thm)],[f196,f146]) ).
fof(f1488,plain,
sdtasdt0(sdtasdt0(sK2_skl,xn),xl) = sdtasdt0(xl,sdtasdt0(sK2_skl,xn)),
inference(resolution,[status(thm)],[f196,f711]) ).
fof(f1557,plain,
sdtasdt0(sK2_skl,xl) = xm,
inference(forward_demodulation,[status(thm)],[f147,f1478]) ).
fof(f1827,plain,
( sK2_skl = sdtsldt0(sdtasdt0(xl,sK2_skl),xl)
| xl = sz00 ),
inference(resolution,[status(thm)],[f1454,f142]) ).
fof(f1976,definition,
( sQ42_spl
<=> xl = sz00 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1977,plain,
( ~ sQ42_spl
| xl = sz00 ),
inference(component_clause,[status(thm)],[f1976]) ).
fof(f1979,definition,
( sQ43_spl
<=> sK2_skl = sdtsldt0(sdtasdt0(xl,sK2_skl),xl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1980,plain,
( ~ sQ43_spl
| sK2_skl = sdtsldt0(sdtasdt0(xl,sK2_skl),xl) ),
inference(component_clause,[status(thm)],[f1979]) ).
fof(f1982,plain,
( sQ43_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1827,f1976,f1979]) ).
fof(f2160,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1977,f145]) ).
fof(f2161,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f2160]) ).
fof(f5719,plain,
( ~ sQ43_spl
| sK2_skl = sdtsldt0(xm,xl) ),
inference(backward_demodulation,[status(thm)],[f147,f1980]) ).
fof(f6074,plain,
( ~ sQ43_spl
| sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtasdt0(sK2_skl,xn) ),
inference(backward_demodulation,[status(thm)],[f5719,f433]) ).
fof(f6167,plain,
( ~ sQ43_spl
| sdtasdt0(xm,xn) != sdtasdt0(xl,sdtasdt0(xn,sK2_skl)) ),
inference(forward_demodulation,[status(thm)],[f5719,f1185]) ).
fof(f6181,plain,
( ~ sQ43_spl
| sdtasdt0(xm,xn) != sdtasdt0(xl,sdtasdt0(sK2_skl,xn)) ),
inference(backward_demodulation,[status(thm)],[f6182,f6167]) ).
fof(f6182,plain,
( ~ sQ43_spl
| sdtasdt0(xn,sK2_skl) = sdtasdt0(sK2_skl,xn) ),
inference(forward_demodulation,[status(thm)],[f5719,f6074]) ).
fof(f7648,plain,
sdtasdt0(sK2_skl,xn) = sdtasdt0(xn,sK2_skl),
inference(resolution,[status(thm)],[f194,f146]) ).
fof(f7762,plain,
! [X0] :
( sdtasdt0(sdtasdt0(X0,sK2_skl),xl) = sdtasdt0(X0,sdtasdt0(sK2_skl,xl))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f238,f142]) ).
fof(f7768,plain,
! [X0] :
( sdtasdt0(sdtasdt0(X0,sK2_skl),xl) = sdtasdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1557,f7762]) ).
fof(f7816,plain,
sdtasdt0(sdtasdt0(xn,sK2_skl),xl) = sdtasdt0(xn,xm),
inference(resolution,[status(thm)],[f7768,f149]) ).
fof(f7887,plain,
sdtasdt0(sdtasdt0(xn,sK2_skl),xl) = sdtasdt0(xm,xn),
inference(forward_demodulation,[status(thm)],[f1152,f7816]) ).
fof(f8080,plain,
sdtasdt0(sdtasdt0(sK2_skl,xn),xl) = sdtasdt0(xm,xn),
inference(forward_demodulation,[status(thm)],[f7648,f7887]) ).
fof(f8081,plain,
sdtasdt0(xl,sdtasdt0(sK2_skl,xn)) = sdtasdt0(xm,xn),
inference(forward_demodulation,[status(thm)],[f1488,f8080]) ).
fof(f8082,plain,
( ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8081,f6181]) ).
fof(f8083,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f8082]) ).
fof(f8084,plain,
$false,
inference(sat_refutation,[status(thm)],[f1982,f2161,f8083]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM478+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 02:33:26 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.02/0.38 % Drodi V4.1.1
% 32.51/4.64 % Refutation found
% 32.51/4.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 32.51/4.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.16/4.70 % Elapsed time: 4.319446 seconds
% 11.16/4.70 % CPU time: 33.732091 seconds
% 11.16/4.70 % Total memory used: 227.124 MB
% 11.16/4.70 % Net memory used: 213.694 MB
%------------------------------------------------------------------------------