%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM490+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 01:40:43 PM UTC 2026
% Result : Theorem 0.11s 10.86s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 22
% Syntax : Number of formulae : 81 ( 22 unt; 14 def)
% Number of atoms : 221 ( 35 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 238 ( 98 ~; 101 |; 18 &)
% ( 16 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 44 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f52,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f55,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f56,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f58,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f90,plain,
! [W0,W1] :
( ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f91,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f90]) ).
fof(f92,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ( sdtpldt0(W0,sK0_skl(W1,W0)) = W1
& aNaturalNumber0(sK0_skl(W1,W0)) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f91]) ).
fof(f95,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f96,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f97,plain,
! [W0,W1] :
( ! [W2] :
( ( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| W2 = sdtmndt0(W1,W0) )
& ( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [W0,W1] :
( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| W2 = sdtmndt0(W1,W0) )
& ! [W2] :
( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(miniscoping,[status(thm)],[f97]) ).
fof(f99,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f167,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f168,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f169,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f174,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f175,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f179,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f180,plain,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f185,plain,
( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[f101,f180]) ).
fof(f190,definition,
( sQ0_spl
<=> aNaturalNumber0(sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ0_spl
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,definition,
( sQ1_spl
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f196,definition,
( sQ2_spl
<=> sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f199,definition,
( sQ3_spl
<=> aNaturalNumber0(sdtasdt0(xr,xm)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( sQ3_spl
| ~ aNaturalNumber0(sdtasdt0(xr,xm)) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
( sQ4_spl
<=> sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ4_spl
| sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f204,plain,
( sQ4_spl
| sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f185,f190,f193,f196,f199,f202]) ).
fof(f213,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f175,f99]) ).
fof(f217,definition,
( sQ5_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( sQ5_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,definition,
( sQ6_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ6_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
( sQ7_spl
<=> sdtlseqdt0(xp,xn) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ7_spl
| ~ sdtlseqdt0(xp,xn) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f230,definition,
( sQ9_spl
<=> aNaturalNumber0(xr) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f213,f217,f220,f223,f230]) ).
fof(f246,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f174]) ).
fof(f247,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f248,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f222,f167]) ).
fof(f249,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f250,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f169]) ).
fof(f251,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f250]) ).
fof(f259,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f204]) ).
fof(f260,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f263,plain,
( sQ3_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f201,f58]) ).
fof(f265,definition,
( sQ14_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( sQ14_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f268,plain,
( sQ3_spl
| ~ sQ14_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f263,f230,f265,f199]) ).
fof(f269,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f168]) ).
fof(f270,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( ~ sQ4_spl
| aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(paramodulation,[status(thm)],[f203,f56]) ).
fof(f277,plain,
( ~ sQ4_spl
| sQ1_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f272,f190,f199,f193,f202]) ).
fof(f278,plain,
( sQ0_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f192,f58]) ).
fof(f280,plain,
( sQ0_spl
| ~ sQ14_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f278,f217,f265,f190]) ).
fof(f302,definition,
( sQ18_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( sQ18_spl
| ~ aNaturalNumber0(sz00) ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f324,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f304,f52]) ).
fof(f325,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f328,definition,
( sQ23_spl
<=> xr = xr ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ23_spl
| xr != xr ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f335,plain,
( sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f330]) ).
fof(f336,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f479,plain,
( ~ sQ4_spl
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[f95,f203]) ).
fof(f490,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f479,f190,f193,f196,f199,f202]) ).
fof(f500,plain,
$false,
inference(sat_refutation,[status(thm)],[f205,f233,f247,f249,f251,f260,f268,f270,f277,f280,f325,f336,f490]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM490+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.81 % Computer : n006.cluster.edu
% 0.11/10.81 % Model : x86_64 x86_64
% 0.11/10.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.81 % Memory : 8046.5625MB
% 0.11/10.81 % OS : Linux 6.8.0-71-generic
% 0.11/10.81 % CPULimit : 300
% 0.11/10.81 % WCLimit : 300
% 0.11/10.81 % DateTime : Mon Sep 21 02:34:40 UTC 2026
% 0.11/10.81 % CPUTime :
% 0.11/10.83 % Drodi V4.1.1
% 0.11/10.86 % Refutation found
% 0.11/10.86 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/10.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/10.89 % Elapsed time: 0.064992 seconds
% 0.11/10.89 % CPU time: 0.228730 seconds
% 0.11/10.89 % Total memory used: 106.206 MB
% 0.11/10.89 % Net memory used: 105.913 MB
%------------------------------------------------------------------------------