%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM457+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 : n018.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 01:40:35 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 59 ( 13 unt; 8 def)
% Number of atoms : 152 ( 51 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 162 ( 69 ~; 66 |; 10 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
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(f9,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 != sz00
=> ! [W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0)
| sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
=> W1 = W2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
( sdtasdt0(xm,xn) = sz00
=> ( xn = sz00
| xm = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ( sdtasdt0(xm,xn) = sz00
=> ( xn = sz00
| xm = sz00 ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f24,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f25,plain,
sz10 != sz00,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f37,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f44,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f45,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f53,plain,
! [W0] :
( ! [W1,W2] :
( W1 = W2
| ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) )
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f54,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f59,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f60,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f61,plain,
( xn != sz00
& xm != sz00
& sdtasdt0(xm,xn) = sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f62,plain,
sdtasdt0(xm,xn) = sz00,
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
xm != sz00,
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f64,plain,
xn != sz00,
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f65,plain,
( aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f62,f29]) ).
fof(f66,definition,
( sQ0_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( sQ0_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,definition,
( sQ1_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( sQ1_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,definition,
( sQ2_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f66,f69,f72]) ).
fof(f76,plain,
( sz00 = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f62,f38]) ).
fof(f78,definition,
( sQ3_spl
<=> sz00 = sdtasdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ3_spl
| sz00 = sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f76,f66,f69,f78]) ).
fof(f83,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f60]) ).
fof(f84,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f83]) ).
fof(f85,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f68,f59]) ).
fof(f86,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f85]) ).
fof(f102,plain,
! [X0] :
( ~ sQ3_spl
| xm = X0
| sz00 != sdtasdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| xn = sz00
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f79,f54]) ).
fof(f107,definition,
( sQ5_spl
<=> xn = sz00 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ5_spl
| xn = sz00 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,definition,
! [X0] :
( sQ6_spl
<=> ( xm = X0
| sz00 != sdtasdt0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f111,plain,
! [X0] :
( ~ sQ6_spl
| xm = X0
| sz00 != sdtasdt0(xn,X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( ~ sQ3_spl
| sQ6_spl
| ~ sQ0_spl
| sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f102,f69,f107,f66,f110,f78]) ).
fof(f114,definition,
( sQ7_spl
<=> xm = sz00 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( ~ sQ7_spl
| xm = sz00 ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f123,definition,
! [X0] :
( sQ9_spl
<=> ( X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f124,plain,
! [X0] :
( ~ sQ9_spl
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f130,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f64]) ).
fof(f131,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f132,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f63]) ).
fof(f133,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f132]) ).
fof(f162,plain,
( ~ sQ9_spl
| sz10 = sz00 ),
inference(resolution,[status(thm)],[f124,f24]) ).
fof(f167,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f25]) ).
fof(f168,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( ~ sQ6_spl
| ~ aNaturalNumber0(xn)
| xm = sz00
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f111,f45]) ).
fof(f176,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| sQ7_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f170,f72,f114,f69,f110]) ).
fof(f178,plain,
$false,
inference(sat_refutation,[status(thm)],[f75,f81,f84,f86,f113,f131,f133,f168,f176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM457+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n018.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 02:33:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.055127 seconds
% 0.14/0.43 % CPU time: 0.152002 seconds
% 0.14/0.43 % Total memory used: 44.741 MB
% 0.14/0.43 % Net memory used: 44.624 MB
%------------------------------------------------------------------------------