%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM474+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 01:40:39 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 16 unt; 5 def)
% Number of atoms : 87 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 74 ( 29 ~; 27 |; 12 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
( xp = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,xp)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
( xq = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( xr = sdtmndt0(xq,xp)
& sdtpldt0(xp,xr) = xq
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f70,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f71,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f140,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f151,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f152,plain,
xm = sdtasdt0(xl,xp),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f155,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f161,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f162,plain,
sdtpldt0(xp,xr) = xq,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f164,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f167,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(xm,xn),
inference(backward_demodulation,[status(thm)],[f152,f164]) ).
fof(f169,plain,
! [X0] :
( sdtasdt0(xl,sdtpldt0(xp,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f152,f71]) ).
fof(f172,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtpldt0(xm,xn),
inference(forward_demodulation,[status(thm)],[f152,f167]) ).
fof(f173,definition,
( sQ0_spl
<=> aNaturalNumber0(xl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( sQ0_spl
| ~ aNaturalNumber0(xl) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f179,definition,
( sQ2_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ2_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f183,definition,
! [X0] :
( sQ3_spl
<=> ( sdtasdt0(xl,sdtpldt0(xp,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f184,plain,
! [X0] :
( ~ sQ3_spl
| sdtasdt0(xl,sdtpldt0(xp,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0))
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( sQ3_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f169,f173,f179,f183]) ).
fof(f195,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f151]) ).
fof(f196,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f195]) ).
fof(f197,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f140]) ).
fof(f198,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f201,definition,
( sQ6_spl
<=> aNaturalNumber0(xr) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( sQ6_spl
| ~ aNaturalNumber0(xr) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f212,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f161]) ).
fof(f213,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f212]) ).
fof(f1138,plain,
( ~ sQ3_spl
| sdtasdt0(xl,xq) = sdtpldt0(xm,sdtasdt0(xl,xr))
| ~ aNaturalNumber0(xr) ),
inference(paramodulation,[status(thm)],[f162,f184]) ).
fof(f1143,definition,
( sQ140_spl
<=> sdtasdt0(xl,xq) = sdtpldt0(xm,sdtasdt0(xl,xr)) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1144,plain,
( ~ sQ140_spl
| sdtasdt0(xl,xq) = sdtpldt0(xm,sdtasdt0(xl,xr)) ),
inference(component_clause,[status(thm)],[f1143]) ).
fof(f1146,plain,
( ~ sQ3_spl
| sQ140_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1138,f201,f1143,f183]) ).
fof(f1147,plain,
( ~ sQ140_spl
| sdtpldt0(xm,xn) = sdtpldt0(xm,sdtasdt0(xl,xr)) ),
inference(forward_demodulation,[status(thm)],[f155,f1144]) ).
fof(f1148,plain,
( ~ sQ140_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1147,f172]) ).
fof(f1149,plain,
~ sQ140_spl,
inference(contradiction_clause,[status(thm)],[f1148]) ).
fof(f1150,plain,
$false,
inference(sat_refutation,[status(thm)],[f186,f196,f198,f213,f1146,f1149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM474+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n009.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 02:33:13 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.11/0.36 % Drodi V4.1.1
% 0.11/0.43 % Refutation found
% 0.11/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.45 % Elapsed time: 0.100946 seconds
% 0.11/0.45 % CPU time: 0.512052 seconds
% 0.11/0.45 % Total memory used: 112.681 MB
% 0.11/0.45 % Net memory used: 111.914 MB
%------------------------------------------------------------------------------