%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM454+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 : n015.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 7.10s 1.52s
% Output : CNFRefutation 7.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 125 ( 52 unt; 4 def)
% Number of atoms : 249 ( 127 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 213 ( 89 ~; 89 |; 20 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 75 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( aInteger0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0] :
( aInteger0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [W0] :
( aInteger0(W0)
=> ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),W0) = smndt0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,conjecture,
( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f55,plain,
aInteger0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f56,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f57,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,plain,
! [W0,W1] :
( aInteger0(sdtasdt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f61,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [W0,W1,W2] :
( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f63,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f65,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f67,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f69,plain,
! [W0] :
( ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f70,plain,
! [X0] :
( sdtpldt0(X0,smndt0(X0)) = sz00
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f76,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f77,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f80,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f85,plain,
! [W0] :
( ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f87,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f88,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f89,plain,
! [X0,X1] :
( X1 = sz00
| X0 = sz00
| sdtasdt0(X0,X1) != sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f230,plain,
aInteger0(xp),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f231,plain,
xp != sz00,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f237,plain,
( sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10)
& sdtpldt0(sz10,xp) = smndt0(sz10) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f238,plain,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f239,plain,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f289,plain,
aInteger0(smndt0(xp)),
inference(resolution,[status(thm)],[f57,f230]) ).
fof(f290,plain,
aInteger0(smndt0(sz10)),
inference(resolution,[status(thm)],[f57,f55]) ).
fof(f294,plain,
! [X0,X1] :
( sdtpldt0(xp,sdtpldt0(X0,X1)) = sdtpldt0(sdtpldt0(xp,X0),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f63,f230]) ).
fof(f295,plain,
! [X0,X1] :
( sdtpldt0(sz10,sdtpldt0(X0,X1)) = sdtpldt0(sdtpldt0(sz10,X0),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f63,f55]) ).
fof(f296,plain,
! [X0] :
( sdtpldt0(xp,X0) = sdtpldt0(X0,xp)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f65,f230]) ).
fof(f303,plain,
! [X0] :
( aInteger0(sdtasdt0(xp,X0))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f61,f230]) ).
fof(f306,plain,
sdtpldt0(xp,sz00) = xp,
inference(resolution,[status(thm)],[f67,f230]) ).
fof(f307,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(resolution,[status(thm)],[f67,f55]) ).
fof(f312,plain,
sdtpldt0(xp,smndt0(xp)) = sz00,
inference(resolution,[status(thm)],[f70,f230]) ).
fof(f313,plain,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(resolution,[status(thm)],[f70,f55]) ).
fof(f315,plain,
sz00 = sdtpldt0(smndt0(xp),xp),
inference(resolution,[status(thm)],[f71,f230]) ).
fof(f316,plain,
sz00 = sdtpldt0(smndt0(sz10),sz10),
inference(resolution,[status(thm)],[f71,f55]) ).
fof(f321,plain,
sdtasdt0(xp,sz10) = xp,
inference(resolution,[status(thm)],[f77,f230]) ).
fof(f331,plain,
smndt0(xp) = sdtpldt0(sz00,smndt0(xp)),
inference(resolution,[status(thm)],[f289,f68]) ).
fof(f340,plain,
! [X0,X1] :
( sdtasdt0(xp,sdtpldt0(X0,X1)) = sdtpldt0(sdtasdt0(xp,X0),sdtasdt0(xp,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f80,f230]) ).
fof(f352,plain,
smndt0(xp) = sdtasdt0(xp,smndt0(sz10)),
inference(resolution,[status(thm)],[f87,f230]) ).
fof(f396,plain,
! [X0] :
( X0 = sz00
| xp = sz00
| sdtasdt0(xp,X0) != sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f89,f230]) ).
fof(f419,definition,
! [X0] :
( sQ6_spl
<=> ( X0 = sz00
| sdtasdt0(xp,X0) != sz00
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f420,plain,
! [X0] :
( ~ sQ6_spl
| X0 = sz00
| sdtasdt0(xp,X0) != sz00
| ~ aInteger0(X0) ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,definition,
( sQ7_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f423,plain,
( ~ sQ7_spl
| xp = sz00 ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f396,f419,f422]) ).
fof(f453,plain,
! [X0] :
( sdtpldt0(xp,sdtpldt0(xp,X0)) = sdtpldt0(sdtpldt0(xp,xp),X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f294,f230]) ).
fof(f454,plain,
! [X0] :
( sdtpldt0(xp,sdtpldt0(sz10,X0)) = sdtpldt0(sdtpldt0(xp,sz10),X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f294,f55]) ).
fof(f458,plain,
! [X0] :
( sdtpldt0(sz10,sdtpldt0(smndt0(xp),X0)) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f295,f289]) ).
fof(f460,plain,
! [X0] :
( sdtpldt0(sz10,sdtpldt0(xp,X0)) = sdtpldt0(sdtpldt0(sz10,xp),X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f295,f230]) ).
fof(f463,plain,
! [X0] :
( sdtpldt0(sz10,sdtpldt0(smndt0(xp),X0)) = sdtpldt0(smndt0(sz10),X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f239,f458]) ).
fof(f465,plain,
! [X0] :
( sdtpldt0(sz10,sdtpldt0(xp,X0)) = sdtpldt0(smndt0(sz10),X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f238,f460]) ).
fof(f593,plain,
sdtpldt0(xp,smndt0(sz10)) = sdtpldt0(smndt0(sz10),xp),
inference(resolution,[status(thm)],[f296,f290]) ).
fof(f596,plain,
sdtpldt0(xp,sz10) = sdtpldt0(sz10,xp),
inference(resolution,[status(thm)],[f296,f55]) ).
fof(f599,plain,
! [X0] :
( sdtpldt0(xp,sdtpldt0(sz10,X0)) = sdtpldt0(smndt0(sz10),X0)
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f601,f454]) ).
fof(f601,plain,
sdtpldt0(xp,sz10) = smndt0(sz10),
inference(forward_demodulation,[status(thm)],[f238,f596]) ).
fof(f603,plain,
sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))) = sdtpldt0(smndt0(sz10),smndt0(sz10)),
inference(resolution,[status(thm)],[f465,f290]) ).
fof(f617,plain,
sdtpldt0(sz10,sdtpldt0(smndt0(xp),xp)) = sdtpldt0(smndt0(sz10),xp),
inference(resolution,[status(thm)],[f463,f230]) ).
fof(f622,plain,
sdtpldt0(sz10,sz00) = sdtpldt0(smndt0(sz10),xp),
inference(forward_demodulation,[status(thm)],[f315,f617]) ).
fof(f623,plain,
sz10 = sdtpldt0(smndt0(sz10),xp),
inference(forward_demodulation,[status(thm)],[f307,f622]) ).
fof(f625,plain,
sdtpldt0(sz10,sz10) = sdtpldt0(smndt0(sz10),smndt0(sz10)),
inference(backward_demodulation,[status(thm)],[f629,f603]) ).
fof(f629,plain,
sz10 = sdtpldt0(xp,smndt0(sz10)),
inference(forward_demodulation,[status(thm)],[f593,f623]) ).
fof(f675,plain,
sdtpldt0(xp,sdtpldt0(sz10,smndt0(sz10))) = sdtpldt0(smndt0(sz10),smndt0(sz10)),
inference(resolution,[status(thm)],[f599,f290]) ).
fof(f677,plain,
sdtpldt0(xp,sdtpldt0(sz10,xp)) = sdtpldt0(smndt0(sz10),xp),
inference(resolution,[status(thm)],[f599,f230]) ).
fof(f678,plain,
sdtpldt0(xp,sdtpldt0(sz10,sz10)) = sdtpldt0(smndt0(sz10),sz10),
inference(resolution,[status(thm)],[f599,f55]) ).
fof(f681,plain,
sdtpldt0(xp,sz00) = sdtpldt0(smndt0(sz10),smndt0(sz10)),
inference(forward_demodulation,[status(thm)],[f313,f675]) ).
fof(f682,plain,
xp = sdtpldt0(smndt0(sz10),smndt0(sz10)),
inference(forward_demodulation,[status(thm)],[f306,f681]) ).
fof(f686,plain,
xp = sdtpldt0(sz10,sz10),
inference(forward_demodulation,[status(thm)],[f625,f682]) ).
fof(f689,plain,
sdtpldt0(xp,smndt0(sz10)) = sdtpldt0(smndt0(sz10),xp),
inference(forward_demodulation,[status(thm)],[f238,f677]) ).
fof(f690,plain,
sz10 = sdtpldt0(smndt0(sz10),xp),
inference(forward_demodulation,[status(thm)],[f629,f689]) ).
fof(f691,plain,
sdtpldt0(xp,xp) = sdtpldt0(smndt0(sz10),sz10),
inference(forward_demodulation,[status(thm)],[f686,f678]) ).
fof(f692,plain,
! [X0] :
( sdtpldt0(xp,sdtpldt0(xp,X0)) = sdtpldt0(sz00,X0)
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f694,f453]) ).
fof(f694,plain,
sdtpldt0(xp,xp) = sz00,
inference(forward_demodulation,[status(thm)],[f316,f691]) ).
fof(f713,plain,
aInteger0(sdtasdt0(xp,xp)),
inference(resolution,[status(thm)],[f303,f230]) ).
fof(f900,plain,
! [X0] :
( sdtasdt0(xp,sdtpldt0(smndt0(sz10),X0)) = sdtpldt0(sdtasdt0(xp,smndt0(sz10)),sdtasdt0(xp,X0))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f340,f290]) ).
fof(f904,plain,
! [X0] :
( sdtasdt0(xp,sdtpldt0(smndt0(sz10),X0)) = sdtpldt0(smndt0(xp),sdtasdt0(xp,X0))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f352,f900]) ).
fof(f969,plain,
sdtasdt0(xp,xp) = sdtpldt0(sz00,sdtasdt0(xp,xp)),
inference(resolution,[status(thm)],[f713,f68]) ).
fof(f997,plain,
sdtpldt0(xp,sdtpldt0(xp,sdtasdt0(xp,xp))) = sdtpldt0(sz00,sdtasdt0(xp,xp)),
inference(resolution,[status(thm)],[f692,f713]) ).
fof(f1000,plain,
sdtpldt0(xp,sdtpldt0(xp,smndt0(xp))) = sdtpldt0(sz00,smndt0(xp)),
inference(resolution,[status(thm)],[f692,f289]) ).
fof(f1005,plain,
sdtpldt0(xp,sdtpldt0(xp,sdtasdt0(xp,xp))) = sdtasdt0(xp,xp),
inference(forward_demodulation,[status(thm)],[f969,f997]) ).
fof(f1084,plain,
sdtpldt0(xp,sz00) = sdtpldt0(sz00,smndt0(xp)),
inference(forward_demodulation,[status(thm)],[f312,f1000]) ).
fof(f1085,plain,
xp = sdtpldt0(sz00,smndt0(xp)),
inference(forward_demodulation,[status(thm)],[f306,f1084]) ).
fof(f1094,plain,
! [X0] :
( sdtasdt0(xp,sdtpldt0(smndt0(sz10),X0)) = sdtpldt0(xp,sdtasdt0(xp,X0))
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f1124,f904]) ).
fof(f1124,plain,
xp = smndt0(xp),
inference(forward_demodulation,[status(thm)],[f331,f1085]) ).
fof(f1261,plain,
sdtasdt0(xp,sdtpldt0(smndt0(sz10),xp)) = sdtpldt0(xp,sdtasdt0(xp,xp)),
inference(resolution,[status(thm)],[f1094,f230]) ).
fof(f1268,plain,
sdtasdt0(xp,sz10) = sdtpldt0(xp,sdtasdt0(xp,xp)),
inference(forward_demodulation,[status(thm)],[f690,f1261]) ).
fof(f1270,plain,
sdtpldt0(xp,xp) = sdtasdt0(xp,xp),
inference(backward_demodulation,[status(thm)],[f1276,f1005]) ).
fof(f1276,plain,
xp = sdtpldt0(xp,sdtasdt0(xp,xp)),
inference(forward_demodulation,[status(thm)],[f321,f1268]) ).
fof(f1321,plain,
sz00 = sdtasdt0(xp,xp),
inference(forward_demodulation,[status(thm)],[f694,f1270]) ).
fof(f1461,plain,
( ~ sQ6_spl
| xp = sz00
| sdtasdt0(xp,xp) != sz00 ),
inference(resolution,[status(thm)],[f420,f230]) ).
fof(f1475,definition,
( sQ26_spl
<=> sdtasdt0(xp,xp) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1477,plain,
( sQ26_spl
| sdtasdt0(xp,xp) != sz00 ),
inference(component_clause,[status(thm)],[f1475]) ).
fof(f1478,plain,
( ~ sQ6_spl
| sQ7_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1461,f1475,f422,f419]) ).
fof(f1479,definition,
( sQ27_spl
<=> sdtasdt0(xp,sz10) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1480,plain,
( ~ sQ27_spl
| sdtasdt0(xp,sz10) = sz00 ),
inference(component_clause,[status(thm)],[f1479]) ).
fof(f1481,plain,
( sQ27_spl
| sdtasdt0(xp,sz10) != sz00 ),
inference(component_clause,[status(thm)],[f1479]) ).
fof(f1573,plain,
( sQ27_spl
| xp != sz00 ),
inference(forward_demodulation,[status(thm)],[f321,f1481]) ).
fof(f1574,plain,
( sQ27_spl
| ~ sQ7_spl
| xp != xp ),
inference(forward_demodulation,[status(thm)],[f423,f1573]) ).
fof(f1575,plain,
( sQ27_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1574]) ).
fof(f1576,plain,
( sQ27_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1575]) ).
fof(f1578,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1321,f1477]) ).
fof(f1579,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f1578]) ).
fof(f1671,plain,
( ~ sQ27_spl
| xp = sz00 ),
inference(forward_demodulation,[status(thm)],[f321,f1480]) ).
fof(f1674,plain,
( ~ sQ27_spl
| xp != xp ),
inference(forward_demodulation,[status(thm)],[f1671,f231]) ).
fof(f1675,plain,
( ~ sQ27_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1674]) ).
fof(f1676,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1675]) ).
fof(f1677,plain,
$false,
inference(sat_refutation,[status(thm)],[f425,f1478,f1576,f1579,f1676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM454+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n015.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 02:34:20 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.49 % Drodi V4.1.1
% 7.10/1.52 % Refutation found
% 7.10/1.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.10/1.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.99/1.57 % Elapsed time: 1.092990 seconds
% 4.99/1.57 % CPU time: 7.891602 seconds
% 4.99/1.57 % Total memory used: 164.706 MB
% 4.99/1.57 % Net memory used: 159.326 MB
%------------------------------------------------------------------------------