%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG049+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:04:47 PM UTC 2026
% Result : Theorem 0.13s 0.52s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 30
% Syntax : Number of formulae : 112 ( 18 unt; 17 def)
% Number of atoms : 324 ( 49 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 356 ( 144 ~; 154 |; 27 &)
% ( 18 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 61 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( sdtlseqdt0(W1,W0)
| sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtlseqdt0(sz0z00,W1)
& sdtlseqdt0(sz0z00,W0) )
=> ( sdtlseqdt0(sz0z00,sdtasdt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtpldt0(W0,W1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [W0] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aVector0(W0) )
=> aScalar0(sdtlbdtrb0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,definition,
! [W0] :
( aVector0(W0)
=> ( aDimensionOf0(W0) != sz00
=> ! [W1] :
( W1 = sziznziztdt0(W0)
<=> ( ! [W2] :
( aNaturalNumber0(W2)
=> sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [W0,W1] :
( ( aVector0(W1)
& aVector0(W0) )
=> ( aDimensionOf0(W0) = aDimensionOf0(W1)
=> aScalar0(sdtasasdt0(W0,W1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
aVector0(xs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
& sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,conjecture,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f64,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f67,plain,
! [W0,W1] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f68,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f99,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f100,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f107,plain,
! [W0,W1] :
( sdtlseqdt0(W1,W0)
| sdtlseqdt0(W0,W1)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f108,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [W0,W1] :
( ( sdtlseqdt0(sz0z00,sdtasdt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtpldt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f110,plain,
! [X0,X1] :
( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f119,plain,
! [W0] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f120,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [W0,W1] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f122,plain,
! [X0,X1] :
( aScalar0(sdtlbdtrb0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [W0] :
( ! [W1] :
( W1 = sziznziztdt0(W0)
<=> ( ! [W2] :
( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2)
| ~ aNaturalNumber0(W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) ) )
| aDimensionOf0(W0) = sz00
| ~ aVector0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f124,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( sdtlbdtrb0(W1,W2) != sdtlbdtrb0(W0,W2)
& aNaturalNumber0(W2) )
| szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
| ~ aVector0(W1)
| W1 = sziznziztdt0(W0) )
& ( ( ! [W2] :
( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2)
| ~ aNaturalNumber0(W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) )
| W1 != sziznziztdt0(W0) ) )
| aDimensionOf0(W0) = sz00
| ~ aVector0(W0) ),
inference(NNF_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( sdtlbdtrb0(W1,W2) != sdtlbdtrb0(W0,W2)
& aNaturalNumber0(W2) )
| szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
| ~ aVector0(W1)
| W1 = sziznziztdt0(W0) )
& ! [W1] :
( ( ! [W2] :
( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2)
| ~ aNaturalNumber0(W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) )
| W1 != sziznziztdt0(W0) ) )
| aDimensionOf0(W0) = sz00
| ~ aVector0(W0) ),
inference(miniscoping,[status(thm)],[f124]) ).
fof(f126,plain,
! [W0] :
( ( ! [W1] :
( ( sdtlbdtrb0(W1,sK1_skl(W1,W0)) != sdtlbdtrb0(W0,sK1_skl(W1,W0))
& aNaturalNumber0(sK1_skl(W1,W0)) )
| szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
| ~ aVector0(W1)
| W1 = sziznziztdt0(W0) )
& ! [W1] :
( ( ! [W2] :
( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2)
| ~ aNaturalNumber0(W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) )
| W1 != sziznziztdt0(W0) ) )
| aDimensionOf0(W0) = sz00
| ~ aVector0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( aVector0(X1)
| X1 != sziznziztdt0(X0)
| aDimensionOf0(X0) = sz00
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f134,plain,
! [W0,W1] :
( aScalar0(sdtasasdt0(W0,W1))
| aDimensionOf0(W0) != aDimensionOf0(W1)
| ~ aVector0(W1)
| ~ aVector0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f135,plain,
! [X0,X1] :
( aScalar0(sdtasasdt0(X0,X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f140,plain,
aVector0(xs),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f143,plain,
aDimensionOf0(xs) != sz00,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f144,plain,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f145,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f146,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f147,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f163,plain,
! [X0] :
( aVector0(sziznziztdt0(X0))
| aDimensionOf0(X0) = sz00
| ~ aVector0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f127]) ).
fof(f166,plain,
( sdtlseqdt0(sdtasasdt0(xs,xs),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(xs,xs)) ),
inference(resolution,[status(thm)],[f108,f147]) ).
fof(f167,definition,
( sQ4_spl
<=> aScalar0(sdtasasdt0(xs,xs)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( sQ4_spl
| ~ aScalar0(sdtasasdt0(xs,xs)) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,definition,
( sQ5_spl
<=> aScalar0(sz0z00) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( sQ5_spl
| ~ aScalar0(sz0z00) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,definition,
( sQ6_spl
<=> sdtlseqdt0(sdtasasdt0(xs,xs),sz0z00) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ6_spl
| sdtlseqdt0(sdtasasdt0(xs,xs),sz0z00) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f166,f167,f170,f173]) ).
fof(f177,plain,
( ~ sQ6_spl
| sz0z00 = sdtasasdt0(xs,xs)
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ aScalar0(sz0z00) ),
inference(resolution,[status(thm)],[f100,f174]) ).
fof(f182,definition,
( sQ7_spl
<=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f185,definition,
( sQ8_spl
<=> sz0z00 = sdtasasdt0(xs,xs) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ8_spl
| sz0z00 = sdtasasdt0(xs,xs) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( ~ sQ6_spl
| sQ8_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f177,f170,f167,f182,f185,f173]) ).
fof(f189,definition,
( sQ9_spl
<=> aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ9_spl
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f203,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f64]) ).
fof(f204,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f203]) ).
fof(f207,definition,
( sQ13_spl
<=> sdtlseqdt0(sz0z00,sz0z00) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( sQ13_spl
| ~ sdtlseqdt0(sz0z00,sz0z00) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f214,plain,
( sQ13_spl
| sdtlseqdt0(sz0z00,sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sz0z00) ),
inference(resolution,[status(thm)],[f209,f108]) ).
fof(f216,plain,
( sQ13_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f214,f170,f207]) ).
fof(f261,definition,
( sQ20_spl
<=> sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ20_spl
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f279,plain,
! [X0] :
( aScalar0(sdtasasdt0(X0,X0))
| ~ aVector0(X0)
| ~ aVector0(X0) ),
inference(equality_resolution,[status(thm)],[f135]) ).
fof(f280,plain,
! [X0] :
( aScalar0(sdtasasdt0(X0,X0))
| ~ aVector0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f279]) ).
fof(f281,plain,
( sQ9_spl
| ~ aVector0(sziznziztdt0(xs)) ),
inference(resolution,[status(thm)],[f280,f191]) ).
fof(f282,plain,
( sQ4_spl
| ~ aVector0(xs) ),
inference(resolution,[status(thm)],[f280,f169]) ).
fof(f283,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f282,f140]) ).
fof(f284,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f283]) ).
fof(f343,plain,
( aVector0(sziznziztdt0(xs))
| ~ aVector0(xs) ),
inference(resolution,[status(thm)],[f163,f143]) ).
fof(f344,definition,
( sQ30_spl
<=> aVector0(xs) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ30_spl
| ~ aVector0(xs) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,definition,
( sQ31_spl
<=> aVector0(sziznziztdt0(xs)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( ~ sQ31_spl
| aVector0(sziznziztdt0(xs)) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,plain,
( sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f343,f344,f347]) ).
fof(f351,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f346,f140]) ).
fof(f352,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f353,plain,
( ~ sQ31_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f348,f281]) ).
fof(f354,plain,
( ~ sQ31_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f492,plain,
( ~ sQ8_spl
| ~ sdtlseqdt0(sz0z00,sz0z00) ),
inference(backward_demodulation,[status(thm)],[f186,f147]) ).
fof(f497,plain,
( ~ sQ8_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f492,f207,f185]) ).
fof(f613,definition,
( sQ61_spl
<=> aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( sQ61_spl
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(component_clause,[status(thm)],[f613]) ).
fof(f688,plain,
( sQ61_spl
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(resolution,[status(thm)],[f615,f68]) ).
fof(f689,definition,
( sQ72_spl
<=> aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f691,plain,
( sQ72_spl
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(component_clause,[status(thm)],[f689]) ).
fof(f692,plain,
( sQ61_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f688,f689,f613]) ).
fof(f783,plain,
( sQ72_spl
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(resolution,[status(thm)],[f691,f122]) ).
fof(f784,definition,
( sQ81_spl
<=> aNaturalNumber0(aDimensionOf0(xs)) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f786,plain,
( sQ81_spl
| ~ aNaturalNumber0(aDimensionOf0(xs)) ),
inference(component_clause,[status(thm)],[f784]) ).
fof(f787,plain,
( sQ72_spl
| ~ sQ81_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f783,f344,f784,f689]) ).
fof(f788,plain,
( sQ81_spl
| ~ aVector0(xs) ),
inference(resolution,[status(thm)],[f786,f120]) ).
fof(f789,plain,
( sQ81_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f788,f344,f784]) ).
fof(f911,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| ~ sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(resolution,[status(thm)],[f146,f100]) ).
fof(f920,definition,
( sQ93_spl
<=> sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f922,plain,
( sQ93_spl
| ~ sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00) ),
inference(component_clause,[status(thm)],[f920]) ).
fof(f923,definition,
( sQ94_spl
<=> sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00 ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f924,plain,
( ~ sQ94_spl
| sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00 ),
inference(component_clause,[status(thm)],[f923]) ).
fof(f926,plain,
( sQ94_spl
| ~ sQ93_spl
| ~ sQ5_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f911,f613,f170,f920,f923]) ).
fof(f929,plain,
( sQ93_spl
| sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00) ),
inference(resolution,[status(thm)],[f922,f108]) ).
fof(f932,definition,
( sQ95_spl
<=> sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f935,plain,
( sQ93_spl
| sQ95_spl
| ~ sQ61_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f929,f170,f613,f932,f920]) ).
fof(f938,plain,
( ~ sQ94_spl
| sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00) ),
inference(backward_demodulation,[status(thm)],[f924,f144]) ).
fof(f1405,plain,
( ~ sQ94_spl
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sz0z00)
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(paramodulation,[status(thm)],[f938,f110]) ).
fof(f1416,plain,
( ~ sQ94_spl
| sQ7_spl
| ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ5_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1405,f189,f170,f261,f207,f182,f923]) ).
fof(f1435,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f145]) ).
fof(f1436,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f1435]) ).
fof(f1484,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(paramodulation,[status(thm)],[f144,f110]) ).
fof(f1490,plain,
( sQ7_spl
| ~ sQ95_spl
| ~ sQ20_spl
| ~ sQ61_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1484,f189,f613,f261,f932,f182]) ).
fof(f1495,plain,
$false,
inference(sat_refutation,[status(thm)],[f176,f188,f204,f216,f284,f350,f352,f354,f497,f692,f787,f789,f926,f935,f1416,f1436,f1490]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG049+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:18:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.52 % Refutation found
% 0.13/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.35/0.55 % Elapsed time: 0.173509 seconds
% 0.35/0.55 % CPU time: 1.083530 seconds
% 0.35/0.55 % Total memory used: 121.214 MB
% 0.35/0.55 % Net memory used: 119.408 MB
%------------------------------------------------------------------------------