%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG071+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 : n019.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 02:04:51 PM UTC 2026
% Result : Theorem 0.28s 1.08s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 63
% Syntax : Number of formulae : 215 ( 45 unt; 36 def)
% Number of atoms : 529 ( 89 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 512 ( 198 ~; 208 |; 52 &)
% ( 37 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 41 ( 39 usr; 36 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 78 ( 76 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W0,W1,W2] :
( ( aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [W0] :
( aScalar0(W0)
=> sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [W0] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aVector0(W0) )
=> aScalar0(sdtlbdtrb0(W0,W1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [W0,W1] :
( ( aVector0(W1)
& aVector0(W0) )
=> ( aDimensionOf0(W0) = aDimensionOf0(W1)
=> aScalar0(sdtasasdt0(W0,W1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [W0] :
( aVector0(W0)
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
( aVector0(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
( xp = sziznziztdt0(xs)
& ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( xq = sziznziztdt0(xt)
& ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,hypothesis,
sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,conjecture,
( sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
& sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,negated_conjecture,
~ ( sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
& sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
inference(negated_conjecture,[status(cth)],[f62]) ).
fof(f84,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f85,plain,
! [W0,W1] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f86,plain,
! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
! [W0,W1] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f88,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f121,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f122,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f129,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(f130,plain,
! [X0,X1] :
( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
! [W0] :
( sdtlseqdt0(sz0z00,sdtasdt0(W0,W0))
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f133,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f139,plain,
! [W0] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f140,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
! [W0,W1] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f142,plain,
! [X0,X1] :
( aScalar0(sdtlbdtrb0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f143,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(f144,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)],[f143]) ).
fof(f145,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)],[f144]) ).
fof(f146,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))],[f145]) ).
fof(f147,plain,
! [X0,X1] :
( aVector0(X1)
| X1 != sziznziztdt0(X0)
| aDimensionOf0(X0) = sz00
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f154,plain,
! [W0,W1] :
( aScalar0(sdtasasdt0(W0,W1))
| aDimensionOf0(W0) != aDimensionOf0(W1)
| ~ aVector0(W1)
| ~ aVector0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f155,plain,
! [X0,X1] :
( aScalar0(sdtasasdt0(X0,X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f160,plain,
! [W0] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f161,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f162,plain,
aVector0(xs),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f163,plain,
aVector0(xt),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f166,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f167,plain,
aDimensionOf0(xs) != sz00,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f168,plain,
( xp = sziznziztdt0(xs)
& ! [W0] :
( sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0)
| ~ aNaturalNumber0(W0) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f170,plain,
szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f172,plain,
xp = sziznziztdt0(xs),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f173,plain,
( xq = sziznziztdt0(xt)
& ! [W0] :
( sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0)
| ~ aNaturalNumber0(W0) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f174,plain,
aVector0(xq),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f177,plain,
xq = sziznziztdt0(xt),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f179,plain,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f181,plain,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f183,plain,
xC = sdtasasdt0(xp,xp),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f185,plain,
xD = sdtasasdt0(xq,xq),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f186,plain,
aScalar0(xE),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f188,plain,
aScalar0(xF),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f189,plain,
xF = sdtasdt0(xA,xA),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f190,plain,
aScalar0(xG),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f191,plain,
xG = sdtasdt0(xB,xB),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f194,plain,
aScalar0(xR),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f195,plain,
xR = sdtasdt0(xC,xG),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f196,plain,
aScalar0(xP),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f198,plain,
aScalar0(xS),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f199,plain,
xS = sdtasdt0(xF,xD),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f207,plain,
sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f208,plain,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f209,plain,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f225,definition,
( sQ4_spl
<=> sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( sQ4_spl
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,definition,
( sQ5_spl
<=> sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ5_spl
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f209,f225,f228]) ).
fof(f253,definition,
( sQ9_spl
<=> aScalar0(sdtpldt0(xR,xS)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( sQ9_spl
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,definition,
( sQ10_spl
<=> aScalar0(sz0z00) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( sQ10_spl
| ~ aScalar0(sz0z00) ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f263,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f84]) ).
fof(f264,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f286,plain,
( sQ9_spl
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(resolution,[status(thm)],[f255,f86]) ).
fof(f287,definition,
( sQ14_spl
<=> aScalar0(xR) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( sQ14_spl
| ~ aScalar0(xR) ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f290,definition,
( sQ15_spl
<=> aScalar0(xS) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ15_spl
| ~ aScalar0(xS) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,plain,
( sQ9_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f286,f287,f290,f253]) ).
fof(f294,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f292,f198]) ).
fof(f295,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f294]) ).
fof(f296,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f289,f194]) ).
fof(f297,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f296]) ).
fof(f298,plain,
! [X0] :
( sQ5_spl
| ~ sdtlseqdt0(X0,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(X0)
| ~ aScalar0(sz0z00) ),
inference(resolution,[status(thm)],[f230,f122]) ).
fof(f300,definition,
! [X0] :
( sQ16_spl
<=> ( ~ sdtlseqdt0(X0,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f301,plain,
! [X0] :
( ~ sQ16_spl
| ~ sdtlseqdt0(X0,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X0) ),
inference(component_clause,[status(thm)],[f300]) ).
fof(f303,definition,
( sQ17_spl
<=> aScalar0(sdtpldt0(xP,xP)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( sQ17_spl
| ~ aScalar0(sdtpldt0(xP,xP)) ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f306,plain,
( sQ5_spl
| ~ sQ17_spl
| sQ16_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f298,f256,f300,f303,f228]) ).
fof(f311,plain,
( sQ17_spl
| ~ aScalar0(xP)
| ~ aScalar0(xP) ),
inference(resolution,[status(thm)],[f305,f86]) ).
fof(f312,definition,
( sQ19_spl
<=> aScalar0(xP) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( sQ19_spl
| ~ aScalar0(xP) ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,plain,
( sQ17_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f311,f312,f303]) ).
fof(f316,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f314,f196]) ).
fof(f317,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f316]) ).
fof(f381,definition,
( sQ30_spl
<=> sdtlseqdt0(sz0z00,xR) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f384,definition,
( sQ31_spl
<=> sdtlseqdt0(sz0z00,xS) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( aVector0(xq)
| aDimensionOf0(xt) = sz00
| ~ aVector0(xt) ),
inference(resolution,[status(thm)],[f147,f177]) ).
fof(f514,plain,
( aVector0(xp)
| aDimensionOf0(xs) = sz00
| ~ aVector0(xs) ),
inference(resolution,[status(thm)],[f147,f172]) ).
fof(f522,definition,
( sQ53_spl
<=> aVector0(xt) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ53_spl
| ~ aVector0(xt) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f525,definition,
( sQ54_spl
<=> aDimensionOf0(xt) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( ~ sQ54_spl
| aDimensionOf0(xt) = sz00 ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,definition,
( sQ55_spl
<=> aVector0(xq) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f531,plain,
( sQ55_spl
| sQ54_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f513,f522,f525,f528]) ).
fof(f532,definition,
( sQ56_spl
<=> aVector0(xs) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f534,plain,
( sQ56_spl
| ~ aVector0(xs) ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f535,definition,
( sQ57_spl
<=> aDimensionOf0(xs) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( ~ sQ57_spl
| aDimensionOf0(xs) = sz00 ),
inference(component_clause,[status(thm)],[f535]) ).
fof(f538,definition,
( sQ58_spl
<=> aVector0(xp) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( sQ58_spl
| sQ57_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f514,f532,f535,f538]) ).
fof(f550,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f167]) ).
fof(f551,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f550]) ).
fof(f552,plain,
( sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f162]) ).
fof(f553,plain,
sQ56_spl,
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f554,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f163]) ).
fof(f555,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f713,plain,
( ~ sQ54_spl
| aDimensionOf0(xs) = sz00 ),
inference(forward_demodulation,[status(thm)],[f526,f166]) ).
fof(f714,plain,
( ~ sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f713,f167]) ).
fof(f715,plain,
~ sQ54_spl,
inference(contradiction_clause,[status(thm)],[f714]) ).
fof(f819,definition,
( sQ105_spl
<=> aNaturalNumber0(aDimensionOf0(xs)) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f924,definition,
( sQ125_spl
<=> aNaturalNumber0(aDimensionOf0(xq)) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f926,plain,
( sQ125_spl
| ~ aNaturalNumber0(aDimensionOf0(xq)) ),
inference(component_clause,[status(thm)],[f924]) ).
fof(f993,plain,
( aScalar0(xA)
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(paramodulation,[status(thm)],[f179,f142]) ).
fof(f1010,definition,
( sQ139_spl
<=> aScalar0(xA) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1013,plain,
( sQ139_spl
| ~ sQ105_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f993,f532,f819,f1010]) ).
fof(f1038,definition,
( sQ144_spl
<=> aScalar0(xB) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1049,plain,
( sdtlseqdt0(sz0z00,xC)
| ~ aVector0(xp) ),
inference(paramodulation,[status(thm)],[f183,f161]) ).
fof(f1051,plain,
( aScalar0(xC)
| aDimensionOf0(xp) != aDimensionOf0(xp)
| ~ aVector0(xp)
| ~ aVector0(xp) ),
inference(paramodulation,[status(thm)],[f183,f155]) ).
fof(f1060,definition,
( sQ147_spl
<=> aDimensionOf0(xp) = aDimensionOf0(xp) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1062,plain,
( sQ147_spl
| aDimensionOf0(xp) != aDimensionOf0(xp) ),
inference(component_clause,[status(thm)],[f1060]) ).
fof(f1071,definition,
( sQ150_spl
<=> sdtlseqdt0(sz0z00,xC) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1074,plain,
( sQ150_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f1049,f538,f1071]) ).
fof(f1079,definition,
( sQ152_spl
<=> aScalar0(xC) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1082,plain,
( sQ152_spl
| ~ sQ147_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f1051,f538,f1060,f1079]) ).
fof(f1083,plain,
( sQ147_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1062]) ).
fof(f1084,plain,
sQ147_spl,
inference(contradiction_clause,[status(thm)],[f1083]) ).
fof(f1164,plain,
( sdtlseqdt0(sz0z00,xD)
| ~ aVector0(xq) ),
inference(paramodulation,[status(thm)],[f185,f161]) ).
fof(f1166,plain,
( aScalar0(xD)
| aDimensionOf0(xq) != aDimensionOf0(xq)
| ~ aVector0(xq)
| ~ aVector0(xq) ),
inference(paramodulation,[status(thm)],[f185,f155]) ).
fof(f1178,definition,
( sQ165_spl
<=> aDimensionOf0(xq) = aDimensionOf0(xq) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1180,plain,
( sQ165_spl
| aDimensionOf0(xq) != aDimensionOf0(xq) ),
inference(component_clause,[status(thm)],[f1178]) ).
fof(f1189,definition,
( sQ168_spl
<=> sdtlseqdt0(sz0z00,xD) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1192,plain,
( sQ168_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f1164,f528,f1189]) ).
fof(f1197,definition,
( sQ170_spl
<=> aScalar0(xD) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1200,plain,
( sQ170_spl
| ~ sQ165_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f1166,f528,f1178,f1197]) ).
fof(f1201,plain,
( sQ165_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1180]) ).
fof(f1202,plain,
sQ165_spl,
inference(contradiction_clause,[status(thm)],[f1201]) ).
fof(f1228,definition,
( sQ175_spl
<=> aScalar0(xE) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f1230,plain,
( sQ175_spl
| ~ aScalar0(xE) ),
inference(component_clause,[status(thm)],[f1228]) ).
fof(f1248,plain,
( sdtlseqdt0(sz0z00,xF)
| ~ aScalar0(xA) ),
inference(paramodulation,[status(thm)],[f189,f133]) ).
fof(f1249,plain,
( aScalar0(xF)
| ~ aScalar0(xA)
| ~ aScalar0(xA) ),
inference(paramodulation,[status(thm)],[f189,f88]) ).
fof(f1262,definition,
( sQ178_spl
<=> sdtlseqdt0(sz0z00,xF) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1302,plain,
( sQ178_spl
| ~ sQ139_spl ),
inference(split_clause,[status(thm)],[f1248,f1010,f1262]) ).
fof(f1303,definition,
( sQ188_spl
<=> aScalar0(xF) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f1306,plain,
( sQ188_spl
| ~ sQ139_spl ),
inference(split_clause,[status(thm)],[f1249,f1010,f1303]) ).
fof(f1359,plain,
( sQ125_spl
| ~ aVector0(xq) ),
inference(resolution,[status(thm)],[f926,f140]) ).
fof(f1360,plain,
( sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1359,f174]) ).
fof(f1361,plain,
sQ125_spl,
inference(contradiction_clause,[status(thm)],[f1360]) ).
fof(f1374,plain,
( sdtlseqdt0(sz0z00,xG)
| ~ aScalar0(xB) ),
inference(paramodulation,[status(thm)],[f191,f133]) ).
fof(f1375,plain,
( aScalar0(xG)
| ~ aScalar0(xB)
| ~ aScalar0(xB) ),
inference(paramodulation,[status(thm)],[f191,f88]) ).
fof(f1388,definition,
( sQ197_spl
<=> sdtlseqdt0(sz0z00,xG) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f1428,plain,
( sQ197_spl
| ~ sQ144_spl ),
inference(split_clause,[status(thm)],[f1374,f1038,f1388]) ).
fof(f1429,definition,
( sQ207_spl
<=> aScalar0(xG) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f1432,plain,
( sQ207_spl
| ~ sQ144_spl ),
inference(split_clause,[status(thm)],[f1375,f1038,f1429]) ).
fof(f2076,plain,
xB = sdtlbdtrb0(xt,aDimensionOf0(xs)),
inference(backward_demodulation,[status(thm)],[f166,f181]) ).
fof(f2083,plain,
( aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xt) ),
inference(paramodulation,[status(thm)],[f166,f140]) ).
fof(f2096,plain,
( sQ105_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f2083,f522,f819]) ).
fof(f2313,plain,
( sQ175_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1230,f186]) ).
fof(f2314,plain,
sQ175_spl,
inference(contradiction_clause,[status(thm)],[f2313]) ).
fof(f2726,plain,
( aScalar0(xB)
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xt) ),
inference(paramodulation,[status(thm)],[f2076,f142]) ).
fof(f2735,plain,
( sQ144_spl
| ~ sQ105_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f2726,f522,f819,f1038]) ).
fof(f2767,plain,
( sdtlseqdt0(sz0z00,xS)
| ~ sdtlseqdt0(sz0z00,xD)
| ~ sdtlseqdt0(sz0z00,xF)
| ~ aScalar0(xD)
| ~ aScalar0(xF) ),
inference(paramodulation,[status(thm)],[f199,f131]) ).
fof(f2787,plain,
( sQ31_spl
| ~ sQ168_spl
| ~ sQ178_spl
| ~ sQ170_spl
| ~ sQ188_spl ),
inference(split_clause,[status(thm)],[f2767,f1303,f1197,f1262,f1189,f384]) ).
fof(f3017,plain,
( sQ4_spl
| ~ sdtlseqdt0(sz0z00,xS)
| ~ sdtlseqdt0(sz0z00,xR)
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(resolution,[status(thm)],[f227,f130]) ).
fof(f3020,plain,
( sQ4_spl
| ~ sQ31_spl
| ~ sQ30_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3017,f287,f290,f381,f384,f225]) ).
fof(f3038,definition,
( sQ449_spl
<=> szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xt) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f3040,plain,
( sQ449_spl
| szszuzczcdt0(aDimensionOf0(xp)) != aDimensionOf0(xt) ),
inference(component_clause,[status(thm)],[f3038]) ).
fof(f3053,plain,
( sQ449_spl
| aDimensionOf0(xs) != aDimensionOf0(xt) ),
inference(forward_demodulation,[status(thm)],[f170,f3040]) ).
fof(f3054,plain,
( sQ449_spl
| aDimensionOf0(xs) != aDimensionOf0(xs) ),
inference(forward_demodulation,[status(thm)],[f166,f3053]) ).
fof(f3055,plain,
( sQ449_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3054]) ).
fof(f3056,plain,
sQ449_spl,
inference(contradiction_clause,[status(thm)],[f3055]) ).
fof(f3198,plain,
( sdtlseqdt0(sz0z00,xR)
| ~ sdtlseqdt0(sz0z00,xG)
| ~ sdtlseqdt0(sz0z00,xC)
| ~ aScalar0(xG)
| ~ aScalar0(xC) ),
inference(paramodulation,[status(thm)],[f195,f131]) ).
fof(f3213,plain,
( sQ30_spl
| ~ sQ197_spl
| ~ sQ150_spl
| ~ sQ207_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f3198,f1079,f1429,f1071,f1388,f381]) ).
fof(f3422,definition,
( sQ491_spl
<=> aScalar0(sdtasdt0(xA,xA)) ),
introduced(definition,[new_symbols(definition,[sQ491_spl])],[split_symbol_definition]) ).
fof(f3424,plain,
( sQ491_spl
| ~ aScalar0(sdtasdt0(xA,xA)) ),
inference(component_clause,[status(thm)],[f3422]) ).
fof(f3429,definition,
( sQ493_spl
<=> aScalar0(sdtasdt0(xB,xB)) ),
introduced(definition,[new_symbols(definition,[sQ493_spl])],[split_symbol_definition]) ).
fof(f3431,plain,
( sQ493_spl
| ~ aScalar0(sdtasdt0(xB,xB)) ),
inference(component_clause,[status(thm)],[f3429]) ).
fof(f3438,plain,
( sQ493_spl
| ~ aScalar0(xG) ),
inference(forward_demodulation,[status(thm)],[f191,f3431]) ).
fof(f3439,plain,
( sQ493_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3438,f190]) ).
fof(f3440,plain,
sQ493_spl,
inference(contradiction_clause,[status(thm)],[f3439]) ).
fof(f3441,plain,
( sQ491_spl
| ~ aScalar0(xF) ),
inference(forward_demodulation,[status(thm)],[f189,f3424]) ).
fof(f3442,plain,
( sQ491_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3441,f188]) ).
fof(f3443,plain,
sQ491_spl,
inference(contradiction_clause,[status(thm)],[f3442]) ).
fof(f4559,plain,
( ~ sQ16_spl
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(resolution,[status(thm)],[f207,f301]) ).
fof(f4564,plain,
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4559,f253,f225,f300]) ).
fof(f4569,plain,
$false,
inference(sat_refutation,[status(thm)],[f231,f264,f293,f295,f297,f306,f315,f317,f531,f541,f551,f553,f555,f715,f1013,f1074,f1082,f1084,f1192,f1200,f1202,f1302,f1306,f1361,f1428,f1432,f2096,f2314,f2735,f2787,f3020,f3056,f3213,f3440,f3443,f4564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG071+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n019.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 04:17:36 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.28/1.08 % Refutation found
% 0.28/1.08 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.28/1.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.51/1.12 % Elapsed time: 0.657906 seconds
% 1.51/1.12 % CPU time: 4.627712 seconds
% 1.51/1.12 % Total memory used: 141.056 MB
% 1.51/1.12 % Net memory used: 138.012 MB
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