%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG071+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 : n017.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 13.46s 12.31s
% Output : CNFRefutation 13.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 60
% Syntax : Number of formulae : 198 ( 39 unt; 33 def)
% Number of atoms : 520 ( 71 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 540 ( 218 ~; 230 |; 42 &)
% ( 34 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 33 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 89 ( 87 !; 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(f25,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( sdtlseqdt0(W1,W0)
| sdtlseqdt0(W0,W1) ) ),
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)
& aVector0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( xq = sziznziztdt0(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(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(f60,hypothesis,
~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
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(f127,plain,
! [W0,W1] :
( sdtlseqdt0(W1,W0)
| sdtlseqdt0(W0,W1)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f128,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
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(f169,plain,
xp = sziznziztdt0(xs),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f171,plain,
xq = sziznziztdt0(xt),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f173,plain,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f174,plain,
aScalar0(xB),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f177,plain,
xC = sdtasasdt0(xp,xp),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f179,plain,
xD = sdtasasdt0(xq,xq),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f182,plain,
aScalar0(xF),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f183,plain,
xF = sdtasdt0(xA,xA),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f184,plain,
aScalar0(xG),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f185,plain,
xG = sdtasdt0(xB,xB),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f188,plain,
aScalar0(xR),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f189,plain,
xR = sdtasdt0(xC,xG),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f190,plain,
aScalar0(xP),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f192,plain,
aScalar0(xS),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f193,plain,
xS = sdtasdt0(xF,xD),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f200,plain,
~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f202,plain,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f203,plain,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f219,definition,
( sQ4_spl
<=> sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( sQ4_spl
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,definition,
( sQ5_spl
<=> sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( sQ5_spl
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f203,f219,f222]) ).
fof(f250,definition,
( sQ10_spl
<=> aScalar0(sz0z00) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( sQ10_spl
| ~ aScalar0(sz0z00) ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f257,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f84]) ).
fof(f258,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f257]) ).
fof(f281,definition,
( sQ14_spl
<=> aScalar0(xR) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( sQ14_spl
| ~ aScalar0(xR) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,definition,
( sQ15_spl
<=> aScalar0(xS) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( sQ15_spl
| ~ aScalar0(xS) ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f288,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f286,f192]) ).
fof(f289,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f288]) ).
fof(f290,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f188]) ).
fof(f291,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f290]) ).
fof(f293,plain,
( sQ5_spl
| sdtlseqdt0(sdtpldt0(xP,xP),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtpldt0(xP,xP)) ),
inference(resolution,[status(thm)],[f224,f128]) ).
fof(f297,definition,
( sQ17_spl
<=> aScalar0(sdtpldt0(xP,xP)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( sQ17_spl
| ~ aScalar0(sdtpldt0(xP,xP)) ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f301,definition,
( sQ18_spl
<=> sdtlseqdt0(sdtpldt0(xP,xP),sz0z00) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( sQ5_spl
| sQ18_spl
| ~ sQ10_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f293,f297,f250,f301,f222]) ).
fof(f305,plain,
( sQ17_spl
| ~ aScalar0(xP)
| ~ aScalar0(xP) ),
inference(resolution,[status(thm)],[f299,f86]) ).
fof(f306,definition,
( sQ19_spl
<=> aScalar0(xP) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( sQ19_spl
| ~ aScalar0(xP) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( sQ17_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f305,f306,f297]) ).
fof(f310,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f190]) ).
fof(f311,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f310]) ).
fof(f364,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X2,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(X2,sz0z00)
| ~ aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(sz0z00)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[f130,f122]) ).
fof(f367,definition,
! [X0,X1,X2] :
( sQ28_spl
<=> ( sdtlseqdt0(X2,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(X2,sz0z00)
| ~ aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f368,plain,
! [X0,X1,X2] :
( ~ sQ28_spl
| sdtlseqdt0(X2,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(X2,sz0z00)
| ~ aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,plain,
( ~ sQ10_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f364,f367,f250]) ).
fof(f375,definition,
( sQ30_spl
<=> sdtlseqdt0(sz0z00,xR) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f378,definition,
( sQ31_spl
<=> sdtlseqdt0(sz0z00,xS) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f382,plain,
! [X0,X1,X2] :
( ~ sQ28_spl
| sdtlseqdt0(X2,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(X2,sz0z00)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f86]) ).
fof(f507,plain,
( aVector0(xq)
| aDimensionOf0(xt) = sz00
| ~ aVector0(xt) ),
inference(resolution,[status(thm)],[f147,f171]) ).
fof(f508,plain,
( aVector0(xp)
| aDimensionOf0(xs) = sz00
| ~ aVector0(xs) ),
inference(resolution,[status(thm)],[f147,f169]) ).
fof(f516,definition,
( sQ53_spl
<=> aVector0(xt) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( sQ53_spl
| ~ aVector0(xt) ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f519,definition,
( sQ54_spl
<=> aDimensionOf0(xt) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( ~ sQ54_spl
| aDimensionOf0(xt) = sz00 ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,definition,
( sQ55_spl
<=> aVector0(xq) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( sQ55_spl
| sQ54_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f507,f516,f519,f522]) ).
fof(f526,definition,
( sQ56_spl
<=> aVector0(xs) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f528,plain,
( sQ56_spl
| ~ aVector0(xs) ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f529,definition,
( sQ57_spl
<=> aDimensionOf0(xs) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( ~ sQ57_spl
| aDimensionOf0(xs) = sz00 ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f532,definition,
( sQ58_spl
<=> aVector0(xp) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( sQ58_spl
| sQ57_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f508,f526,f529,f532]) ).
fof(f544,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f530,f167]) ).
fof(f545,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f544]) ).
fof(f546,plain,
( sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f162]) ).
fof(f547,plain,
sQ56_spl,
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f548,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f163]) ).
fof(f549,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f707,plain,
( ~ sQ54_spl
| aDimensionOf0(xs) = sz00 ),
inference(forward_demodulation,[status(thm)],[f520,f166]) ).
fof(f708,plain,
( ~ sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f707,f167]) ).
fof(f709,plain,
~ sQ54_spl,
inference(contradiction_clause,[status(thm)],[f708]) ).
fof(f785,plain,
( aScalar0(xA)
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(paramodulation,[status(thm)],[f173,f142]) ).
fof(f797,definition,
( sQ102_spl
<=> aNaturalNumber0(aDimensionOf0(xs)) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f799,plain,
( sQ102_spl
| ~ aNaturalNumber0(aDimensionOf0(xs)) ),
inference(component_clause,[status(thm)],[f797]) ).
fof(f805,definition,
( sQ104_spl
<=> aScalar0(xA) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f808,plain,
( sQ104_spl
| ~ sQ102_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f785,f526,f797,f805]) ).
fof(f898,definition,
( sQ121_spl
<=> aScalar0(xB) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f900,plain,
( sQ121_spl
| ~ aScalar0(xB) ),
inference(component_clause,[status(thm)],[f898]) ).
fof(f908,plain,
( sdtlseqdt0(sz0z00,xC)
| ~ aVector0(xp) ),
inference(paramodulation,[status(thm)],[f177,f161]) ).
fof(f910,plain,
( aScalar0(xC)
| aDimensionOf0(xp) != aDimensionOf0(xp)
| ~ aVector0(xp)
| ~ aVector0(xp) ),
inference(paramodulation,[status(thm)],[f177,f155]) ).
fof(f922,definition,
( sQ125_spl
<=> aDimensionOf0(xp) = aDimensionOf0(xp) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f924,plain,
( sQ125_spl
| aDimensionOf0(xp) != aDimensionOf0(xp) ),
inference(component_clause,[status(thm)],[f922]) ).
fof(f933,definition,
( sQ128_spl
<=> sdtlseqdt0(sz0z00,xC) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f936,plain,
( sQ128_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f908,f532,f933]) ).
fof(f944,definition,
( sQ131_spl
<=> aScalar0(xC) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f947,plain,
( sQ131_spl
| ~ sQ125_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f910,f532,f922,f944]) ).
fof(f948,plain,
( sQ125_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f924]) ).
fof(f949,plain,
sQ125_spl,
inference(contradiction_clause,[status(thm)],[f948]) ).
fof(f954,plain,
( sdtlseqdt0(sz0z00,xD)
| ~ aVector0(xq) ),
inference(paramodulation,[status(thm)],[f179,f161]) ).
fof(f956,plain,
( aScalar0(xD)
| aDimensionOf0(xq) != aDimensionOf0(xq)
| ~ aVector0(xq)
| ~ aVector0(xq) ),
inference(paramodulation,[status(thm)],[f179,f155]) ).
fof(f968,definition,
( sQ135_spl
<=> aDimensionOf0(xq) = aDimensionOf0(xq) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f970,plain,
( sQ135_spl
| aDimensionOf0(xq) != aDimensionOf0(xq) ),
inference(component_clause,[status(thm)],[f968]) ).
fof(f979,definition,
( sQ138_spl
<=> sdtlseqdt0(sz0z00,xD) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f982,plain,
( sQ138_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f954,f522,f979]) ).
fof(f990,definition,
( sQ141_spl
<=> aScalar0(xD) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f993,plain,
( sQ141_spl
| ~ sQ135_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f956,f522,f968,f990]) ).
fof(f994,plain,
( sQ135_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f970]) ).
fof(f995,plain,
sQ135_spl,
inference(contradiction_clause,[status(thm)],[f994]) ).
fof(f1015,plain,
( sQ102_spl
| ~ aVector0(xs) ),
inference(resolution,[status(thm)],[f799,f140]) ).
fof(f1016,plain,
( sQ102_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f1015,f526,f797]) ).
fof(f1057,plain,
( sdtlseqdt0(sz0z00,xF)
| ~ aScalar0(xA) ),
inference(paramodulation,[status(thm)],[f183,f133]) ).
fof(f1058,plain,
( aScalar0(xF)
| ~ aScalar0(xA)
| ~ aScalar0(xA) ),
inference(paramodulation,[status(thm)],[f183,f88]) ).
fof(f1071,definition,
( sQ150_spl
<=> sdtlseqdt0(sz0z00,xF) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1111,plain,
( sQ150_spl
| ~ sQ104_spl ),
inference(split_clause,[status(thm)],[f1057,f805,f1071]) ).
fof(f1112,definition,
( sQ160_spl
<=> aScalar0(xF) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f1115,plain,
( sQ160_spl
| ~ sQ104_spl ),
inference(split_clause,[status(thm)],[f1058,f805,f1112]) ).
fof(f1144,plain,
( sdtlseqdt0(sz0z00,xG)
| ~ aScalar0(xB) ),
inference(paramodulation,[status(thm)],[f185,f133]) ).
fof(f1145,plain,
( aScalar0(xG)
| ~ aScalar0(xB)
| ~ aScalar0(xB) ),
inference(paramodulation,[status(thm)],[f185,f88]) ).
fof(f1158,definition,
( sQ167_spl
<=> sdtlseqdt0(sz0z00,xG) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1198,plain,
( sQ167_spl
| ~ sQ121_spl ),
inference(split_clause,[status(thm)],[f1144,f898,f1158]) ).
fof(f1199,definition,
( sQ177_spl
<=> aScalar0(xG) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1202,plain,
( sQ177_spl
| ~ sQ121_spl ),
inference(split_clause,[status(thm)],[f1145,f898,f1199]) ).
fof(f1219,plain,
( sQ121_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f900,f174]) ).
fof(f1220,plain,
sQ121_spl,
inference(contradiction_clause,[status(thm)],[f1219]) ).
fof(f1568,definition,
( sQ246_spl
<=> aScalar0(sdtasdt0(xB,xB)) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f1570,plain,
( sQ246_spl
| ~ aScalar0(sdtasdt0(xB,xB)) ),
inference(component_clause,[status(thm)],[f1568]) ).
fof(f1578,definition,
( sQ249_spl
<=> aScalar0(sdtasdt0(xA,xA)) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f1580,plain,
( sQ249_spl
| ~ aScalar0(sdtasdt0(xA,xA)) ),
inference(component_clause,[status(thm)],[f1578]) ).
fof(f1587,plain,
( sQ249_spl
| ~ aScalar0(xF) ),
inference(forward_demodulation,[status(thm)],[f183,f1580]) ).
fof(f1588,plain,
( sQ249_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1587,f182]) ).
fof(f1589,plain,
sQ249_spl,
inference(contradiction_clause,[status(thm)],[f1588]) ).
fof(f1601,plain,
( sdtlseqdt0(sz0z00,xS)
| ~ sdtlseqdt0(sz0z00,xD)
| ~ sdtlseqdt0(sz0z00,xF)
| ~ aScalar0(xD)
| ~ aScalar0(xF) ),
inference(paramodulation,[status(thm)],[f193,f131]) ).
fof(f1616,plain,
( sQ31_spl
| ~ sQ138_spl
| ~ sQ150_spl
| ~ sQ141_spl
| ~ sQ160_spl ),
inference(split_clause,[status(thm)],[f1601,f1112,f990,f1071,f979,f378]) ).
fof(f1982,plain,
( sdtlseqdt0(sz0z00,xR)
| ~ sdtlseqdt0(sz0z00,xG)
| ~ sdtlseqdt0(sz0z00,xC)
| ~ aScalar0(xG)
| ~ aScalar0(xC) ),
inference(paramodulation,[status(thm)],[f189,f131]) ).
fof(f1997,plain,
( sQ30_spl
| ~ sQ167_spl
| ~ sQ128_spl
| ~ sQ177_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f1982,f944,f1199,f933,f1158,f375]) ).
fof(f3952,plain,
( sQ4_spl
| ~ sdtlseqdt0(sz0z00,xS)
| ~ sdtlseqdt0(sz0z00,xR)
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(resolution,[status(thm)],[f221,f130]) ).
fof(f3958,plain,
( sQ4_spl
| ~ sQ31_spl
| ~ sQ30_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f3952,f281,f284,f375,f378,f219]) ).
fof(f4923,plain,
( sQ246_spl
| ~ aScalar0(xG) ),
inference(forward_demodulation,[status(thm)],[f185,f1570]) ).
fof(f4924,plain,
( sQ246_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4923,f184]) ).
fof(f4925,plain,
sQ246_spl,
inference(contradiction_clause,[status(thm)],[f4924]) ).
fof(f5367,plain,
( ~ sQ28_spl
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sz0z00)
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,xS)
| ~ sdtlseqdt0(sz0z00,xR)
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(resolution,[status(thm)],[f382,f200]) ).
fof(f5381,plain,
( ~ sQ28_spl
| ~ sQ18_spl
| ~ sQ17_spl
| ~ sQ31_spl
| ~ sQ30_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f5367,f281,f284,f375,f378,f297,f301,f367]) ).
fof(f5398,plain,
$false,
inference(sat_refutation,[status(thm)],[f225,f258,f289,f291,f304,f309,f311,f370,f525,f535,f545,f547,f549,f709,f808,f936,f947,f949,f982,f993,f995,f1016,f1111,f1115,f1198,f1202,f1220,f1589,f1616,f1997,f3958,f4925,f5381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG071+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n017.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Mon Sep 21 04:13:08 UTC 2026
% 0.08/10.38 % CPUTime :
% 0.08/10.40 % Drodi V4.1.1
% 13.46/12.31 % Refutation found
% 13.46/12.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 13.46/12.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.46/12.35 % Elapsed time: 1.958816 seconds
% 13.46/12.35 % CPU time: 15.176656 seconds
% 13.46/12.35 % Total memory used: 189.127 MB
% 13.46/12.35 % Net memory used: 181.768 MB
%------------------------------------------------------------------------------