TSTP Solution File: RNG081+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:37:55 EDT 2024
% Result : Theorem 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 25
% Syntax : Number of formulae : 119 ( 30 unt; 0 def)
% Number of atoms : 457 ( 161 equ)
% Maximal formula atoms : 40 ( 3 avg)
% Number of connectives : 452 ( 114 ~; 111 |; 198 &)
% ( 14 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 15 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 18 con; 0-2 aty)
% Number of variables : 98 ( 42 !; 56 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( aNaturalNumber0(szszuzczcdt0(W0))
& szszuzczcdt0(W0) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0] :
( aScalar0(W0)
=> aScalar0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0] :
( aScalar0(W0)
=> ( sdtpldt0(W0,sz0z00) = W0
& sdtpldt0(sz0z00,W0) = W0
& sdtasdt0(W0,sz0z00) = sz0z00
& sdtasdt0(sz0z00,W0) = sz0z00
& sdtpldt0(W0,smndt0(W0)) = sz0z00
& sdtpldt0(smndt0(W0),W0) = sz0z00
& smndt0(smndt0(W0)) = W0
& smndt0(sz0z00) = sz0z00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [W0,W1] :
( ( aVector0(W0)
& aNaturalNumber0(W1) )
=> aScalar0(sdtlbdtrb0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [W0,W1] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1)
& aDimensionOf0(W1) = sz00 )
=> sdtasasdt0(W0,W1) = sz0z00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,conjecture,
( ( aDimensionOf0(xs) != sz00
=> ? [W0] :
( aVector0(W0)
& szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs)
& ! [W1] :
( aNaturalNumber0(W1)
=> sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) )
& W0 = sziznziztdt0(xs)
& ? [W1] :
( aVector0(W1)
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt)
& ! [W2] :
( aNaturalNumber0(W2)
=> sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) )
& W1 = sziznziztdt0(xt)
& ? [W2] :
( aScalar0(W2)
& W2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& ? [W3] :
( aScalar0(W3)
& W3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& ? [W4] :
( aScalar0(W4)
& W4 = sdtasasdt0(W0,W0)
& ? [W5] :
( aScalar0(W5)
& W5 = sdtasasdt0(W1,W1)
& ? [W6] :
( aScalar0(W6)
& W6 = sdtasasdt0(W0,W1)
& ? [W7] :
( aScalar0(W7)
& W7 = sdtasdt0(W2,W2)
& ? [W8] :
( aScalar0(W8)
& W8 = sdtasdt0(W3,W3)
& ? [W9] :
( aScalar0(W9)
& W9 = sdtasdt0(W2,W3)
& ? [W10] :
( aScalar0(W10)
& W10 = sdtasdt0(W4,W8)
& ? [W11] :
( aScalar0(W11)
& W11 = sdtasdt0(W6,W9)
& ? [W12] :
( aScalar0(W12)
& W12 = sdtasdt0(W7,W5)
& ? [W13] :
( aScalar0(W13)
& W13 = sdtasdt0(W10,W12)
& sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
& sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
~ ( ( aDimensionOf0(xs) != sz00
=> ? [W0] :
( aVector0(W0)
& szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs)
& ! [W1] :
( aNaturalNumber0(W1)
=> sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) )
& W0 = sziznziztdt0(xs)
& ? [W1] :
( aVector0(W1)
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt)
& ! [W2] :
( aNaturalNumber0(W2)
=> sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) )
& W1 = sziznziztdt0(xt)
& ? [W2] :
( aScalar0(W2)
& W2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& ? [W3] :
( aScalar0(W3)
& W3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& ? [W4] :
( aScalar0(W4)
& W4 = sdtasasdt0(W0,W0)
& ? [W5] :
( aScalar0(W5)
& W5 = sdtasasdt0(W1,W1)
& ? [W6] :
( aScalar0(W6)
& W6 = sdtasasdt0(W0,W1)
& ? [W7] :
( aScalar0(W7)
& W7 = sdtasdt0(W2,W2)
& ? [W8] :
( aScalar0(W8)
& W8 = sdtasdt0(W3,W3)
& ? [W9] :
( aScalar0(W9)
& W9 = sdtasdt0(W2,W3)
& ? [W10] :
( aScalar0(W10)
& W10 = sdtasdt0(W4,W8)
& ? [W11] :
( aScalar0(W11)
& W11 = sdtasdt0(W6,W9)
& ? [W12] :
( aScalar0(W12)
& W12 = sdtasdt0(W7,W5)
& ? [W13] :
( aScalar0(W13)
& W13 = sdtasdt0(W10,W12)
& sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
& sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f46,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f47,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( aNaturalNumber0(szszuzczcdt0(W0))
& szszuzczcdt0(W0) != sz00 ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f48,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(szszuzczcdt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f63,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f68,plain,
! [W0] :
( ~ aScalar0(W0)
| aScalar0(smndt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f69,plain,
! [X0] :
( ~ aScalar0(X0)
| aScalar0(smndt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
! [W0] :
( ~ aScalar0(W0)
| ( sdtpldt0(W0,sz0z00) = W0
& sdtpldt0(sz0z00,W0) = W0
& sdtasdt0(W0,sz0z00) = sz0z00
& sdtasdt0(sz0z00,W0) = sz0z00
& sdtpldt0(W0,smndt0(W0)) = sz0z00
& sdtpldt0(smndt0(W0),W0) = sz0z00
& smndt0(smndt0(W0)) = W0
& smndt0(sz0z00) = sz0z00 ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f73,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(X0,sz0z00) = sz0z00 ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f96,plain,
! [W0] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f97,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f96]) ).
fof(f120,plain,
! [W0,W1] :
( ~ aVector0(W0)
| ~ aNaturalNumber0(W1)
| aScalar0(sdtlbdtrb0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f121,plain,
! [X0,X1] :
( ~ aVector0(X0)
| ~ aNaturalNumber0(X1)
| aScalar0(sdtlbdtrb0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f120]) ).
fof(f135,plain,
! [W0,W1] :
( ~ aVector0(W0)
| ~ aVector0(W1)
| aDimensionOf0(W0) != aDimensionOf0(W1)
| aDimensionOf0(W1) != sz00
| sdtasasdt0(W0,W1) = sz0z00 ),
inference(pre_NNF_transformation,[status(esa)],[f35]) ).
fof(f136,plain,
! [X0,X1] :
( ~ aVector0(X0)
| ~ aVector0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aDimensionOf0(X1) != sz00
| sdtasasdt0(X0,X1) = sz0z00 ),
inference(cnf_transformation,[status(esa)],[f135]) ).
fof(f141,plain,
aVector0(xs),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f142,plain,
aVector0(xt),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f145,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f146,plain,
( ( aDimensionOf0(xs) = sz00
| ? [W0] :
( aVector0(W0)
& szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs)
& ! [W1] :
( ~ aNaturalNumber0(W1)
| sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) )
& W0 = sziznziztdt0(xs)
& ? [W1] :
( aVector0(W1)
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt)
& ! [W2] :
( ~ aNaturalNumber0(W2)
| sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) )
& W1 = sziznziztdt0(xt)
& ? [W2] :
( aScalar0(W2)
& W2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& ? [W3] :
( aScalar0(W3)
& W3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& ? [W4] :
( aScalar0(W4)
& W4 = sdtasasdt0(W0,W0)
& ? [W5] :
( aScalar0(W5)
& W5 = sdtasasdt0(W1,W1)
& ? [W6] :
( aScalar0(W6)
& W6 = sdtasasdt0(W0,W1)
& ? [W7] :
( aScalar0(W7)
& W7 = sdtasdt0(W2,W2)
& ? [W8] :
( aScalar0(W8)
& W8 = sdtasdt0(W3,W3)
& ? [W9] :
( aScalar0(W9)
& W9 = sdtasdt0(W2,W3)
& ? [W10] :
( aScalar0(W10)
& W10 = sdtasdt0(W4,W8)
& ? [W11] :
( aScalar0(W11)
& W11 = sdtasdt0(W6,W9)
& ? [W12] :
( aScalar0(W12)
& W12 = sdtasdt0(W7,W5)
& ? [W13] :
( aScalar0(W13)
& W13 = sdtasdt0(W10,W12)
& sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
& sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f147,plain,
( ( aDimensionOf0(xs) = sz00
| ? [W0] :
( aVector0(W0)
& szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs)
& ! [W1] :
( ~ aNaturalNumber0(W1)
| sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) )
& W0 = sziznziztdt0(xs)
& ? [W1] :
( aVector0(W1)
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt)
& ! [W2] :
( ~ aNaturalNumber0(W2)
| sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) )
& W1 = sziznziztdt0(xt)
& ? [W2] :
( aScalar0(W2)
& W2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& ? [W3] :
( aScalar0(W3)
& W3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& ? [W4] :
( aScalar0(W4)
& W4 = sdtasasdt0(W0,W0)
& ? [W5] :
( aScalar0(W5)
& W5 = sdtasasdt0(W1,W1)
& ? [W6] :
( aScalar0(W6)
& W6 = sdtasasdt0(W0,W1)
& ? [W7] :
( aScalar0(W7)
& W7 = sdtasdt0(W2,W2)
& ? [W8] :
( aScalar0(W8)
& W8 = sdtasdt0(W3,W3)
& ? [W9] :
( aScalar0(W9)
& W9 = sdtasdt0(W2,W3)
& ? [W10] :
( aScalar0(W10)
& W10 = sdtasdt0(W4,W8)
& ? [W11] :
( aScalar0(W11)
& W11 = sdtasdt0(W6,W9)
& ? [W12] :
( aScalar0(W12)
& W12 = sdtasdt0(W7,W5)
& ? [W13] :
( aScalar0(W13)
& W13 = sdtasdt0(W10,W12) )
& sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
& sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(miniscoping,[status(esa)],[f146]) ).
fof(f148,plain,
( ( aDimensionOf0(xs) = sz00
| ( aVector0(sk0_2)
& szszuzczcdt0(aDimensionOf0(sk0_2)) = aDimensionOf0(xs)
& ! [W1] :
( ~ aNaturalNumber0(W1)
| sdtlbdtrb0(sk0_2,W1) = sdtlbdtrb0(xs,W1) )
& sk0_2 = sziznziztdt0(xs)
& aVector0(sk0_3)
& szszuzczcdt0(aDimensionOf0(sk0_3)) = aDimensionOf0(xt)
& ! [W2] :
( ~ aNaturalNumber0(W2)
| sdtlbdtrb0(sk0_3,W2) = sdtlbdtrb0(xt,W2) )
& sk0_3 = sziznziztdt0(xt)
& aScalar0(sk0_4)
& sk0_4 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(sk0_5)
& sk0_5 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(sk0_6)
& sk0_6 = sdtasasdt0(sk0_2,sk0_2)
& aScalar0(sk0_7)
& sk0_7 = sdtasasdt0(sk0_3,sk0_3)
& aScalar0(sk0_8)
& sk0_8 = sdtasasdt0(sk0_2,sk0_3)
& aScalar0(sk0_9)
& sk0_9 = sdtasdt0(sk0_4,sk0_4)
& aScalar0(sk0_10)
& sk0_10 = sdtasdt0(sk0_5,sk0_5)
& aScalar0(sk0_11)
& sk0_11 = sdtasdt0(sk0_4,sk0_5)
& aScalar0(sk0_12)
& sk0_12 = sdtasdt0(sk0_6,sk0_10)
& aScalar0(sk0_13)
& sk0_13 = sdtasdt0(sk0_8,sk0_11)
& aScalar0(sk0_14)
& sk0_14 = sdtasdt0(sk0_9,sk0_7)
& aScalar0(sk0_15)
& sk0_15 = sdtasdt0(sk0_12,sk0_14)
& sdtlseqdt0(sdtasdt0(sk0_8,sk0_8),sdtasdt0(sk0_6,sk0_7))
& sdtlseqdt0(sdtpldt0(sk0_13,sk0_13),sdtpldt0(sk0_12,sk0_14))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sk0_8,sk0_11),sdtpldt0(sk0_8,sk0_11)),sdtasdt0(sdtpldt0(sk0_6,sk0_9),sdtpldt0(sk0_7,sk0_10)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) )
& ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(skolemization,[status(esa)],[f147]) ).
fof(f184,plain,
( aDimensionOf0(xs) = sz00
| sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(cnf_transformation,[status(esa)],[f148]) ).
fof(f185,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(cnf_transformation,[status(esa)],[f148]) ).
fof(f201,plain,
( spl0_4
<=> aDimensionOf0(xs) = sz00 ),
introduced(split_symbol_definition) ).
fof(f202,plain,
( aDimensionOf0(xs) = sz00
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f344,plain,
( spl0_40
<=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
introduced(split_symbol_definition) ).
fof(f345,plain,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| ~ spl0_40 ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,plain,
( spl0_4
| spl0_40 ),
inference(split_clause,[status(thm)],[f184,f201,f344]) ).
fof(f351,plain,
aNaturalNumber0(szszuzczcdt0(sz00)),
inference(resolution,[status(thm)],[f48,f46]) ).
fof(f370,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(resolution,[status(thm)],[f63,f97]) ).
fof(f469,plain,
( sz00 = aDimensionOf0(xt)
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f202,f145]) ).
fof(f696,plain,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(resolution,[status(thm)],[f73,f63]) ).
fof(f948,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| aScalar0(sdtlbdtrb0(xt,X0)) ),
inference(resolution,[status(thm)],[f121,f142]) ).
fof(f949,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| aScalar0(sdtlbdtrb0(xs,X0)) ),
inference(resolution,[status(thm)],[f121,f141]) ).
fof(f956,plain,
aScalar0(sdtlbdtrb0(xt,szszuzczcdt0(sz00))),
inference(resolution,[status(thm)],[f948,f351]) ).
fof(f957,plain,
aScalar0(sdtlbdtrb0(xt,sz00)),
inference(resolution,[status(thm)],[f948,f46]) ).
fof(f971,plain,
aScalar0(smndt0(sdtlbdtrb0(xt,sz00))),
inference(resolution,[status(thm)],[f957,f69]) ).
fof(f977,plain,
sdtlseqdt0(sdtlbdtrb0(xt,sz00),sdtlbdtrb0(xt,sz00)),
inference(resolution,[status(thm)],[f957,f97]) ).
fof(f986,plain,
aScalar0(sdtlbdtrb0(xs,szszuzczcdt0(sz00))),
inference(resolution,[status(thm)],[f949,f351]) ).
fof(f987,plain,
aScalar0(sdtlbdtrb0(xs,sz00)),
inference(resolution,[status(thm)],[f949,f46]) ).
fof(f1001,plain,
aScalar0(smndt0(sdtlbdtrb0(xs,sz00))),
inference(resolution,[status(thm)],[f987,f69]) ).
fof(f1007,plain,
sdtlseqdt0(sdtlbdtrb0(xs,sz00),sdtlbdtrb0(xs,sz00)),
inference(resolution,[status(thm)],[f987,f97]) ).
fof(f1019,plain,
( spl0_117
<=> sz0z00 = sdtasasdt0(xs,xs) ),
introduced(split_symbol_definition) ).
fof(f1020,plain,
( sz0z00 = sdtasasdt0(xs,xs)
| ~ spl0_117 ),
inference(component_clause,[status(thm)],[f1019]) ).
fof(f1030,plain,
( spl0_120
<=> sz0z00 = sdtasasdt0(xt,xt) ),
introduced(split_symbol_definition) ).
fof(f1031,plain,
( sz0z00 = sdtasasdt0(xt,xt)
| ~ spl0_120 ),
inference(component_clause,[status(thm)],[f1030]) ).
fof(f1350,plain,
( $false
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[status(thm)],[f345,f185]) ).
fof(f1351,plain,
~ spl0_40,
inference(contradiction_clause,[status(thm)],[f1350]) ).
fof(f1599,plain,
( spl0_145
<=> aDimensionOf0(xt) = sz00 ),
introduced(split_symbol_definition) ).
fof(f1601,plain,
( aDimensionOf0(xt) != sz00
| spl0_145 ),
inference(component_clause,[status(thm)],[f1599]) ).
fof(f1805,plain,
( spl0_182
<=> aScalar0(sdtlbdtrb0(xt,sz00)) ),
introduced(split_symbol_definition) ).
fof(f1807,plain,
( ~ aScalar0(sdtlbdtrb0(xt,sz00))
| spl0_182 ),
inference(component_clause,[status(thm)],[f1805]) ).
fof(f1828,plain,
( spl0_187
<=> sdtlseqdt0(sdtlbdtrb0(xt,sz00),sdtlbdtrb0(xt,sz00)) ),
introduced(split_symbol_definition) ).
fof(f1830,plain,
( ~ sdtlseqdt0(sdtlbdtrb0(xt,sz00),sdtlbdtrb0(xt,sz00))
| spl0_187 ),
inference(component_clause,[status(thm)],[f1828]) ).
fof(f1836,plain,
( $false
| spl0_182 ),
inference(forward_subsumption_resolution,[status(thm)],[f1807,f957]) ).
fof(f1837,plain,
spl0_182,
inference(contradiction_clause,[status(thm)],[f1836]) ).
fof(f1838,plain,
( $false
| spl0_187 ),
inference(forward_subsumption_resolution,[status(thm)],[f1830,f977]) ).
fof(f1839,plain,
spl0_187,
inference(contradiction_clause,[status(thm)],[f1838]) ).
fof(f1877,plain,
( spl0_191
<=> aScalar0(sdtlbdtrb0(xs,sz00)) ),
introduced(split_symbol_definition) ).
fof(f1879,plain,
( ~ aScalar0(sdtlbdtrb0(xs,sz00))
| spl0_191 ),
inference(component_clause,[status(thm)],[f1877]) ).
fof(f1900,plain,
( spl0_196
<=> sdtlseqdt0(sdtlbdtrb0(xs,sz00),sdtlbdtrb0(xs,sz00)) ),
introduced(split_symbol_definition) ).
fof(f1902,plain,
( ~ sdtlseqdt0(sdtlbdtrb0(xs,sz00),sdtlbdtrb0(xs,sz00))
| spl0_196 ),
inference(component_clause,[status(thm)],[f1900]) ).
fof(f1908,plain,
( $false
| spl0_191 ),
inference(forward_subsumption_resolution,[status(thm)],[f1879,f987]) ).
fof(f1909,plain,
spl0_191,
inference(contradiction_clause,[status(thm)],[f1908]) ).
fof(f1910,plain,
( $false
| spl0_196 ),
inference(forward_subsumption_resolution,[status(thm)],[f1902,f1007]) ).
fof(f1911,plain,
spl0_196,
inference(contradiction_clause,[status(thm)],[f1910]) ).
fof(f2141,plain,
( spl0_235
<=> aScalar0(sdtlbdtrb0(xt,szszuzczcdt0(sz00))) ),
introduced(split_symbol_definition) ).
fof(f2143,plain,
( ~ aScalar0(sdtlbdtrb0(xt,szszuzczcdt0(sz00)))
| spl0_235 ),
inference(component_clause,[status(thm)],[f2141]) ).
fof(f2189,plain,
( $false
| spl0_235 ),
inference(forward_subsumption_resolution,[status(thm)],[f2143,f956]) ).
fof(f2190,plain,
spl0_235,
inference(contradiction_clause,[status(thm)],[f2189]) ).
fof(f2191,plain,
( spl0_245
<=> aScalar0(sdtlbdtrb0(xs,szszuzczcdt0(sz00))) ),
introduced(split_symbol_definition) ).
fof(f2193,plain,
( ~ aScalar0(sdtlbdtrb0(xs,szszuzczcdt0(sz00)))
| spl0_245 ),
inference(component_clause,[status(thm)],[f2191]) ).
fof(f2239,plain,
( $false
| spl0_245 ),
inference(forward_subsumption_resolution,[status(thm)],[f2193,f986]) ).
fof(f2240,plain,
spl0_245,
inference(contradiction_clause,[status(thm)],[f2239]) ).
fof(f2241,plain,
( spl0_255
<=> aScalar0(smndt0(sdtlbdtrb0(xt,sz00))) ),
introduced(split_symbol_definition) ).
fof(f2243,plain,
( ~ aScalar0(smndt0(sdtlbdtrb0(xt,sz00)))
| spl0_255 ),
inference(component_clause,[status(thm)],[f2241]) ).
fof(f2289,plain,
( $false
| spl0_255 ),
inference(forward_subsumption_resolution,[status(thm)],[f2243,f971]) ).
fof(f2290,plain,
spl0_255,
inference(contradiction_clause,[status(thm)],[f2289]) ).
fof(f2291,plain,
( spl0_265
<=> aScalar0(smndt0(sdtlbdtrb0(xs,sz00))) ),
introduced(split_symbol_definition) ).
fof(f2293,plain,
( ~ aScalar0(smndt0(sdtlbdtrb0(xs,sz00)))
| spl0_265 ),
inference(component_clause,[status(thm)],[f2291]) ).
fof(f2339,plain,
( $false
| spl0_265 ),
inference(forward_subsumption_resolution,[status(thm)],[f2293,f1001]) ).
fof(f2340,plain,
spl0_265,
inference(contradiction_clause,[status(thm)],[f2339]) ).
fof(f2736,plain,
! [X0] :
( ~ aVector0(X0)
| aDimensionOf0(xt) != aDimensionOf0(X0)
| aDimensionOf0(X0) != sz00
| sdtasasdt0(xt,X0) = sz0z00 ),
inference(resolution,[status(thm)],[f136,f142]) ).
fof(f2737,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 != aDimensionOf0(X0)
| aDimensionOf0(X0) != sz00
| sdtasasdt0(xt,X0) = sz0z00
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f469,f2736]) ).
fof(f2738,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 != aDimensionOf0(X0)
| sdtasasdt0(xt,X0) = sz0z00
| ~ spl0_4 ),
inference(duplicate_literals_removal,[status(esa)],[f2737]) ).
fof(f2739,plain,
! [X0] :
( ~ aVector0(X0)
| aDimensionOf0(xs) != aDimensionOf0(X0)
| aDimensionOf0(X0) != sz00
| sdtasasdt0(xs,X0) = sz0z00 ),
inference(resolution,[status(thm)],[f136,f141]) ).
fof(f2740,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 != aDimensionOf0(X0)
| aDimensionOf0(X0) != sz00
| sdtasasdt0(xs,X0) = sz0z00
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f202,f2739]) ).
fof(f2741,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 != aDimensionOf0(X0)
| sdtasasdt0(xs,X0) = sz0z00
| ~ spl0_4 ),
inference(duplicate_literals_removal,[status(esa)],[f2740]) ).
fof(f3391,plain,
( sz00 != sz00
| ~ spl0_4
| spl0_145 ),
inference(forward_demodulation,[status(thm)],[f469,f1601]) ).
fof(f3392,plain,
( $false
| ~ spl0_4
| spl0_145 ),
inference(trivial_equality_resolution,[status(esa)],[f3391]) ).
fof(f3393,plain,
( ~ spl0_4
| spl0_145 ),
inference(contradiction_clause,[status(thm)],[f3392]) ).
fof(f3513,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sz0z00))
| ~ spl0_120 ),
inference(backward_demodulation,[status(thm)],[f1031,f185]) ).
fof(f3564,plain,
( spl0_359
<=> sz0z00 = sdtasasdt0(xs,xt) ),
introduced(split_symbol_definition) ).
fof(f3565,plain,
( sz0z00 = sdtasasdt0(xs,xt)
| ~ spl0_359 ),
inference(component_clause,[status(thm)],[f3564]) ).
fof(f3626,plain,
( ~ sdtlseqdt0(sdtasdt0(sz0z00,sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sz0z00))
| ~ spl0_359
| ~ spl0_120 ),
inference(forward_demodulation,[status(thm)],[f3565,f3513]) ).
fof(f3627,plain,
( ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sz0z00))
| ~ spl0_359
| ~ spl0_120 ),
inference(forward_demodulation,[status(thm)],[f3565,f3626]) ).
fof(f3628,plain,
( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00))
| ~ spl0_359
| ~ spl0_120 ),
inference(forward_demodulation,[status(thm)],[f696,f3627]) ).
fof(f3629,plain,
( ~ sdtlseqdt0(sz0z00,sdtasdt0(sz0z00,sz0z00))
| ~ spl0_117
| ~ spl0_359
| ~ spl0_120 ),
inference(forward_demodulation,[status(thm)],[f1020,f3628]) ).
fof(f3630,plain,
( ~ sdtlseqdt0(sz0z00,sz0z00)
| ~ spl0_117
| ~ spl0_359
| ~ spl0_120 ),
inference(forward_demodulation,[status(thm)],[f696,f3629]) ).
fof(f3631,plain,
( $false
| ~ spl0_117
| ~ spl0_359
| ~ spl0_120 ),
inference(forward_subsumption_resolution,[status(thm)],[f3630,f370]) ).
fof(f3632,plain,
( ~ spl0_117
| ~ spl0_359
| ~ spl0_120 ),
inference(contradiction_clause,[status(thm)],[f3631]) ).
fof(f3726,plain,
( sz00 != aDimensionOf0(xt)
| sdtasasdt0(xt,xt) = sz0z00
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f2738,f142]) ).
fof(f3727,plain,
( ~ spl0_145
| spl0_120
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f3726,f1599,f1030,f201]) ).
fof(f3730,plain,
( sz00 != aDimensionOf0(xt)
| sdtasasdt0(xs,xt) = sz0z00
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f2741,f142]) ).
fof(f3731,plain,
( ~ spl0_145
| spl0_359
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f3730,f1599,f3564,f201]) ).
fof(f3732,plain,
( sz00 != aDimensionOf0(xs)
| sdtasasdt0(xs,xs) = sz0z00
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f2741,f141]) ).
fof(f3733,plain,
( ~ spl0_4
| spl0_117 ),
inference(split_clause,[status(thm)],[f3732,f201,f1019]) ).
fof(f3734,plain,
$false,
inference(sat_refutation,[status(thm)],[f347,f1351,f1837,f1839,f1909,f1911,f2190,f2240,f2290,f2340,f3393,f3632,f3727,f3731,f3733]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35 % Computer : n010.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Apr 29 22:08:35 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Drodi V3.6.0
% 0.18/0.48 % Refutation found
% 0.18/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.49 % Elapsed time: 0.137972 seconds
% 0.18/0.49 % CPU time: 0.974478 seconds
% 0.18/0.49 % Total memory used: 77.965 MB
% 0.18/0.49 % Net memory used: 77.187 MB
%------------------------------------------------------------------------------