%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG081+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Sun Sep 27 08:26:35 AM UTC 2026
% Result : Theorem 15.88s 2.71s
% Output : CNFRefutation 15.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 22 unt; 0 def)
% Number of atoms : 161 ( 88 equ)
% Maximal formula atoms : 40 ( 3 avg)
% Number of connectives : 153 ( 35 ~; 26 |; 80 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 8 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mScZero,axiom,
! [W0] :
( aScalar0(W0)
=> ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(W0)) = W0
& sdtpldt0(smndt0(W0),W0) = sz0z00
& sdtpldt0(W0,smndt0(W0)) = sz0z00
& sdtasdt0(sz0z00,W0) = sz0z00
& sdtasdt0(W0,sz0z00) = sz0z00
& sdtpldt0(sz0z00,W0) = W0
& sdtpldt0(W0,sz0z00) = W0 ) ),
file('theBenchmark.p',mScZero) ).
fof(mLERef,axiom,
! [W0] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) ),
file('theBenchmark.p',mLERef) ).
fof(mDefSPZ,axiom,
! [W0,W1] :
( ( aVector0(W1)
& aVector0(W0) )
=> ( ( aDimensionOf0(W1) = sz00
& aDimensionOf0(W0) = aDimensionOf0(W1) )
=> sdtasasdt0(W0,W1) = sz0z00 ) ),
file('theBenchmark.p',mDefSPZ) ).
fof(m__1678,axiom,
( aVector0(xt)
& aVector0(xs) ),
file('theBenchmark.p',m__1678) ).
fof(m__,conjecture,
( ( aDimensionOf0(xs) != sz00
=> ? [W0] :
( ? [W1] :
( ? [W2] :
( ? [W3] :
( ? [W4] :
( ? [W5] :
( ? [W6] :
( ? [W7] :
( ? [W8] :
( ? [W9] :
( ? [W10] :
( ? [W11] :
( ? [W12] :
( ? [W13] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
& sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
& sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
& W13 = sdtasdt0(W10,W12)
& aScalar0(W13) )
& W12 = sdtasdt0(W7,W5)
& aScalar0(W12) )
& W11 = sdtasdt0(W6,W9)
& aScalar0(W11) )
& W10 = sdtasdt0(W4,W8)
& aScalar0(W10) )
& W9 = sdtasdt0(W2,W3)
& aScalar0(W9) )
& W8 = sdtasdt0(W3,W3)
& aScalar0(W8) )
& W7 = sdtasdt0(W2,W2)
& aScalar0(W7) )
& W6 = sdtasasdt0(W0,W1)
& aScalar0(W6) )
& W5 = sdtasasdt0(W1,W1)
& aScalar0(W5) )
& W4 = sdtasasdt0(W0,W0)
& aScalar0(W4) )
& W3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(W3) )
& W2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(W2) )
& W1 = sziznziztdt0(xt)
& ! [W2] :
( aNaturalNumber0(W2)
=> sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt)
& aVector0(W1) )
& W0 = sziznziztdt0(xs)
& ! [W1] :
( aNaturalNumber0(W1)
=> sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) )
& szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs)
& aVector0(W0) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( aDimensionOf0(xs) != sz00
=> ? [W0] :
( ? [W1] :
( ? [W2] :
( ? [W3] :
( ? [W4] :
( ? [W5] :
( ? [W6] :
( ? [W7] :
( ? [W8] :
( ? [W9] :
( ? [W10] :
( ? [W11] :
( ? [W12] :
( ? [W13] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
& sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
& sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
& W13 = sdtasdt0(W10,W12)
& aScalar0(W13) )
& W12 = sdtasdt0(W7,W5)
& aScalar0(W12) )
& W11 = sdtasdt0(W6,W9)
& aScalar0(W11) )
& W10 = sdtasdt0(W4,W8)
& aScalar0(W10) )
& W9 = sdtasdt0(W2,W3)
& aScalar0(W9) )
& W8 = sdtasdt0(W3,W3)
& aScalar0(W8) )
& W7 = sdtasdt0(W2,W2)
& aScalar0(W7) )
& W6 = sdtasasdt0(W0,W1)
& aScalar0(W6) )
& W5 = sdtasasdt0(W1,W1)
& aScalar0(W5) )
& W4 = sdtasasdt0(W0,W0)
& aScalar0(W4) )
& W3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(W3) )
& W2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(W2) )
& W1 = sziznziztdt0(xt)
& ! [W2] :
( aNaturalNumber0(W2)
=> sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt)
& aVector0(W1) )
& W0 = sziznziztdt0(xs)
& ! [W1] :
( aNaturalNumber0(W1)
=> sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) )
& szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs)
& aVector0(W0) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('theBenchmark.p',mSZeroSc) ).
cnf(c_46,plain,
aScalar0(sz0z00),
inference(clausify,[status(thm)],[mSZeroSc]) ).
cnf(c_52,plain,
( sdtasdt0(A,sz0z00) = sz0z00
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mScZero]) ).
cnf(c_71,plain,
( sdtlseqdt0(A,A)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mLERef]) ).
cnf(c_90,plain,
( sdtasasdt0(A,B) = sz0z00
| aDimensionOf0(B) != sz00
| aDimensionOf0(B) != aDimensionOf0(A)
| ~ aVector0(B)
| ~ aVector0(A) ),
inference(clausify,[status(thm)],[mDefSPZ]) ).
cnf(c_94,plain,
aVector0(xs),
inference(clausify,[status(thm)],[m__1678]) ).
cnf(c_95,plain,
aVector0(xt),
inference(clausify,[status(thm)],[m__1678]) ).
fof(m__1678_01,axiom,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('theBenchmark.p',m__1678_01) ).
cnf(c_97,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(clausify,[status(thm)],[m__1678_01]) ).
cnf(c_98,plain,
aDimensionOf0(xt) = aDimensionOf0(xs),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_139,negated_conjecture,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| aDimensionOf0(xs) = sz00 ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_140,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_3292,plain,
( sdtasasdt0(A,A) = sz0z00
| aDimensionOf0(A) != sz00
| aDimensionOf0(A) != aDimensionOf0(A)
| ~ aVector0(A) ),
inference(factor,[status(thm)],[c_90]) ).
cnf(c_186,plain,
( sdtasasdt0(A,A) = sz0z00
| aDimensionOf0(A) != sz00
| ~ aVector0(A) ),
inference(copy,[status(thm)],[c_3292]) ).
cnf(c_189,negated_conjecture,
aDimensionOf0(xs) = sz00,
inference(resolve,[status(thm)],[c_140,c_139]) ).
cnf(c_223,plain,
aDimensionOf0(xt) = sz00,
inference(paramod,[status(thm)],[c_189,c_98]) ).
cnf(c_236,plain,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(resolve,[status(thm)],[c_52,c_46]) ).
cnf(c_294,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(resolve,[status(thm)],[c_71,c_46]) ).
cnf(c_3293,plain,
( sdtasasdt0(xs,A) = sz0z00
| aDimensionOf0(A) != sz00
| aDimensionOf0(A) != aDimensionOf0(xs)
| ~ aVector0(A) ),
inference(resolve,[status(thm)],[c_94,c_90]) ).
cnf(c_3294,plain,
( sdtasasdt0(xs,A) = sz0z00
| aDimensionOf0(A) != sz00
| aDimensionOf0(A) != sz00
| ~ aVector0(A) ),
inference(paramod,[status(thm)],[c_189,c_3293]) ).
cnf(c_355,plain,
( sdtasasdt0(xs,A) = sz0z00
| aDimensionOf0(A) != sz00
| ~ aVector0(A) ),
inference(copy,[status(thm)],[c_3294]) ).
cnf(c_3295,plain,
( sdtasasdt0(xt,xt) = sz0z00
| aDimensionOf0(xt) != sz00 ),
inference(resolve,[status(thm)],[c_186,c_95]) ).
cnf(c_3296,plain,
( sdtasasdt0(xt,xt) = sz0z00
| sz00 != sz00 ),
inference(paramod,[status(thm)],[c_223,c_3295]) ).
cnf(c_412,plain,
sdtasasdt0(xt,xt) = sz0z00,
inference(copy,[status(thm)],[c_3296]) ).
cnf(c_3297,plain,
( sdtasasdt0(xs,xs) = sz0z00
| aDimensionOf0(xs) != sz00 ),
inference(resolve,[status(thm)],[c_186,c_94]) ).
cnf(c_3298,plain,
( sdtasasdt0(xs,xs) = sz0z00
| sz00 != sz00 ),
inference(paramod,[status(thm)],[c_189,c_3297]) ).
cnf(c_413,plain,
sdtasasdt0(xs,xs) = sz0z00,
inference(copy,[status(thm)],[c_3298]) ).
cnf(c_3299,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sz0z00,sdtasasdt0(xt,xt))),
inference(paramod,[status(thm)],[c_413,c_140]) ).
cnf(c_3300,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sz0z00,sz0z00)),
inference(paramod,[status(thm)],[c_412,c_3299]) ).
cnf(c_414,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sz0z00),
inference(paramod,[status(thm)],[c_236,c_3300]) ).
cnf(c_3301,plain,
( sdtasasdt0(xs,xt) = sz0z00
| aDimensionOf0(xt) != sz00 ),
inference(resolve,[status(thm)],[c_355,c_95]) ).
cnf(c_3302,plain,
( sdtasasdt0(xs,xt) = sz0z00
| sz00 != sz00 ),
inference(paramod,[status(thm)],[c_223,c_3301]) ).
cnf(c_3290,plain,
sdtasasdt0(xs,xt) = sz0z00,
inference(copy,[status(thm)],[c_3302]) ).
cnf(c_3303,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sz0z00,sdtasasdt0(xs,xt)),sz0z00),
inference(paramod,[status(thm)],[c_3290,c_414]) ).
cnf(c_3304,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sz0z00),
inference(paramod,[status(thm)],[c_3290,c_3303]) ).
cnf(c_3305,negated_conjecture,
~ sdtlseqdt0(sz0z00,sz0z00),
inference(paramod,[status(thm)],[c_236,c_3304]) ).
cnf(c_3291,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_294,c_3305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG081+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n011.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 06:00:45 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3945363 was started by sandbox2 on n011,
% 0.07/0.35 % Sat Sep 26 06:00:45 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 15.88/2.71
% 15.88/2.71 % SZS status Theorem for theBenchmark
% 15.88/2.71
% 15.88/2.71 % Proof 1 at 2.15 (+ 0.15) seconds.
% 15.88/2.71 % Length of proof is 26.
% 15.88/2.71 % Level of proof is 6.
% 15.88/2.71 % Maximum clause weight is 34.000.
% 15.88/2.71 % Given clauses 213.
% 15.88/2.71
% 15.88/2.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------