%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : RNG052+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n019.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 : Wed Apr 9 08:31:23 PM UTC 2025
% Result : Theorem 30.00s 16.20s
% Output : CNFRefutation 30.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 33 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 71 ( 29 ~; 22 |; 11 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 18 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aVector0 > aScalar0 > aNaturalNumber0 > sdtpldt0 > sdtlbdtrb0 > sdtasdt0 > sdtasasdt0 > #nlpp > szszuzczcdt0 > sziznziztdt0 > smndt0 > aDimensionOf0 > xt > xs > xq > xp > xS > xR > xP > xN > xH > xG > xF > xE > xD > xC > xB > xA > sz0z00 > sz00 > #skF_1 > #skF_2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xq,type,
xq: $i ).
tff(xt,type,
xt: $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
tff(sdtlbdtrb0,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(xG,type,
xG: $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(xE,type,
xE: $i ).
tff(sziznziztdt0,type,
sziznziztdt0: $i > $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xS,type,
xS: $i ).
tff(sz00,type,
sz00: $i ).
tff(xR,type,
xR: $i ).
tff(xH,type,
xH: $i ).
tff(xP,type,
xP: $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aDimensionOf0,type,
aDimensionOf0: $i > $i ).
tff(xB,type,
xB: $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff(sz0z00,type,
sz0z00: $i ).
tff(smndt0,type,
smndt0: $i > $i ).
tff(aScalar0,type,
aScalar0: $i > $o ).
tff(xs,type,
xs: $i ).
tff(xN,type,
xN: $i ).
tff(xC,type,
xC: $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(xp,type,
xp: $i ).
tff(sdtasasdt0,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff(xA,type,
xA: $i ).
tff(xD,type,
xD: $i ).
tff(xF,type,
xF: $i ).
tff(aVector0,type,
aVector0: $i > $o ).
tff(f_399,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_351,hypothesis,
( aVector0(xp)
& ( szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs) )
& ! [W0] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0) ) )
& ( xp = sziznziztdt0(xs) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
tff(f_361,hypothesis,
( aVector0(xq)
& ( szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt) )
& ! [W0] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0) ) )
& ( xq = sziznziztdt0(xt) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
tff(f_258,axiom,
! [W0] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
tff(f_66,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
tff(f_376,hypothesis,
( aScalar0(xE)
& ( xE = sdtasasdt0(xp,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
tff(f_373,hypothesis,
( aScalar0(xD)
& ( xD = sdtasasdt0(xq,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
tff(f_370,hypothesis,
( aScalar0(xC)
& ( xC = sdtasasdt0(xp,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
tff(f_338,hypothesis,
! [W0,W1] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1652) ).
tff(f_339,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
tff(f_55,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
tff(c_188,plain,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_130,plain,
aVector0(xp),
inference(cnfTransformation,[status(thm)],[f_351]) ).
tff(c_138,plain,
aVector0(xq),
inference(cnfTransformation,[status(thm)],[f_361]) ).
tff(c_90,plain,
! [W0_55] :
( aNaturalNumber0(aDimensionOf0(W0_55))
| ~ aVector0(W0_55) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_128,plain,
szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs),
inference(cnfTransformation,[status(thm)],[f_351]) ).
tff(c_490,plain,
! [W0_89] :
( iLess0(W0_89,szszuzczcdt0(W0_89))
| ~ aNaturalNumber0(W0_89) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_496,plain,
( iLess0(aDimensionOf0(xp),aDimensionOf0(xs))
| ~ aNaturalNumber0(aDimensionOf0(xp)) ),
inference(superposition,[status(thm),theory(equality)],[c_128,c_490]) ).
tff(c_1505,plain,
~ aNaturalNumber0(aDimensionOf0(xp)),
inference(splitLeft,[status(thm)],[c_496]) ).
tff(c_1509,plain,
~ aVector0(xp),
inference(resolution,[status(thm)],[c_90,c_1505]) ).
tff(c_1513,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_130,c_1509]) ).
tff(c_1514,plain,
iLess0(aDimensionOf0(xp),aDimensionOf0(xs)),
inference(splitRight,[status(thm)],[c_496]) ).
tff(c_156,plain,
sdtasasdt0(xp,xq) = xE,
inference(cnfTransformation,[status(thm)],[f_376]) ).
tff(c_152,plain,
sdtasasdt0(xq,xq) = xD,
inference(cnfTransformation,[status(thm)],[f_373]) ).
tff(c_148,plain,
sdtasasdt0(xp,xp) = xC,
inference(cnfTransformation,[status(thm)],[f_370]) ).
tff(c_14438,plain,
! [W0_190,W1_191] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0_190,W1_191),sdtasasdt0(W0_190,W1_191)),sdtasdt0(sdtasasdt0(W0_190,W0_190),sdtasasdt0(W1_191,W1_191)))
| ~ iLess0(aDimensionOf0(W0_190),aDimensionOf0(xs))
| ( aDimensionOf0(W1_191) != aDimensionOf0(W0_190) )
| ~ aVector0(W1_191)
| ~ aVector0(W0_190) ),
inference(cnfTransformation,[status(thm)],[f_338]) ).
tff(c_14469,plain,
( sdtlseqdt0(sdtasdt0(xE,sdtasasdt0(xp,xq)),sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq)))
| ~ iLess0(aDimensionOf0(xp),aDimensionOf0(xs))
| ( aDimensionOf0(xq) != aDimensionOf0(xp) )
| ~ aVector0(xq)
| ~ aVector0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_156,c_14438]) ).
tff(c_14496,plain,
( sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
| ( aDimensionOf0(xq) != aDimensionOf0(xp) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_138,c_1514,c_156,c_152,c_148,c_14469]) ).
tff(c_14497,plain,
aDimensionOf0(xq) != aDimensionOf0(xp),
inference(negUnitSimplification,[status(thm)],[c_188,c_14496]) ).
tff(c_1515,plain,
aNaturalNumber0(aDimensionOf0(xp)),
inference(splitRight,[status(thm)],[c_496]) ).
tff(c_120,plain,
aDimensionOf0(xt) = aDimensionOf0(xs),
inference(cnfTransformation,[status(thm)],[f_339]) ).
tff(c_136,plain,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt),
inference(cnfTransformation,[status(thm)],[f_361]) ).
tff(c_190,plain,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xs),
inference(demodulation,[status(thm),theory(equality)],[c_120,c_136]) ).
tff(c_493,plain,
( iLess0(aDimensionOf0(xq),aDimensionOf0(xs))
| ~ aNaturalNumber0(aDimensionOf0(xq)) ),
inference(superposition,[status(thm),theory(equality)],[c_190,c_490]) ).
tff(c_1533,plain,
~ aNaturalNumber0(aDimensionOf0(xq)),
inference(splitLeft,[status(thm)],[c_493]) ).
tff(c_1557,plain,
~ aVector0(xq),
inference(resolution,[status(thm)],[c_90,c_1533]) ).
tff(c_1561,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_138,c_1557]) ).
tff(c_1563,plain,
aNaturalNumber0(aDimensionOf0(xq)),
inference(splitRight,[status(thm)],[c_493]) ).
tff(c_1659,plain,
! [W1_118,W0_119] :
( ( W1_118 = W0_119 )
| ( szszuzczcdt0(W1_118) != szszuzczcdt0(W0_119) )
| ~ aNaturalNumber0(W1_118)
| ~ aNaturalNumber0(W0_119) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_1665,plain,
! [W0_119] :
( ( aDimensionOf0(xq) = W0_119 )
| ( szszuzczcdt0(W0_119) != aDimensionOf0(xs) )
| ~ aNaturalNumber0(aDimensionOf0(xq))
| ~ aNaturalNumber0(W0_119) ),
inference(superposition,[status(thm),theory(equality)],[c_190,c_1659]) ).
tff(c_42912,plain,
! [W0_221] :
( ( aDimensionOf0(xq) = W0_221 )
| ( szszuzczcdt0(W0_221) != aDimensionOf0(xs) )
| ~ aNaturalNumber0(W0_221) ),
inference(demodulation,[status(thm),theory(equality)],[c_1563,c_1665]) ).
tff(c_42921,plain,
( ( aDimensionOf0(xq) = aDimensionOf0(xp) )
| ( szszuzczcdt0(aDimensionOf0(xp)) != aDimensionOf0(xs) ) ),
inference(resolution,[status(thm)],[c_1515,c_42912]) ).
tff(c_42944,plain,
aDimensionOf0(xq) = aDimensionOf0(xp),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_42921]) ).
tff(c_42946,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14497,c_42944]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : RNG052+2 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 8 18:32:47 EDT 2025
% 0.14/0.37 % CPUTime :
% 30.00/16.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.00/16.21
% 30.00/16.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------