TSTP Solution File: NUM558+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM558+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n005.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 Aug 22 10:52:07 EDT 2023
% Result : Theorem 7.75s 2.65s
% Output : CNFRefutation 7.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 52
% Syntax : Number of formulae : 74 ( 14 unt; 45 typ; 0 def)
% Number of atoms : 102 ( 15 equ)
% Maximal formula atoms : 43 ( 3 avg)
% Number of connectives : 95 ( 22 ~; 18 |; 36 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 59 ( 34 >; 25 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 37 ( 37 usr; 11 con; 0-3 aty)
% Number of variables : 24 (; 23 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > slbdtrb0 > sbrdtbr0 > xy > xx > xk > xT > xS > xQ > xP > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_16 > #skF_18 > #skF_17 > #skF_6 > #skF_19 > #skF_1 > #skF_4 > #skF_12 > #skF_5 > #skF_10 > #skF_8 > #skF_15 > #skF_13 > #skF_14 > #skF_3 > #skF_2 > #skF_9
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': $i > $i ).
tff(sbrdtbr0,type,
sbrdtbr0: $i > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff(szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': $i > $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff(szNzAzT0,type,
szNzAzT0: $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xS,type,
xS: $i ).
tff(sz00,type,
sz00: $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(xP,type,
xP: $i ).
tff(xy,type,
xy: $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(slbdtsldtrb0,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xx,type,
xx: $i ).
tff(aSubsetOf0,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(isCountable0,type,
isCountable0: $i > $o ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(xT,type,
xT: $i ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff(slcrc0,type,
slcrc0: $i ).
tff(isFinite0,type,
isFinite0: $i > $o ).
tff(xQ,type,
xQ: $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff(szmzizndt0,type,
szmzizndt0: $i > $i ).
tff(szmzazxdt0,type,
szmzazxdt0: $i > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff(slbdtrb0,type,
slbdtrb0: $i > $i ).
tff(f_683,hypothesis,
( ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xP,xS)
& ( sbrdtbr0(xP) = xk )
& aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2378) ).
tff(f_624,hypothesis,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ~ ( ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
=> ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
| ( slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
tff(f_685,negated_conjecture,
~ aElementOf0(xx,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_673,hypothesis,
( aSet0(sdtmndt0(xQ,xy))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xQ,xy))
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != xy ) ) )
& aSet0(xP)
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )
& ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2357) ).
tff(f_526,hypothesis,
( aSet0(xS)
& aSet0(xT)
& ( xk != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
tff(f_625,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).
tff(f_39,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
tff(c_364,plain,
sbrdtbr0(xP) = xk,
inference(cnfTransformation,[status(thm)],[f_683]) ).
tff(c_362,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnfTransformation,[status(thm)],[f_683]) ).
tff(c_1632,plain,
! [W0_275] :
( aElementOf0(W0_275,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(W0_275,slbdtsldtrb0(xS,xk)) ),
inference(cnfTransformation,[status(thm)],[f_624]) ).
tff(c_288,plain,
! [W0_176] :
( aSubsetOf0(W0_176,xT)
| ~ aElementOf0(W0_176,slbdtsldtrb0(xT,xk)) ),
inference(cnfTransformation,[status(thm)],[f_624]) ).
tff(c_1696,plain,
! [W0_277] :
( aSubsetOf0(W0_277,xT)
| ~ aElementOf0(W0_277,slbdtsldtrb0(xS,xk)) ),
inference(resolution,[status(thm)],[c_1632,c_288]) ).
tff(c_1722,plain,
aSubsetOf0(xP,xT),
inference(resolution,[status(thm)],[c_362,c_1696]) ).
tff(c_294,plain,
! [W0_176] :
( ~ aSubsetOf0(W0_176,xT)
| aElementOf0(W0_176,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0_176) != xk ) ),
inference(cnfTransformation,[status(thm)],[f_624]) ).
tff(c_370,plain,
~ aElementOf0(xx,xT),
inference(cnfTransformation,[status(thm)],[f_685]) ).
tff(c_352,plain,
( aElementOf0(xx,xP)
| ~ aElement0(xx) ),
inference(cnfTransformation,[status(thm)],[f_673]) ).
tff(c_413,plain,
~ aElement0(xx),
inference(splitLeft,[status(thm)],[c_352]) ).
tff(c_258,plain,
aSet0(xS),
inference(cnfTransformation,[status(thm)],[f_526]) ).
tff(c_314,plain,
aElementOf0(xx,xS),
inference(cnfTransformation,[status(thm)],[f_625]) ).
tff(c_588,plain,
! [W1_212,W0_213] :
( aElement0(W1_212)
| ~ aElementOf0(W1_212,W0_213)
| ~ aSet0(W0_213) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_609,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_314,c_588]) ).
tff(c_639,plain,
aElement0(xx),
inference(demodulation,[status(thm),theory(equality)],[c_258,c_609]) ).
tff(c_641,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_413,c_639]) ).
tff(c_642,plain,
aElementOf0(xx,xP),
inference(splitRight,[status(thm)],[c_352]) ).
tff(c_2271,plain,
! [W1_308,W0_309] :
( aElementOf0(W1_308,xT)
| ~ aElementOf0(W1_308,W0_309)
| ~ aElementOf0(W0_309,slbdtsldtrb0(xT,xk)) ),
inference(cnfTransformation,[status(thm)],[f_624]) ).
tff(c_2301,plain,
( aElementOf0(xx,xT)
| ~ aElementOf0(xP,slbdtsldtrb0(xT,xk)) ),
inference(resolution,[status(thm)],[c_642,c_2271]) ).
tff(c_2332,plain,
~ aElementOf0(xP,slbdtsldtrb0(xT,xk)),
inference(negUnitSimplification,[status(thm)],[c_370,c_2301]) ).
tff(c_2344,plain,
( ~ aSubsetOf0(xP,xT)
| ( sbrdtbr0(xP) != xk ) ),
inference(resolution,[status(thm)],[c_294,c_2332]) ).
tff(c_2351,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_364,c_1722,c_2344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM558+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 3 15:22:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 7.75/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.75/2.65
% 7.75/2.65 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.98/2.68
% 7.98/2.68 Inference rules
% 7.98/2.68 ----------------------
% 7.98/2.68 #Ref : 0
% 7.98/2.68 #Sup : 374
% 7.98/2.68 #Fact : 0
% 7.98/2.68 #Define : 0
% 7.98/2.68 #Split : 26
% 7.98/2.68 #Chain : 0
% 7.98/2.68 #Close : 0
% 7.98/2.68
% 7.98/2.68 Ordering : KBO
% 7.98/2.68
% 7.98/2.68 Simplification rules
% 7.98/2.68 ----------------------
% 7.98/2.68 #Subsume : 79
% 7.98/2.68 #Demod : 391
% 7.98/2.68 #Tautology : 157
% 7.98/2.68 #SimpNegUnit : 35
% 7.98/2.68 #BackRed : 73
% 7.98/2.68
% 7.98/2.68 #Partial instantiations: 0
% 7.98/2.68 #Strategies tried : 1
% 7.98/2.68
% 7.98/2.68 Timing (in seconds)
% 7.98/2.68 ----------------------
% 7.98/2.68 Preprocessing : 0.83
% 7.98/2.68 Parsing : 0.40
% 7.98/2.68 CNF conversion : 0.08
% 7.98/2.68 Main loop : 0.87
% 7.98/2.68 Inferencing : 0.27
% 7.98/2.68 Reduction : 0.31
% 7.98/2.68 Demodulation : 0.21
% 7.98/2.68 BG Simplification : 0.07
% 7.98/2.68 Subsumption : 0.17
% 7.98/2.69 Abstraction : 0.03
% 7.98/2.69 MUC search : 0.00
% 7.98/2.69 Cooper : 0.00
% 7.98/2.69 Total : 1.75
% 7.98/2.69 Index Insertion : 0.00
% 7.98/2.69 Index Deletion : 0.00
% 7.98/2.69 Index Matching : 0.00
% 7.98/2.69 BG Taut test : 0.00
%------------------------------------------------------------------------------