%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COM022+1 : 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 : n025.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 05:50:36 PM UTC 2025
% Result : Theorem 4.71s 2.22s
% Output : CNFRefutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 24 unt; 0 typ; 2 def)
% Number of atoms : 124 ( 7 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 135 ( 58 ~; 48 |; 22 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-4 aty)
% Number of variables : 26 ( 20 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtmndtplgtdt0 > sdtmndtasgtdt0 > aReductOfIn0 > aNormalFormOfIn0 > iLess0 > isTerminating0 > isLocallyConfluent0 > isConfluent0 > aRewritingSystem0 > aElement0 > #nlpp > xc > xb > xa > xR > #skF_9 > #skF_7 > #skF_5 > #skF_1 > #skF_4 > #skF_18 > #skF_17 > #skF_15 > #skF_12 > #skF_8 > #skF_13 > #skF_16 > #skF_10 > #skF_2 > #skF_6 > #skF_14 > #skF_3 > #skF_11
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(sdtmndtplgtdt0,type,
sdtmndtplgtdt0: ( $i * $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff(aReductOfIn0,type,
aReductOfIn0: ( $i * $i * $i ) > $o ).
tff(xa,type,
xa: $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(isTerminating0,type,
isTerminating0: $i > $o ).
tff(aNormalFormOfIn0,type,
aNormalFormOfIn0: ( $i * $i * $i ) > $o ).
tff(xR,type,
xR: $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff(xc,type,
xc: $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i * $i ) > $i ).
tff(xb,type,
xb: $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff(aRewritingSystem0,type,
aRewritingSystem0: $i > $o ).
tff(isConfluent0,type,
isConfluent0: $i > $o ).
tff(isLocallyConfluent0,type,
isLocallyConfluent0: $i > $o ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff(sdtmndtasgtdt0,type,
sdtmndtasgtdt0: ( $i * $i * $i ) > $o ).
tff(f_268,negated_conjecture,
~ ( ( ( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtasgtdt0(W0,xR,xb)
& ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xa,xR)
& sdtmndtasgtdt0(W1,xR,xc)
& ? [W2] :
( aElement0(W2)
& sdtmndtasgtdt0(W0,xR,W2)
& sdtmndtasgtdt0(W1,xR,W2)
& ? [W3] :
( aNormalFormOfIn0(W3,W2,xR)
& sdtmndtasgtdt0(xb,xR,W3)
& sdtmndtasgtdt0(xc,xR,W3) ) ) ) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& sdtmndtasgtdt0(xb,xR,W0)
& sdtmndtasgtdt0(xc,xR,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_206,hypothesis,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
tff(f_198,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
tff(f_101,definition,
! [W0,W1,W2] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2) )
=> ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( ( W0 = W2 )
| sdtmndtplgtdt0(W0,W1,W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRDef) ).
tff(f_187,definition,
! [W0,W1] :
( ( aElement0(W0)
& aRewritingSystem0(W1) )
=> ! [W2] :
( aNormalFormOfIn0(W2,W0,W1)
<=> ( aElement0(W2)
& sdtmndtasgtdt0(W0,W1,W2)
& ~ ? [W3] : aReductOfIn0(W3,W2,W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNFRDef) ).
tff(c_108,plain,
sdtmndtasgtdt0(xa,xR,xc),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_98,plain,
aElement0(xa),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_88,plain,
aRewritingSystem0(xR),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_96,plain,
aElement0(xb),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_110,plain,
sdtmndtasgtdt0(xa,xR,xb),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_301,plain,
! [W0_160,W1_161,W2_162] :
( sdtmndtplgtdt0(W0_160,W1_161,W2_162)
| ( W2_162 = W0_160 )
| ~ sdtmndtasgtdt0(W0_160,W1_161,W2_162)
| ~ aElement0(W2_162)
| ~ aRewritingSystem0(W1_161)
| ~ aElement0(W0_160) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_134,plain,
( aElement0('#skF_15')
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_136,plain,
~ sdtmndtplgtdt0(xa,xR,xb),
inference(splitLeft,[status(thm)],[c_134]) ).
tff(c_310,plain,
( ( xb = xa )
| ~ sdtmndtasgtdt0(xa,xR,xb)
| ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[c_301,c_136]) ).
tff(c_315,plain,
xb = xa,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_88,c_96,c_110,c_310]) ).
tff(c_94,plain,
aElement0(xc),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_28,plain,
! [W2_24,W1_23] :
( sdtmndtasgtdt0(W2_24,W1_23,W2_24)
| ~ aRewritingSystem0(W1_23)
| ~ aElement0(W2_24) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_145,plain,
! [W0_113] :
( ~ sdtmndtasgtdt0(xc,xR,W0_113)
| ~ sdtmndtasgtdt0(xb,xR,W0_113)
| ~ aElement0(W0_113) ),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_149,plain,
( ~ sdtmndtasgtdt0(xb,xR,xc)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xc) ),
inference(resolution,[status(thm)],[c_28,c_145]) ).
tff(c_152,plain,
~ sdtmndtasgtdt0(xb,xR,xc),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_88,c_149]) ).
tff(c_344,plain,
~ sdtmndtasgtdt0(xa,xR,xc),
inference(demodulation,[status(thm),theory(equality)],[c_315,c_152]) ).
tff(c_351,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_108,c_344]) ).
tff(c_353,plain,
sdtmndtplgtdt0(xa,xR,xb),
inference(splitRight,[status(thm)],[c_134]) ).
tff(c_554,plain,
! [W0_221,W1_222,W2_223] :
( sdtmndtplgtdt0(W0_221,W1_222,W2_223)
| ( W2_223 = W0_221 )
| ~ sdtmndtasgtdt0(W0_221,W1_222,W2_223)
| ~ aElement0(W2_223)
| ~ aRewritingSystem0(W1_222)
| ~ aElement0(W0_221) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_352,plain,
( ~ sdtmndtplgtdt0(xa,xR,xc)
| aElement0('#skF_15') ),
inference(splitRight,[status(thm)],[c_134]) ).
tff(c_354,plain,
~ sdtmndtplgtdt0(xa,xR,xc),
inference(splitLeft,[status(thm)],[c_352]) ).
tff(c_563,plain,
( ( xc = xa )
| ~ sdtmndtasgtdt0(xa,xR,xc)
| ~ aElement0(xc)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[c_554,c_354]) ).
tff(c_568,plain,
xc = xa,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_88,c_94,c_108,c_563]) ).
tff(c_106,plain,
! [W0_102] :
( ~ sdtmndtasgtdt0(xc,xR,W0_102)
| ~ sdtmndtasgtdt0(xb,xR,W0_102)
| ~ aElement0(W0_102) ),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_632,plain,
! [W0_226] :
( ~ sdtmndtasgtdt0(xa,xR,W0_226)
| ~ sdtmndtasgtdt0(xb,xR,W0_226)
| ~ aElement0(W0_226) ),
inference(demodulation,[status(thm),theory(equality)],[c_568,c_106]) ).
tff(c_644,plain,
( ~ sdtmndtasgtdt0(xa,xR,xb)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[c_28,c_632]) ).
tff(c_654,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_96,c_88,c_110,c_644]) ).
tff(c_656,plain,
sdtmndtplgtdt0(xa,xR,xc),
inference(splitRight,[status(thm)],[c_352]) ).
tff(c_122,plain,
( aElement0('#skF_17')
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_692,plain,
aElement0('#skF_17'),
inference(demodulation,[status(thm),theory(equality)],[c_353,c_656,c_122]) ).
tff(c_116,plain,
( aNormalFormOfIn0('#skF_18','#skF_17',xR)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_706,plain,
aNormalFormOfIn0('#skF_18','#skF_17',xR),
inference(demodulation,[status(thm),theory(equality)],[c_353,c_656,c_116]) ).
tff(c_84,plain,
! [W2_77,W0_70,W1_71] :
( aElement0(W2_77)
| ~ aNormalFormOfIn0(W2_77,W0_70,W1_71)
| ~ aRewritingSystem0(W1_71)
| ~ aElement0(W0_70) ),
inference(cnfTransformation,[status(thm)],[f_187]) ).
tff(c_709,plain,
( aElement0('#skF_18')
| ~ aRewritingSystem0(xR)
| ~ aElement0('#skF_17') ),
inference(resolution,[status(thm)],[c_706,c_84]) ).
tff(c_712,plain,
aElement0('#skF_18'),
inference(demodulation,[status(thm),theory(equality)],[c_692,c_88,c_709]) ).
tff(c_112,plain,
( sdtmndtasgtdt0(xc,xR,'#skF_18')
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_759,plain,
sdtmndtasgtdt0(xc,xR,'#skF_18'),
inference(demodulation,[status(thm),theory(equality)],[c_353,c_656,c_112]) ).
tff(c_762,plain,
( ~ sdtmndtasgtdt0(xb,xR,'#skF_18')
| ~ aElement0('#skF_18') ),
inference(resolution,[status(thm)],[c_759,c_106]) ).
tff(c_765,plain,
~ sdtmndtasgtdt0(xb,xR,'#skF_18'),
inference(demodulation,[status(thm),theory(equality)],[c_712,c_762]) ).
tff(c_114,plain,
( sdtmndtasgtdt0(xb,xR,'#skF_18')
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_784,plain,
sdtmndtasgtdt0(xb,xR,'#skF_18'),
inference(demodulation,[status(thm),theory(equality)],[c_353,c_656,c_114]) ).
tff(c_785,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_765,c_784]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM022+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 16:13:50 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.71/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.71/2.23
% 4.71/2.23 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------