%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COM022+4 : 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 : n007.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 05:50:37 PM UTC 2025
% Result : Theorem 13.38s 4.24s
% Output : CNFRefutation 13.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 30 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 140 ( 15 equ)
% Maximal formula atoms : 96 ( 4 avg)
% Number of connectives : 132 ( 22 ~; 43 |; 64 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 3 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 : 36 ( 36 usr; 17 con; 0-4 aty)
% Number of variables : 20 ( 1 !; 19 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtmndtplgtdt0 > sdtmndtasgtdt0 > aReductOfIn0 > aNormalFormOfIn0 > iLess0 > isTerminating0 > isLocallyConfluent0 > isConfluent0 > aRewritingSystem0 > aElement0 > #nlpp > xc > xb > xa > xR > #skF_9 > #skF_7 > #skF_5 > #skF_17 > #skF_1 > #skF_20 > #skF_4 > #skF_31 > #skF_25 > #skF_18 > #skF_12 > #skF_8 > #skF_13 > #skF_26 > #skF_10 > #skF_2 > #skF_19 > #skF_6 > #skF_21 > #skF_32 > #skF_15 > #skF_30 > #skF_14 > #skF_3 > #skF_11 > #skF_22 > #skF_29 > #skF_28 > #skF_24 > #skF_27 > #skF_23 > #skF_16
%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_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(aReductOfIn0,type,
aReductOfIn0: ( $i * $i * $i ) > $o ).
tff(xa,type,
xa: $i ).
tff('#skF_31',type,
'#skF_31': $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $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_26',type,
'#skF_26': $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(xb,type,
xb: $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': $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('#skF_22',type,
'#skF_22': $i ).
tff(aRewritingSystem0,type,
aRewritingSystem0: $i > $o ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
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('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(f_551,negated_conjecture,
~ ( ( ( ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) )
| sdtmndtplgtdt0(xa,xR,xb) )
& ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) )
| sdtmndtplgtdt0(xa,xR,xc) ) )
=> ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& ( ( W0 = xb )
| ( ( aReductOfIn0(xb,W0,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,W0,xR)
& sdtmndtplgtdt0(W1,xR,xb) ) )
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtasgtdt0(W0,xR,xb)
& ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xa,xR)
& ( ( W1 = xc )
| ( ( aReductOfIn0(xc,W1,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W1,xR)
& sdtmndtplgtdt0(W2,xR,xc) ) )
& sdtmndtplgtdt0(W1,xR,xc) ) )
& sdtmndtasgtdt0(W1,xR,xc)
& ? [W2] :
( aElement0(W2)
& ( ( W0 = W2 )
| ( ( aReductOfIn0(W2,W0,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W0,xR)
& sdtmndtplgtdt0(W3,xR,W2) ) )
& sdtmndtplgtdt0(W0,xR,W2) ) )
& sdtmndtasgtdt0(W0,xR,W2)
& ( ( W1 = W2 )
| ( ( aReductOfIn0(W2,W1,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W1,xR)
& sdtmndtplgtdt0(W3,xR,W2) ) )
& sdtmndtplgtdt0(W1,xR,W2) ) )
& sdtmndtasgtdt0(W1,xR,W2)
& ? [W3] :
( aElement0(W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3)
& ~ ? [W4] : aReductOfIn0(W4,W3,xR)
& aNormalFormOfIn0(W3,W2,xR)
& ( ( xb = W3 )
| ( ( aReductOfIn0(W3,xb,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xb,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(xb,xR,W3) ) )
& sdtmndtasgtdt0(xb,xR,W3)
& ( ( xc = W3 )
| ( ( aReductOfIn0(W3,xc,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xc,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(xc,xR,W3) ) )
& sdtmndtasgtdt0(xc,xR,W3) ) ) ) ) )
=> ( ( ( ( xa = xb )
| ( ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( ( xa = xc )
| ( ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& ( ( xb = W0 )
| aReductOfIn0(W0,xb,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xb,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xb,xR,W0)
| sdtmndtasgtdt0(xb,xR,W0) )
& ( ( xc = W0 )
| aReductOfIn0(W0,xc,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xc,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xc,xR,W0)
| sdtmndtasgtdt0(xc,xR,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_268,hypothesis,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
tff(c_680,plain,
sdtmndtasgtdt0(xa,xR,xb),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_732,plain,
( sdtmndtplgtdt0(xa,xR,xc)
| ( xc = xa ) ),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_1539,plain,
xc = xa,
inference(splitLeft,[status(thm)],[c_732]) ).
tff(c_124,plain,
aElement0(xb),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_690,plain,
( ~ sdtmndtasgtdt0(xc,xR,xb)
| ~ aElement0(xb) ),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_1528,plain,
~ sdtmndtasgtdt0(xc,xR,xb),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_690]) ).
tff(c_1540,plain,
~ sdtmndtasgtdt0(xa,xR,xb),
inference(demodulation,[status(thm),theory(equality)],[c_1539,c_1528]) ).
tff(c_1551,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_680,c_1540]) ).
tff(c_1552,plain,
sdtmndtplgtdt0(xa,xR,xc),
inference(splitRight,[status(thm)],[c_732]) ).
tff(c_678,plain,
sdtmndtasgtdt0(xa,xR,xc),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_740,plain,
( sdtmndtplgtdt0(xa,xR,xb)
| ( xb = xa ) ),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_1554,plain,
xb = xa,
inference(splitLeft,[status(thm)],[c_740]) ).
tff(c_122,plain,
aElement0(xc),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_722,plain,
( ~ sdtmndtasgtdt0(xb,xR,xc)
| ~ aElement0(xc) ),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_1532,plain,
~ sdtmndtasgtdt0(xb,xR,xc),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_722]) ).
tff(c_1558,plain,
~ sdtmndtasgtdt0(xa,xR,xc),
inference(demodulation,[status(thm),theory(equality)],[c_1554,c_1532]) ).
tff(c_1566,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_678,c_1558]) ).
tff(c_1567,plain,
sdtmndtplgtdt0(xa,xR,xb),
inference(splitRight,[status(thm)],[c_740]) ).
tff(c_1054,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| aElement0('#skF_27') ),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_2627,plain,
aElement0('#skF_27'),
inference(demodulation,[status(thm),theory(equality)],[c_1552,c_1567,c_1054]) ).
tff(c_748,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(xc,xR,'#skF_27') ),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_2865,plain,
sdtmndtasgtdt0(xc,xR,'#skF_27'),
inference(demodulation,[status(thm),theory(equality)],[c_1552,c_1567,c_748]) ).
tff(c_682,plain,
! [W0_207] :
( ~ sdtmndtasgtdt0(xb,xR,W0_207)
| ~ sdtmndtasgtdt0(xc,xR,W0_207)
| ~ aElement0(W0_207) ),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_2871,plain,
( ~ sdtmndtasgtdt0(xb,xR,'#skF_27')
| ~ aElement0('#skF_27') ),
inference(resolution,[status(thm)],[c_2865,c_682]) ).
tff(c_2877,plain,
~ sdtmndtasgtdt0(xb,xR,'#skF_27'),
inference(demodulation,[status(thm),theory(equality)],[c_2627,c_2871]) ).
tff(c_838,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(xb,xR,'#skF_27') ),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_2883,plain,
sdtmndtasgtdt0(xb,xR,'#skF_27'),
inference(demodulation,[status(thm),theory(equality)],[c_1552,c_1567,c_838]) ).
tff(c_2884,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2877,c_2883]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM022+4 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.13 % 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 : n007.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 16:13:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 13.38/4.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.38/4.25
% 13.38/4.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------