TSTP Solution File: COM023+4 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : COM023+4 : 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 : n016.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 10:35:20 EDT 2023
% Result : Theorem 23.43s 8.94s
% Output : CNFRefutation 23.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 41
% Syntax : Number of formulae : 134 ( 33 unt; 35 typ; 2 def)
% Number of atoms : 402 ( 37 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 496 ( 193 ~; 229 |; 64 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 29 >; 32 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-4 aty)
% Number of variables : 89 (; 74 !; 15 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtmndtplgtdt0 > sdtmndtasgtdt0 > aReductOfIn0 > aNormalFormOfIn0 > iLess0 > isTerminating0 > isLocallyConfluent0 > isConfluent0 > aRewritingSystem0 > aElement0 > #nlpp > xR > #skF_9 > #skF_7 > #skF_5 > #skF_17 > #skF_1 > #skF_20 > #skF_4 > #skF_18 > #skF_12 > #skF_8 > #skF_13 > #skF_10 > #skF_2 > #skF_19 > #skF_6 > #skF_21 > #skF_15 > #skF_14 > #skF_3 > #skF_11 > #skF_22 > #skF_24 > #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('#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('#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_15',type,
'#skF_15': ( $i * $i * $i ) > $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_24',type,
'#skF_24': $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_404,negated_conjecture,
~ ( ! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& ( ( W0 = W1 )
| ( ( aReductOfIn0(W1,W0,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W0,xR)
& sdtmndtplgtdt0(W3,xR,W1) ) )
& sdtmndtplgtdt0(W0,xR,W1) ) )
& sdtmndtasgtdt0(W0,xR,W1)
& ( ( 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) )
=> ? [W3] :
( aElement0(W3)
& ( ( W1 = W3 )
| aReductOfIn0(W3,W1,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) )
| sdtmndtplgtdt0(W1,xR,W3)
| sdtmndtasgtdt0(W1,xR,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) ) ) )
| isConfluent0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_198,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
tff(f_137,definition,
! [W0] :
( aRewritingSystem0(W0)
=> ( isConfluent0(W0)
<=> ! [W1,W2,W3] :
( ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& sdtmndtasgtdt0(W1,W0,W2)
& sdtmndtasgtdt0(W1,W0,W3) )
=> ? [W4] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCRDef) ).
tff(f_332,hypothesis,
! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& ( ( W0 = W1 )
| aReductOfIn0(W1,W0,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W0,xR)
& sdtmndtplgtdt0(W3,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1)
| sdtmndtasgtdt0(W0,xR,W1) )
& ( ( 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) ) )
=> ? [W3] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,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) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__715) ).
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/sandbox/benchmark/theBenchmark.p',mTCRDef) ).
tff(f_263,hypothesis,
( ! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,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) ) )
& isLocallyConfluent0(xR)
& ! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( aReductOfIn0(W1,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1) )
=> iLess0(W1,W0) ) )
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
tff(c_672,plain,
~ isConfluent0(xR),
inference(cnfTransformation,[status(thm)],[f_404]) ).
tff(c_88,plain,
aRewritingSystem0(xR),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_40,plain,
! [W0_29] :
( aElement0('#skF_4'(W0_29))
| isConfluent0(W0_29)
| ~ aRewritingSystem0(W0_29) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_42,plain,
! [W0_29] :
( aElement0('#skF_3'(W0_29))
| isConfluent0(W0_29)
| ~ aRewritingSystem0(W0_29) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_38,plain,
! [W0_29] :
( aElement0('#skF_5'(W0_29))
| isConfluent0(W0_29)
| ~ aRewritingSystem0(W0_29) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_420,plain,
! [W2_103] :
( sdtmndtasgtdt0(W2_103,xR,'#skF_17'(W2_103,W2_103,W2_103))
| ~ aElement0(W2_103) ),
inference(cnfTransformation,[status(thm)],[f_332]) ).
tff(c_1886,plain,
! [W0_255,W4_256] :
( ~ sdtmndtasgtdt0('#skF_5'(W0_255),W0_255,W4_256)
| ~ sdtmndtasgtdt0('#skF_4'(W0_255),W0_255,W4_256)
| ~ aElement0(W4_256)
| isConfluent0(W0_255)
| ~ aRewritingSystem0(W0_255) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_1946,plain,
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_17'('#skF_5'(xR),'#skF_5'(xR),'#skF_5'(xR)))
| ~ aElement0('#skF_17'('#skF_5'(xR),'#skF_5'(xR),'#skF_5'(xR)))
| isConfluent0(xR)
| ~ aRewritingSystem0(xR)
| ~ aElement0('#skF_5'(xR)) ),
inference(resolution,[status(thm)],[c_420,c_1886]) ).
tff(c_2003,plain,
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_17'('#skF_5'(xR),'#skF_5'(xR),'#skF_5'(xR)))
| ~ aElement0('#skF_17'('#skF_5'(xR),'#skF_5'(xR),'#skF_5'(xR)))
| isConfluent0(xR)
| ~ aElement0('#skF_5'(xR)) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_1946]) ).
tff(c_2004,plain,
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_17'('#skF_5'(xR),'#skF_5'(xR),'#skF_5'(xR)))
| ~ aElement0('#skF_17'('#skF_5'(xR),'#skF_5'(xR),'#skF_5'(xR)))
| ~ aElement0('#skF_5'(xR)) ),
inference(negUnitSimplification,[status(thm)],[c_672,c_2003]) ).
tff(c_2177,plain,
~ aElement0('#skF_5'(xR)),
inference(splitLeft,[status(thm)],[c_2004]) ).
tff(c_2180,plain,
( isConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c_38,c_2177]) ).
tff(c_2183,plain,
isConfluent0(xR),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2180]) ).
tff(c_2185,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_672,c_2183]) ).
tff(c_2187,plain,
aElement0('#skF_5'(xR)),
inference(splitRight,[status(thm)],[c_2004]) ).
tff(c_34,plain,
! [W0_29] :
( sdtmndtasgtdt0('#skF_3'(W0_29),W0_29,'#skF_5'(W0_29))
| isConfluent0(W0_29)
| ~ aRewritingSystem0(W0_29) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_2017,plain,
! [W0_258,W1_259,W2_260] :
( sdtmndtplgtdt0(W0_258,W1_259,W2_260)
| ( W2_260 = W0_258 )
| ~ sdtmndtasgtdt0(W0_258,W1_259,W2_260)
| ~ aElement0(W2_260)
| ~ aRewritingSystem0(W1_259)
| ~ aElement0(W0_258) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_94,plain,
! [W0_87,W1_88] :
( ~ sdtmndtplgtdt0(W0_87,xR,W1_88)
| iLess0(W1_88,W0_87)
| ~ aElement0(W1_88)
| ~ aElement0(W0_87) ),
inference(cnfTransformation,[status(thm)],[f_263]) ).
tff(c_2055,plain,
! [W2_260,W0_258] :
( iLess0(W2_260,W0_258)
| ( W2_260 = W0_258 )
| ~ sdtmndtasgtdt0(W0_258,xR,W2_260)
| ~ aElement0(W2_260)
| ~ aRewritingSystem0(xR)
| ~ aElement0(W0_258) ),
inference(resolution,[status(thm)],[c_2017,c_94]) ).
tff(c_2326,plain,
! [W2_267,W0_268] :
( iLess0(W2_267,W0_268)
| ( W2_267 = W0_268 )
| ~ sdtmndtasgtdt0(W0_268,xR,W2_267)
| ~ aElement0(W2_267)
| ~ aElement0(W0_268) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2055]) ).
tff(c_2374,plain,
( iLess0('#skF_5'(xR),'#skF_3'(xR))
| ( '#skF_5'(xR) = '#skF_3'(xR) )
| ~ aElement0('#skF_5'(xR))
| ~ aElement0('#skF_3'(xR))
| isConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c_34,c_2326]) ).
tff(c_2412,plain,
( iLess0('#skF_5'(xR),'#skF_3'(xR))
| ( '#skF_5'(xR) = '#skF_3'(xR) )
| ~ aElement0('#skF_3'(xR))
| isConfluent0(xR) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2187,c_2374]) ).
tff(c_2413,plain,
( iLess0('#skF_5'(xR),'#skF_3'(xR))
| ( '#skF_5'(xR) = '#skF_3'(xR) )
| ~ aElement0('#skF_3'(xR)) ),
inference(negUnitSimplification,[status(thm)],[c_672,c_2412]) ).
tff(c_2431,plain,
~ aElement0('#skF_3'(xR)),
inference(splitLeft,[status(thm)],[c_2413]) ).
tff(c_2434,plain,
( isConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c_42,c_2431]) ).
tff(c_2437,plain,
isConfluent0(xR),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2434]) ).
tff(c_2439,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_672,c_2437]) ).
tff(c_2441,plain,
aElement0('#skF_3'(xR)),
inference(splitRight,[status(thm)],[c_2413]) ).
tff(c_36,plain,
! [W0_29] :
( sdtmndtasgtdt0('#skF_3'(W0_29),W0_29,'#skF_4'(W0_29))
| isConfluent0(W0_29)
| ~ aRewritingSystem0(W0_29) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_2378,plain,
( iLess0('#skF_4'(xR),'#skF_3'(xR))
| ( '#skF_4'(xR) = '#skF_3'(xR) )
| ~ aElement0('#skF_4'(xR))
| ~ aElement0('#skF_3'(xR))
| isConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c_36,c_2326]) ).
tff(c_2416,plain,
( iLess0('#skF_4'(xR),'#skF_3'(xR))
| ( '#skF_4'(xR) = '#skF_3'(xR) )
| ~ aElement0('#skF_4'(xR))
| ~ aElement0('#skF_3'(xR))
| isConfluent0(xR) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2378]) ).
tff(c_2417,plain,
( iLess0('#skF_4'(xR),'#skF_3'(xR))
| ( '#skF_4'(xR) = '#skF_3'(xR) )
| ~ aElement0('#skF_4'(xR))
| ~ aElement0('#skF_3'(xR)) ),
inference(negUnitSimplification,[status(thm)],[c_672,c_2416]) ).
tff(c_2442,plain,
~ aElement0('#skF_3'(xR)),
inference(splitLeft,[status(thm)],[c_2417]) ).
tff(c_2444,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2441,c_2442]) ).
tff(c_2445,plain,
( ~ aElement0('#skF_4'(xR))
| ( '#skF_4'(xR) = '#skF_3'(xR) )
| iLess0('#skF_4'(xR),'#skF_3'(xR)) ),
inference(splitRight,[status(thm)],[c_2417]) ).
tff(c_2587,plain,
~ aElement0('#skF_4'(xR)),
inference(splitLeft,[status(thm)],[c_2445]) ).
tff(c_2590,plain,
( isConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c_40,c_2587]) ).
tff(c_2593,plain,
isConfluent0(xR),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2590]) ).
tff(c_2595,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_672,c_2593]) ).
tff(c_2597,plain,
aElement0('#skF_4'(xR)),
inference(splitRight,[status(thm)],[c_2445]) ).
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_2596,plain,
( iLess0('#skF_4'(xR),'#skF_3'(xR))
| ( '#skF_4'(xR) = '#skF_3'(xR) ) ),
inference(splitRight,[status(thm)],[c_2445]) ).
tff(c_2598,plain,
'#skF_4'(xR) = '#skF_3'(xR),
inference(splitLeft,[status(thm)],[c_2596]) ).
tff(c_2005,plain,
! [W1_23] :
( ~ sdtmndtasgtdt0('#skF_4'(W1_23),W1_23,'#skF_5'(W1_23))
| isConfluent0(W1_23)
| ~ aRewritingSystem0(W1_23)
| ~ aElement0('#skF_5'(W1_23)) ),
inference(resolution,[status(thm)],[c_28,c_1886]) ).
tff(c_2604,plain,
( ~ sdtmndtasgtdt0('#skF_3'(xR),xR,'#skF_5'(xR))
| isConfluent0(xR)
| ~ aRewritingSystem0(xR)
| ~ aElement0('#skF_5'(xR)) ),
inference(superposition,[status(thm),theory(equality)],[c_2598,c_2005]) ).
tff(c_2614,plain,
( ~ sdtmndtasgtdt0('#skF_3'(xR),xR,'#skF_5'(xR))
| isConfluent0(xR) ),
inference(demodulation,[status(thm),theory(equality)],[c_2187,c_88,c_2604]) ).
tff(c_2615,plain,
~ sdtmndtasgtdt0('#skF_3'(xR),xR,'#skF_5'(xR)),
inference(negUnitSimplification,[status(thm)],[c_672,c_2614]) ).
tff(c_2632,plain,
( isConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c_34,c_2615]) ).
tff(c_2641,plain,
isConfluent0(xR),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2632]) ).
tff(c_2643,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_672,c_2641]) ).
tff(c_2645,plain,
'#skF_4'(xR) != '#skF_3'(xR),
inference(splitRight,[status(thm)],[c_2596]) ).
tff(c_24,plain,
! [W0_22,W1_23,W2_24] :
( sdtmndtplgtdt0(W0_22,W1_23,W2_24)
| ( W2_24 = W0_22 )
| ~ sdtmndtasgtdt0(W0_22,W1_23,W2_24)
| ~ aElement0(W2_24)
| ~ aRewritingSystem0(W1_23)
| ~ aElement0(W0_22) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_634,plain,
! [W0_101,W1_102,W2_103] :
( ~ sdtmndtplgtdt0(W0_101,xR,W1_102)
| ~ sdtmndtplgtdt0(W0_101,xR,W2_103)
| aElement0('#skF_17'(W0_101,W1_102,W2_103))
| ~ aElement0(W2_103)
| ~ aElement0(W1_102)
| ~ aElement0(W0_101) ),
inference(cnfTransformation,[status(thm)],[f_332]) ).
tff(c_134,plain,
! [W0_101,W1_102,W2_103] :
( ~ sdtmndtplgtdt0(W0_101,xR,W1_102)
| ~ sdtmndtplgtdt0(W0_101,xR,W2_103)
| sdtmndtasgtdt0(W2_103,xR,'#skF_17'(W0_101,W1_102,W2_103))
| ~ aElement0(W2_103)
| ~ aElement0(W1_102)
| ~ aElement0(W0_101) ),
inference(cnfTransformation,[status(thm)],[f_332]) ).
tff(c_28239,plain,
! [W0_858,W1_859,W2_860] :
( ~ sdtmndtplgtdt0(W0_858,xR,W1_859)
| ~ sdtmndtplgtdt0(W0_858,xR,W2_860)
| sdtmndtasgtdt0(W1_859,xR,'#skF_17'(W0_858,W1_859,W2_860))
| ~ aElement0(W2_860)
| ~ aElement0(W1_859)
| ~ aElement0(W0_858) ),
inference(cnfTransformation,[status(thm)],[f_332]) ).
tff(c_32,plain,
! [W0_29,W4_45] :
( ~ sdtmndtasgtdt0('#skF_5'(W0_29),W0_29,W4_45)
| ~ sdtmndtasgtdt0('#skF_4'(W0_29),W0_29,W4_45)
| ~ aElement0(W4_45)
| isConfluent0(W0_29)
| ~ aRewritingSystem0(W0_29) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_28403,plain,
! [W0_858,W2_860] :
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_17'(W0_858,'#skF_5'(xR),W2_860))
| ~ aElement0('#skF_17'(W0_858,'#skF_5'(xR),W2_860))
| isConfluent0(xR)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(W0_858,xR,'#skF_5'(xR))
| ~ sdtmndtplgtdt0(W0_858,xR,W2_860)
| ~ aElement0(W2_860)
| ~ aElement0('#skF_5'(xR))
| ~ aElement0(W0_858) ),
inference(resolution,[status(thm)],[c_28239,c_32]) ).
tff(c_28550,plain,
! [W0_858,W2_860] :
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_17'(W0_858,'#skF_5'(xR),W2_860))
| ~ aElement0('#skF_17'(W0_858,'#skF_5'(xR),W2_860))
| isConfluent0(xR)
| ~ sdtmndtplgtdt0(W0_858,xR,'#skF_5'(xR))
| ~ sdtmndtplgtdt0(W0_858,xR,W2_860)
| ~ aElement0(W2_860)
| ~ aElement0(W0_858) ),
inference(demodulation,[status(thm),theory(equality)],[c_2187,c_88,c_28403]) ).
tff(c_41670,plain,
! [W0_1061,W2_1062] :
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_17'(W0_1061,'#skF_5'(xR),W2_1062))
| ~ aElement0('#skF_17'(W0_1061,'#skF_5'(xR),W2_1062))
| ~ sdtmndtplgtdt0(W0_1061,xR,'#skF_5'(xR))
| ~ sdtmndtplgtdt0(W0_1061,xR,W2_1062)
| ~ aElement0(W2_1062)
| ~ aElement0(W0_1061) ),
inference(negUnitSimplification,[status(thm)],[c_672,c_28550]) ).
tff(c_41696,plain,
! [W0_101] :
( ~ aElement0('#skF_17'(W0_101,'#skF_5'(xR),'#skF_4'(xR)))
| ~ sdtmndtplgtdt0(W0_101,xR,'#skF_5'(xR))
| ~ sdtmndtplgtdt0(W0_101,xR,'#skF_4'(xR))
| ~ aElement0('#skF_4'(xR))
| ~ aElement0('#skF_5'(xR))
| ~ aElement0(W0_101) ),
inference(resolution,[status(thm)],[c_134,c_41670]) ).
tff(c_42511,plain,
! [W0_1067] :
( ~ aElement0('#skF_17'(W0_1067,'#skF_5'(xR),'#skF_4'(xR)))
| ~ sdtmndtplgtdt0(W0_1067,xR,'#skF_5'(xR))
| ~ sdtmndtplgtdt0(W0_1067,xR,'#skF_4'(xR))
| ~ aElement0(W0_1067) ),
inference(demodulation,[status(thm),theory(equality)],[c_2187,c_2597,c_41696]) ).
tff(c_42559,plain,
! [W0_101] :
( ~ sdtmndtplgtdt0(W0_101,xR,'#skF_5'(xR))
| ~ sdtmndtplgtdt0(W0_101,xR,'#skF_4'(xR))
| ~ aElement0('#skF_4'(xR))
| ~ aElement0('#skF_5'(xR))
| ~ aElement0(W0_101) ),
inference(resolution,[status(thm)],[c_634,c_42511]) ).
tff(c_42645,plain,
! [W0_1068] :
( ~ sdtmndtplgtdt0(W0_1068,xR,'#skF_5'(xR))
| ~ sdtmndtplgtdt0(W0_1068,xR,'#skF_4'(xR))
| ~ aElement0(W0_1068) ),
inference(demodulation,[status(thm),theory(equality)],[c_2187,c_2597,c_42559]) ).
tff(c_42677,plain,
! [W0_22] :
( ~ sdtmndtplgtdt0(W0_22,xR,'#skF_4'(xR))
| ( W0_22 = '#skF_5'(xR) )
| ~ sdtmndtasgtdt0(W0_22,xR,'#skF_5'(xR))
| ~ aElement0('#skF_5'(xR))
| ~ aRewritingSystem0(xR)
| ~ aElement0(W0_22) ),
inference(resolution,[status(thm)],[c_24,c_42645]) ).
tff(c_42774,plain,
! [W0_1071] :
( ~ sdtmndtplgtdt0(W0_1071,xR,'#skF_4'(xR))
| ( W0_1071 = '#skF_5'(xR) )
| ~ sdtmndtasgtdt0(W0_1071,xR,'#skF_5'(xR))
| ~ aElement0(W0_1071) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2187,c_42677]) ).
tff(c_42806,plain,
! [W0_22] :
( ( W0_22 = '#skF_5'(xR) )
| ~ sdtmndtasgtdt0(W0_22,xR,'#skF_5'(xR))
| ( W0_22 = '#skF_4'(xR) )
| ~ sdtmndtasgtdt0(W0_22,xR,'#skF_4'(xR))
| ~ aElement0('#skF_4'(xR))
| ~ aRewritingSystem0(xR)
| ~ aElement0(W0_22) ),
inference(resolution,[status(thm)],[c_24,c_42774]) ).
tff(c_43989,plain,
! [W0_1080] :
( ( W0_1080 = '#skF_5'(xR) )
| ~ sdtmndtasgtdt0(W0_1080,xR,'#skF_5'(xR))
| ( W0_1080 = '#skF_4'(xR) )
| ~ sdtmndtasgtdt0(W0_1080,xR,'#skF_4'(xR))
| ~ aElement0(W0_1080) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2597,c_42806]) ).
tff(c_44057,plain,
( ( '#skF_5'(xR) = '#skF_3'(xR) )
| ( '#skF_4'(xR) = '#skF_3'(xR) )
| ~ sdtmndtasgtdt0('#skF_3'(xR),xR,'#skF_4'(xR))
| ~ aElement0('#skF_3'(xR))
| isConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c_34,c_43989]) ).
tff(c_44112,plain,
( ( '#skF_5'(xR) = '#skF_3'(xR) )
| ( '#skF_4'(xR) = '#skF_3'(xR) )
| ~ sdtmndtasgtdt0('#skF_3'(xR),xR,'#skF_4'(xR))
| isConfluent0(xR) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2441,c_44057]) ).
tff(c_44113,plain,
( ( '#skF_5'(xR) = '#skF_3'(xR) )
| ~ sdtmndtasgtdt0('#skF_3'(xR),xR,'#skF_4'(xR)) ),
inference(negUnitSimplification,[status(thm)],[c_672,c_2645,c_44112]) ).
tff(c_44117,plain,
~ sdtmndtasgtdt0('#skF_3'(xR),xR,'#skF_4'(xR)),
inference(splitLeft,[status(thm)],[c_44113]) ).
tff(c_44150,plain,
( isConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c_36,c_44117]) ).
tff(c_44183,plain,
isConfluent0(xR),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_44150]) ).
tff(c_44185,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_672,c_44183]) ).
tff(c_44187,plain,
sdtmndtasgtdt0('#skF_3'(xR),xR,'#skF_4'(xR)),
inference(splitRight,[status(thm)],[c_44113]) ).
tff(c_44186,plain,
'#skF_5'(xR) = '#skF_3'(xR),
inference(splitRight,[status(thm)],[c_44113]) ).
tff(c_412,plain,
! [W2_103,W1_102] :
( ~ sdtmndtasgtdt0(W2_103,xR,W1_102)
| sdtmndtasgtdt0(W1_102,xR,'#skF_17'(W2_103,W1_102,W2_103))
| ~ aElement0(W1_102)
| ~ aElement0(W2_103) ),
inference(cnfTransformation,[status(thm)],[f_332]) ).
tff(c_162,plain,
! [W2_103,W1_102] :
( ~ sdtmndtasgtdt0(W2_103,xR,W1_102)
| sdtmndtasgtdt0(W2_103,xR,'#skF_17'(W2_103,W1_102,W2_103))
| ~ aElement0(W1_102)
| ~ aElement0(W2_103) ),
inference(cnfTransformation,[status(thm)],[f_332]) ).
tff(c_1914,plain,
! [W1_102] :
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_17'('#skF_5'(xR),W1_102,'#skF_5'(xR)))
| ~ aElement0('#skF_17'('#skF_5'(xR),W1_102,'#skF_5'(xR)))
| isConfluent0(xR)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0('#skF_5'(xR),xR,W1_102)
| ~ aElement0(W1_102)
| ~ aElement0('#skF_5'(xR)) ),
inference(resolution,[status(thm)],[c_162,c_1886]) ).
tff(c_1977,plain,
! [W1_102] :
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_17'('#skF_5'(xR),W1_102,'#skF_5'(xR)))
| ~ aElement0('#skF_17'('#skF_5'(xR),W1_102,'#skF_5'(xR)))
| isConfluent0(xR)
| ~ sdtmndtasgtdt0('#skF_5'(xR),xR,W1_102)
| ~ aElement0(W1_102)
| ~ aElement0('#skF_5'(xR)) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_1914]) ).
tff(c_1978,plain,
! [W1_102] :
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_17'('#skF_5'(xR),W1_102,'#skF_5'(xR)))
| ~ aElement0('#skF_17'('#skF_5'(xR),W1_102,'#skF_5'(xR)))
| ~ sdtmndtasgtdt0('#skF_5'(xR),xR,W1_102)
| ~ aElement0(W1_102)
| ~ aElement0('#skF_5'(xR)) ),
inference(negUnitSimplification,[status(thm)],[c_672,c_1977]) ).
tff(c_4867,plain,
! [W1_383] :
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_17'('#skF_5'(xR),W1_383,'#skF_5'(xR)))
| ~ aElement0('#skF_17'('#skF_5'(xR),W1_383,'#skF_5'(xR)))
| ~ sdtmndtasgtdt0('#skF_5'(xR),xR,W1_383)
| ~ aElement0(W1_383) ),
inference(demodulation,[status(thm),theory(equality)],[c_2187,c_1978]) ).
tff(c_4879,plain,
( ~ aElement0('#skF_17'('#skF_5'(xR),'#skF_4'(xR),'#skF_5'(xR)))
| ~ sdtmndtasgtdt0('#skF_5'(xR),xR,'#skF_4'(xR))
| ~ aElement0('#skF_4'(xR))
| ~ aElement0('#skF_5'(xR)) ),
inference(resolution,[status(thm)],[c_412,c_4867]) ).
tff(c_4894,plain,
( ~ aElement0('#skF_17'('#skF_5'(xR),'#skF_4'(xR),'#skF_5'(xR)))
| ~ sdtmndtasgtdt0('#skF_5'(xR),xR,'#skF_4'(xR)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2187,c_2597,c_4879]) ).
tff(c_4901,plain,
~ sdtmndtasgtdt0('#skF_5'(xR),xR,'#skF_4'(xR)),
inference(splitLeft,[status(thm)],[c_4894]) ).
tff(c_44260,plain,
~ sdtmndtasgtdt0('#skF_3'(xR),xR,'#skF_4'(xR)),
inference(demodulation,[status(thm),theory(equality)],[c_44186,c_4901]) ).
tff(c_45680,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_44187,c_44260]) ).
tff(c_45682,plain,
sdtmndtasgtdt0('#skF_5'(xR),xR,'#skF_4'(xR)),
inference(splitRight,[status(thm)],[c_4894]) ).
tff(c_45697,plain,
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_4'(xR))
| ~ aElement0('#skF_4'(xR))
| isConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c_45682,c_32]) ).
tff(c_45712,plain,
( ~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_4'(xR))
| isConfluent0(xR) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2597,c_45697]) ).
tff(c_45713,plain,
~ sdtmndtasgtdt0('#skF_4'(xR),xR,'#skF_4'(xR)),
inference(negUnitSimplification,[status(thm)],[c_672,c_45712]) ).
tff(c_45722,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0('#skF_4'(xR)) ),
inference(resolution,[status(thm)],[c_28,c_45713]) ).
tff(c_45732,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2597,c_88,c_45722]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COM023+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 4 00:04:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 23.43/8.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.43/8.95
% 23.43/8.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.97/8.98
% 23.97/8.98 Inference rules
% 23.97/8.98 ----------------------
% 23.97/8.98 #Ref : 0
% 23.97/8.98 #Sup : 7762
% 23.97/8.98 #Fact : 0
% 23.97/8.98 #Define : 0
% 23.97/8.98 #Split : 59
% 23.97/8.98 #Chain : 0
% 23.97/8.98 #Close : 0
% 23.97/8.98
% 23.97/8.98 Ordering : KBO
% 23.97/8.99
% 23.97/8.99 Simplification rules
% 23.97/8.99 ----------------------
% 23.97/8.99 #Subsume : 3735
% 23.97/8.99 #Demod : 11753
% 23.97/8.99 #Tautology : 644
% 23.97/8.99 #SimpNegUnit : 476
% 23.97/8.99 #BackRed : 112
% 23.97/8.99
% 23.97/8.99 #Partial instantiations: 0
% 23.97/8.99 #Strategies tried : 1
% 23.97/8.99
% 23.97/8.99 Timing (in seconds)
% 23.97/8.99 ----------------------
% 23.97/8.99 Preprocessing : 0.83
% 23.97/8.99 Parsing : 0.34
% 23.97/8.99 CNF conversion : 0.08
% 23.97/8.99 Main loop : 7.08
% 23.97/8.99 Inferencing : 1.61
% 23.97/8.99 Reduction : 2.15
% 23.97/8.99 Demodulation : 1.47
% 23.97/8.99 BG Simplification : 0.17
% 23.97/8.99 Subsumption : 2.79
% 23.97/8.99 Abstraction : 0.14
% 23.97/8.99 MUC search : 0.00
% 23.97/8.99 Cooper : 0.00
% 23.97/8.99 Total : 7.98
% 23.97/8.99 Index Insertion : 0.00
% 23.97/8.99 Index Deletion : 0.00
% 23.97/8.99 Index Matching : 0.00
% 23.97/8.99 BG Taut test : 0.00
%------------------------------------------------------------------------------