%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COM018+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/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 : n003.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 05:50:35 PM UTC 2025
% Result : Theorem 4.01s 1.98s
% Output : CNFRefutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 5 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-4 aty)
% Number of variables : 7 ( 5 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtmndtplgtdt0 > sdtmndtasgtdt0 > aReductOfIn0 > aNormalFormOfIn0 > iLess0 > isTerminating0 > isLocallyConfluent0 > isConfluent0 > aRewritingSystem0 > aElement0 > #nlpp > xw > xv > xu > xc > xb > xa > xR > #skF_9 > #skF_7 > #skF_5 > #skF_1 > #skF_4 > #skF_12 > #skF_8 > #skF_13 > #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(aReductOfIn0,type,
aReductOfIn0: ( $i * $i * $i ) > $o ).
tff(xa,type,
xa: $i ).
tff(xw,type,
xw: $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(xu,type,
xu: $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_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(xv,type,
xv: $i ).
tff(f_198,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
tff(f_201,hypothesis,
( isLocallyConfluent0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
tff(f_243,hypothesis,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw)
& sdtmndtasgtdt0(xv,xR,xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
tff(f_197,axiom,
! [W0] :
( ( aRewritingSystem0(W0)
& isTerminating0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).
tff(f_246,negated_conjecture,
~ ? [W0] : aNormalFormOfIn0(W0,xw,xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(c_88,plain,
aRewritingSystem0(xR),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_90,plain,
isTerminating0(xR),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_126,plain,
aElement0(xw),
inference(cnfTransformation,[status(thm)],[f_243]) ).
tff(c_187,plain,
! [W0_125,W1_126] :
( aNormalFormOfIn0('#skF_13'(W0_125,W1_126),W1_126,W0_125)
| ~ aElement0(W1_126)
| ~ isTerminating0(W0_125)
| ~ aRewritingSystem0(W0_125) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_128,plain,
! [W0_91] : ~ aNormalFormOfIn0(W0_91,xw,xR),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_194,plain,
( ~ aElement0(xw)
| ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c_187,c_128]) ).
tff(c_199,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_88,c_90,c_126,c_194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM018+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.13 % 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
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 7 16:12:33 EDT 2025
% 0.14/0.34 % CPUTime :
% 4.01/1.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.01/1.98
% 4.01/1.98 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------