%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET794+4 : TPTP v9.0.0. Released v3.2.0.
% 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 : n032.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 08:39:15 PM UTC 2025
% Result : Theorem 34.00s 20.26s
% Output : CNFRefutation 34.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 44 ~; 53 |; 6 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 14 ( 12 usr; 1 prp; 0-4 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-4 aty)
% Number of variables : 70 ( 70 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ least_upper_bound > greatest_lower_bound > upper_bound > min > max > lower_bound > least > greatest > apply > total_order > order > member > #nlpp > #skF_13 > #skF_6 > #skF_18 > #skF_17 > #skF_12 > #skF_19 > #skF_3 > #skF_15 > #skF_16 > #skF_8 > #skF_11 > #skF_9 > #skF_14 > #skF_2 > #skF_7 > #skF_1 > #skF_5 > #skF_4 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff(upper_bound,type,
upper_bound: ( $i * $i * $i ) > $o ).
tff(greatest_lower_bound,type,
greatest_lower_bound: ( $i * $i * $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(apply,type,
apply: ( $i * $i * $i ) > $o ).
tff('#skF_17',type,
'#skF_17': $i ).
tff(least_upper_bound,type,
least_upper_bound: ( $i * $i * $i * $i ) > $o ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': $i ).
tff(total_order,type,
total_order: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i * $i ) > $i ).
tff(greatest,type,
greatest: ( $i * $i * $i ) > $o ).
tff(lower_bound,type,
lower_bound: ( $i * $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff(min,type,
min: ( $i * $i * $i ) > $o ).
tff(least,type,
least: ( $i * $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(order,type,
order: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(max,type,
max: ( $i * $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_182,negated_conjecture,
~ ! [R,E,M] :
( ( total_order(R,E)
& min(M,R,E) )
=> least(M,R,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV6) ).
tff(f_147,axiom,
! [R,E,M] :
( min(M,R,E)
<=> ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,X,M) )
=> ( M = X ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',min) ).
tff(f_93,axiom,
! [R,E] :
( total_order(R,E)
<=> ( order(R,E)
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( apply(R,X,Y)
| apply(R,Y,X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',total_order) ).
tff(f_107,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',lower_bound) ).
tff(f_125,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',least) ).
tff(c_216,plain,
total_order('#skF_17','#skF_18'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_214,plain,
min('#skF_19','#skF_17','#skF_18'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_225,plain,
! [M_90,E_91,R_92] :
( member(M_90,E_91)
| ~ min(M_90,R_92,E_91) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_229,plain,
member('#skF_19','#skF_18'),
inference(resolution,[status(thm)],[c_214,c_225]) ).
tff(c_586,plain,
! [R_246,Y_247,X_248,E_249] :
( apply(R_246,Y_247,X_248)
| apply(R_246,X_248,Y_247)
| ~ member(Y_247,E_249)
| ~ member(X_248,E_249)
| ~ total_order(R_246,E_249) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_613,plain,
! [R_246,X_248] :
( apply(R_246,'#skF_19',X_248)
| apply(R_246,X_248,'#skF_19')
| ~ member(X_248,'#skF_18')
| ~ total_order(R_246,'#skF_18') ),
inference(resolution,[status(thm)],[c_229,c_586]) ).
tff(c_625,plain,
! [R_246] :
( ~ member('#skF_19','#skF_18')
| ~ total_order(R_246,'#skF_18')
| apply(R_246,'#skF_19','#skF_19') ),
inference(factorization,[status(thm),theory(equality)],[c_613]) ).
tff(c_628,plain,
! [R_246] :
( ~ total_order(R_246,'#skF_18')
| apply(R_246,'#skF_19','#skF_19') ),
inference(demodulation,[status(thm),theory(equality)],[c_229,c_625]) ).
tff(c_212,plain,
~ least('#skF_19','#skF_17','#skF_18'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_150,plain,
! [R_35,E_36,M_37] :
( member('#skF_10'(R_35,E_36,M_37),E_36)
| lower_bound(M_37,R_35,E_36) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_632,plain,
! [R_250,X_251] :
( apply(R_250,'#skF_19',X_251)
| apply(R_250,X_251,'#skF_19')
| ~ member(X_251,'#skF_18')
| ~ total_order(R_250,'#skF_18') ),
inference(resolution,[status(thm)],[c_229,c_586]) ).
tff(c_178,plain,
! [X_64,M_61,R_59,E_60] :
( ( X_64 = M_61 )
| ~ apply(R_59,X_64,M_61)
| ~ member(X_64,E_60)
| ~ min(M_61,R_59,E_60) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_1105,plain,
! [X_347,E_348,R_349] :
( ( X_347 = '#skF_19' )
| ~ member(X_347,E_348)
| ~ min('#skF_19',R_349,E_348)
| apply(R_349,'#skF_19',X_347)
| ~ member(X_347,'#skF_18')
| ~ total_order(R_349,'#skF_18') ),
inference(resolution,[status(thm)],[c_632,c_178]) ).
tff(c_74947,plain,
! [R_4809,E_4810,M_4811,R_4812] :
( ( '#skF_10'(R_4809,E_4810,M_4811) = '#skF_19' )
| ~ min('#skF_19',R_4812,E_4810)
| apply(R_4812,'#skF_19','#skF_10'(R_4809,E_4810,M_4811))
| ~ member('#skF_10'(R_4809,E_4810,M_4811),'#skF_18')
| ~ total_order(R_4812,'#skF_18')
| lower_bound(M_4811,R_4809,E_4810) ),
inference(resolution,[status(thm)],[c_150,c_1105]) ).
tff(c_148,plain,
! [R_35,M_37,E_36] :
( ~ apply(R_35,M_37,'#skF_10'(R_35,E_36,M_37))
| lower_bound(M_37,R_35,E_36) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_74974,plain,
! [R_4813,E_4814] :
( ( '#skF_10'(R_4813,E_4814,'#skF_19') = '#skF_19' )
| ~ min('#skF_19',R_4813,E_4814)
| ~ member('#skF_10'(R_4813,E_4814,'#skF_19'),'#skF_18')
| ~ total_order(R_4813,'#skF_18')
| lower_bound('#skF_19',R_4813,E_4814) ),
inference(resolution,[status(thm)],[c_74947,c_148]) ).
tff(c_75050,plain,
! [R_4818] :
( ( '#skF_10'(R_4818,'#skF_18','#skF_19') = '#skF_19' )
| ~ min('#skF_19',R_4818,'#skF_18')
| ~ total_order(R_4818,'#skF_18')
| lower_bound('#skF_19',R_4818,'#skF_18') ),
inference(resolution,[status(thm)],[c_150,c_74974]) ).
tff(c_75065,plain,
( ( '#skF_10'('#skF_17','#skF_18','#skF_19') = '#skF_19' )
| ~ total_order('#skF_17','#skF_18')
| lower_bound('#skF_19','#skF_17','#skF_18') ),
inference(resolution,[status(thm)],[c_214,c_75050]) ).
tff(c_75077,plain,
( ( '#skF_10'('#skF_17','#skF_18','#skF_19') = '#skF_19' )
| lower_bound('#skF_19','#skF_17','#skF_18') ),
inference(demodulation,[status(thm),theory(equality)],[c_216,c_75065]) ).
tff(c_75078,plain,
lower_bound('#skF_19','#skF_17','#skF_18'),
inference(splitLeft,[status(thm)],[c_75077]) ).
tff(c_393,plain,
! [R_176,E_177,M_178] :
( member('#skF_12'(R_176,E_177,M_178),E_177)
| least(M_178,R_176,E_177)
| ~ member(M_178,E_177) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_146,plain,
! [R_35,M_37,X_40,E_36] :
( apply(R_35,M_37,X_40)
| ~ member(X_40,E_36)
| ~ lower_bound(M_37,R_35,E_36) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_1486,plain,
! [M_403,E_402,M_405,R_404,R_401] :
( apply(R_404,M_405,'#skF_12'(R_401,E_402,M_403))
| ~ lower_bound(M_405,R_404,E_402)
| least(M_403,R_401,E_402)
| ~ member(M_403,E_402) ),
inference(resolution,[status(thm)],[c_393,c_146]) ).
tff(c_164,plain,
! [R_47,M_49,E_48] :
( ~ apply(R_47,M_49,'#skF_12'(R_47,E_48,M_49))
| least(M_49,R_47,E_48)
| ~ member(M_49,E_48) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_1506,plain,
! [M_403,R_401,E_402] :
( ~ lower_bound(M_403,R_401,E_402)
| least(M_403,R_401,E_402)
| ~ member(M_403,E_402) ),
inference(resolution,[status(thm)],[c_1486,c_164]) ).
tff(c_75110,plain,
( least('#skF_19','#skF_17','#skF_18')
| ~ member('#skF_19','#skF_18') ),
inference(resolution,[status(thm)],[c_75078,c_1506]) ).
tff(c_75162,plain,
least('#skF_19','#skF_17','#skF_18'),
inference(demodulation,[status(thm),theory(equality)],[c_229,c_75110]) ).
tff(c_75164,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_212,c_75162]) ).
tff(c_75166,plain,
~ lower_bound('#skF_19','#skF_17','#skF_18'),
inference(splitRight,[status(thm)],[c_75077]) ).
tff(c_75165,plain,
'#skF_10'('#skF_17','#skF_18','#skF_19') = '#skF_19',
inference(splitRight,[status(thm)],[c_75077]) ).
tff(c_75285,plain,
( ~ apply('#skF_17','#skF_19','#skF_19')
| lower_bound('#skF_19','#skF_17','#skF_18') ),
inference(superposition,[status(thm),theory(equality)],[c_75165,c_148]) ).
tff(c_75382,plain,
~ apply('#skF_17','#skF_19','#skF_19'),
inference(negUnitSimplification,[status(thm)],[c_75166,c_75285]) ).
tff(c_75581,plain,
~ total_order('#skF_17','#skF_18'),
inference(resolution,[status(thm)],[c_628,c_75382]) ).
tff(c_75603,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_216,c_75581]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SET794+4 : TPTP v9.0.0. Released v3.2.0.
% 0.05/0.10 % 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
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue Apr 8 21:39:30 EDT 2025
% 0.09/0.29 % CPUTime :
% 34.00/20.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.00/20.26
% 34.00/20.26 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------