TSTP Solution File: DAT053_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : DAT053_1 : TPTP v8.1.2. Released v5.0.0.
% 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 : n020.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 10:37:03 EDT 2023
% Result : Theorem 9.70s 3.30s
% Output : CNFRefutation 10.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 65
% Syntax : Number of formulae : 229 ( 109 unt; 55 typ; 0 def)
% Number of atoms : 265 ( 139 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 185 ( 94 ~; 74 |; 7 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 315 ( 20 atm; 135 fun; 160 num; 0 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 59 ( 53 usr; 51 con; 0-2 aty)
% Number of variables : 32 (; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
%$ isrecord > #nlpp > split2 > split1 > next > length > data > b > a
%Foreground sorts:
tff(record,type,
record: $tType ).
%Background operators:
tff('#skE_46',type,
'#skE_46': $int ).
tff('#skE_7',type,
'#skE_7': $int ).
tff('#skE_21',type,
'#skE_21': $int ).
tff('#skE_30',type,
'#skE_30': $int ).
tff('#skE_11',type,
'#skE_11': $int ).
tff('#skE_25',type,
'#skE_25': $int ).
tff('#skE_28',type,
'#skE_28': $int ).
tff('#skE_23',type,
'#skE_23': $int ).
tff('#skE_12',type,
'#skE_12': $int ).
tff('#skE_41',type,
'#skE_41': $int ).
tff('#skE_43',type,
'#skE_43': $int ).
tff('#skE_37',type,
'#skE_37': $int ).
tff('#skE_42',type,
'#skE_42': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_33',type,
'#skE_33': $int ).
tff('#skE_20',type,
'#skE_20': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_13',type,
'#skE_13': $int ).
tff('#skE_26',type,
'#skE_26': $int ).
tff('#skE_32',type,
'#skE_32': $int ).
tff('#skE_10',type,
'#skE_10': $int ).
tff('#skE_24',type,
'#skE_24': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_38',type,
'#skE_38': $int ).
tff('#skE_31',type,
'#skE_31': $int ).
tff('#skE_15',type,
'#skE_15': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skE_36',type,
'#skE_36': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skE_22',type,
'#skE_22': $int ).
tff('#skE_16',type,
'#skE_16': $int ).
tff('#skE_17',type,
'#skE_17': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skE_40',type,
'#skE_40': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
tff('#skE_29',type,
'#skE_29': $int ).
tff('#skE_44',type,
'#skE_44': $int ).
tff('#skE_34',type,
'#skE_34': $int ).
tff('#skE_45',type,
'#skE_45': $int ).
tff('#skE_27',type,
'#skE_27': $int ).
tff('#skE_18',type,
'#skE_18': $int ).
tff('#skE_35',type,
'#skE_35': $int ).
tff('#skE_39',type,
'#skE_39': $int ).
tff('#skE_19',type,
'#skE_19': $int ).
tff('#skE_14',type,
'#skE_14': $int ).
%Foreground operators:
tff(split2,type,
split2: record > record ).
tff(next,type,
next: record > record ).
tff(a,type,
a: record ).
tff(b,type,
b: record ).
tff(isrecord,type,
isrecord: record > $o ).
tff(split1,type,
split1: record > record ).
tff(data,type,
data: record > $int ).
tff(length,type,
length: record > $int ).
tff(f_144,negated_conjecture,
~ ( ( isrecord(b)
& isrecord(next(b))
& ( next(next(b)) = a )
& ( ( $product(2,length(split1(a))) = $sum(length(a),1) )
| ( $product(2,length(split1(a))) = length(a) ) ) )
=> ( ( $product(2,length(split1(b))) = $sum(length(b),1) )
| ( $product(2,length(split1(b))) = length(b) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_62,axiom,
! [U: record] :
( ~ isrecord(U)
=> ( length(U) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT003_0.ax',ax1) ).
tff(f_122,axiom,
! [U: record] :
( ( isrecord(U)
& isrecord(next(U)) )
=> ( data(split2(U)) = data(next(U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT003_0.ax',ax12) ).
tff(f_66,axiom,
! [U: record] :
( isrecord(U)
=> $greatereq(length(U),1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT003_0.ax',ax2) ).
tff(f_110,axiom,
! [U: record] :
( ~ isrecord(next(U))
=> ~ isrecord(split2(U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT003_0.ax',ax10) ).
tff(f_116,axiom,
! [U: record] :
( ( isrecord(U)
& isrecord(next(U)) )
=> isrecord(split2(U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT003_0.ax',ax11) ).
tff(f_70,axiom,
! [U: record] :
( isrecord(U)
=> ( length(U) = $sum(length(next(U)),1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT003_0.ax',ax3) ).
tff(f_98,axiom,
! [U: record] :
( ( isrecord(U)
& isrecord(next(U)) )
=> ( next(split1(U)) = split1(next(next(U))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT003_0.ax',ax8) ).
tff(f_80,axiom,
! [U: record] :
( isrecord(U)
=> isrecord(split1(U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT003_0.ax',ax5) ).
tff(f_128,axiom,
! [U: record] :
( ( isrecord(U)
& isrecord(next(U)) )
=> ( next(split2(U)) = split2(next(next(U))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT003_0.ax',ax13) ).
tff(c_40,plain,
isrecord(next(b)),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_50,plain,
! [U_1: record] :
( ( length(U_1) = 0 )
| isrecord(U_1) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_38,plain,
next(next(b)) = a,
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_777,plain,
! [U_35: record] :
( ( data(split2(U_35)) = data(next(U_35)) )
| ~ isrecord(next(U_35))
| ~ isrecord(U_35) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_804,plain,
( ( data(split2(next(b))) = data(next(next(b))) )
| ~ isrecord(a)
| ~ isrecord(next(b)) ),
inference(superposition,[status(thm),theory(equality)],[c_38,c_777]) ).
tff(c_826,plain,
( ( data(split2(next(b))) = data(a) )
| ~ isrecord(a) ),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_38,c_804]) ).
tff(c_868,plain,
data(a) = '#skE_15',
inference(define,[status(thm),theory(equality)],[c_826]) ).
tff(c_867,plain,
data(split2(next(b))) = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_826]) ).
tff(c_873,plain,
( ( '#skE_15' = '#skE_14' )
| ~ isrecord(a) ),
inference(demodulation,[status(thm),theory(equality)],[c_868,c_867,c_826]) ).
tff(c_886,plain,
~ isrecord(a),
inference(splitLeft,[status(thm)],[c_873]) ).
tff(c_921,plain,
length(a) = 0,
inference(resolution,[status(thm)],[c_50,c_886]) ).
tff(c_35,plain,
( ( $product(2,length(split1(a))) = length(a) )
| ( $product(2,length(split1(a))) = $sum(length(a),1) ) ),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_43,plain,
( ( $product(2,length(split1(a))) = length(a) )
| ( $sum($uminus(1),$product(2,length(split1(a)))) = length(a) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_578,plain,
length(a) = '#skE_11',
inference(define,[status(thm),theory(equality)],[c_43]) ).
tff(c_924,plain,
'#skE_11' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_921,c_578]) ).
tff(c_4,plain,
! [U_2: record] :
( $greatereq(length(U_2),1)
| ~ isrecord(U_2) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_79,plain,
! [U_19: record] :
( ~ $less(length(U_19),1)
| ~ isrecord(U_19) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).
tff(c_95,plain,
! [U_1: record] :
( ~ $less(length(U_1),1)
| ( length(U_1) = 0 ) ),
inference(resolution,[status(thm)],[c_50,c_79]) ).
tff(c_583,plain,
( ~ $less('#skE_11',1)
| ( length(a) = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_578,c_95]) ).
tff(c_588,plain,
( ~ $less('#skE_11',1)
| ( '#skE_11' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578,c_583]) ).
tff(c_603,plain,
~ $less('#skE_11',1),
inference(splitLeft,[status(thm)],[c_588]) ).
tff(c_957,plain,
~ $less(0,1),
inference(demodulation,[status(thm),theory(equality)],[c_924,c_603]) ).
tff(c_966,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_957]) ).
tff(c_968,plain,
isrecord(a),
inference(splitRight,[status(thm)],[c_873]) ).
tff(c_73,plain,
! [U_18: record] :
( ~ isrecord(split2(U_18))
| isrecord(next(U_18)) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_336,plain,
! [U_26: record] :
( isrecord(next(U_26))
| ( length(split2(U_26)) = 0 ) ),
inference(resolution,[status(thm)],[c_50,c_73]) ).
tff(c_355,plain,
( isrecord(a)
| ( length(split2(next(b))) = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_38,c_336]) ).
tff(c_356,plain,
length(split2(next(b))) = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_355]) ).
tff(c_360,plain,
( isrecord(a)
| ( '#skE_9' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_356,c_355]) ).
tff(c_362,plain,
'#skE_9' = 0,
inference(splitLeft,[status(thm)],[c_360]) ).
tff(c_359,plain,
length(split2(next(b))) = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_355]) ).
tff(c_364,plain,
length(split2(next(b))) = 0,
inference(demodulation,[status(thm),theory(equality)],[c_362,c_359]) ).
tff(c_229,plain,
! [U_23: record] :
( isrecord(split2(U_23))
| ~ isrecord(next(U_23))
| ~ isrecord(U_23) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_49,plain,
! [U_2: record] :
( ~ $less(length(U_2),1)
| ~ isrecord(U_2) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).
tff(c_2360,plain,
! [U_50: record] :
( ~ $less(length(split2(U_50)),1)
| ~ isrecord(next(U_50))
| ~ isrecord(U_50) ),
inference(resolution,[status(thm)],[c_229,c_49]) ).
tff(c_2423,plain,
( ~ $less(length(split2(next(b))),1)
| ~ isrecord(a)
| ~ isrecord(next(b)) ),
inference(superposition,[status(thm),theory(equality)],[c_38,c_2360]) ).
tff(c_2468,plain,
~ $less(0,1),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_968,c_364,c_2423]) ).
tff(c_2471,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2468]) ).
tff(c_2474,plain,
'#skE_11' = 0,
inference(splitRight,[status(thm)],[c_588]) ).
tff(c_2478,plain,
length(a) = 0,
inference(demodulation,[status(thm),theory(equality)],[c_2474,c_578]) ).
tff(c_97,plain,
~ $less(length(next(b)),1),
inference(resolution,[status(thm)],[c_40,c_79]) ).
tff(c_124,plain,
length(next(b)) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_97]) ).
tff(c_7,plain,
! [U_3: record] :
( ( $sum(length(next(U_3)),1) = length(U_3) )
| ~ isrecord(U_3) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_2525,plain,
! [U_51: record] :
( ( length(next(U_51)) = $sum($uminus(1),length(U_51)) )
| ~ isrecord(U_51) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_2558,plain,
length(next(next(b))) = $sum($uminus(1),length(next(b))),
inference(resolution,[status(thm)],[c_40,c_2525]) ).
tff(c_2583,plain,
$sum($uminus(1),'#skE_3') = 0,
inference(demodulation,[status(thm),theory(equality)],[c_2478,c_38,c_124,c_2558]) ).
tff(c_2585,plain,
'#skE_3' = 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2583]) ).
tff(c_45,plain,
$product(2,length(split1(b))) != length(b),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_105,plain,
length(b) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_45]) ).
tff(c_42,plain,
isrecord(b),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_2561,plain,
length(next(b)) = $sum($uminus(1),length(b)),
inference(resolution,[status(thm)],[c_42,c_2525]) ).
tff(c_2588,plain,
'#skE_3' = $sum($uminus(1),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_105,c_124,c_2561]) ).
tff(c_2607,plain,
$sum($uminus(1),'#skE_2') = 1,
inference(demodulation,[status(thm),theory(equality)],[c_2585,c_2588]) ).
tff(c_2609,plain,
'#skE_2' = 2,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2607]) ).
tff(c_101,plain,
length(b) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_45]) ).
tff(c_100,plain,
length(split1(b)) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_45]) ).
tff(c_106,plain,
'#skE_2' != $product(2,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_101,c_100,c_45]) ).
tff(c_2616,plain,
$product(2,'#skE_1') != 2,
inference(demodulation,[status(thm),theory(equality)],[c_2609,c_106]) ).
tff(c_2622,plain,
'#skE_1' != 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2616]) ).
tff(c_104,plain,
length(split1(b)) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_45]) ).
tff(c_574,plain,
length(a) = '#skE_11',
inference(define,[status(thm),theory(equality)],[c_43]) ).
tff(c_573,plain,
length(split1(a)) = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_43]) ).
tff(c_579,plain,
( ( '#skE_11' = $product(2,'#skE_10') )
| ( '#skE_11' = $sum($uminus(1),$product(2,'#skE_10')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_574,c_573,c_574,c_573,c_43]) ).
tff(c_2494,plain,
( ( $product(2,'#skE_10') = 0 )
| ( $sum($uminus(1),$product(2,'#skE_10')) = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2474,c_2474,c_579]) ).
tff(c_2496,plain,
( ( '#skE_10' = 0 )
| ( $product(2,'#skE_10') = 1 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2494]) ).
tff(c_2498,plain,
$product(2,'#skE_10') = 1,
inference(splitLeft,[status(thm)],[c_2496]) ).
tff(c_2499,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2498]) ).
tff(c_2502,plain,
'#skE_10' = 0,
inference(splitRight,[status(thm)],[c_2496]) ).
tff(c_577,plain,
length(split1(a)) = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_43]) ).
tff(c_2506,plain,
length(split1(a)) = 0,
inference(demodulation,[status(thm),theory(equality)],[c_2502,c_577]) ).
tff(c_3099,plain,
! [U_57: record] :
( ( split1(next(next(U_57))) = next(split1(U_57)) )
| ~ isrecord(next(U_57))
| ~ isrecord(U_57) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_3132,plain,
( ( split1(next(next(b))) = next(split1(b)) )
| ~ isrecord(b) ),
inference(resolution,[status(thm)],[c_40,c_3099]) ).
tff(c_3155,plain,
next(split1(b)) = split1(a),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_38,c_3132]) ).
tff(c_12,plain,
! [U_5: record] :
( isrecord(split1(U_5))
| ~ isrecord(U_5) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_78,plain,
! [U_18: record] :
( isrecord(next(U_18))
| ( length(split2(U_18)) = 0 ) ),
inference(resolution,[status(thm)],[c_50,c_73]) ).
tff(c_3180,plain,
( isrecord(split1(a))
| ( length(split2(split1(b))) = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_3155,c_78]) ).
tff(c_3244,plain,
length(split2(split1(b))) = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_3180]) ).
tff(c_3248,plain,
( isrecord(split1(a))
| ( '#skE_18' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3244,c_3180]) ).
tff(c_3261,plain,
'#skE_18' = 0,
inference(splitLeft,[status(thm)],[c_3248]) ).
tff(c_3247,plain,
length(split2(split1(b))) = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_3180]) ).
tff(c_3264,plain,
length(split2(split1(b))) = 0,
inference(demodulation,[status(thm),theory(equality)],[c_3261,c_3247]) ).
tff(c_4160,plain,
! [U_66: record] :
( ~ $less(length(split2(U_66)),1)
| ~ isrecord(next(U_66))
| ~ isrecord(U_66) ),
inference(resolution,[status(thm)],[c_229,c_49]) ).
tff(c_4181,plain,
( ~ $less(length(split2(split1(b))),1)
| ~ isrecord(split1(a))
| ~ isrecord(split1(b)) ),
inference(superposition,[status(thm),theory(equality)],[c_3155,c_4160]) ).
tff(c_4227,plain,
( ~ $less(0,1)
| ~ isrecord(split1(a))
| ~ isrecord(split1(b)) ),
inference(demodulation,[status(thm),theory(equality)],[c_3264,c_4181]) ).
tff(c_4229,plain,
( ~ isrecord(split1(a))
| ~ isrecord(split1(b)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4227]) ).
tff(c_4284,plain,
~ isrecord(split1(b)),
inference(splitLeft,[status(thm)],[c_4229]) ).
tff(c_4314,plain,
~ isrecord(b),
inference(resolution,[status(thm)],[c_12,c_4284]) ).
tff(c_4339,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_42,c_4314]) ).
tff(c_4341,plain,
isrecord(split1(b)),
inference(splitRight,[status(thm)],[c_4229]) ).
tff(c_48,plain,
! [U_3: record] :
( ( length(next(U_3)) = $sum($uminus(1),length(U_3)) )
| ~ isrecord(U_3) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_4350,plain,
length(next(split1(b))) = $sum($uminus(1),length(split1(b))),
inference(resolution,[status(thm)],[c_4341,c_48]) ).
tff(c_4369,plain,
$sum($uminus(1),'#skE_1') = 0,
inference(demodulation,[status(thm),theory(equality)],[c_104,c_2506,c_3155,c_4350]) ).
tff(c_4371,plain,
'#skE_1' = 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4369]) ).
tff(c_4380,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2622,c_4371]) ).
tff(c_4381,plain,
isrecord(a),
inference(splitRight,[status(thm)],[c_360]) ).
tff(c_4398,plain,
~ $less(length(a),1),
inference(resolution,[status(thm)],[c_4381,c_49]) ).
tff(c_4413,plain,
length(a) = '#skE_11',
inference(define,[status(thm),theory(equality)],[c_4398]) ).
tff(c_4426,plain,
( ( $product(2,length(split1(a))) = '#skE_11' )
| ( $sum($uminus(1),$product(2,length(split1(a)))) = '#skE_11' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4413,c_4413,c_43]) ).
tff(c_4428,plain,
( ( $product(2,length(split1(a))) = '#skE_11' )
| ( $product(2,length(split1(a))) = $sum(1,'#skE_11') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4426]) ).
tff(c_4429,plain,
length(split1(a)) = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_4428]) ).
tff(c_4431,plain,
( ( '#skE_11' = $product(2,'#skE_10') )
| ( $sum(1,'#skE_11') = $product(2,'#skE_10') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4429,c_4429,c_4428]) ).
tff(c_4434,plain,
( ( '#skE_11' = $product(2,'#skE_10') )
| ( '#skE_11' = $sum($uminus(1),$product(2,'#skE_10')) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4431]) ).
tff(c_4503,plain,
'#skE_11' = $sum($uminus(1),$product(2,'#skE_10')),
inference(splitLeft,[status(thm)],[c_4434]) ).
tff(c_4738,plain,
length(a) = $sum($uminus(1),$product(2,'#skE_10')),
inference(demodulation,[status(thm),theory(equality)],[c_4503,c_4413]) ).
tff(c_5308,plain,
! [U_87: record] :
( ( length(next(U_87)) = $sum($uminus(1),length(U_87)) )
| ~ isrecord(U_87) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_5374,plain,
length(next(next(b))) = $sum($uminus(1),length(next(b))),
inference(resolution,[status(thm)],[c_40,c_5308]) ).
tff(c_5423,plain,
$sum($uminus(1),'#skE_3') = $sum($uminus(1),$product(2,'#skE_10')),
inference(demodulation,[status(thm),theory(equality)],[c_4738,c_38,c_124,c_5374]) ).
tff(c_5425,plain,
'#skE_3' = $product(2,'#skE_10'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5423]) ).
tff(c_5377,plain,
length(next(b)) = $sum($uminus(1),length(b)),
inference(resolution,[status(thm)],[c_42,c_5308]) ).
tff(c_5428,plain,
'#skE_3' = $sum($uminus(1),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_105,c_124,c_5377]) ).
tff(c_5436,plain,
$sum($uminus(1),'#skE_2') = $product(2,'#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_5425,c_5428]) ).
tff(c_5439,plain,
'#skE_2' = $sum(1,$product(2,'#skE_10')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5436]) ).
tff(c_32,plain,
$product(2,length(split1(b))) != $sum(length(b),1),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_44,plain,
$product(2,length(split1(b))) != $sum(1,length(b)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_32]) ).
tff(c_174,plain,
$sum(1,'#skE_2') != $product(2,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_104,c_105,c_44]) ).
tff(c_176,plain,
'#skE_2' != $sum($uminus(1),$product(2,'#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_174]) ).
tff(c_5458,plain,
$sum(1,$product(2,'#skE_10')) != $sum($uminus(1),$product(2,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_5439,c_176]) ).
tff(c_5467,plain,
'#skE_10' != $sum($uminus(1),'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5458]) ).
tff(c_4432,plain,
length(split1(a)) = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_4428]) ).
tff(c_6148,plain,
! [U_92: record] :
( ( split1(next(next(U_92))) = next(split1(U_92)) )
| ~ isrecord(next(U_92))
| ~ isrecord(U_92) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_6214,plain,
( ( split1(next(next(b))) = next(split1(b)) )
| ~ isrecord(b) ),
inference(resolution,[status(thm)],[c_40,c_6148]) ).
tff(c_6257,plain,
next(split1(b)) = split1(a),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_38,c_6214]) ).
tff(c_6290,plain,
( isrecord(split1(a))
| ( length(split2(split1(b))) = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_6257,c_78]) ).
tff(c_6326,plain,
length(split2(split1(b))) = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_6290]) ).
tff(c_6330,plain,
( isrecord(split1(a))
| ( '#skE_18' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6326,c_6290]) ).
tff(c_6364,plain,
'#skE_18' = 0,
inference(splitLeft,[status(thm)],[c_6330]) ).
tff(c_6329,plain,
length(split2(split1(b))) = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_6290]) ).
tff(c_6367,plain,
length(split2(split1(b))) = 0,
inference(demodulation,[status(thm),theory(equality)],[c_6364,c_6329]) ).
tff(c_6510,plain,
! [U_93: record] :
( ~ $less(length(split2(U_93)),1)
| ~ isrecord(next(U_93))
| ~ isrecord(U_93) ),
inference(resolution,[status(thm)],[c_229,c_49]) ).
tff(c_6516,plain,
( ~ $less(length(split2(split1(b))),1)
| ~ isrecord(split1(a))
| ~ isrecord(split1(b)) ),
inference(superposition,[status(thm),theory(equality)],[c_6257,c_6510]) ).
tff(c_6584,plain,
( ~ $less(0,1)
| ~ isrecord(split1(a))
| ~ isrecord(split1(b)) ),
inference(demodulation,[status(thm),theory(equality)],[c_6367,c_6516]) ).
tff(c_6586,plain,
( ~ isrecord(split1(a))
| ~ isrecord(split1(b)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6584]) ).
tff(c_6670,plain,
~ isrecord(split1(b)),
inference(splitLeft,[status(thm)],[c_6586]) ).
tff(c_6715,plain,
~ isrecord(b),
inference(resolution,[status(thm)],[c_12,c_6670]) ).
tff(c_6750,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_42,c_6715]) ).
tff(c_6752,plain,
isrecord(split1(b)),
inference(splitRight,[status(thm)],[c_6586]) ).
tff(c_6758,plain,
length(next(split1(b))) = $sum($uminus(1),length(split1(b))),
inference(resolution,[status(thm)],[c_6752,c_48]) ).
tff(c_6778,plain,
'#skE_10' = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_104,c_4432,c_6257,c_6758]) ).
tff(c_6780,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5467,c_6778]) ).
tff(c_6783,plain,
'#skE_11' = $product(2,'#skE_10'),
inference(splitRight,[status(thm)],[c_4434]) ).
tff(c_6790,plain,
length(a) = $product(2,'#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_6783,c_4413]) ).
tff(c_7219,plain,
! [U_105: record] :
( ( length(next(U_105)) = $sum($uminus(1),length(U_105)) )
| ~ isrecord(U_105) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_7261,plain,
length(next(next(b))) = $sum($uminus(1),length(next(b))),
inference(resolution,[status(thm)],[c_40,c_7219]) ).
tff(c_7293,plain,
$sum($uminus(1),'#skE_3') = $product(2,'#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_6790,c_38,c_124,c_7261]) ).
tff(c_7295,plain,
'#skE_3' = $sum(1,$product(2,'#skE_10')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7293]) ).
tff(c_7264,plain,
length(next(b)) = $sum($uminus(1),length(b)),
inference(resolution,[status(thm)],[c_42,c_7219]) ).
tff(c_7298,plain,
'#skE_3' = $sum($uminus(1),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_105,c_124,c_7264]) ).
tff(c_7360,plain,
$sum($uminus(1),'#skE_2') = $sum(1,$product(2,'#skE_10')),
inference(demodulation,[status(thm),theory(equality)],[c_7295,c_7298]) ).
tff(c_7363,plain,
'#skE_2' = $sum(2,$product(2,'#skE_10')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7360]) ).
tff(c_7461,plain,
$sum(2,$product(2,'#skE_10')) != $product(2,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_7363,c_106]) ).
tff(c_7468,plain,
'#skE_10' != $sum($uminus(1),'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7461]) ).
tff(c_7863,plain,
! [U_110: record] :
( ( split1(next(next(U_110))) = next(split1(U_110)) )
| ~ isrecord(next(U_110))
| ~ isrecord(U_110) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_7911,plain,
( ( split1(next(next(b))) = next(split1(b)) )
| ~ isrecord(b) ),
inference(resolution,[status(thm)],[c_40,c_7863]) ).
tff(c_7942,plain,
next(split1(b)) = split1(a),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_38,c_7911]) ).
tff(c_28,plain,
! [U_13: record] :
( ( split2(next(next(U_13))) = next(split2(U_13)) )
| ~ isrecord(next(U_13))
| ~ isrecord(U_13) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_7949,plain,
( ( split2(next(next(split1(b)))) = next(split2(split1(b))) )
| ~ isrecord(split1(a))
| ~ isrecord(split1(b)) ),
inference(superposition,[status(thm),theory(equality)],[c_7942,c_28]) ).
tff(c_7968,plain,
( ( next(split2(split1(b))) = split2(next(split1(a))) )
| ~ isrecord(split1(a))
| ~ isrecord(split1(b)) ),
inference(demodulation,[status(thm),theory(equality)],[c_7942,c_7949]) ).
tff(c_10172,plain,
~ isrecord(split1(b)),
inference(splitLeft,[status(thm)],[c_7968]) ).
tff(c_10217,plain,
~ isrecord(b),
inference(resolution,[status(thm)],[c_12,c_10172]) ).
tff(c_10252,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_42,c_10217]) ).
tff(c_10254,plain,
isrecord(split1(b)),
inference(splitRight,[status(thm)],[c_7968]) ).
tff(c_10260,plain,
length(next(split1(b))) = $sum($uminus(1),length(split1(b))),
inference(resolution,[status(thm)],[c_10254,c_48]) ).
tff(c_10280,plain,
'#skE_10' = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_104,c_4432,c_7942,c_10260]) ).
tff(c_10282,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7468,c_10280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : DAT053_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.14 % 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
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 13:12:22 EDT 2023
% 0.15/0.36 % CPUTime :
% 9.70/3.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.70/3.32
% 9.70/3.32 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.19/3.42
% 10.19/3.42 Inference rules
% 10.19/3.42 ----------------------
% 10.19/3.42 #Ref : 0
% 10.19/3.42 #Sup : 2005
% 10.19/3.42 #Fact : 0
% 10.19/3.42 #Define : 80
% 10.19/3.42 #Split : 36
% 10.19/3.42 #Chain : 0
% 10.19/3.42 #Close : 1
% 10.19/3.42
% 10.19/3.42 Ordering : LPO
% 10.19/3.42
% 10.19/3.42 Simplification rules
% 10.19/3.42 ----------------------
% 10.19/3.42 #Subsume : 107
% 10.19/3.42 #Demod : 992
% 10.19/3.42 #Tautology : 692
% 10.19/3.42 #SimpNegUnit : 7
% 10.19/3.42 #BackRed : 71
% 10.19/3.42
% 10.19/3.42 #Partial instantiations: 0
% 10.19/3.42 #Strategies tried : 1
% 10.19/3.42
% 10.19/3.42 Timing (in seconds)
% 10.19/3.42 ----------------------
% 10.19/3.42 Preprocessing : 0.54
% 10.19/3.42 Parsing : 0.29
% 10.19/3.42 CNF conversion : 0.03
% 10.19/3.42 Main loop : 1.71
% 10.19/3.42 Inferencing : 0.45
% 10.19/3.42 Reduction : 0.45
% 10.19/3.42 Demodulation : 0.31
% 10.19/3.42 BG Simplification : 0.18
% 10.19/3.42 Subsumption : 0.36
% 10.19/3.42 Abstraction : 0.05
% 10.19/3.42 MUC search : 0.01
% 10.19/3.42 Cooper : 0.11
% 10.19/3.42 Total : 2.39
% 10.19/3.42 Index Insertion : 0.00
% 10.19/3.42 Index Deletion : 0.00
% 10.19/3.42 Index Matching : 0.00
% 10.19/3.42 BG Taut test : 0.00
%------------------------------------------------------------------------------