TSTP Solution File: SWW626_2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW626_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : n019.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 11:07:50 EDT 2023
% Result : Theorem 124.08s 86.88s
% Output : CNFRefutation 124.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 121
% Syntax : Number of formulae : 230 ( 79 unt; 106 typ; 0 def)
% Number of atoms : 212 ( 91 equ)
% Maximal formula atoms : 29 ( 1 avg)
% Number of connectives : 143 ( 55 ~; 46 |; 15 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 369 ( 63 atm; 101 fun; 156 num; 49 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 80 ( 39 >; 41 *; 0 +; 0 <<)
% Number of predicates : 9 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 103 ( 95 usr; 65 con; 0-5 aty)
% Number of variables : 100 (; 100 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
%$ permut > mem > sort > le > sorted > match_list > match_bool > rev_append > prefix > num_occ > infix_plpl > cons > reverse > mod > length > div > cons_proj_2 > cons_proj_1 > #nlpp > witness > tb2t1 > tb2t > t2tb1 > t2tb > nil > list > abs > tuple02 > tuple01 > true > real > qtmark > int > false > elt1 > bool1 > #skF_3 > #skF_19 > #skF_13 > #skF_5 > #skF_6 > #skF_16 > #skF_4 > #skF_12 > #skF_8 > #skF_10 > #skF_18 > #skF_15 > #skF_17 > #skF_11 > #skF_1 > #skF_9 > #skF_7 > #skF_2
%Foreground sorts:
tff(elt,type,
elt: $tType ).
tff(bool,type,
bool: $tType ).
tff(tuple0,type,
tuple0: $tType ).
tff(list_elt,type,
list_elt: $tType ).
tff(ty,type,
ty: $tType ).
tff(uni,type,
uni: $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('#skF_14',type,
'#skF_14': $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(list,type,
list: ty > ty ).
tff('#skF_3',type,
'#skF_3': ( ty * uni * uni ) > uni ).
tff(prefix,type,
prefix: ( ty * $int * uni ) > uni ).
tff(elt1,type,
elt1: ty ).
tff('#skF_19',type,
'#skF_19': list_elt ).
tff(cons_proj_1,type,
cons_proj_1: ( ty * uni ) > uni ).
tff(cons,type,
cons: ( ty * uni * uni ) > uni ).
tff(t2tb,type,
t2tb: list_elt > uni ).
tff(nil,type,
nil: ty > uni ).
tff('#skF_13',type,
'#skF_13': ( list_elt * list_elt ) > elt ).
tff(permut,type,
permut: ( ty * uni * uni ) > $o ).
tff('#skF_5',type,
'#skF_5': list_elt > elt ).
tff(tuple02,type,
tuple02: tuple0 ).
tff(div,type,
div: ( $int * $int ) > $int ).
tff(tuple01,type,
tuple01: ty ).
tff(int,type,
int: ty ).
tff('#skF_6',type,
'#skF_6': list_elt > elt ).
tff(abs,type,
abs: $int > $int ).
tff(rev_append,type,
rev_append: ( ty * uni * uni ) > uni ).
tff(real,type,
real: ty ).
tff(sorted,type,
sorted: list_elt > $o ).
tff(match_bool,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(false,type,
false: bool ).
tff('#skF_16',type,
'#skF_16': list_elt ).
tff('#skF_4',type,
'#skF_4': list_elt > elt ).
tff('#skF_12',type,
'#skF_12': ( list_elt * list_elt ) > elt ).
tff('#skF_8',type,
'#skF_8': ( elt * list_elt ) > elt ).
tff(mod,type,
mod: ( $int * $int ) > $int ).
tff(tb2t,type,
tb2t: uni > list_elt ).
tff(reverse,type,
reverse: ( ty * uni ) > uni ).
tff('#skF_10',type,
'#skF_10': ( list_elt * list_elt ) > elt ).
tff(length,type,
length: ( ty * uni ) > $int ).
tff(le,type,
le: ( elt * elt ) > $o ).
tff(qtmark,type,
qtmark: ty ).
tff(t2tb1,type,
t2tb1: elt > uni ).
tff(num_occ,type,
num_occ: ( ty * uni * uni ) > $int ).
tff(bool1,type,
bool1: ty ).
tff('#skF_18',type,
'#skF_18': list_elt ).
tff('#skF_15',type,
'#skF_15': list_elt ).
tff('#skF_17',type,
'#skF_17': list_elt ).
tff('#skF_11',type,
'#skF_11': ( list_elt * elt ) > elt ).
tff('#skF_1',type,
'#skF_1': ( ty * uni * uni ) > uni ).
tff('#skF_9',type,
'#skF_9': ( list_elt * list_elt ) > elt ).
tff('#skF_7',type,
'#skF_7': list_elt > list_elt ).
tff(match_list,type,
match_list: ( ty * ty * uni * uni * uni ) > uni ).
tff(sort,type,
sort: ( ty * uni ) > $o ).
tff(true,type,
true: bool ).
tff(cons_proj_2,type,
cons_proj_2: ( ty * uni ) > uni ).
tff(mem,type,
mem: ( ty * uni * uni ) > $o ).
tff(tb2t1,type,
tb2t1: uni > elt ).
tff(witness,type,
witness: ty > uni ).
tff(infix_plpl,type,
infix_plpl: ( ty * uni * uni ) > uni ).
tff('#skF_2',type,
'#skF_2': ( ty * uni * uni ) > uni ).
tff(f_540,negated_conjecture,
~ ! [Na: $int,L: list_elt] :
( ( $lesseq(2,Na)
& $lesseq(Na,length(elt1,t2tb(L))) )
=> ( ( Na != 2 )
=> ( ( Na != 3 )
=> ( ( 2 != 0 )
=> ( ( $lesseq(0,div(Na,2))
& $lesseq(div(Na,2),length(elt1,t2tb(L))) )
=> ! [L2: list_elt] :
( ( L = tb2t(infix_plpl(elt1,prefix(elt1,div(Na,2),t2tb(L)),t2tb(L2))) )
=> ( ( tb2t(infix_plpl(elt1,prefix(elt1,div(Na,2),t2tb(L)),prefix(elt1,$difference(Na,div(Na,2)),t2tb(L2)))) = tb2t(prefix(elt1,Na,t2tb(L))) )
=> ( ( $lesseq(2,div(Na,2))
& $lesseq(div(Na,2),length(elt1,t2tb(L))) )
=> ! [S1: list_elt] :
( ( sorted(S1)
& permut(elt1,t2tb(S1),prefix(elt1,div(Na,2),t2tb(L))) )
=> ( ( $lesseq(2,$difference(Na,div(Na,2)))
& $lesseq($difference(Na,div(Na,2)),length(elt1,t2tb(L2))) )
=> ! [S2: list_elt] :
( ( sorted(S2)
& permut(elt1,t2tb(S2),prefix(elt1,$difference(Na,div(Na,2)),t2tb(L2))) )
=> ( ( sorted(tb2t(reverse(elt1,nil(elt1))))
& sorted(S1)
& sorted(S2)
& ! [X: elt,Y: elt] :
( mem(elt1,t2tb1(X),nil(elt1))
=> ( mem(elt1,t2tb1(Y),t2tb(S1))
=> le(X,Y) ) )
& ! [X: elt,Y: elt] :
( mem(elt1,t2tb1(X),nil(elt1))
=> ( mem(elt1,t2tb1(Y),t2tb(S2))
=> le(X,Y) ) ) )
=> ! [Result: list_elt] :
( ( sorted(tb2t(reverse(elt1,t2tb(Result))))
& permut(elt1,t2tb(Result),infix_plpl(elt1,infix_plpl(elt1,nil(elt1),t2tb(S1)),t2tb(S2))) )
=> permut(elt1,t2tb(Result),prefix(elt1,Na,t2tb(L))) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_rev_sort) ).
tff(f_442,axiom,
! [Xa: $int] : ( div(Xa,1) = Xa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_1) ).
tff(f_394,axiom,
! [Xa: $int,Ya: $int] :
( ( Ya != 0 )
=> ( Xa = $sum($product(Ya,div(Xa,Ya)),mod(Xa,Ya)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_mod) ).
tff(f_444,axiom,
! [Xa: $int] : ( mod(Xa,1) = 0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_1) ).
tff(f_6283,axiom,
! [M: $int,N: $int] : ( $product($sum(1,M),N) = $sum(N,$product(M,N)) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',mult_def_2) ).
tff(f_381,axiom,
! [Xa: $int] :
( ( $lesseq(0,Xa)
=> ( abs(Xa) = Xa ) )
& ( ~ $lesseq(0,Xa)
=> ( abs(Xa) = $uminus(Xa) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abs_def) ).
tff(f_6286,axiom,
! [A: $int,B: $int] : ( $product(A,B) = $product(B,A) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',mult_comm) ).
tff(f_409,axiom,
! [Xa: $int,Ya: $int] :
( ( Ya != 0 )
=> ( $less($uminus(abs(Ya)),mod(Xa,Ya))
& $less(mod(Xa,Ya),abs(Ya)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_bound) ).
tff(f_440,axiom,
! [Xa: $int,Ya: $int] :
( ( Ya != 0 )
=> $lesseq(abs($product(div(Xa,Ya),Ya)),abs(Xa)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rounds_toward_zero) ).
tff(f_6311,axiom,
! [A: $int,B: $int] :
( ( $less(0,A)
& $less(0,B) )
=> $less(0,$product(A,B)) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',mult_nonneg_nonneg) ).
tff(f_251,axiom,
! [J: uni] : ( t2tb(tb2t(J)) = J ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR) ).
tff(f_103,axiom,
! [A: ty,L2: uni] :
( ( infix_plpl(A,nil(A),L2) = L2 )
& ! [X: uni,X1: uni] : ( infix_plpl(A,cons(A,X,X1),L2) = cons(A,X,infix_plpl(A,X1,L2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infix_plpl_def) ).
tff(f_105,axiom,
! [A: ty,L1: uni,L2: uni,L3: uni] : ( infix_plpl(A,L1,infix_plpl(A,L2,L3)) = infix_plpl(A,infix_plpl(A,L1,L2),L3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',append_assoc) ).
tff(f_221,axiom,
! [A: ty,L1: uni,L2: uni,K1: uni,K2: uni] :
( permut(A,L1,K1)
=> ( permut(A,L2,K2)
=> permut(A,infix_plpl(A,L1,L2),infix_plpl(A,K1,K2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_append) ).
tff(f_205,axiom,
! [A: ty,L1: uni,L2: uni,L3: uni] :
( permut(A,L1,L2)
=> ( permut(A,L2,L3)
=> permut(A,L1,L3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_trans) ).
tff(c_387,plain,
permut(elt1,t2tb('#skF_17'),prefix(elt1,div('#skF_14',2),t2tb('#skF_15'))),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_645,plain,
div('#skF_14',2) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_387]) ).
tff(c_473,plain,
permut(elt1,t2tb('#skF_17'),prefix(elt1,div('#skF_14',2),t2tb('#skF_15'))),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_1407,plain,
permut(elt1,t2tb('#skF_17'),prefix(elt1,'#skE_1',t2tb('#skF_15'))),
inference(demodulation,[status(thm),theory(equality)],[c_645,c_473]) ).
tff(c_409,plain,
! [X_282a: $int] : ( div(X_282a,1) = X_282a ),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_244,plain,
! [Y_267a: $int,X_266a: $int] :
( ( $sum($product(Y_267a,div(X_266a,Y_267a)),mod(X_266a,Y_267a)) = X_266a )
| ( Y_267a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_394]) ).
tff(c_5987,plain,
! [X_1991a: $int,Y_1992a: $int] :
( ( mod(X_1991a,Y_1992a) = $sum(X_1991a,$uminus($product(Y_1992a,div(X_1991a,Y_1992a)))) )
| ( Y_1992a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_244]) ).
tff(c_408,plain,
! [X_283a: $int] : ( mod(X_283a,1) = 0 ),
inference(cnfTransformation,[status(thm)],[f_444]) ).
tff(c_6015,plain,
! [X_1991a: $int] :
( ( $sum(X_1991a,$uminus($product(1,div(X_1991a,1)))) = 0 )
| ( 1 = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_5987,c_408]) ).
tff(c_6041,plain,
! [X_1991a: $int] :
( ( $sum(X_1991a,$uminus($product(1,X_1991a))) = 0 )
| ( 1 = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_409,c_6015]) ).
tff(c_6056,plain,
! [X_1993a: $int] : ( $product(1,X_1993a) = X_1993a ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6041]) ).
tff(c_465,plain,
! [X_452: $int,N_387: $int,M_386: $int] :
( ( $product(X_452,N_387) = $sum(N_387,$product(M_386,N_387)) )
| ( X_452 != $sum(1,M_386) ) ),
inference(cnfTransformation,[status(thm)],[f_6283]) ).
tff(c_6141,plain,
! [X_1993a: $int] : ( $product($sum(1,1),X_1993a) = $sum(X_1993a,X_1993a) ),
inference(superposition,[status(thm),theory(equality)],[c_6056,c_465]) ).
tff(c_6366,plain,
! [X_2009a: $int] : ( $product(2,X_2009a) = $product(2,X_2009a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6141]) ).
tff(c_231,plain,
! [X_262a: $int] :
( ( abs(X_262a) = X_262a )
| ~ $lesseq(0,X_262a) ),
inference(cnfTransformation,[status(thm)],[f_381]) ).
tff(c_426,plain,
! [X_262a: $int] :
( ( abs(X_262a) = X_262a )
| $less(X_262a,0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_231]) ).
tff(c_463,plain,
! [B_390: $int,A_391: $int] : ( $product(B_390,A_391) = $product(A_391,B_390) ),
inference(cnfTransformation,[status(thm)],[f_6286]) ).
tff(c_652,plain,
div('#skF_14',2) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_387]) ).
tff(c_874,plain,
! [X_683a: $int,Y_684a: $int] :
( $less(mod(X_683a,Y_684a),abs(Y_684a))
| ( Y_684a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_409]) ).
tff(c_884,plain,
( $less(0,abs(1))
| ( 1 = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_408,c_874]) ).
tff(c_890,plain,
$less(0,abs(1)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_884]) ).
tff(c_894,plain,
abs(1) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_890]) ).
tff(c_941,plain,
( ( '#skE_2' = 1 )
| $less(1,0) ),
inference(superposition,[status(thm),theory(equality)],[c_894,c_426]) ).
tff(c_961,plain,
'#skE_2' = 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_941]) ).
tff(c_971,plain,
abs(1) = 1,
inference(demodulation,[status(thm),theory(equality)],[c_961,c_894]) ).
tff(c_261,plain,
! [X_280a: $int,Y_281a: $int] :
( $lesseq(abs($product(div(X_280a,Y_281a),Y_281a)),abs(X_280a))
| ( Y_281a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_440]) ).
tff(c_410,plain,
! [X_280a: $int,Y_281a: $int] :
( ~ $less(abs(X_280a),abs($product(div(X_280a,Y_281a),Y_281a)))
| ( Y_281a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_261]) ).
tff(c_2583,plain,
! [X_1307a: $int,Y_1308a: $int] :
( ~ $less(abs(X_1307a),abs($product(Y_1308a,div(X_1307a,Y_1308a))))
| ( Y_1308a = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_463,c_410]) ).
tff(c_2772,plain,
! [Y_1320a: $int] :
( ~ $less(1,abs($product(Y_1320a,div(1,Y_1320a))))
| ( Y_1320a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_971,c_2583]) ).
tff(c_2801,plain,
( ~ $less(1,abs($product(2,'#skE_1')))
| ( 2 = 0 )
| ( '#skF_14' != 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_652,c_2772]) ).
tff(c_2804,plain,
( ~ $less(1,abs($product(2,'#skE_1')))
| ( '#skF_14' != 1 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2801]) ).
tff(c_2831,plain,
$product(2,'#skE_1') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_2804]) ).
tff(c_2997,plain,
$product('#skE_1',2) = '#skE_7',
inference(superposition,[status(thm),theory(equality)],[c_463,c_2831]) ).
tff(c_2603,plain,
! [X_282a: $int] :
( ~ $less(abs(X_282a),abs($product(1,X_282a)))
| ( 1 = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_409,c_2583]) ).
tff(c_2637,plain,
! [X_1313a: $int] : ~ $less(abs(X_1313a),abs($product(1,X_1313a))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2603]) ).
tff(c_2673,plain,
! [X_262a: $int] :
( ~ $less(X_262a,abs($product(1,X_262a)))
| $less(X_262a,0) ),
inference(superposition,[status(thm),theory(equality)],[c_426,c_2637]) ).
tff(c_3085,plain,
( ~ $less(2,abs('#skE_7'))
| $less(2,0)
| ( '#skE_1' != 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2997,c_2673]) ).
tff(c_3088,plain,
( ~ $less(2,abs('#skE_7'))
| ( '#skE_1' != 1 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3085]) ).
tff(c_5033,plain,
abs('#skE_7') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_3088]) ).
tff(c_5130,plain,
( ( '#skE_7' = '#skE_10' )
| $less('#skE_7',0) ),
inference(superposition,[status(thm),theory(equality)],[c_426,c_5033]) ).
tff(c_5135,plain,
$less('#skE_7',0),
inference(splitLeft,[status(thm)],[c_5130]) ).
tff(c_454,plain,
! [A_410: $int,B_411: $int] :
( $less(0,$product(A_410,B_411))
| ~ $less(0,A_410)
| ~ $less(0,B_411) ),
inference(cnfTransformation,[status(thm)],[f_6311]) ).
tff(c_2940,plain,
( $less(0,'#skE_7')
| ~ $less(0,2)
| ~ $less(0,'#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_2831,c_454]) ).
tff(c_2942,plain,
( $less(0,'#skE_7')
| ~ $less(0,'#skE_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2940]) ).
tff(c_2990,plain,
~ $less(0,'#skE_1'),
inference(splitLeft,[status(thm)],[c_2942]) ).
tff(c_713,plain,
div('#skF_14',2) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_387]) ).
tff(c_309,plain,
$lesseq(2,div('#skF_14',2)),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_379,plain,
~ $less(div('#skF_14',2),2),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_309]) ).
tff(c_822,plain,
~ $less('#skE_1',2),
inference(demodulation,[status(thm),theory(equality)],[c_713,c_379]) ).
tff(c_2991,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2990,c_822]) ).
tff(c_2994,plain,
$less(0,'#skE_7'),
inference(splitRight,[status(thm)],[c_2942]) ).
tff(c_5200,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5135,c_2994]) ).
tff(c_5203,plain,
'#skE_7' = '#skE_10',
inference(splitRight,[status(thm)],[c_5130]) ).
tff(c_2825,plain,
$product(2,'#skE_1') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_2804]) ).
tff(c_5317,plain,
$product(2,'#skE_1') = '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_5203,c_2825]) ).
tff(c_6456,plain,
'#skE_10' = $product(2,'#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_6366,c_5317]) ).
tff(c_6723,plain,
'#skE_7' = $product(2,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_6456,c_5203]) ).
tff(c_2818,plain,
$product(2,'#skE_1') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_2804]) ).
tff(c_2817,plain,
( ~ $less(1,abs($product(2,'#skE_1')))
| ( '#skF_14' != 1 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2801]) ).
tff(c_2828,plain,
( ~ $less(1,abs('#skE_7'))
| ( '#skF_14' != 1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2818,c_2817]) ).
tff(c_12288,plain,
( ~ $less(1,abs($product(2,'#skE_1')))
| ( '#skF_14' != 1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6723,c_2828]) ).
tff(c_12301,plain,
abs($product(2,'#skE_1')) = '#skE_11',
inference(define,[status(thm),theory(equality)],[c_12288]) ).
tff(c_12380,plain,
( ( '#skE_11' = $product(2,'#skE_1') )
| $less($product(2,'#skE_1'),0) ),
inference(superposition,[status(thm),theory(equality)],[c_12301,c_426]) ).
tff(c_12382,plain,
( ( '#skE_11' = $product(2,'#skE_1') )
| $less('#skE_1',0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12380]) ).
tff(c_12395,plain,
$less('#skE_1',0),
inference(splitLeft,[status(thm)],[c_12382]) ).
tff(c_12410,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_12395,c_822]) ).
tff(c_12413,plain,
'#skE_11' = $product(2,'#skE_1'),
inference(splitRight,[status(thm)],[c_12382]) ).
tff(c_12296,plain,
abs($product(2,'#skE_1')) = '#skE_11',
inference(define,[status(thm),theory(equality)],[c_12288]) ).
tff(c_39158,plain,
abs($product(2,'#skE_1')) = $product(2,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_12413,c_12296]) ).
tff(c_6143,plain,
! [X_1993a: $int] : ( $product(2,X_1993a) = $product(2,X_1993a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6141]) ).
tff(c_2622,plain,
( ~ $less(abs('#skF_14'),abs($product(2,'#skE_1')))
| ( 2 = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_652,c_2583]) ).
tff(c_2625,plain,
~ $less(abs('#skF_14'),abs($product(2,'#skE_1'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2622]) ).
tff(c_61871,plain,
~ $less(abs('#skF_14'),$product(2,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_39158,c_6143,c_2625]) ).
tff(c_61883,plain,
abs('#skF_14') = '#skE_15',
inference(define,[status(thm),theory(equality)],[c_61871]) ).
tff(c_61973,plain,
( ( '#skF_14' = '#skE_15' )
| $less('#skF_14',0) ),
inference(superposition,[status(thm),theory(equality)],[c_61883,c_426]) ).
tff(c_61990,plain,
$less('#skF_14',0),
inference(splitLeft,[status(thm)],[c_61973]) ).
tff(c_328,plain,
$lesseq(2,'#skF_14'),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_353,plain,
~ $less('#skF_14',2),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_328]) ).
tff(c_61991,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_61990,c_353]) ).
tff(c_61994,plain,
'#skF_14' = '#skE_15',
inference(splitRight,[status(thm)],[c_61973]) ).
tff(c_399,plain,
permut(elt1,t2tb('#skF_18'),prefix(elt1,$sum('#skF_14',$uminus(div('#skF_14',2))),t2tb('#skF_16'))),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_1029,plain,
permut(elt1,t2tb('#skF_18'),prefix(elt1,$sum('#skF_14',$uminus('#skE_1')),t2tb('#skF_16'))),
inference(demodulation,[status(thm),theory(equality)],[c_713,c_399]) ).
tff(c_1032,plain,
permut(elt1,t2tb('#skF_18'),prefix(elt1,$sum($uminus('#skE_1'),'#skF_14'),t2tb('#skF_16'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1029]) ).
tff(c_62137,plain,
permut(elt1,t2tb('#skF_18'),prefix(elt1,$sum($uminus('#skE_1'),'#skE_15'),t2tb('#skF_16'))),
inference(demodulation,[status(thm),theory(equality)],[c_61994,c_1032]) ).
tff(c_62243,plain,
permut(elt1,t2tb('#skF_18'),prefix(elt1,$sum('#skE_15',$uminus('#skE_1')),t2tb('#skF_16'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_62137]) ).
tff(c_135275,plain,
permut(elt1,t2tb('#skF_18'),prefix(elt1,$sum($uminus('#skE_1'),'#skE_15'),t2tb('#skF_16'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_62243]) ).
tff(c_154,plain,
! [J_184: uni] : ( t2tb(tb2t(J_184)) = J_184 ),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_375,plain,
tb2t(infix_plpl(elt1,prefix(elt1,div('#skF_14',2),t2tb('#skF_15')),prefix(elt1,$sum('#skF_14',$uminus(div('#skF_14',2))),t2tb('#skF_16')))) = tb2t(prefix(elt1,'#skF_14',t2tb('#skF_15'))),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_1091,plain,
tb2t(infix_plpl(elt1,prefix(elt1,'#skE_1',t2tb('#skF_15')),prefix(elt1,$sum('#skF_14',$uminus('#skE_1')),t2tb('#skF_16')))) = tb2t(prefix(elt1,'#skF_14',t2tb('#skF_15'))),
inference(demodulation,[status(thm),theory(equality)],[c_713,c_713,c_375]) ).
tff(c_1096,plain,
tb2t(infix_plpl(elt1,prefix(elt1,'#skE_1',t2tb('#skF_15')),prefix(elt1,$sum($uminus('#skE_1'),'#skF_14'),t2tb('#skF_16')))) = tb2t(prefix(elt1,'#skF_14',t2tb('#skF_15'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1091]) ).
tff(c_1105,plain,
infix_plpl(elt1,prefix(elt1,'#skE_1',t2tb('#skF_15')),prefix(elt1,$sum($uminus('#skE_1'),'#skF_14'),t2tb('#skF_16'))) = t2tb(tb2t(prefix(elt1,'#skF_14',t2tb('#skF_15')))),
inference(superposition,[status(thm),theory(equality)],[c_1096,c_154]) ).
tff(c_1136,plain,
infix_plpl(elt1,prefix(elt1,'#skE_1',t2tb('#skF_15')),prefix(elt1,$sum($uminus('#skE_1'),'#skF_14'),t2tb('#skF_16'))) = prefix(elt1,'#skF_14',t2tb('#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_154,c_1105]) ).
tff(c_1139,plain,
infix_plpl(elt1,prefix(elt1,'#skE_1',t2tb('#skF_15')),prefix(elt1,$sum('#skF_14',$uminus('#skE_1')),t2tb('#skF_16'))) = prefix(elt1,'#skF_14',t2tb('#skF_15')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1136]) ).
tff(c_349042,plain,
infix_plpl(elt1,prefix(elt1,'#skE_1',t2tb('#skF_15')),prefix(elt1,$sum('#skE_15',$uminus('#skE_1')),t2tb('#skF_16'))) = prefix(elt1,'#skE_15',t2tb('#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_61994,c_61994,c_1139]) ).
tff(c_349047,plain,
infix_plpl(elt1,prefix(elt1,'#skE_1',t2tb('#skF_15')),prefix(elt1,$sum($uminus('#skE_1'),'#skE_15'),t2tb('#skF_16'))) = prefix(elt1,'#skE_15',t2tb('#skF_15')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_349042]) ).
tff(c_53,plain,
! [A_63: ty,L2_64: uni] : ( infix_plpl(A_63,nil(A_63),L2_64) = L2_64 ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_57,plain,
! [A_69: ty,L1_70: uni,L2_71: uni,L3_72: uni] : ( infix_plpl(A_69,infix_plpl(A_69,L1_70,L2_71),L3_72) = infix_plpl(A_69,L1_70,infix_plpl(A_69,L2_71,L3_72)) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_278,plain,
permut(elt1,t2tb('#skF_19'),infix_plpl(elt1,infix_plpl(elt1,nil(elt1),t2tb('#skF_17')),t2tb('#skF_18'))),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_508,plain,
permut(elt1,t2tb('#skF_19'),infix_plpl(elt1,nil(elt1),infix_plpl(elt1,t2tb('#skF_17'),t2tb('#skF_18')))),
inference(demodulation,[status(thm),theory(equality)],[c_57,c_278]) ).
tff(c_512,plain,
permut(elt1,t2tb('#skF_19'),infix_plpl(elt1,t2tb('#skF_17'),t2tb('#skF_18'))),
inference(demodulation,[status(thm),theory(equality)],[c_53,c_508]) ).
tff(c_14574,plain,
! [A_2807: ty,L1_2804: uni,K2_2805: uni,L2_2808: uni,K1_2806: uni] :
( permut(A_2807,infix_plpl(A_2807,L1_2804,L2_2808),infix_plpl(A_2807,K1_2806,K2_2805))
| ~ permut(A_2807,L2_2808,K2_2805)
| ~ permut(A_2807,L1_2804,K1_2806) ),
inference(cnfTransformation,[status(thm)],[f_221]) ).
tff(c_126,plain,
! [A_141: ty,L1_142: uni,L3_144: uni,L2_143: uni] :
( permut(A_141,L1_142,L3_144)
| ~ permut(A_141,L2_143,L3_144)
| ~ permut(A_141,L1_142,L2_143) ),
inference(cnfTransformation,[status(thm)],[f_205]) ).
tff(c_315346,plain,
! [K1_37555: uni,A_37556: ty,L2_37551: uni,L1_37553: uni,L1_37554: uni,K2_37552: uni] :
( permut(A_37556,L1_37554,infix_plpl(A_37556,K1_37555,K2_37552))
| ~ permut(A_37556,L1_37554,infix_plpl(A_37556,L1_37553,L2_37551))
| ~ permut(A_37556,L2_37551,K2_37552)
| ~ permut(A_37556,L1_37553,K1_37555) ),
inference(resolution,[status(thm)],[c_14574,c_126]) ).
tff(c_315715,plain,
! [K1_37555: uni,K2_37552: uni] :
( permut(elt1,t2tb('#skF_19'),infix_plpl(elt1,K1_37555,K2_37552))
| ~ permut(elt1,t2tb('#skF_18'),K2_37552)
| ~ permut(elt1,t2tb('#skF_17'),K1_37555) ),
inference(resolution,[status(thm)],[c_512,c_315346]) ).
tff(c_349185,plain,
( permut(elt1,t2tb('#skF_19'),prefix(elt1,'#skE_15',t2tb('#skF_15')))
| ~ permut(elt1,t2tb('#skF_18'),prefix(elt1,$sum($uminus('#skE_1'),'#skE_15'),t2tb('#skF_16')))
| ~ permut(elt1,t2tb('#skF_17'),prefix(elt1,'#skE_1',t2tb('#skF_15'))) ),
inference(superposition,[status(thm),theory(equality)],[c_349047,c_315715]) ).
tff(c_350779,plain,
permut(elt1,t2tb('#skF_19'),prefix(elt1,'#skE_15',t2tb('#skF_15'))),
inference(demodulation,[status(thm),theory(equality)],[c_1407,c_135275,c_349185]) ).
tff(c_403,plain,
~ permut(elt1,t2tb('#skF_19'),prefix(elt1,'#skF_14',t2tb('#skF_15'))),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_62253,plain,
~ permut(elt1,t2tb('#skF_19'),prefix(elt1,'#skE_15',t2tb('#skF_15'))),
inference(demodulation,[status(thm),theory(equality)],[c_61994,c_403]) ).
tff(c_350782,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_350779,c_62253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWW626_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.15 % 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
% 0.16/0.37 % Computer : n019.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 3 19:42:31 EDT 2023
% 0.16/0.37 % CPUTime :
% 124.08/86.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 124.08/86.89
% 124.08/86.89 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 124.08/86.93
% 124.08/86.93 Inference rules
% 124.08/86.93 ----------------------
% 124.08/86.93 #Ref : 8
% 124.08/86.93 #Sup : 56585
% 124.08/86.93 #Fact : 17
% 124.08/86.93 #Define : 105
% 124.08/86.93 #Split : 332
% 124.08/86.93 #Chain : 0
% 124.08/86.93 #Close : 16
% 124.08/86.93
% 124.08/86.93 Ordering : LPO
% 124.08/86.93
% 124.08/86.93 Simplification rules
% 124.08/86.93 ----------------------
% 124.08/86.93 #Subsume : 4948
% 124.08/86.93 #Demod : 32072
% 124.08/86.93 #Tautology : 20462
% 124.08/86.93 #SimpNegUnit : 901
% 124.08/86.93 #BackRed : 1627
% 124.08/86.93
% 124.08/86.93 #Partial instantiations: 1823
% 124.08/86.93 #Strategies tried : 1
% 124.08/86.93
% 124.08/86.93 Timing (in seconds)
% 124.08/86.93 ----------------------
% 124.08/86.94 Preprocessing : 1.00
% 124.08/86.94 Parsing : 0.52
% 124.08/86.94 CNF conversion : 0.08
% 124.08/86.94 Main loop : 84.84
% 124.08/86.94 Inferencing : 6.64
% 124.08/86.94 Reduction : 34.37
% 124.08/86.94 Demodulation : 26.67
% 124.08/86.94 BG Simplification : 2.07
% 124.08/86.94 Subsumption : 24.31
% 124.08/86.94 Abstraction : 1.41
% 124.08/86.94 MUC search : 1.33
% 124.08/86.94 Cooper : 10.76
% 124.08/86.94 Total : 85.91
% 124.08/86.94 Index Insertion : 0.00
% 124.08/86.94 Index Deletion : 0.00
% 124.08/86.94 Index Matching : 0.00
% 124.08/86.94 BG Taut test : 0.00
%------------------------------------------------------------------------------