TSTP Solution File: SWW670_2 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW670_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 : n014.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 11:07:55 EDT 2023
% Result : Theorem 72.35s 44.15s
% Output : CNFRefutation 72.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 66
% Syntax : Number of formulae : 167 ( 65 unt; 57 typ; 0 def)
% Number of atoms : 195 ( 95 equ)
% Maximal formula atoms : 17 ( 1 avg)
% Number of connectives : 164 ( 79 ~; 60 |; 13 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 278 ( 73 atm; 99 fun; 78 num; 28 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 58 ( 31 >; 27 *; 0 +; 0 <<)
% Number of predicates : 7 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 53 ( 48 usr; 22 con; 0-5 aty)
% Number of variables : 67 (; 65 !; 2 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
%$ zero_at1 > sort1 > no_zero1 > match_option1 > match_list1 > match_bool1 > nth1 > cons > tl > some_proj_11 > some > mk_ref > length1 > hd > contents > cons_proj_21 > cons_proj_11 > #nlpp > witness1 > tb2t2 > tb2t1 > tb2t > t2tb2 > t2tb1 > t2tb > ref > option > none > nil > list > tuple03 > tuple0 > true1 > real > qtmark > int > false1 > bool > #skF_3 > #skF_8 > #skF_2 > #skF_1 > #skF_4
%Foreground sorts:
tff(option_int,type,
option_int: $tType ).
tff(tuple02,type,
tuple02: $tType ).
tff(list_int,type,
list_int: $tType ).
tff(bool1,type,
bool1: $tType ).
tff(ty,type,
ty: $tType ).
tff(uni,type,
uni: $tType ).
%Background operators:
tff('#skF_6',type,
'#skF_6': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skF_5',type,
'#skF_5': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skF_7',type,
'#skF_7': $int ).
%Foreground operators:
tff(list,type,
list: ty > ty ).
tff(tb2t1,type,
tb2t1: uni > list_int ).
tff(length1,type,
length1: ( ty * uni ) > $int ).
tff(cons,type,
cons: ( ty * uni * uni ) > uni ).
tff(some_proj_11,type,
some_proj_11: ( ty * uni ) > uni ).
tff(t2tb2,type,
t2tb2: $int > uni ).
tff(no_zero1,type,
no_zero1: list_int > $o ).
tff(nil,type,
nil: ty > uni ).
tff('#skF_3',type,
'#skF_3': list_int ).
tff(true1,type,
true1: bool1 ).
tff(match_list1,type,
match_list1: ( ty * ty * uni * uni * uni ) > uni ).
tff(int,type,
int: ty ).
tff(false1,type,
false1: bool1 ).
tff(zero_at1,type,
zero_at1: ( list_int * $int ) > $o ).
tff(sort1,type,
sort1: ( ty * uni ) > $o ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff('#skF_8',type,
'#skF_8': list_int ).
tff(witness1,type,
witness1: ty > uni ).
tff(real,type,
real: ty ).
tff('#skF_2',type,
'#skF_2': list_int > $int ).
tff(hd,type,
hd: ( ty * uni ) > uni ).
tff(match_bool1,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(t2tb,type,
t2tb: option_int > uni ).
tff(option,type,
option: ty > ty ).
tff(none,type,
none: ty > uni ).
tff(tuple0,type,
tuple0: ty ).
tff(qtmark,type,
qtmark: ty ).
tff('#skF_1',type,
'#skF_1': ( list_int * $int ) > $int ).
tff(bool,type,
bool: ty ).
tff('#skF_4',type,
'#skF_4': list_int ).
tff(some,type,
some: ( ty * uni ) > uni ).
tff(t2tb1,type,
t2tb1: list_int > uni ).
tff(nth1,type,
nth1: ( ty * $int * uni ) > uni ).
tff(tl,type,
tl: ( ty * uni ) > uni ).
tff(tb2t,type,
tb2t: uni > option_int ).
tff(tuple03,type,
tuple03: tuple02 ).
tff(cons_proj_11,type,
cons_proj_11: ( ty * uni ) > uni ).
tff(ref,type,
ref: ty > ty ).
tff(tb2t2,type,
tb2t2: uni > $int ).
tff(cons_proj_21,type,
cons_proj_21: ( ty * uni ) > uni ).
tff(match_option1,type,
match_option1: ( ty * ty * uni * uni * uni ) > uni ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(f_249,negated_conjecture,
~ ! [L: list_int,S: list_int,Ia: $int] :
( ( $lesseq(0,Ia)
& ( $sum(Ia,length1(int,t2tb1(S))) = length1(int,t2tb1(L)) )
& ! [Ja: $int] :
( $lesseq(0,Ja)
=> ( tb2t(nth1(int,Ja,t2tb1(S))) = tb2t(nth1(int,$sum(Ia,Ja),t2tb1(L))) ) )
& ! [Ja: $int] :
( ( $lesseq(0,Ja)
& $less(Ja,Ia) )
=> ( tb2t(nth1(int,Ja,t2tb1(L))) != tb2t(some(int,t2tb2(0))) ) ) )
=> ( ( S != tb2t1(nil(int)) )
=> ( ( S != tb2t1(nil(int)) )
=> ! [Oa: $int] :
( ? [Xa: $int,X1: list_int] :
( ( S = tb2t1(cons(int,t2tb2(Xa),t2tb1(X1))) )
& ( Oa = Xa ) )
=> ( ( Oa != 0 )
=> ( ( $lesseq(0,Ia)
& $less(Ia,length1(int,t2tb1(L)))
& zero_at1(L,Ia) )
| ( ( Ia = length1(int,t2tb1(L)) )
& no_zero1(L) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_search_loop) ).
tff(f_151,axiom,
! [J: uni] : ( t2tb1(tb2t1(J)) = J ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR1) ).
tff(f_198,axiom,
! [A: ty] :
( ( hd(A,nil(A)) = none(A) )
& ! [X: uni,X1: uni] : ( hd(A,cons(A,X,X1)) = some(A,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hd_def) ).
tff(f_139,axiom,
! [A: ty,Na: $int] :
( ( nth1(A,Na,nil(A)) = none(A) )
& ! [X: uni,X1: uni] :
( ( ( Na = 0 )
=> ( nth1(A,Na,cons(A,X,X1)) = some(A,X) ) )
& ( ( Na != 0 )
=> ( nth1(A,Na,cons(A,X,X1)) = nth1(A,$difference(Na,1),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nth_def) ).
tff(f_169,axiom,
! [L: list_int,Ia: $int] :
( zero_at1(L,Ia)
<=> ( ( tb2t(nth1(int,Ia,t2tb1(L))) = tb2t(some(int,t2tb2(0))) )
& ! [Ja: $int] :
( ( $lesseq(0,Ja)
& $less(Ja,Ia) )
=> ( tb2t(nth1(int,Ja,t2tb1(L))) != tb2t(some(int,t2tb2(0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_at_def) ).
tff(f_92,axiom,
! [A: ty,L: uni] : $lesseq(0,length1(A,L)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_nonnegative) ).
tff(f_145,axiom,
! [J: uni] : ( t2tb(tb2t(J)) = J ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR) ).
tff(f_96,axiom,
! [A: ty,L: uni] :
( ( length1(A,L) = 0 )
<=> ( L = nil(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_nil) ).
tff(f_149,axiom,
! [I: list_int] : ( tb2t1(t2tb1(I)) = I ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeL1) ).
tff(c_144,plain,
tb2t1(nil(int)) != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_191,plain,
'#skF_6' = 0,
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_190,plain,
'#skF_7' = '#skF_6',
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_189,plain,
tb2t1(cons(int,t2tb2('#skF_7'),t2tb1('#skF_8'))) = '#skF_4',
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_245,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_8'))) = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_190,c_189]) ).
tff(c_251,plain,
tb2t1(cons(int,t2tb2(0),t2tb1('#skF_8'))) = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_191,c_245]) ).
tff(c_86,plain,
! [J_99: uni] : ( t2tb1(tb2t1(J_99)) = J_99 ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_538,plain,
cons(int,t2tb2(0),t2tb1('#skF_8')) = t2tb1('#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_251,c_86]) ).
tff(c_1034,plain,
! [A_435: ty,X_436: uni,X1_437: uni] : ( hd(A_435,cons(A_435,X_436,X1_437)) = some(A_435,X_436) ),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_1050,plain,
some(int,t2tb2(0)) = hd(int,t2tb1('#skF_4')),
inference(superposition,[status(thm),theory(equality)],[c_538,c_1034]) ).
tff(c_1284,plain,
! [A_452: ty,X_453: uni,X1_454: uni] : ( nth1(A_452,0,cons(A_452,X_453,X1_454)) = some(A_452,X_453) ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_1296,plain,
nth1(int,0,t2tb1('#skF_4')) = some(int,t2tb2(0)),
inference(superposition,[status(thm),theory(equality)],[c_538,c_1284]) ).
tff(c_1301,plain,
nth1(int,0,t2tb1('#skF_4')) = hd(int,t2tb1('#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_1050,c_1296]) ).
tff(c_180,plain,
length1(int,t2tb1('#skF_3')) = $sum('#skF_5',length1(int,t2tb1('#skF_4'))),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_309,plain,
length1(int,t2tb1('#skF_4')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_180]) ).
tff(c_308,plain,
length1(int,t2tb1('#skF_3')) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_180]) ).
tff(c_234,plain,
length1(int,t2tb1('#skF_3')) = $sum('#skF_5',length1(int,t2tb1('#skF_4'))),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_311,plain,
$sum('#skF_5','#skE_2') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_309,c_308,c_234]) ).
tff(c_315,plain,
'#skF_5' = $sum($uminus('#skE_2'),'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_311]) ).
tff(c_147,plain,
! [J_141a: $int] :
( ( tb2t(nth1(int,$sum('#skF_5',J_141a),t2tb1('#skF_3'))) = tb2t(nth1(int,J_141a,t2tb1('#skF_4'))) )
| ~ $lesseq(0,J_141a) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_184,plain,
! [J_141a: $int] :
( ( tb2t(nth1(int,$sum('#skF_5',J_141a),t2tb1('#skF_3'))) = tb2t(nth1(int,J_141a,t2tb1('#skF_4'))) )
| $less(J_141a,0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_147]) ).
tff(c_452,plain,
! [J_141a: $int] :
( ( tb2t(nth1(int,$sum($sum($uminus('#skE_2'),'#skE_1'),J_141a),t2tb1('#skF_3'))) = tb2t(nth1(int,J_141a,t2tb1('#skF_4'))) )
| $less(J_141a,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_315,c_184]) ).
tff(c_455,plain,
! [J_141a: $int] :
( ( tb2t(nth1(int,$sum(J_141a,$sum('#skE_1',$uminus('#skE_2'))),t2tb1('#skF_3'))) = tb2t(nth1(int,J_141a,t2tb1('#skF_4'))) )
| $less(J_141a,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_452]) ).
tff(c_1320,plain,
( ( tb2t(nth1(int,$sum(0,$sum('#skE_1',$uminus('#skE_2'))),t2tb1('#skF_3'))) = tb2t(hd(int,t2tb1('#skF_4'))) )
| $less(0,0) ),
inference(superposition,[status(thm),theory(equality)],[c_1301,c_455]) ).
tff(c_1321,plain,
tb2t(nth1(int,$sum('#skE_1',$uminus('#skE_2')),t2tb1('#skF_3'))) = tb2t(hd(int,t2tb1('#skF_4'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1320]) ).
tff(c_1378,plain,
tb2t(nth1(int,$sum($uminus('#skE_2'),'#skE_1'),t2tb1('#skF_3'))) = tb2t(hd(int,t2tb1('#skF_4'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1321]) ).
tff(c_102,plain,
! [L_103: list_int,I_104a: $int] :
( $lesseq(0,'#skF_1'(L_103,I_104a))
| zero_at1(L_103,I_104a)
| ( tb2t(nth1(int,I_104a,t2tb1(L_103))) != tb2t(some(int,t2tb2(0))) ) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_201,plain,
! [L_103: list_int,I_104a: $int] :
( ~ $less('#skF_1'(L_103,I_104a),0)
| zero_at1(L_103,I_104a)
| ( tb2t(nth1(int,I_104a,t2tb1(L_103))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_102]) ).
tff(c_7632,plain,
! [L_892: list_int,I_893a: $int] :
( ~ $less('#skF_1'(L_892,I_893a),0)
| zero_at1(L_892,I_893a)
| ( tb2t(nth1(int,I_893a,t2tb1(L_892))) != tb2t(hd(int,t2tb1('#skF_4'))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1050,c_201]) ).
tff(c_313,plain,
length1(int,t2tb1('#skF_4')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_180]) ).
tff(c_151,plain,
$lesseq(0,'#skF_5'),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_176,plain,
~ $less('#skF_5',0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_151]) ).
tff(c_135,plain,
( ~ zero_at1('#skF_3','#skF_5')
| ~ $less('#skF_5',length1(int,t2tb1('#skF_3')))
| ~ $lesseq(0,'#skF_5') ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_195,plain,
( ~ zero_at1('#skF_3','#skF_5')
| ~ $less('#skF_5',length1(int,t2tb1('#skF_3')))
| $less('#skF_5',0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_135]) ).
tff(c_254,plain,
( ~ zero_at1('#skF_3','#skF_5')
| ~ $less('#skF_5',$sum('#skF_5',length1(int,t2tb1('#skF_4'))))
| $less('#skF_5',0) ),
inference(demodulation,[status(thm),theory(equality)],[c_234,c_195]) ).
tff(c_256,plain,
( ~ zero_at1('#skF_3','#skF_5')
| ~ $less('#skF_5',$sum('#skF_5',length1(int,t2tb1('#skF_4')))) ),
inference(negUnitSimplification,[status(thm)],[c_176,c_254]) ).
tff(c_259,plain,
( ~ zero_at1('#skF_3','#skF_5')
| ~ $less(0,length1(int,t2tb1('#skF_4'))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_256]) ).
tff(c_806,plain,
( ~ zero_at1('#skF_3',$sum($uminus('#skE_2'),'#skE_1'))
| ~ $less(0,'#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_313,c_315,c_259]) ).
tff(c_809,plain,
( ~ zero_at1('#skF_3',$sum('#skE_1',$uminus('#skE_2')))
| ~ $less(0,'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_806]) ).
tff(c_812,plain,
~ $less(0,'#skE_2'),
inference(splitLeft,[status(thm)],[c_809]) ).
tff(c_196,plain,
( ~ no_zero1('#skF_3')
| ( length1(int,t2tb1('#skF_3')) != '#skF_5' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_263,plain,
( ~ no_zero1('#skF_3')
| ( $sum('#skF_5',length1(int,t2tb1('#skF_4'))) != '#skF_5' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_234,c_196]) ).
tff(c_265,plain,
( ~ no_zero1('#skF_3')
| ( length1(int,t2tb1('#skF_4')) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_263]) ).
tff(c_520,plain,
( ~ no_zero1('#skF_3')
| ( '#skE_2' != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_313,c_265]) ).
tff(c_522,plain,
'#skE_2' != 0,
inference(splitLeft,[status(thm)],[c_520]) ).
tff(c_44,plain,
! [A_56: ty,L_57: uni] : $lesseq(0,length1(A_56,L_57)),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_218,plain,
! [A_56: ty,L_57: uni] : ~ $less(length1(A_56,L_57),0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_44]) ).
tff(c_397,plain,
~ $less('#skE_2',0),
inference(superposition,[status(thm),theory(equality)],[c_313,c_218]) ).
tff(c_813,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_812,c_522,c_397]) ).
tff(c_816,plain,
~ zero_at1('#skF_3',$sum('#skE_1',$uminus('#skE_2'))),
inference(splitRight,[status(thm)],[c_809]) ).
tff(c_819,plain,
~ zero_at1('#skF_3',$sum($uminus('#skE_2'),'#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_816]) ).
tff(c_7639,plain,
( ~ $less('#skF_1'('#skF_3',$sum($uminus('#skE_2'),'#skE_1')),0)
| ( tb2t(nth1(int,$sum($uminus('#skE_2'),'#skE_1'),t2tb1('#skF_3'))) != tb2t(hd(int,t2tb1('#skF_4'))) ) ),
inference(resolution,[status(thm)],[c_7632,c_819]) ).
tff(c_7646,plain,
~ $less('#skF_1'('#skF_3',$sum($uminus('#skE_2'),'#skE_1')),0),
inference(demodulation,[status(thm),theory(equality)],[c_1378,c_7639]) ).
tff(c_7649,plain,
~ $less('#skF_1'('#skF_3',$sum('#skE_1',$uminus('#skE_2'))),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7646]) ).
tff(c_7652,plain,
'#skF_1'('#skF_3',$sum('#skE_1',$uminus('#skE_2'))) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_7649]) ).
tff(c_7651,plain,
~ $less('#skF_1'('#skF_3',$sum('#skE_1',$uminus('#skE_2'))),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7646]) ).
tff(c_7660,plain,
~ $less('#skE_3',0),
inference(demodulation,[status(thm),theory(equality)],[c_7652,c_7651]) ).
tff(c_7656,plain,
'#skF_1'('#skF_3',$sum('#skE_1',$uminus('#skE_2'))) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_7649]) ).
tff(c_7662,plain,
'#skF_1'('#skF_3',$sum($uminus('#skE_2'),'#skE_1')) = '#skE_3',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7656]) ).
tff(c_203,plain,
! [L_103: list_int,I_104a: $int] :
( ( tb2t(nth1(int,'#skF_1'(L_103,I_104a),t2tb1(L_103))) = tb2t(some(int,t2tb2(0))) )
| zero_at1(L_103,I_104a)
| ( tb2t(nth1(int,I_104a,t2tb1(L_103))) != tb2t(some(int,t2tb2(0))) ) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_8592,plain,
! [L_1000: list_int,I_1001a: $int] :
( ( tb2t(nth1(int,'#skF_1'(L_1000,I_1001a),t2tb1(L_1000))) = tb2t(hd(int,t2tb1('#skF_4'))) )
| zero_at1(L_1000,I_1001a)
| ( tb2t(nth1(int,I_1001a,t2tb1(L_1000))) != tb2t(hd(int,t2tb1('#skF_4'))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1050,c_1050,c_203]) ).
tff(c_8602,plain,
( ( tb2t(nth1(int,'#skF_1'('#skF_3',$sum($uminus('#skE_2'),'#skE_1')),t2tb1('#skF_3'))) = tb2t(hd(int,t2tb1('#skF_4'))) )
| ( tb2t(nth1(int,$sum($uminus('#skE_2'),'#skE_1'),t2tb1('#skF_3'))) != tb2t(hd(int,t2tb1('#skF_4'))) ) ),
inference(resolution,[status(thm)],[c_8592,c_819]) ).
tff(c_12628,plain,
tb2t(nth1(int,'#skE_3',t2tb1('#skF_3'))) = tb2t(hd(int,t2tb1('#skF_4'))),
inference(demodulation,[status(thm),theory(equality)],[c_1378,c_7662,c_8602]) ).
tff(c_12715,plain,
! [J_141a: $int] :
( ( tb2t(nth1(int,J_141a,t2tb1('#skF_4'))) = tb2t(hd(int,t2tb1('#skF_4'))) )
| $less(J_141a,0)
| ( $sum(J_141a,$sum('#skE_1',$uminus('#skE_2'))) != '#skE_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_12628,c_455]) ).
tff(c_12717,plain,
( ( tb2t(nth1(int,$sum('#skE_2',$sum($uminus('#skE_1'),'#skE_3')),t2tb1('#skF_4'))) = tb2t(hd(int,t2tb1('#skF_4'))) )
| $less($sum('#skE_2',$sum($uminus('#skE_1'),'#skE_3')),0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12715]) ).
tff(c_12720,plain,
( ( tb2t(nth1(int,$sum($uminus('#skE_1'),$sum('#skE_3','#skE_2')),t2tb1('#skF_4'))) = tb2t(hd(int,t2tb1('#skF_4'))) )
| $less($sum('#skE_3','#skE_2'),'#skE_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12717]) ).
tff(c_23157,plain,
$less($sum('#skE_3','#skE_2'),'#skE_1'),
inference(splitLeft,[status(thm)],[c_12720]) ).
tff(c_23159,plain,
$less($sum('#skE_2','#skE_3'),'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_23157]) ).
tff(c_80,plain,
! [J_96: uni] : ( t2tb(tb2t(J_96)) = J_96 ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_12655,plain,
nth1(int,'#skE_3',t2tb1('#skF_3')) = t2tb(tb2t(hd(int,t2tb1('#skF_4')))),
inference(superposition,[status(thm),theory(equality)],[c_12628,c_80]) ).
tff(c_12726,plain,
nth1(int,'#skE_3',t2tb1('#skF_3')) = hd(int,t2tb1('#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_12655]) ).
tff(c_145,plain,
! [J_142a: $int] :
( ( tb2t(nth1(int,J_142a,t2tb1('#skF_3'))) != tb2t(some(int,t2tb2(0))) )
| ~ $lesseq(0,J_142a)
| ~ $less(J_142a,'#skF_5') ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_185,plain,
! [J_142a: $int] :
( ( tb2t(nth1(int,J_142a,t2tb1('#skF_3'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_142a,0)
| ~ $less(J_142a,'#skF_5') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_145]) ).
tff(c_422,plain,
! [J_142a: $int] :
( ( tb2t(nth1(int,J_142a,t2tb1('#skF_3'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_142a,0)
| ~ $less(J_142a,$sum($uminus('#skE_2'),'#skE_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_315,c_185]) ).
tff(c_424,plain,
! [J_142a: $int] :
( ( tb2t(nth1(int,J_142a,t2tb1('#skF_3'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_142a,0)
| ~ $less($sum('#skE_2',J_142a),'#skE_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_422]) ).
tff(c_429,plain,
! [J_142a: $int] :
( ( tb2t(nth1(int,J_142a,t2tb1('#skF_3'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_142a,0)
| ~ $less($sum(J_142a,'#skE_2'),'#skE_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_424]) ).
tff(c_1051,plain,
! [J_142a: $int] :
( ( tb2t(nth1(int,J_142a,t2tb1('#skF_3'))) != tb2t(hd(int,t2tb1('#skF_4'))) )
| $less(J_142a,0)
| ~ $less($sum(J_142a,'#skE_2'),'#skE_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_1050,c_429]) ).
tff(c_1053,plain,
! [J_142a: $int] :
( ( tb2t(nth1(int,J_142a,t2tb1('#skF_3'))) != tb2t(hd(int,t2tb1('#skF_4'))) )
| $less(J_142a,0)
| ~ $less($sum('#skE_2',J_142a),'#skE_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1051]) ).
tff(c_220515,plain,
! [J_17413a: $int] :
( ( tb2t(nth1(int,J_17413a,t2tb1('#skF_3'))) != tb2t(hd(int,t2tb1('#skF_4'))) )
| $less(J_17413a,0)
| ~ $less($sum(J_17413a,'#skE_2'),'#skE_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1053]) ).
tff(c_220670,plain,
( $less('#skE_3',0)
| ~ $less($sum('#skE_3','#skE_2'),'#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_12726,c_220515]) ).
tff(c_220672,plain,
( $less('#skE_3',0)
| ~ $less($sum('#skE_2','#skE_3'),'#skE_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_220670]) ).
tff(c_220704,plain,
$less('#skE_3',0),
inference(demodulation,[status(thm),theory(equality)],[c_23159,c_220672]) ).
tff(c_220705,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7660,c_220704]) ).
tff(c_220707,plain,
~ $less($sum('#skE_3','#skE_2'),'#skE_1'),
inference(splitRight,[status(thm)],[c_12720]) ).
tff(c_220713,plain,
~ $less($sum('#skE_2','#skE_3'),'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_220707]) ).
tff(c_202,plain,
! [L_103: list_int,I_104a: $int] :
( $less('#skF_1'(L_103,I_104a),I_104a)
| zero_at1(L_103,I_104a)
| ( tb2t(nth1(int,I_104a,t2tb1(L_103))) != tb2t(some(int,t2tb2(0))) ) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_6853,plain,
! [L_830: list_int,I_831a: $int] :
( $less('#skF_1'(L_830,I_831a),I_831a)
| zero_at1(L_830,I_831a)
| ( tb2t(nth1(int,I_831a,t2tb1(L_830))) != tb2t(hd(int,t2tb1('#skF_4'))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1050,c_202]) ).
tff(c_6860,plain,
( $less('#skF_1'('#skF_3',$sum($uminus('#skE_2'),'#skE_1')),$sum($uminus('#skE_2'),'#skE_1'))
| ( tb2t(nth1(int,$sum($uminus('#skE_2'),'#skE_1'),t2tb1('#skF_3'))) != tb2t(hd(int,t2tb1('#skF_4'))) ) ),
inference(resolution,[status(thm)],[c_6853,c_819]) ).
tff(c_6867,plain,
$less('#skF_1'('#skF_3',$sum($uminus('#skE_2'),'#skE_1')),$sum($uminus('#skE_2'),'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_1378,c_6860]) ).
tff(c_6870,plain,
$less($sum('#skE_2','#skF_1'('#skF_3',$sum('#skE_1',$uminus('#skE_2')))),'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6867]) ).
tff(c_235445,plain,
'#skF_1'('#skF_3',$sum('#skE_1',$uminus('#skE_2'))) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_6870]) ).
tff(c_235444,plain,
$less($sum('#skE_2','#skF_1'('#skF_3',$sum('#skE_1',$uminus('#skE_2')))),'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6867]) ).
tff(c_235447,plain,
$less($sum('#skE_2','#skE_3'),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_235445,c_235444]) ).
tff(c_235454,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_220713,c_235447]) ).
tff(c_235457,plain,
'#skE_2' = 0,
inference(splitRight,[status(thm)],[c_520]) ).
tff(c_235490,plain,
length1(int,t2tb1('#skF_4')) = 0,
inference(demodulation,[status(thm),theory(equality)],[c_235457,c_313]) ).
tff(c_235512,plain,
! [A_18729: ty,L_18730: uni] :
( ( nil(A_18729) = L_18730 )
| ( length1(A_18729,L_18730) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_235523,plain,
t2tb1('#skF_4') = nil(int),
inference(superposition,[status(thm),theory(equality)],[c_235490,c_235512]) ).
tff(c_84,plain,
! [I_98: list_int] : ( tb2t1(t2tb1(I_98)) = I_98 ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_235535,plain,
tb2t1(nil(int)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_235523,c_84]) ).
tff(c_235539,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_144,c_235535]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW670_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 19:22:48 EDT 2023
% 0.13/0.34 % CPUTime :
% 72.35/44.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 72.35/44.16
% 72.35/44.16 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 72.35/44.20
% 72.35/44.20 Inference rules
% 72.35/44.20 ----------------------
% 72.35/44.20 #Ref : 46
% 72.35/44.20 #Sup : 39730
% 72.35/44.20 #Fact : 9
% 72.35/44.20 #Define : 7
% 72.35/44.20 #Split : 25
% 72.35/44.20 #Chain : 0
% 72.35/44.20 #Close : 1
% 72.35/44.20
% 72.35/44.20 Ordering : LPO
% 72.35/44.20
% 72.35/44.20 Simplification rules
% 72.35/44.20 ----------------------
% 72.35/44.20 #Subsume : 6816
% 72.35/44.20 #Demod : 19588
% 72.35/44.20 #Tautology : 13493
% 72.35/44.20 #SimpNegUnit : 1656
% 72.35/44.20 #BackRed : 121
% 72.35/44.20
% 72.35/44.20 #Partial instantiations: 864
% 72.35/44.20 #Strategies tried : 1
% 72.35/44.20
% 72.35/44.20 Timing (in seconds)
% 72.35/44.20 ----------------------
% 72.35/44.20 Preprocessing : 0.81
% 72.35/44.20 Parsing : 0.44
% 72.35/44.20 CNF conversion : 0.06
% 72.35/44.20 Main loop : 42.23
% 72.35/44.20 Inferencing : 4.12
% 72.35/44.20 Reduction : 22.18
% 72.35/44.20 Demodulation : 19.68
% 72.35/44.20 BG Simplification : 1.32
% 72.35/44.20 Subsumption : 10.38
% 72.35/44.20 Abstraction : 1.09
% 72.35/44.20 MUC search : 0.01
% 72.35/44.20 Cooper : 0.08
% 72.35/44.20 Total : 43.11
% 72.35/44.20 Index Insertion : 0.00
% 72.35/44.20 Index Deletion : 0.00
% 72.35/44.20 Index Matching : 0.00
% 72.35/44.20 BG Taut test : 0.00
%------------------------------------------------------------------------------