TSTP Solution File: SWW624_2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW624_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 : n017.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 50.46s 25.17s
% Output : CNFRefutation 50.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 84
% Syntax : Number of formulae : 140 ( 51 unt; 70 typ; 0 def)
% Number of atoms : 90 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 35 ~; 11 |; 4 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 129 ( 22 atm; 50 fun; 55 num; 2 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 : 68 ( 59 usr; 30 con; 0-5 aty)
% Number of variables : 122 (; 122 !; 0 ?; 122 :)
% 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_13 > #skF_5 > #skF_6 > #skF_4 > #skF_12 > #skF_8 > #skF_10 > #skF_14 > #skF_15 > #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_7',type,
'#skE_7': $int ).
tff('#skE_11',type,
'#skE_11': $int ).
tff('#skE_12',type,
'#skE_12': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_13',type,
'#skE_13': $int ).
tff('#skE_10',type,
'#skE_10': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skE_9',type,
'#skE_9': $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(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_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_14',type,
'#skF_14': elt ).
tff('#skF_15',type,
'#skF_15': 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_195,axiom,
! [A: ty,L: uni] : permut(A,L,L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_refl) ).
tff(f_356,axiom,
! [A: ty,L: uni] : ( prefix(A,0,L) = nil(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prefix_def1) ).
tff(f_96,axiom,
! [A: ty,L: uni] :
( ( length(A,L) = 0 )
<=> ( L = nil(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_nil) ).
tff(f_479,negated_conjecture,
~ ( permut(elt1,prefix(elt1,length(elt1,nil(elt1)),nil(elt1)),nil(elt1))
& ! [X: elt,X1: list_elt] :
( permut(elt1,prefix(elt1,length(elt1,t2tb(X1)),t2tb(X1)),t2tb(X1))
=> permut(elt1,prefix(elt1,length(elt1,cons(elt1,t2tb1(X),t2tb(X1))),cons(elt1,t2tb1(X),t2tb(X1))),cons(elt1,t2tb1(X),t2tb(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_prefix) ).
tff(f_199,axiom,
! [A: ty,L1: uni,L2: uni] :
( permut(A,L1,L2)
=> permut(A,L2,L1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_sym) ).
tff(f_209,axiom,
! [A: ty,X: uni,L1: uni,L2: uni] :
( permut(A,L1,L2)
=> permut(A,cons(A,X,L1),cons(A,X,L2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_cons) ).
tff(f_360,axiom,
! [A: ty,Na: $int,X: uni,L: uni] :
( $less(0,Na)
=> ( prefix(A,Na,cons(A,X,L)) = cons(A,X,prefix(A,$difference(Na,1),L)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prefix_def2) ).
tff(f_90,axiom,
! [A: ty] :
( ( length(A,nil(A)) = 0 )
& ! [X: uni,X1: uni] : ( length(A,cons(A,X,X1)) = $sum(1,length(A,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_def) ).
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_167,axiom,
! [A: ty] :
( ( reverse(A,nil(A)) = nil(A) )
& ! [X: uni,X1: uni] : ( reverse(A,cons(A,X,X1)) = infix_plpl(A,reverse(A,X1),cons(A,X,nil(A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reverse_def) ).
tff(f_171,axiom,
! [A: ty,L: uni,X: uni] : ( reverse(A,cons(A,X,L)) = infix_plpl(A,reverse(A,L),cons(A,X,nil(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reverse_cons) ).
tff(f_179,axiom,
! [A: ty,L: uni] : ( length(A,reverse(A,L)) = length(A,L) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reverse_length) ).
tff(f_109,axiom,
! [A: ty,L1: uni,L2: uni] : ( length(A,infix_plpl(A,L1,L2)) = $sum(length(A,L1),length(A,L2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',append_length) ).
tff(f_92,axiom,
! [A: ty,L: uni] : $lesseq(0,length(A,L)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_nonnegative) ).
tff(c_122,plain,
! [A_136: ty,L_137: uni] : permut(A_136,L_137,L_137),
inference(cnfTransformation,[status(thm)],[f_195]) ).
tff(c_333,plain,
! [A_249: ty,L_250: uni] : ( prefix(A_249,0,L_250) = nil(A_249) ),
inference(cnfTransformation,[status(thm)],[f_356]) ).
tff(c_348,plain,
! [A_58: ty] : ( length(A_58,nil(A_58)) = 0 ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_302,plain,
( permut(elt1,prefix(elt1,length(elt1,t2tb('#skF_15')),t2tb('#skF_15')),t2tb('#skF_15'))
| ~ permut(elt1,prefix(elt1,length(elt1,nil(elt1)),nil(elt1)),nil(elt1)) ),
inference(cnfTransformation,[status(thm)],[f_479]) ).
tff(c_387,plain,
( permut(elt1,prefix(elt1,length(elt1,t2tb('#skF_15')),t2tb('#skF_15')),t2tb('#skF_15'))
| ~ permut(elt1,prefix(elt1,0,nil(elt1)),nil(elt1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_348,c_302]) ).
tff(c_393,plain,
permut(elt1,prefix(elt1,length(elt1,t2tb('#skF_15')),t2tb('#skF_15')),t2tb('#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_333,c_387]) ).
tff(c_449,plain,
length(elt1,t2tb('#skF_15')) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_393]) ).
tff(c_456,plain,
permut(elt1,prefix(elt1,'#skE_1',t2tb('#skF_15')),t2tb('#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_449,c_393]) ).
tff(c_762,plain,
! [A_554: ty,L2_555: uni,L1_556: uni] :
( permut(A_554,L2_555,L1_556)
| ~ permut(A_554,L1_556,L2_555) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_769,plain,
permut(elt1,t2tb('#skF_15'),prefix(elt1,'#skE_1',t2tb('#skF_15'))),
inference(resolution,[status(thm)],[c_456,c_762]) ).
tff(c_4486,plain,
! [A_1114: ty,X_1115: uni,L1_1116: uni,L2_1117: uni] :
( permut(A_1114,cons(A_1114,X_1115,L1_1116),cons(A_1114,X_1115,L2_1117))
| ~ permut(A_1114,L1_1116,L2_1117) ),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_124,plain,
! [A_138: ty,L2_140: uni,L1_139: uni] :
( permut(A_138,L2_140,L1_139)
| ~ permut(A_138,L1_139,L2_140) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_87123,plain,
! [A_4980: ty,X_4981: uni,L2_4982: uni,L1_4983: uni] :
( permut(A_4980,cons(A_4980,X_4981,L2_4982),cons(A_4980,X_4981,L1_4983))
| ~ permut(A_4980,L1_4983,L2_4982) ),
inference(resolution,[status(thm)],[c_4486,c_124]) ).
tff(c_93328,plain,
! [X_4981: uni] : permut(elt1,cons(elt1,X_4981,prefix(elt1,'#skE_1',t2tb('#skF_15'))),cons(elt1,X_4981,t2tb('#skF_15'))),
inference(resolution,[status(thm)],[c_769,c_87123]) ).
tff(c_21007,plain,
! [A_2248: ty,N_2249a: $int,X_2251: uni,L_2250: uni] :
( ( prefix(A_2248,N_2249a,cons(A_2248,X_2251,L_2250)) = cons(A_2248,X_2251,prefix(A_2248,$sum($uminus(1),N_2249a),L_2250)) )
| ~ $less(0,N_2249a) ),
inference(cnfTransformation,[status(thm)],[f_360]) ).
tff(c_453,plain,
length(elt1,t2tb('#skF_15')) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_393]) ).
tff(c_351,plain,
! [A_51: ty,X_54: uni,X1_55: uni] : ( length(A_51,cons(A_51,X_54,X1_55)) = $sum(1,length(A_51,X1_55)) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_303,plain,
( ~ permut(elt1,prefix(elt1,length(elt1,cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15')))
| ~ permut(elt1,prefix(elt1,length(elt1,nil(elt1)),nil(elt1)),nil(elt1)) ),
inference(cnfTransformation,[status(thm)],[f_479]) ).
tff(c_385,plain,
( ~ permut(elt1,prefix(elt1,length(elt1,cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15')))
| ~ permut(elt1,prefix(elt1,0,nil(elt1)),nil(elt1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_348,c_303]) ).
tff(c_390,plain,
~ permut(elt1,prefix(elt1,length(elt1,cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_333,c_385]) ).
tff(c_395,plain,
~ permut(elt1,prefix(elt1,$sum(1,length(elt1,t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),
inference(demodulation,[status(thm),theory(equality)],[c_351,c_390]) ).
tff(c_569,plain,
~ permut(elt1,prefix(elt1,$sum(1,'#skE_1'),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),
inference(demodulation,[status(thm),theory(equality)],[c_453,c_395]) ).
tff(c_21236,plain,
( ~ permut(elt1,cons(elt1,t2tb1('#skF_14'),prefix(elt1,$sum($uminus(1),$sum(1,'#skE_1')),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15')))
| ~ $less(0,$sum(1,'#skE_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_21007,c_569]) ).
tff(c_21239,plain,
( ~ permut(elt1,cons(elt1,t2tb1('#skF_14'),prefix(elt1,'#skE_1',t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15')))
| ~ $less($uminus(1),'#skE_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_21236]) ).
tff(c_194365,plain,
~ $less($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_93328,c_21239]) ).
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_98,plain,
! [A_108: ty] : ( reverse(A_108,nil(A_108)) = nil(A_108) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_8283,plain,
! [A_1447: ty,L_1448: uni,X_1449: uni] : ( infix_plpl(A_1447,reverse(A_1447,L_1448),cons(A_1447,X_1449,nil(A_1447))) = reverse(A_1447,cons(A_1447,X_1449,L_1448)) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_8330,plain,
! [A_108: ty,X_1449: uni] : ( infix_plpl(A_108,nil(A_108),cons(A_108,X_1449,nil(A_108))) = reverse(A_108,cons(A_108,X_1449,nil(A_108))) ),
inference(superposition,[status(thm),theory(equality)],[c_98,c_8283]) ).
tff(c_8354,plain,
! [A_108: ty,X_1449: uni] : ( reverse(A_108,cons(A_108,X_1449,nil(A_108))) = cons(A_108,X_1449,nil(A_108)) ),
inference(demodulation,[status(thm),theory(equality)],[c_53,c_8330]) ).
tff(c_340,plain,
! [A_125: ty,L_126: uni] : ( length(A_125,reverse(A_125,L_126)) = length(A_125,L_126) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_347,plain,
! [A_75: ty,L1_76: uni,L2_77: uni] : ( length(A_75,infix_plpl(A_75,L1_76,L2_77)) = $sum(length(A_75,L1_76),length(A_75,L2_77)) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_8301,plain,
! [A_1447: ty,X_1449: uni,L_1448: uni] : ( length(A_1447,reverse(A_1447,cons(A_1447,X_1449,L_1448))) = $sum(length(A_1447,reverse(A_1447,L_1448)),length(A_1447,cons(A_1447,X_1449,nil(A_1447)))) ),
inference(superposition,[status(thm),theory(equality)],[c_8283,c_347]) ).
tff(c_8346,plain,
! [A_1447: ty,X_1449: uni,L_1448: uni] : ( length(A_1447,reverse(A_1447,cons(A_1447,X_1449,L_1448))) = $sum(length(A_1447,L_1448),$sum(1,0)) ),
inference(demodulation,[status(thm),theory(equality)],[c_348,c_351,c_340,c_8301]) ).
tff(c_63319,plain,
! [A_4147: ty,X_4148: uni,L_4149: uni] : ( length(A_4147,reverse(A_4147,cons(A_4147,X_4148,L_4149))) = $sum(1,length(A_4147,L_4149)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8346]) ).
tff(c_63563,plain,
! [A_108: ty,X_1449: uni] : ( length(A_108,cons(A_108,X_1449,nil(A_108))) = $sum(1,length(A_108,nil(A_108))) ),
inference(superposition,[status(thm),theory(equality)],[c_8354,c_63319]) ).
tff(c_63811,plain,
! [A_108: ty,X_1449: uni] : ( length(A_108,cons(A_108,X_1449,nil(A_108))) = $sum(1,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_348,c_63563]) ).
tff(c_63827,plain,
! [A_4204: ty,X_4205: uni] : ( length(A_4204,cons(A_4204,X_4205,nil(A_4204))) = 1 ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_63811]) ).
tff(c_3651,plain,
! [A_1036: ty,L1_1037: uni,L2_1038: uni] : ( length(A_1036,infix_plpl(A_1036,L1_1037,L2_1038)) = $sum(length(A_1036,L1_1037),length(A_1036,L2_1038)) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_44,plain,
! [A_56: ty,L_57: uni] : $lesseq(0,length(A_56,L_57)),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_350,plain,
! [A_56: ty,L_57: uni] : ~ $less(length(A_56,L_57),0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_44]) ).
tff(c_3659,plain,
! [A_1036: ty,L1_1037: uni,L2_1038: uni] : ~ $less($sum(length(A_1036,L1_1037),length(A_1036,L2_1038)),0),
inference(superposition,[status(thm),theory(equality)],[c_3651,c_350]) ).
tff(c_3683,plain,
! [A_1039: ty,L2_1040: uni,L1_1041: uni] : ~ $less($sum(length(A_1039,L2_1040),length(A_1039,L1_1041)),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3659]) ).
tff(c_3752,plain,
! [L1_1051: uni] : ~ $less($sum('#skE_1',length(elt1,L1_1051)),0),
inference(superposition,[status(thm),theory(equality)],[c_453,c_3683]) ).
tff(c_3863,plain,
! [L1_1058: uni,L2_1059: uni] : ~ $less($sum('#skE_1',$sum(length(elt1,L1_1058),length(elt1,L2_1059))),0),
inference(superposition,[status(thm),theory(equality)],[c_347,c_3752]) ).
tff(c_3944,plain,
! [L1_1058: uni] : ~ $less($sum('#skE_1',$sum(length(elt1,L1_1058),'#skE_1')),0),
inference(superposition,[status(thm),theory(equality)],[c_453,c_3863]) ).
tff(c_4304,plain,
! [L1_1101: uni] : ~ $less($sum($product(2,'#skE_1'),length(elt1,L1_1101)),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3944]) ).
tff(c_6861,plain,
! [L1_1354: uni,L2_1355: uni] : ~ $less($sum($product(2,'#skE_1'),$sum(length(elt1,L1_1354),length(elt1,L2_1355))),0),
inference(superposition,[status(thm),theory(equality)],[c_347,c_4304]) ).
tff(c_6974,plain,
! [L1_1354: uni] : ~ $less($sum($product(2,'#skE_1'),$sum(length(elt1,L1_1354),'#skE_1')),0),
inference(superposition,[status(thm),theory(equality)],[c_453,c_6861]) ).
tff(c_7431,plain,
! [L1_1400: uni] : ~ $less($sum($product(3,'#skE_1'),length(elt1,L1_1400)),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6974]) ).
tff(c_8604,plain,
! [L1_1466: uni,L2_1467: uni] : ~ $less($sum($product(3,'#skE_1'),$sum(length(elt1,L1_1466),length(elt1,L2_1467))),0),
inference(superposition,[status(thm),theory(equality)],[c_347,c_7431]) ).
tff(c_8717,plain,
! [L1_1466: uni] : ~ $less($sum($product(3,'#skE_1'),$sum(length(elt1,L1_1466),'#skE_1')),0),
inference(superposition,[status(thm),theory(equality)],[c_453,c_8604]) ).
tff(c_8720,plain,
! [L1_1466: uni] : ~ $less($sum($product(4,'#skE_1'),length(elt1,L1_1466)),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8717]) ).
tff(c_64181,plain,
~ $less($sum($product(4,'#skE_1'),1),0),
inference(superposition,[status(thm),theory(equality)],[c_63827,c_8720]) ).
tff(c_64183,plain,
~ $less($product(2,'#skE_1'),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_64181]) ).
tff(c_194366,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_194365,c_64183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW624_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14 % 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
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 18:51:51 EDT 2023
% 0.13/0.35 % CPUTime :
% 50.46/25.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.46/25.18
% 50.46/25.18 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 50.46/25.21
% 50.46/25.21 Inference rules
% 50.46/25.21 ----------------------
% 50.46/25.21 #Ref : 4
% 50.46/25.21 #Sup : 29778
% 50.46/25.21 #Fact : 25
% 50.46/25.21 #Define : 22
% 50.46/25.21 #Split : 107
% 50.46/25.21 #Chain : 0
% 50.46/25.21 #Close : 3
% 50.46/25.21
% 50.46/25.21 Ordering : LPO
% 50.46/25.21
% 50.46/25.21 Simplification rules
% 50.46/25.21 ----------------------
% 50.46/25.21 #Subsume : 1454
% 50.46/25.21 #Demod : 10062
% 50.46/25.21 #Tautology : 15734
% 50.46/25.21 #SimpNegUnit : 209
% 50.46/25.21 #BackRed : 19
% 50.46/25.21
% 50.46/25.21 #Partial instantiations: 896
% 50.46/25.21 #Strategies tried : 1
% 50.46/25.21
% 50.46/25.21 Timing (in seconds)
% 50.46/25.21 ----------------------
% 50.46/25.21 Preprocessing : 0.96
% 50.46/25.21 Parsing : 0.51
% 50.46/25.21 CNF conversion : 0.07
% 50.46/25.21 Main loop : 23.16
% 50.46/25.21 Inferencing : 2.96
% 50.46/25.21 Reduction : 9.47
% 50.46/25.21 Demodulation : 7.46
% 50.46/25.21 BG Simplification : 1.12
% 50.46/25.21 Subsumption : 7.66
% 50.46/25.21 Abstraction : 0.57
% 50.46/25.21 MUC search : 0.04
% 50.46/25.22 Cooper : 0.12
% 50.46/25.22 Total : 24.18
% 50.46/25.22 Index Insertion : 0.00
% 50.46/25.22 Index Deletion : 0.00
% 50.46/25.22 Index Matching : 0.00
% 50.46/25.22 BG Taut test : 0.00
%------------------------------------------------------------------------------