TSTP Solution File: NUM925^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM925^1 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.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 May 21 02:14:28 EDT 2024
% Result : Theorem 0.11s 0.37s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 131
% Syntax : Number of formulae : 351 ( 181 unt; 31 typ; 0 def)
% Number of atoms : 1731 ( 385 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 408 ( 171 ~; 135 |; 26 &; 0 @)
% ( 72 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 36 ( 35 >; 1 *; 0 +; 0 <<)
% Number of symbols : 82 ( 79 usr; 60 con; 0-6 aty)
% Number of variables : 259 ( 0 ^ 253 !; 0 ?; 259 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
int: $tType ).
thf(type_def_6,type,
nat: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
int: $tType ).
thf(func_def_1,type,
nat: $tType ).
thf(func_def_2,type,
one_one_int: int ).
thf(func_def_3,type,
one_one_nat: nat ).
thf(func_def_4,type,
plus_plus_int: int > int > int ).
thf(func_def_5,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_6,type,
zero_zero_int: int ).
thf(func_def_7,type,
zero_zero_nat: nat ).
thf(func_def_8,type,
bit0: int > int ).
thf(func_def_9,type,
bit1: int > int ).
thf(func_def_10,type,
pls: int ).
thf(func_def_11,type,
number_number_of_int: int > int ).
thf(func_def_12,type,
number_number_of_nat: int > nat ).
thf(func_def_13,type,
semiri1621563631at_int: nat > int ).
thf(func_def_14,type,
semiri984289939at_nat: nat > nat ).
thf(func_def_15,type,
ord_less_int: int > int > $o ).
thf(func_def_16,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_17,type,
power_power_int: int > nat > int ).
thf(func_def_18,type,
power_power_nat: nat > nat > nat ).
thf(func_def_19,type,
n: nat ).
thf(func_def_20,type,
t: int ).
thf(func_def_25,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_26,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_27,type,
vAND: $o > $o > $o ).
thf(func_def_28,type,
vOR: $o > $o > $o ).
thf(func_def_29,type,
vIMP: $o > $o > $o ).
thf(func_def_30,type,
vNOT: $o > $o ).
thf(func_def_31,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f917,plain,
$false,
inference(avatar_sat_refutation,[],[f564,f568,f601,f606,f610,f614,f619,f624,f629,f635,f639,f643,f648,f654,f658,f662,f666,f670,f684,f689,f693,f698,f706,f712,f718,f723,f735,f743,f748,f753,f757,f762,f782,f787,f791,f795,f817,f829,f833,f837,f861,f869,f876,f883,f887,f891,f895,f899,f903,f907,f912,f916]) ).
thf(f916,plain,
( ~ spl0_2
| spl0_13
| ~ spl0_30
| ~ spl0_51 ),
inference(avatar_contradiction_clause,[],[f915]) ).
thf(f915,plain,
( $false
| ~ spl0_2
| spl0_13
| ~ spl0_30
| ~ spl0_51 ),
inference(trivial_inequality_removal,[],[f914]) ).
thf(f914,plain,
( ( $true = $false )
| ~ spl0_2
| spl0_13
| ~ spl0_30
| ~ spl0_51 ),
inference(forward_demodulation,[],[f913,f650]) ).
thf(f650,plain,
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) )
| ~ spl0_2
| spl0_13 ),
inference(trivial_inequality_removal,[],[f649]) ).
thf(f649,plain,
( ( $true != $true )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) )
| ~ spl0_2
| spl0_13 ),
inference(superposition,[],[f647,f567]) ).
thf(f567,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f566]) ).
thf(f566,plain,
( spl0_2
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f647,plain,
( ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) )
| spl0_13 ),
inference(avatar_component_clause,[],[f645]) ).
thf(f645,plain,
( spl0_13
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f913,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int) )
| ~ spl0_30
| ~ spl0_51 ),
inference(forward_demodulation,[],[f911,f752]) ).
thf(f752,plain,
( ( zero_zero_int = vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),n)) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f750]) ).
thf(f750,plain,
( spl0_30
<=> ( zero_zero_int = vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),n)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
thf(f911,plain,
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),n))) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f909]) ).
thf(f909,plain,
( spl0_51
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),n))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
thf(f912,plain,
spl0_51,
inference(avatar_split_clause,[],[f559,f909]) ).
thf(f559,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),n))),
inference(forward_demodulation,[],[f469,f333]) ).
thf(f333,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri1621563631at_int,X0)),vAPP(nat,int,semiri1621563631at_int,X1)) ),
inference(cnf_transformation,[],[f209]) ).
thf(f209,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri1621563631at_int,X0)),vAPP(nat,int,semiri1621563631at_int,X1)) ),
inference(rectify,[],[f28]) ).
thf(f28,axiom,
! [X12: nat,X13: nat] : ( vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X12),X13)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri1621563631at_int,X12)),vAPP(nat,int,semiri1621563631at_int,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_zadd__int) ).
thf(f469,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),vAPP(nat,int,semiri1621563631at_int,n))),
inference(definition_unfolding,[],[f387,f389]) ).
thf(f389,plain,
one_one_int = vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),
inference(definition_unfolding,[],[f261,f388]) ).
thf(f388,plain,
one_one_nat = vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f268,f257]) ).
thf(f257,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f79]) ).
thf(f79,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Pls__def) ).
thf(f268,plain,
one_one_nat = vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,pls)),
inference(cnf_transformation,[],[f44]) ).
thf(f44,axiom,
one_one_nat = vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Numeral1__eq1__nat) ).
thf(f261,plain,
one_one_int = vAPP(nat,int,semiri1621563631at_int,one_one_nat),
inference(cnf_transformation,[],[f29]) ).
thf(f29,axiom,
one_one_int = vAPP(nat,int,semiri1621563631at_int,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_int__1) ).
thf(f387,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(nat,int,semiri1621563631at_int,n))) = $true,
inference(cnf_transformation,[],[f176]) ).
thf(f176,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(nat,int,semiri1621563631at_int,n))) = $true,
inference(fool_elimination,[],[f175]) ).
thf(f175,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(nat,int,semiri1621563631at_int,n))),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(nat,int,semiri1621563631at_int,n))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(f907,plain,
spl0_50,
inference(avatar_split_clause,[],[f535,f905]) ).
thf(f905,plain,
( spl0_50
<=> ! [X0: int] : ( vAPP(int,int,bit1,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
thf(f535,plain,
! [X0: int] : ( vAPP(int,int,bit1,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0)),X0) ),
inference(forward_demodulation,[],[f422,f402]) ).
thf(f402,plain,
vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)),
inference(definition_unfolding,[],[f270,f389,f257]) ).
thf(f270,plain,
one_one_int = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,pls)),
inference(cnf_transformation,[],[f17]) ).
thf(f17,axiom,
one_one_int = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_semiring__norm_I110_J) ).
thf(f422,plain,
! [X0: int] : ( vAPP(int,int,bit1,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),X0)),X0) ),
inference(definition_unfolding,[],[f295,f389]) ).
thf(f295,plain,
! [X0: int] : ( vAPP(int,int,bit1,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)),X0) ),
inference(cnf_transformation,[],[f192]) ).
thf(f192,plain,
! [X0: int] : ( vAPP(int,int,bit1,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)),X0) ),
inference(rectify,[],[f100]) ).
thf(f100,axiom,
! [X6: int] : ( vAPP(int,int,bit1,X6) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X6)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Bit1__def) ).
thf(f903,plain,
spl0_49,
inference(avatar_split_clause,[],[f448,f901]) ).
thf(f901,plain,
( spl0_49
<=> ! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
thf(f448,plain,
! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))))),zero_zero_int) ),
inference(definition_unfolding,[],[f327,f257]) ).
thf(f327,plain,
! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_int) ),
inference(cnf_transformation,[],[f203]) ).
thf(f203,plain,
! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_int) ),
inference(flattening,[],[f142]) ).
thf(f142,plain,
! [X0: int] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_int) ),
inference(fool_elimination,[],[f141]) ).
thf(f141,plain,
! [X0: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_int),
inference(rectify,[],[f105]) ).
thf(f105,axiom,
! [X46: int] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X46),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls))))),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_power2__less__0) ).
thf(f899,plain,
spl0_48,
inference(avatar_split_clause,[],[f339,f897]) ).
thf(f897,plain,
( spl0_48
<=> ! [X0: int,X1: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
thf(f339,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ),
inference(cnf_transformation,[],[f215]) ).
thf(f215,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,X0)),vAPP(int,int,bit0,X1)) ),
inference(rectify,[],[f98]) ).
thf(f98,axiom,
! [X6: int,X7: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit1,X6)),vAPP(int,int,bit0,X7)) = vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X6),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_add__Bit1__Bit0) ).
thf(f895,plain,
spl0_47,
inference(avatar_split_clause,[],[f338,f893]) ).
thf(f893,plain,
( spl0_47
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
thf(f338,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) ),
inference(cnf_transformation,[],[f214]) ).
thf(f214,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit0,X1)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) ),
inference(rectify,[],[f83]) ).
thf(f83,axiom,
! [X6: int,X7: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X6)),vAPP(int,int,bit0,X7)) = vAPP(int,int,bit0,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X6),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_add__Bit0__Bit0) ).
thf(f891,plain,
spl0_46,
inference(avatar_split_clause,[],[f335,f889]) ).
thf(f889,plain,
( spl0_46
<=> ! [X0: int,X1: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
thf(f335,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ),
inference(cnf_transformation,[],[f211]) ).
thf(f211,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X0)),vAPP(int,int,bit1,X1)) ),
inference(rectify,[],[f99]) ).
thf(f99,axiom,
! [X6: int,X7: int] : ( vAPP(int,int,bit1,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X6),X7)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,bit0,X6)),vAPP(int,int,bit1,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_add__Bit0__Bit1) ).
thf(f887,plain,
spl0_45,
inference(avatar_split_clause,[],[f334,f885]) ).
thf(f885,plain,
( spl0_45
<=> ! [X0: int,X1: int] : ( vAPP(int,int,number_number_of_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
thf(f334,plain,
! [X0: int,X1: int] : ( vAPP(int,int,number_number_of_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) ),
inference(cnf_transformation,[],[f210]) ).
thf(f210,plain,
! [X0: int,X1: int] : ( vAPP(int,int,number_number_of_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X0)),vAPP(int,int,number_number_of_int,X1)) ),
inference(rectify,[],[f97]) ).
thf(f97,axiom,
! [X42: int,X43: int] : ( vAPP(int,int,number_number_of_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X42),X43)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,X42)),vAPP(int,int,number_number_of_int,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_number__of__add) ).
thf(f883,plain,
spl0_44,
inference(avatar_split_clause,[],[f333,f881]) ).
thf(f881,plain,
( spl0_44
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri1621563631at_int,X0)),vAPP(nat,int,semiri1621563631at_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
thf(f876,plain,
spl0_43,
inference(avatar_split_clause,[],[f406,f873]) ).
thf(f873,plain,
( spl0_43
<=> ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
thf(f406,plain,
vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f274,f390,f390,f257]) ).
thf(f390,plain,
zero_zero_nat = vAPP(int,nat,number_number_of_nat,zero_zero_int),
inference(definition_unfolding,[],[f258,f257]) ).
thf(f258,plain,
zero_zero_nat = vAPP(int,nat,number_number_of_nat,pls),
inference(cnf_transformation,[],[f88]) ).
thf(f88,axiom,
zero_zero_nat = vAPP(int,nat,number_number_of_nat,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_semiring__numeral__0__eq__0) ).
thf(f274,plain,
zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f7]) ).
thf(f7,axiom,
zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,zero_zero_nat),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_zero__power2) ).
thf(f869,plain,
spl0_42,
inference(avatar_split_clause,[],[f453,f867]) ).
thf(f867,plain,
( spl0_42
<=> ! [X0: nat,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
thf(f453,plain,
! [X0: nat,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f357,f390,f390]) ).
thf(f357,plain,
! [X0: nat,X1: int] :
( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(cnf_transformation,[],[f246]) ).
thf(f246,plain,
! [X0: nat,X1: int] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_nat != X0 ) )
& ( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_nat = X0 ) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(flattening,[],[f245]) ).
thf(f245,plain,
! [X0: nat,X1: int] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_nat != X0 ) )
& ( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_nat = X0 ) )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(nnf_transformation,[],[f223]) ).
thf(f223,plain,
! [X0: nat,X1: int] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_nat = X0 ) ) ),
inference(rectify,[],[f94]) ).
thf(f94,axiom,
! [X35: nat,X36: int] :
( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X35),vAPP(int,nat,number_number_of_nat,X36)) )
<=> ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X36) )
& ( zero_zero_nat = X35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_power__eq__0__iff__number__of) ).
thf(f861,plain,
( ~ spl0_41
| ~ spl0_10
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f812,f793,f632,f858]) ).
thf(f858,plain,
( spl0_41
<=> ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
thf(f632,plain,
( spl0_10
<=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),n))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f793,plain,
( spl0_36
<=> ! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
thf(f812,plain,
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl0_10
| ~ spl0_36 ),
inference(trivial_inequality_removal,[],[f808]) ).
thf(f808,plain,
( ( zero_zero_int != zero_zero_int )
| ( vAPP(int,nat,number_number_of_nat,zero_zero_int) != vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int))) )
| ~ spl0_10
| ~ spl0_36 ),
inference(superposition,[],[f794,f634]) ).
thf(f634,plain,
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),n))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f632]) ).
thf(f794,plain,
( ! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( vAPP(int,nat,number_number_of_nat,X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f793]) ).
thf(f837,plain,
spl0_40,
inference(avatar_split_clause,[],[f551,f835]) ).
thf(f835,plain,
( spl0_40
<=> ! [X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
thf(f551,plain,
! [X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)))) ),
inference(forward_demodulation,[],[f488,f402]) ).
thf(f488,plain,
! [X1: int] : ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))))) ),
inference(equality_resolution,[],[f460]) ).
thf(f460,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))))) )
| ( X0 != X1 ) ),
inference(definition_unfolding,[],[f375,f389]) ).
thf(f375,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f252,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( ( X0 != X1 )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) != $true ) ) )
& ( ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) ) ) ),
inference(flattening,[],[f251]) ).
thf(f251,plain,
! [X0: int,X1: int] :
( ( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
| ( ( X0 != X1 )
& ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) != $true ) ) )
& ( ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = $true )
| ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) ) ) ),
inference(nnf_transformation,[],[f164]) ).
thf(f164,plain,
! [X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int)) )
<=> ( ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = $true ) ) ),
inference(fool_elimination,[],[f163]) ).
thf(f163,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),one_one_int))
<=> ( ( X0 = X1 )
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ) ),
inference(rectify,[],[f66]) ).
thf(f66,axiom,
! [X9: int,X14: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X9),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X14),one_one_int))
<=> ( ( X9 = X14 )
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X9),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zless__add1__eq) ).
thf(f833,plain,
spl0_39,
inference(avatar_split_clause,[],[f534,f831]) ).
thf(f831,plain,
( spl0_39
<=> ! [X0: int] : ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
thf(f534,plain,
! [X0: int] : ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),X0)),X0) ),
inference(forward_demodulation,[],[f421,f402]) ).
thf(f421,plain,
! [X0: int] : ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),X0)),X0) ),
inference(definition_unfolding,[],[f294,f389]) ).
thf(f294,plain,
! [X0: int] : ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)),X0) ),
inference(cnf_transformation,[],[f191]) ).
thf(f191,plain,
! [X0: int] : ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X0)),X0) ),
inference(rectify,[],[f101]) ).
thf(f101,axiom,
! [X14: int] : ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),X14)),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_odd__nonzero) ).
thf(f829,plain,
spl0_38,
inference(avatar_split_clause,[],[f331,f827]) ).
thf(f827,plain,
( spl0_38
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,semiri1621563631at_int,X0)),X1) = vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
thf(f331,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,semiri1621563631at_int,X0)),X1) = vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ),
inference(cnf_transformation,[],[f207]) ).
thf(f207,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,semiri1621563631at_int,X0)),X1) = vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),X1)) ),
inference(rectify,[],[f25]) ).
thf(f25,axiom,
! [X12: nat,X13: nat] : ( vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,semiri1621563631at_int,X12)),X13) = vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X12),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_zpower__int) ).
thf(f817,plain,
spl0_37,
inference(avatar_split_clause,[],[f343,f815]) ).
thf(f815,plain,
( spl0_37
<=> ! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) = $true )
| ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
thf(f343,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) = $true )
| ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = $true ) ),
inference(cnf_transformation,[],[f146]) ).
thf(f146,plain,
! [X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0) = $true )
| ( X0 = X1 )
| ( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) = $true ) ),
inference(fool_elimination,[],[f145]) ).
thf(f145,plain,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0)
| ( X0 = X1 )
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
! [X0: int,X1: int] :
( vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X1),X0)
| ( X0 = X1 )
| vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_zless__linear) ).
thf(f795,plain,
spl0_36,
inference(avatar_split_clause,[],[f456,f793]) ).
thf(f456,plain,
! [X0: int,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,X1) != vAPP(int,nat,number_number_of_nat,zero_zero_int) )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(definition_unfolding,[],[f360,f390]) ).
thf(f360,plain,
! [X0: int,X1: int] :
( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(cnf_transformation,[],[f248]) ).
thf(f248,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(flattening,[],[f247]) ).
thf(f247,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X1) )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
inference(nnf_transformation,[],[f224]) ).
thf(f224,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) )
<=> ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X1) )
& ( zero_zero_int = X0 ) ) ),
inference(rectify,[],[f93]) ).
thf(f93,axiom,
! [X35: int,X36: int] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X35),vAPP(int,nat,number_number_of_nat,X36)) )
<=> ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X36) )
& ( zero_zero_int = X35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_power__eq__0__iff__number__of) ).
thf(f791,plain,
spl0_35,
inference(avatar_split_clause,[],[f454,f789]) ).
thf(f789,plain,
( spl0_35
<=> ! [X0: nat,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
thf(f454,plain,
! [X0: nat,X1: int] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) != vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f356,f390,f390]) ).
thf(f356,plain,
! [X0: nat,X1: int] :
( ( zero_zero_nat = X0 )
| ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),power_power_nat,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(cnf_transformation,[],[f246]) ).
thf(f787,plain,
spl0_34,
inference(avatar_split_clause,[],[f428,f785]) ).
thf(f785,plain,
( spl0_34
<=> ! [X0: int] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
thf(f428,plain,
! [X0: int] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) )
| ( vAPP(int,nat,number_number_of_nat,X0) = vAPP(int,nat,number_number_of_nat,zero_zero_int) ) ),
inference(definition_unfolding,[],[f302,f390]) ).
thf(f302,plain,
! [X0: int] :
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) ) ),
inference(cnf_transformation,[],[f230]) ).
thf(f230,plain,
! [X0: int] :
( ( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) ) )
& ( ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) )
| ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) ) ) ),
inference(ennf_transformation,[],[f196]) ).
thf(f196,plain,
! [X0: int] :
( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X0) )
=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) ) )
& ( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X0) )
=> ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X0)) ) ) ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
! [X5: int] :
( ( ( zero_zero_nat != vAPP(int,nat,number_number_of_nat,X5) )
=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X5)) ) )
& ( ( zero_zero_nat = vAPP(int,nat,number_number_of_nat,X5) )
=> ( one_one_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_power__0__left__number__of) ).
thf(f782,plain,
spl0_33,
inference(avatar_split_clause,[],[f408,f779]) ).
thf(f779,plain,
( spl0_33
<=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
thf(f408,plain,
zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f276,f257]) ).
thf(f276,plain,
zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f6]) ).
thf(f6,axiom,
zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,zero_zero_int),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__power2) ).
thf(f762,plain,
spl0_32,
inference(avatar_split_clause,[],[f402,f759]) ).
thf(f759,plain,
( spl0_32
<=> ( vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) = vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
thf(f757,plain,
spl0_31,
inference(avatar_split_clause,[],[f330,f755]) ).
thf(f755,plain,
( spl0_31
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
thf(f330,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) ),
inference(cnf_transformation,[],[f206]) ).
thf(f206,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) ),
inference(rectify,[],[f53]) ).
thf(f53,axiom,
! [X14: int,X9: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X14),X9) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X9),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_zadd__commute) ).
thf(f753,plain,
( spl0_30
| ~ spl0_10
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f738,f733,f632,f750]) ).
thf(f733,plain,
( spl0_27
<=> ! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
thf(f738,plain,
( ( zero_zero_int = vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),n)) )
| ~ spl0_10
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f737]) ).
thf(f737,plain,
( ( zero_zero_int != zero_zero_int )
| ( zero_zero_int = vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),n)) )
| ~ spl0_10
| ~ spl0_27 ),
inference(superposition,[],[f734,f634]) ).
thf(f734,plain,
( ! [X0: int,X1: int] :
( ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) )
| ( zero_zero_int = X0 ) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f733]) ).
thf(f748,plain,
spl0_29,
inference(avatar_split_clause,[],[f558,f745]) ).
thf(f745,plain,
( spl0_29
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
thf(f558,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),
inference(forward_demodulation,[],[f468,f402]) ).
thf(f468,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f386,f389]) ).
thf(f386,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),one_one_int) = $true,
inference(cnf_transformation,[],[f174]) ).
thf(f174,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),one_one_int) = $true,
inference(fool_elimination,[],[f173]) ).
thf(f173,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),one_one_int),
inference(rectify,[],[f65]) ).
thf(f65,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_int__0__less__1) ).
thf(f743,plain,
spl0_28,
inference(avatar_split_clause,[],[f557,f740]) ).
thf(f740,plain,
( spl0_28
<=> ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
thf(f557,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(int,int,number_number_of_int,vAPP(int,int,bit1,zero_zero_int))),t),
inference(forward_demodulation,[],[f467,f402]) ).
thf(f467,plain,
$true = vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),t),
inference(definition_unfolding,[],[f385,f389]) ).
thf(f385,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),t) = $true,
inference(cnf_transformation,[],[f172]) ).
thf(f172,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),t) = $true,
inference(fool_elimination,[],[f171]) ).
thf(f171,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),t),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,one_one_int),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_t1) ).
thf(f735,plain,
spl0_27,
inference(avatar_split_clause,[],[f359,f733]) ).
thf(f359,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,X0),vAPP(int,nat,number_number_of_nat,X1)) ) ),
inference(cnf_transformation,[],[f248]) ).
thf(f723,plain,
spl0_26,
inference(avatar_split_clause,[],[f466,f720]) ).
thf(f720,plain,
( spl0_26
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
thf(f466,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(int,nat,number_number_of_nat,zero_zero_int)),n),
inference(definition_unfolding,[],[f384,f390]) ).
thf(f384,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),n) = $true,
inference(cnf_transformation,[],[f170]) ).
thf(f170,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),n) = $true,
inference(fool_elimination,[],[f169]) ).
thf(f169,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),n),
inference(rectify,[],[f19]) ).
thf(f19,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,zero_zero_nat),n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_n0) ).
thf(f718,plain,
spl0_25,
inference(avatar_split_clause,[],[f326,f716]) ).
thf(f716,plain,
( spl0_25
<=> ! [X0: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,semiri1621563631at_int,X0)),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
thf(f326,plain,
! [X0: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,semiri1621563631at_int,X0)),zero_zero_int) ),
inference(cnf_transformation,[],[f202]) ).
thf(f202,plain,
! [X0: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,semiri1621563631at_int,X0)),zero_zero_int) ),
inference(flattening,[],[f140]) ).
thf(f140,plain,
! [X0: nat] : ( $true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,semiri1621563631at_int,X0)),zero_zero_int) ),
inference(fool_elimination,[],[f139]) ).
thf(f139,plain,
! [X0: nat] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,semiri1621563631at_int,X0)),zero_zero_int),
inference(rectify,[],[f67]) ).
thf(f67,axiom,
! [X6: nat] : ~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,vAPP(nat,int,semiri1621563631at_int,X6)),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_int__less__0__conv) ).
thf(f712,plain,
spl0_24,
inference(avatar_split_clause,[],[f291,f710]) ).
thf(f710,plain,
( spl0_24
<=> ! [X0: int] : ( vAPP(int,int,bit0,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
thf(f291,plain,
! [X0: int] : ( vAPP(int,int,bit0,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) ),
inference(cnf_transformation,[],[f188]) ).
thf(f188,plain,
! [X0: int] : ( vAPP(int,int,bit0,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) ),
inference(rectify,[],[f84]) ).
thf(f84,axiom,
! [X6: int] : ( vAPP(int,int,bit0,X6) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X6),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
thf(f706,plain,
spl0_23,
inference(avatar_split_clause,[],[f309,f704]) ).
thf(f704,plain,
( spl0_23
<=> ! [X0: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
thf(f309,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) ) ),
inference(cnf_transformation,[],[f236]) ).
thf(f236,plain,
! [X0: int] :
( ( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) )
| ( zero_zero_int != X0 ) )
& ( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) ) ) ),
inference(nnf_transformation,[],[f200]) ).
thf(f200,plain,
! [X0: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X0) )
<=> ( zero_zero_int = X0 ) ),
inference(rectify,[],[f71]) ).
thf(f71,axiom,
! [X32: int] :
( ( zero_zero_int = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X32),X32) )
<=> ( zero_zero_int = X32 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_double__eq__0__iff) ).
thf(f698,plain,
~ spl0_22,
inference(avatar_split_clause,[],[f393,f695]) ).
thf(f695,plain,
( spl0_22
<=> ( zero_zero_int = vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f393,plain,
zero_zero_int != vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),
inference(definition_unfolding,[],[f256,f389]) ).
thf(f256,plain,
zero_zero_int != one_one_int,
inference(cnf_transformation,[],[f80]) ).
thf(f80,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_int__0__neq__1) ).
thf(f693,plain,
spl0_21,
inference(avatar_split_clause,[],[f290,f691]) ).
thf(f691,plain,
( spl0_21
<=> ! [X0: nat] : ( vAPP(int,nat,number_number_of_nat,vAPP(nat,int,semiri1621563631at_int,X0)) = vAPP(nat,nat,semiri984289939at_nat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f290,plain,
! [X0: nat] : ( vAPP(int,nat,number_number_of_nat,vAPP(nat,int,semiri1621563631at_int,X0)) = vAPP(nat,nat,semiri984289939at_nat,X0) ),
inference(cnf_transformation,[],[f187]) ).
thf(f187,plain,
! [X0: nat] : ( vAPP(int,nat,number_number_of_nat,vAPP(nat,int,semiri1621563631at_int,X0)) = vAPP(nat,nat,semiri984289939at_nat,X0) ),
inference(rectify,[],[f102]) ).
thf(f102,axiom,
! [X44: nat] : ( vAPP(int,nat,number_number_of_nat,vAPP(nat,int,semiri1621563631at_int,X44)) = vAPP(nat,nat,semiri984289939at_nat,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_number__of__int) ).
thf(f689,plain,
spl0_20,
inference(avatar_split_clause,[],[f289,f687]) ).
thf(f687,plain,
( spl0_20
<=> ! [X0: nat] : ( vAPP(nat,int,semiri1621563631at_int,X0) = vAPP(int,int,number_number_of_int,vAPP(nat,int,semiri1621563631at_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f289,plain,
! [X0: nat] : ( vAPP(nat,int,semiri1621563631at_int,X0) = vAPP(int,int,number_number_of_int,vAPP(nat,int,semiri1621563631at_int,X0)) ),
inference(cnf_transformation,[],[f186]) ).
thf(f186,plain,
! [X0: nat] : ( vAPP(nat,int,semiri1621563631at_int,X0) = vAPP(int,int,number_number_of_int,vAPP(nat,int,semiri1621563631at_int,X0)) ),
inference(rectify,[],[f103]) ).
thf(f103,axiom,
! [X44: nat] : ( vAPP(nat,int,semiri1621563631at_int,X44) = vAPP(int,int,number_number_of_int,vAPP(nat,int,semiri1621563631at_int,X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_number__of__int) ).
thf(f684,plain,
( spl0_19
| ~ spl0_3
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f674,f656,f598,f682]) ).
thf(f682,plain,
( spl0_19
<=> ! [X0: int] :
( ( zero_zero_int != vAPP(int,int,number_number_of_int,X0) )
| ( zero_zero_int = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
thf(f598,plain,
( spl0_3
<=> ( zero_zero_int = vAPP(int,int,number_number_of_int,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f656,plain,
( spl0_15
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,int,number_number_of_int,X0) != vAPP(int,int,number_number_of_int,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f674,plain,
( ! [X0: int] :
( ( zero_zero_int != vAPP(int,int,number_number_of_int,X0) )
| ( zero_zero_int = X0 ) )
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f657,f600]) ).
thf(f600,plain,
( ( zero_zero_int = vAPP(int,int,number_number_of_int,zero_zero_int) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f598]) ).
thf(f657,plain,
( ! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,X0) != vAPP(int,int,number_number_of_int,X1) )
| ( X0 = X1 ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f656]) ).
thf(f670,plain,
spl0_18,
inference(avatar_split_clause,[],[f431,f668]) ).
thf(f668,plain,
( spl0_18
<=> ! [X0: nat] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 )
| ( zero_zero_int != vAPP(nat,int,semiri1621563631at_int,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f431,plain,
! [X0: nat] :
( ( vAPP(int,nat,number_number_of_nat,zero_zero_int) = X0 )
| ( zero_zero_int != vAPP(nat,int,semiri1621563631at_int,X0) ) ),
inference(definition_unfolding,[],[f303,f390]) ).
thf(f303,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( zero_zero_int != vAPP(nat,int,semiri1621563631at_int,X0) ) ),
inference(cnf_transformation,[],[f233]) ).
thf(f233,plain,
! [X0: nat] :
( ( ( zero_zero_int = vAPP(nat,int,semiri1621563631at_int,X0) )
| ( zero_zero_nat != X0 ) )
& ( ( zero_zero_nat = X0 )
| ( zero_zero_int != vAPP(nat,int,semiri1621563631at_int,X0) ) ) ),
inference(nnf_transformation,[],[f197]) ).
thf(f197,plain,
! [X0: nat] :
( ( zero_zero_int = vAPP(nat,int,semiri1621563631at_int,X0) )
<=> ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f32]) ).
thf(f32,axiom,
! [X13: nat] :
( ( zero_zero_int = vAPP(nat,int,semiri1621563631at_int,X13) )
<=> ( zero_zero_nat = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_int__eq__0__conv) ).
thf(f666,plain,
spl0_17,
inference(avatar_split_clause,[],[f354,f664]) ).
thf(f664,plain,
( spl0_17
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,int,bit1,X0) != vAPP(int,int,bit1,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f354,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,int,bit1,X0) != vAPP(int,int,bit1,X1) ) ),
inference(cnf_transformation,[],[f244]) ).
thf(f244,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,int,bit1,X0) = vAPP(int,int,bit1,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(int,int,bit1,X0) != vAPP(int,int,bit1,X1) ) ) ),
inference(nnf_transformation,[],[f222]) ).
thf(f222,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit1,X0) = vAPP(int,int,bit1,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f48]) ).
thf(f48,axiom,
! [X6: int,X7: int] :
( ( vAPP(int,int,bit1,X6) = vAPP(int,int,bit1,X7) )
<=> ( X6 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_rel__simps_I51_J) ).
thf(f662,plain,
spl0_16,
inference(avatar_split_clause,[],[f352,f660]) ).
thf(f660,plain,
( spl0_16
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,int,bit0,X0) != vAPP(int,int,bit0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f352,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,int,bit0,X0) != vAPP(int,int,bit0,X1) ) ),
inference(cnf_transformation,[],[f243]) ).
thf(f243,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,int,bit0,X0) = vAPP(int,int,bit0,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(int,int,bit0,X0) != vAPP(int,int,bit0,X1) ) ) ),
inference(nnf_transformation,[],[f221]) ).
thf(f221,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,bit0,X0) = vAPP(int,int,bit0,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
! [X6: int,X7: int] :
( ( vAPP(int,int,bit0,X6) = vAPP(int,int,bit0,X7) )
<=> ( X6 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_rel__simps_I48_J) ).
thf(f658,plain,
spl0_15,
inference(avatar_split_clause,[],[f350,f656]) ).
thf(f350,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,int,number_number_of_int,X0) != vAPP(int,int,number_number_of_int,X1) ) ),
inference(cnf_transformation,[],[f242]) ).
thf(f242,plain,
! [X0: int,X1: int] :
( ( ( vAPP(int,int,number_number_of_int,X0) = vAPP(int,int,number_number_of_int,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(int,int,number_number_of_int,X0) != vAPP(int,int,number_number_of_int,X1) ) ) ),
inference(nnf_transformation,[],[f220]) ).
thf(f220,plain,
! [X0: int,X1: int] :
( ( vAPP(int,int,number_number_of_int,X0) = vAPP(int,int,number_number_of_int,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f45]) ).
thf(f45,axiom,
! [X20: int,X21: int] :
( ( vAPP(int,int,number_number_of_int,X20) = vAPP(int,int,number_number_of_int,X21) )
<=> ( X20 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_eq__number__of) ).
thf(f654,plain,
spl0_14,
inference(avatar_split_clause,[],[f348,f652]) ).
thf(f652,plain,
( spl0_14
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,int,semiri1621563631at_int,X0) != vAPP(nat,int,semiri1621563631at_int,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f348,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,int,semiri1621563631at_int,X0) != vAPP(nat,int,semiri1621563631at_int,X1) ) ),
inference(cnf_transformation,[],[f241]) ).
thf(f241,plain,
! [X0: nat,X1: nat] :
( ( ( vAPP(nat,int,semiri1621563631at_int,X0) = vAPP(nat,int,semiri1621563631at_int,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( vAPP(nat,int,semiri1621563631at_int,X0) != vAPP(nat,int,semiri1621563631at_int,X1) ) ) ),
inference(nnf_transformation,[],[f219]) ).
thf(f219,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,int,semiri1621563631at_int,X0) = vAPP(nat,int,semiri1621563631at_int,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f54]) ).
thf(f54,axiom,
! [X12: nat,X13: nat] :
( ( vAPP(nat,int,semiri1621563631at_int,X12) = vAPP(nat,int,semiri1621563631at_int,X13) )
<=> ( X12 = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_int__int__eq) ).
thf(f648,plain,
~ spl0_13,
inference(avatar_split_clause,[],[f413,f645]) ).
thf(f413,plain,
$true != vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,zero_zero_int),zero_zero_int),
inference(definition_unfolding,[],[f281,f257]) ).
thf(f281,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),zero_zero_int) != $true,
inference(cnf_transformation,[],[f178]) ).
thf(f178,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),zero_zero_int) != $true,
inference(flattening,[],[f112]) ).
thf(f112,plain,
vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),zero_zero_int) != $true,
inference(fool_elimination,[],[f111]) ).
thf(f111,plain,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),zero_zero_int),
inference(rectify,[],[f63]) ).
thf(f63,axiom,
~ vAPP(int,$o,vAPP(int,sTfun(int,$o),ord_less_int,pls),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_bin__less__0__simps_I1_J) ).
thf(f643,plain,
spl0_12,
inference(avatar_split_clause,[],[f287,f641]) ).
thf(f641,plain,
( spl0_12
<=> ! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),zero_zero_int) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f287,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),zero_zero_int) = X0 ),
inference(cnf_transformation,[],[f184]) ).
thf(f184,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),zero_zero_int) = X0 ),
inference(rectify,[],[f85]) ).
thf(f85,axiom,
! [X14: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X14),zero_zero_int) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_zadd__0__right) ).
thf(f639,plain,
spl0_11,
inference(avatar_split_clause,[],[f285,f637]) ).
thf(f637,plain,
( spl0_11
<=> ! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,zero_zero_int),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f285,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,zero_zero_int),X0) = X0 ),
inference(cnf_transformation,[],[f182]) ).
thf(f182,plain,
! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,zero_zero_int),X0) = X0 ),
inference(rectify,[],[f86]) ).
thf(f86,axiom,
! [X14: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,zero_zero_int),X14) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_zadd__0) ).
thf(f635,plain,
( spl0_10
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f630,f626,f632]) ).
thf(f626,plain,
( spl0_9
<=> ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),vAPP(nat,int,semiri1621563631at_int,n))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f630,plain,
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(nat,int,semiri1621563631at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int))),n))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl0_9 ),
inference(forward_demodulation,[],[f628,f333]) ).
thf(f628,plain,
( ( zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),vAPP(nat,int,semiri1621563631at_int,n))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f626]) ).
thf(f629,plain,
spl0_9,
inference(avatar_split_clause,[],[f392,f626]) ).
thf(f392,plain,
zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit1,zero_zero_int)))),vAPP(nat,int,semiri1621563631at_int,n))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,zero_zero_int)))),
inference(definition_unfolding,[],[f255,f389,f257]) ).
thf(f255,plain,
zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(nat,int,semiri1621563631at_int,n))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f177]) ).
thf(f177,plain,
zero_zero_int = vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(nat,int,semiri1621563631at_int,n))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
inference(flattening,[],[f108]) ).
thf(f108,negated_conjecture,
~ ( ( zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(nat,int,semiri1621563631at_int,n))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))) ) ),
inference(negated_conjecture,[],[f107]) ).
thf(f107,conjecture,
zero_zero_int != vAPP(nat,int,vAPP(int,sTfun(nat,int),power_power_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,one_one_int),vAPP(nat,int,semiri1621563631at_int,n))),vAPP(int,nat,number_number_of_nat,vAPP(int,int,bit0,vAPP(int,int,bit1,pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f624,plain,
spl0_8,
inference(avatar_split_clause,[],[f396,f621]) ).
thf(f621,plain,
( spl0_8
<=> ( zero_zero_int = vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f396,plain,
zero_zero_int = vAPP(nat,int,semiri1621563631at_int,vAPP(int,nat,number_number_of_nat,zero_zero_int)),
inference(definition_unfolding,[],[f262,f390]) ).
thf(f262,plain,
zero_zero_int = vAPP(nat,int,semiri1621563631at_int,zero_zero_nat),
inference(cnf_transformation,[],[f33]) ).
thf(f33,axiom,
zero_zero_int = vAPP(nat,int,semiri1621563631at_int,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_int__0) ).
thf(f619,plain,
spl0_7,
inference(avatar_split_clause,[],[f328,f617]) ).
thf(f617,plain,
( spl0_7
<=> ! [X0: int,X1: int] : ( vAPP(int,int,bit1,X0) != vAPP(int,int,bit0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f328,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,X0) != vAPP(int,int,bit0,X1) ),
inference(cnf_transformation,[],[f204]) ).
thf(f204,plain,
! [X0: int,X1: int] : ( vAPP(int,int,bit1,X0) != vAPP(int,int,bit0,X1) ),
inference(rectify,[],[f74]) ).
thf(f74,axiom,
! [X6: int,X7: int] : ( vAPP(int,int,bit1,X6) != vAPP(int,int,bit0,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_rel__simps_I50_J) ).
thf(f614,plain,
spl0_6,
inference(avatar_split_clause,[],[f433,f612]) ).
thf(f612,plain,
( spl0_6
<=> ! [X0: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(int,int,bit0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f433,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != vAPP(int,int,bit0,X0) ) ),
inference(definition_unfolding,[],[f305,f257,f257]) ).
thf(f305,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != vAPP(int,int,bit0,X0) ) ),
inference(cnf_transformation,[],[f234]) ).
thf(f234,plain,
! [X0: int] :
( ( ( pls = vAPP(int,int,bit0,X0) )
| ( pls != X0 ) )
& ( ( pls = X0 )
| ( pls != vAPP(int,int,bit0,X0) ) ) ),
inference(nnf_transformation,[],[f198]) ).
thf(f198,plain,
! [X0: int] :
( ( pls = vAPP(int,int,bit0,X0) )
<=> ( pls = X0 ) ),
inference(rectify,[],[f76]) ).
thf(f76,axiom,
! [X6: int] :
( ( pls = vAPP(int,int,bit0,X6) )
<=> ( pls = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I44_J) ).
thf(f610,plain,
spl0_5,
inference(avatar_split_clause,[],[f415,f608]) ).
thf(f608,plain,
( spl0_5
<=> ! [X0: int] : ( zero_zero_int != vAPP(int,int,bit1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f415,plain,
! [X0: int] : ( zero_zero_int != vAPP(int,int,bit1,X0) ),
inference(definition_unfolding,[],[f283,f257]) ).
thf(f283,plain,
! [X0: int] : ( pls != vAPP(int,int,bit1,X0) ),
inference(cnf_transformation,[],[f180]) ).
thf(f180,plain,
! [X0: int] : ( pls != vAPP(int,int,bit1,X0) ),
inference(rectify,[],[f73]) ).
thf(f73,axiom,
! [X7: int] : ( pls != vAPP(int,int,bit1,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rel__simps_I39_J) ).
thf(f606,plain,
spl0_4,
inference(avatar_split_clause,[],[f400,f603]) ).
thf(f603,plain,
( spl0_4
<=> ( zero_zero_int = vAPP(int,int,bit0,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f400,plain,
zero_zero_int = vAPP(int,int,bit0,zero_zero_int),
inference(definition_unfolding,[],[f267,f257,f257]) ).
thf(f267,plain,
pls = vAPP(int,int,bit0,pls),
inference(cnf_transformation,[],[f78]) ).
thf(f78,axiom,
pls = vAPP(int,int,bit0,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Bit0__Pls) ).
thf(f601,plain,
spl0_3,
inference(avatar_split_clause,[],[f391,f598]) ).
thf(f391,plain,
zero_zero_int = vAPP(int,int,number_number_of_int,zero_zero_int),
inference(definition_unfolding,[],[f263,f257]) ).
thf(f263,plain,
zero_zero_int = vAPP(int,int,number_number_of_int,pls),
inference(cnf_transformation,[],[f87]) ).
thf(f87,axiom,
zero_zero_int = vAPP(int,int,number_number_of_int,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_semiring__numeral__0__eq__0) ).
thf(f568,plain,
spl0_2,
inference(avatar_split_clause,[],[f110,f566]) ).
thf(f110,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f564,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f109,f561]) ).
thf(f561,plain,
( spl0_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f109,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : NUM925^1 : TPTP v8.2.0. Released v5.3.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n026.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 20 07:13:53 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.11/0.32 % (18192)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (18196)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 % (18195)WARNING: value z3 for option sas not known
% 0.11/0.34 % (18197)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.34 % (18193)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34 % (18199)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.34 % (18195)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.34 % (18194)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.34 % (18198)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.34 % Exception at run slice level
% 0.11/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.34 % (18199)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.34 % Exception at run slice level
% 0.11/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.34 % Exception at run slice level
% 0.11/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.35 % (18200)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.11/0.36 % (18200)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.36 % Exception at run slice level
% 0.11/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.36 % (18201)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.11/0.36 % (18202)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.11/0.36 % (18197)First to succeed.
% 0.11/0.36 % (18198)Also succeeded, but the first one will report.
% 0.11/0.36 % (18201)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.37 % (18197)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18192"
% 0.11/0.37 % (18195)Also succeeded, but the first one will report.
% 0.11/0.37 % (18197)Refutation found. Thanks to Tanya!
% 0.11/0.37 % SZS status Theorem for theBenchmark
% 0.11/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.37 % (18197)------------------------------
% 0.11/0.37 % (18197)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.37 % (18197)Termination reason: Refutation
% 0.11/0.37
% 0.11/0.37 % (18197)Memory used [KB]: 1129
% 0.11/0.37 % (18197)Time elapsed: 0.029 s
% 0.11/0.37 % (18197)Instructions burned: 61 (million)
% 0.11/0.37 % (18192)Success in time 0.047 s
%------------------------------------------------------------------------------