%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP103^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:21 AM UTC 2026
% Result : Theorem 0.20s 0.36s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 83 ( 28 unt; 0 typ; 4 def)
% Number of atoms : 269 ( 95 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 415 ( 68 ~; 48 |; 0 &; 277 @)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 61 usr; 10 con; 0-4 aty)
% Number of variables : 71 ( 0 sgn 71 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
list_P1891567085od_a_a: $tType ).
thf(type_def_6,type,
list_P1458844246od_a_a: $tType ).
thf(type_def_7,type,
list_P319927492_a_a_a: $tType ).
thf(type_def_8,type,
list_P1467822637od_a_a: $tType ).
thf(type_def_9,type,
list_a: $tType ).
thf(type_def_10,type,
nat: $tType ).
thf(type_def_11,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
times_times_nat: nat > nat > nat ).
thf(func_def_1,type,
zero_zero_nat: nat ).
thf(func_def_2,type,
produc1055075589od_a_a: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1891567085od_a_a ).
thf(func_def_3,type,
produc778776796_a_a_a: list_P1467822637od_a_a > list_a > list_P319927492_a_a_a ).
thf(func_def_4,type,
produc16441326od_a_a: list_a > list_P1467822637od_a_a > list_P1458844246od_a_a ).
thf(func_def_5,type,
product_a_a: list_a > list_a > list_P1467822637od_a_a ).
thf(func_def_6,type,
suc: nat > nat ).
thf(func_def_7,type,
size_s1052379225od_a_a: list_P1891567085od_a_a > nat ).
thf(func_def_8,type,
size_s736232240_a_a_a: list_P319927492_a_a_a > nat ).
thf(func_def_9,type,
size_s1875148994od_a_a: list_P1458844246od_a_a > nat ).
thf(func_def_10,type,
size_s642698393od_a_a: list_P1467822637od_a_a > nat ).
thf(func_def_11,type,
size_size_list_a: list_a > nat ).
thf(func_def_12,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_13,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_14,type,
divide_divide_nat: nat > nat > nat ).
thf(func_def_15,type,
k: nat ).
thf(func_def_16,type,
n: nat ).
thf(func_def_17,type,
xs: list_a ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_22,type,
vAND: $o > $o > $o ).
thf(func_def_23,type,
vOR: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vIMP: $o > $o > $o ).
thf(func_def_26,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_31,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
sK0: nat > nat > nat ).
thf(func_def_33,type,
sK1: ( nat > $o ) > nat > nat ).
thf(func_def_34,type,
sK2: ( nat > $o ) > nat > nat ).
thf(func_def_35,type,
sK3: ( nat > $o ) > nat ).
thf(func_def_36,type,
sK4: nat > nat ).
thf(func_def_37,type,
sK5: ( nat > $o ) > nat ).
thf(func_def_38,type,
sK6: ( nat > $o ) > nat ).
thf(func_def_39,type,
sK7: ( list_a > $o ) > list_a ).
thf(func_def_40,type,
sK8: ( nat > nat > $o ) > nat ).
thf(func_def_41,type,
sK9: ( nat > nat > $o ) > nat ).
thf(func_def_42,type,
sK10: ( nat > nat > $o ) > nat ).
thf(func_def_43,type,
sK11: ( nat > nat > $o ) > nat ).
thf(func_def_44,type,
sK12: ( nat > $o ) > nat ).
thf(func_def_45,type,
sK13: ( nat > nat ) > nat ).
thf(func_def_46,type,
sK14: nat > nat ).
thf(func_def_47,type,
sK15: nat > nat > nat ).
thf(func_def_48,type,
sK16: ( nat > nat > $o ) > nat ).
thf(func_def_49,type,
sK17: ( nat > nat > $o ) > nat ).
thf(func_def_50,type,
sK18: ( nat > nat > $o ) > nat ).
thf(func_def_51,type,
sK19: ( nat > nat > $o ) > nat ).
thf(func_def_52,type,
sK20: nat > nat ).
thf(func_def_53,type,
sK21: nat > nat ).
thf(func_def_54,type,
sK22: ( nat > nat ) > nat ).
thf(func_def_55,type,
sK23: ( nat > $o ) > nat ).
thf(func_def_56,type,
sK24: ( nat > $o ) > nat ).
thf(func_def_57,type,
sK25: ( nat > $o ) > nat ).
thf(func_def_58,type,
sK26: nat > list_a ).
thf(f28,axiom,
! [X0: nat] :
( X0
!= ( suc @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_n__not__Suc__n) ).
thf(f30,axiom,
! [X1: nat,X0: nat] :
( ( X0 != X1 )
=> ( ~ ( ord_less_nat @ X0 @ X1 )
=> ( ord_less_nat @ X1 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_linorder__neqE__nat) ).
thf(f36,axiom,
! [X0: nat] :
~ ( ord_less_nat @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_less__not__refl) ).
thf(f71,axiom,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X0 @ X1 )
=> ( ord_less_nat @ X0 @ ( suc @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_less__SucI) ).
thf(f99,axiom,
! [X1: nat,X0: nat] :
( ( X0 != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ X1 @ X0 ) @ X0 )
= X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_nonzero__mult__div__cancel__right) ).
thf(f126,axiom,
! [X1: nat,X0: nat,X2: nat] :
( ( ord_less_nat @ zero_zero_nat @ X0 )
=> ( ( ord_less_nat @ ( divide_divide_nat @ X1 @ X0 ) @ X2 )
= ( ord_less_nat @ X1 @ ( times_times_nat @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_div__less__conv) ).
thf(f138,axiom,
! [X1: nat,X0: nat] :
( ( ord_less_nat @ X0 @ X1 )
=> ( X1 != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_gr__implies__not__zero) ).
thf(f184,axiom,
( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
= ( suc @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f185,axiom,
k != zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(f186,conjecture,
ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(f187,negated_conjecture,
~ ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) ),
inference(negated_conjecture,[status(cth)],[f186]) ).
thf(f200,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X1 @ X0 )
=> ( zero_zero_nat != X0 ) ),
inference(rectify,[],[f138]) ).
thf(f201,plain,
! [X1: nat,X0: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
= $true )
=> ( zero_zero_nat != X0 ) ),
inference(fool_elimination,[],[f200]) ).
thf(f238,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ord_less_nat @ zero_zero_nat @ X1 )
=> ( ( ord_less_nat @ ( divide_divide_nat @ X0 @ X1 ) @ X2 )
= ( ord_less_nat @ X0 @ ( times_times_nat @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f126]) ).
thf(f239,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ X1 )
= $true )
=> ( ( ord_less_nat @ ( divide_divide_nat @ X0 @ X1 ) @ X2 )
= ( ord_less_nat @ X0 @ ( times_times_nat @ X2 @ X1 ) ) ) ),
inference(fool_elimination,[],[f238]) ).
thf(f256,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ( ord_less_nat @ X1 @ X0 )
=> ( ord_less_nat @ X0 @ X1 ) ) ),
inference(rectify,[],[f30]) ).
thf(f257,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( ( ord_less_nat @ X1 @ X0 )
!= $true )
=> ( ( ord_less_nat @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f256]) ).
thf(f276,plain,
! [X0: nat] :
~ ( ord_less_nat @ X0 @ X0 ),
inference(rectify,[],[f36]) ).
thf(f277,plain,
! [X0: nat] :
( ( ord_less_nat @ X0 @ X0 )
!= $true ),
inference(fool_elimination,[],[f276]) ).
thf(f286,plain,
~ ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) ),
inference(rectify,[],[f187]) ).
thf(f287,plain,
( ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) )
!= $true ),
inference(fool_elimination,[],[f286]) ).
thf(f293,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X0 @ X1 )
=> ( ord_less_nat @ X0 @ ( suc @ X1 ) ) ),
inference(rectify,[],[f71]) ).
thf(f294,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
= $true )
=> ( ( ord_less_nat @ X0 @ ( suc @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f293]) ).
thf(f445,plain,
( ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) )
!= $true ),
inference(flattening,[],[f287]) ).
thf(f463,plain,
! [X0: nat] :
( ( ord_less_nat @ X0 @ X0 )
!= $true ),
inference(flattening,[],[f277]) ).
thf(f464,plain,
! [X1: nat,X0: nat] :
( ( X0 != X1 )
=> ( ( ( ord_less_nat @ X1 @ X0 )
!= $true )
=> ( ( ord_less_nat @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[],[f257]) ).
thf(f493,plain,
! [X1: nat,X0: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
= $true )
| ( ( ord_less_nat @ X1 @ X0 )
= $true )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f464]) ).
thf(f494,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( ( ord_less_nat @ X0 @ X1 )
= $true )
| ( ( ord_less_nat @ X1 @ X0 )
= $true ) ),
inference(flattening,[],[f493]) ).
thf(f503,plain,
! [X1: nat,X0: nat] :
( ( ( ord_less_nat @ X0 @ ( suc @ X1 ) )
= $true )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f294]) ).
thf(f529,plain,
! [X1: nat,X0: nat,X2: nat] :
( ( ( ord_less_nat @ ( divide_divide_nat @ X0 @ X1 ) @ X2 )
= ( ord_less_nat @ X0 @ ( times_times_nat @ X2 @ X1 ) ) )
| ( ( ord_less_nat @ zero_zero_nat @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f239]) ).
thf(f570,plain,
! [X0: nat,X1: nat] :
( ( ( divide_divide_nat @ ( times_times_nat @ X1 @ X0 ) @ X0 )
= X1 )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f99]) ).
thf(f575,plain,
! [X1: nat,X0: nat] :
( ( zero_zero_nat != X0 )
| ( ( ord_less_nat @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f201]) ).
thf(f585,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X1 )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(rectify,[],[f575]) ).
thf(f608,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ ( suc @ X0 ) )
= $true )
| ( ( ord_less_nat @ X1 @ X0 )
!= $true ) ),
inference(rectify,[],[f503]) ).
thf(f625,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ord_less_nat @ ( divide_divide_nat @ X1 @ X0 ) @ X2 )
= ( ord_less_nat @ X1 @ ( times_times_nat @ X2 @ X0 ) ) )
| ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true ) ),
inference(rectify,[],[f529]) ).
thf(f656,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X1 )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f585]) ).
thf(f673,plain,
( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
= ( suc @ n ) ),
inference(cnf_transformation,[],[f184]) ).
thf(f674,plain,
! [X0: nat,X1: nat] :
( ( ( divide_divide_nat @ ( times_times_nat @ X1 @ X0 ) @ X0 )
= X1 )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f570]) ).
thf(f687,plain,
! [X0: nat] :
( ( ord_less_nat @ X0 @ X0 )
!= $true ),
inference(cnf_transformation,[],[f463]) ).
thf(f713,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ ( suc @ X0 ) )
= $true )
| ( ( ord_less_nat @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f608]) ).
thf(f719,plain,
( ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) )
!= $true ),
inference(cnf_transformation,[],[f445]) ).
thf(f720,plain,
! [X0: nat] :
( ( suc @ X0 )
!= X0 ),
inference(cnf_transformation,[],[f28]) ).
thf(f724,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
= $true )
| ( ( ord_less_nat @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f494]) ).
thf(f749,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( ord_less_nat @ ( divide_divide_nat @ X1 @ X0 ) @ X2 )
= ( ord_less_nat @ X1 @ ( times_times_nat @ X2 @ X0 ) ) )
| ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f625]) ).
thf(f757,plain,
zero_zero_nat != k,
inference(cnf_transformation,[],[f185]) ).
thf(f799,plain,
! [X0: nat] :
( ( ord_less_nat @ X0 @ zero_zero_nat )
!= $true ),
inference(equality_resolution,[],[f656]) ).
thf(f810,plain,
( ( $true != $true )
| ( ( size_size_list_a @ xs )
= ( times_times_nat @ n @ k ) )
| ( $true
= ( ord_less_nat @ ( size_size_list_a @ xs ) @ ( times_times_nat @ n @ k ) ) ) ),
inference(superposition,[],[f719,f724]) ).
thf(f812,plain,
( ( $true
= ( ord_less_nat @ ( size_size_list_a @ xs ) @ ( times_times_nat @ n @ k ) ) )
| ( ( size_size_list_a @ xs )
= ( times_times_nat @ n @ k ) ) ),
inference(trivial_inequality_removal,[],[f810]) ).
thf(f815,definition,
( spl27_1
<=> ( $true
= ( ord_less_nat @ ( size_size_list_a @ xs ) @ ( times_times_nat @ n @ k ) ) ) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
thf(f817,plain,
( ( $true
= ( ord_less_nat @ ( size_size_list_a @ xs ) @ ( times_times_nat @ n @ k ) ) )
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f815]) ).
thf(f819,definition,
( spl27_2
<=> ( ( size_size_list_a @ xs )
= ( times_times_nat @ n @ k ) ) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
thf(f821,plain,
( ( ( size_size_list_a @ xs )
= ( times_times_nat @ n @ k ) )
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f819]) ).
thf(f822,plain,
( spl27_1
| spl27_2 ),
inference(avatar_split_clause,[],[f812,f819,f815]) ).
thf(f833,plain,
( ( zero_zero_nat = k )
| ( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
= n )
| ~ spl27_2 ),
inference(superposition,[],[f674,f821]) ).
thf(f959,definition,
( spl27_8
<=> ( ( ord_less_nat @ zero_zero_nat @ k )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl27_8])],[avatar_definition]) ).
thf(f960,plain,
( ( ( ord_less_nat @ zero_zero_nat @ k )
= $true )
| ~ spl27_8 ),
inference(avatar_component_clause,[],[f959]) ).
thf(f961,plain,
( ( ( ord_less_nat @ zero_zero_nat @ k )
!= $true )
| spl27_8 ),
inference(avatar_component_clause,[],[f959]) ).
thf(f1006,plain,
( ( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
= n )
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f833,f757]) ).
thf(f1085,definition,
( spl27_30
<=> ( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
= n ) ),
introduced(definition,[new_symbols(definition,[spl27_30])],[avatar_definition]) ).
thf(f1102,plain,
( spl27_30
| ~ spl27_2 ),
inference(avatar_split_clause,[],[f1006,f819,f1085]) ).
thf(f1138,plain,
! [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) )
= $true )
| ( $true
!= ( ord_less_nat @ X0 @ n ) ) ),
inference(superposition,[],[f713,f673]) ).
thf(f1139,plain,
( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
!= n ),
inference(superposition,[],[f720,f673]) ).
thf(f1311,plain,
~ spl27_30,
inference(avatar_split_clause,[],[f1139,f1085]) ).
thf(f1352,plain,
( ( $true
= ( ord_less_nat @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) @ n ) )
| ( ( ord_less_nat @ zero_zero_nat @ k )
!= $true )
| ~ spl27_1 ),
inference(superposition,[],[f749,f817]) ).
thf(f1530,plain,
( ( ( ord_less_nat @ k @ zero_zero_nat )
= $true )
| ( zero_zero_nat = k )
| ( $true != $true )
| spl27_8 ),
inference(superposition,[],[f961,f724]) ).
thf(f1536,plain,
( ( ( ord_less_nat @ k @ zero_zero_nat )
= $true )
| ( zero_zero_nat = k )
| spl27_8 ),
inference(trivial_inequality_removal,[],[f1530]) ).
thf(f1541,plain,
( ( zero_zero_nat = k )
| spl27_8 ),
inference(forward_subsumption_resolution,[],[f1536,f799]) ).
thf(f1542,plain,
( $false
| spl27_8 ),
inference(forward_subsumption_resolution,[],[f1541,f757]) ).
thf(f1543,plain,
spl27_8,
inference(avatar_contradiction_clause,[],[f1542]) ).
thf(f1550,plain,
( ( $true
= ( ord_less_nat @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) @ n ) )
| ~ spl27_1
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f1352,f960]) ).
thf(f1558,plain,
( ( $true != $true )
| ( $true
!= ( ord_less_nat @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) @ n ) ) ),
inference(superposition,[],[f687,f1138]) ).
thf(f1595,plain,
( $true
!= ( ord_less_nat @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) @ n ) ),
inference(trivial_inequality_removal,[],[f1558]) ).
thf(f1603,plain,
( $false
| ~ spl27_1
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f1595,f1550]) ).
thf(f1604,plain,
( ~ spl27_1
| ~ spl27_8 ),
inference(avatar_contradiction_clause,[],[f1603]) ).
cnf(s1,plain,
( spl27_1
| spl27_2 ),
inference(sat_conversion,[],[f822]) ).
cnf(s47,plain,
( ~ spl27_2
| spl27_30 ),
inference(sat_conversion,[],[f1102]) ).
cnf(s69,plain,
~ spl27_30,
inference(sat_conversion,[],[f1311]) ).
cnf(s80,plain,
spl27_8,
inference(sat_conversion,[],[f1543]) ).
cnf(s86,plain,
( ~ spl27_1
| ~ spl27_8 ),
inference(sat_conversion,[],[f1604]) ).
cnf(s87,plain,
~ spl27_1,
inference(rat,[],[s86,s80]) ).
cnf(s90,plain,
~ spl27_2,
inference(rat,[],[s47,s69]) ).
cnf(s91,plain,
$false,
inference(rat,[],[s1,s90,s87]) ).
thf(f1605,plain,
$false,
inference(avatar_sat_refutation,[],[s91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP103^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n003.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:55:44 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.36 % (2980902)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.36 % (2980912)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1720750676:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.36 % (2980913)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.36 % (2980913)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.36 % (2980908)lrs+10_16_si=on:nwc=1.5:random_seed=3027792283:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.36 % (2980909)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=200547723:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.36 % (2980910)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2827184113:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.36 % (2980907)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3340679796:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.36 % (2980911)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2393515478:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.36 % (2980913)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3325092643:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.36 % (2980909)Instruction limit reached!
% 0.20/0.36 % (2980909)------------------------------
% 0.20/0.36 % (2980909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980909)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980909)Termination reason: Instruction limit
% 0.20/0.36 % (2980909)Termination phase: shuffling
% 0.20/0.36 % (2980909)Time elapsed: 0.002 s
% 0.20/0.36 % (2980909)Peak memory usage: 10 MB
% 0.20/0.36 % (2980909)Instructions burned: 3 (million)
% 0.20/0.36 % (2980908)Instruction limit reached!
% 0.20/0.36 % (2980908)------------------------------
% 0.20/0.36 % (2980908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980908)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980908)Termination reason: Instruction limit
% 0.20/0.36 % (2980908)Termination phase: Preprocessing 3
% 0.20/0.36 % (2980908)Time elapsed: 0.009 s
% 0.20/0.36 % (2980908)Peak memory usage: 10 MB
% 0.20/0.36 % (2980908)Instructions burned: 20 (million)
% 0.20/0.36 % (2980912)Instruction limit reached!
% 0.20/0.36 % (2980912)------------------------------
% 0.20/0.36 % (2980912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980912)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980912)Termination reason: Instruction limit
% 0.20/0.36 % (2980912)Termination phase: Saturation
% 0.20/0.36 % (2980912)Time elapsed: 0.018 s
% 0.20/0.36 % (2980912)Peak memory usage: 12 MB
% 0.20/0.36 % (2980912)Instructions burned: 78 (million)
% 0.20/0.36 % (2980911)Instruction limit reached!
% 0.20/0.36 % (2980911)------------------------------
% 0.20/0.36 % (2980911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980911)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980911)Termination reason: Instruction limit
% 0.20/0.36 % (2980911)Termination phase: Property scanning
% 0.20/0.36 % (2980911)Time elapsed: 0.013 s
% 0.20/0.36 % (2980911)Peak memory usage: 11 MB
% 0.20/0.36 % (2980911)Instructions burned: 30 (million)
% 0.20/0.36 % (2980923)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.36 % (2980921)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3232697631:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.36 % (2980923)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=995894759:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.36 % (2980923)Instruction limit reached!
% 0.20/0.36 % (2980923)------------------------------
% 0.20/0.36 % (2980923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980923)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980923)Termination reason: Instruction limit
% 0.20/0.36 % (2980923)Termination phase: shuffling
% 0.20/0.36 % (2980923)Time elapsed: 0.002 s
% 0.20/0.36 % (2980923)Peak memory usage: 10 MB
% 0.20/0.36 % (2980923)Instructions burned: 8 (million)
% 0.20/0.36 % (2980921)Instruction limit reached!
% 0.20/0.36 % (2980921)------------------------------
% 0.20/0.36 % (2980921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980921)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980921)Termination reason: Instruction limit
% 0.20/0.36 % (2980921)Termination phase: shuffling
% 0.20/0.36 % (2980921)Time elapsed: 0.003 s
% 0.20/0.36 % (2980921)Peak memory usage: 10 MB
% 0.20/0.36 % (2980921)Instructions burned: 6 (million)
% 0.20/0.36 % (2980922)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2161941063:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.36 % (2980922)Instruction limit reached!
% 0.20/0.36 % (2980922)------------------------------
% 0.20/0.36 % (2980922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980922)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980922)Termination reason: Instruction limit
% 0.20/0.36 % (2980922)Termination phase: shuffling
% 0.20/0.36 % (2980922)Time elapsed: 0.003 s
% 0.20/0.36 % (2980922)Peak memory usage: 10 MB
% 0.20/0.36 % (2980922)Instructions burned: 7 (million)
% 0.20/0.36 % (2980927)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.36 % (2980927)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.36 % (2980924)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1947549771:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.36 % (2980927)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2782131643:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.36 % (2980907)Instruction limit reached!
% 0.20/0.36 % (2980907)------------------------------
% 0.20/0.36 % (2980907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980907)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980907)Termination reason: Instruction limit
% 0.20/0.36 % (2980907)Termination phase: Saturation
% 0.20/0.36 % (2980907)Time elapsed: 0.038 s
% 0.20/0.36 % (2980907)Peak memory usage: 12 MB
% 0.20/0.36 % (2980907)Instructions burned: 87 (million)
% 0.20/0.36 % (2980924)Instruction limit reached!
% 0.20/0.36 % (2980924)------------------------------
% 0.20/0.36 % (2980924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980924)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980924)Termination reason: Instruction limit
% 0.20/0.36 % (2980924)Termination phase: Property scanning
% 0.20/0.36 % (2980924)Time elapsed: 0.006 s
% 0.20/0.36 % (2980924)Peak memory usage: 10 MB
% 0.20/0.36 % (2980924)Instructions burned: 13 (million)
% 0.20/0.36 % (2980927)Instruction limit reached!
% 0.20/0.36 % (2980927)------------------------------
% 0.20/0.36 % (2980927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980927)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980927)Termination reason: Instruction limit
% 0.20/0.36 % (2980927)Termination phase: Property scanning
% 0.20/0.36 % (2980927)Time elapsed: 0.007 s
% 0.20/0.36 % (2980927)Peak memory usage: 10 MB
% 0.20/0.36 % (2980927)Instructions burned: 31 (million)
% 0.20/0.36 % (2980928)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=574119065:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.36 % (2980931)lrs+10_1_si=on:cs=on:random_seed=2937209793:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.20/0.36 % (2980935)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2014017735:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.20/0.36 % (2980933)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.20/0.36 % (2980931)Instruction limit reached!
% 0.20/0.36 % (2980931)------------------------------
% 0.20/0.36 % (2980931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980931)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980931)Termination reason: Instruction limit
% 0.20/0.36 % (2980931)Termination phase: Property scanning
% 0.20/0.36 % (2980931)Time elapsed: 0.004 s
% 0.20/0.36 % (2980931)Peak memory usage: 10 MB
% 0.20/0.36 % (2980931)Instructions burned: 9 (million)
% 0.20/0.36 % (2980933)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1037309233:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.36 % (2980934)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=904958672:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.20/0.36 % (2980933)Instruction limit reached!
% 0.20/0.36 % (2980933)------------------------------
% 0.20/0.36 % (2980933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980933)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980933)Termination reason: Instruction limit
% 0.20/0.36 % (2980933)Termination phase: shuffling
% 0.20/0.36 % (2980933)Time elapsed: 0.002 s
% 0.20/0.36 % (2980933)Peak memory usage: 10 MB
% 0.20/0.36 % (2980933)Instructions burned: 3 (million)
% 0.20/0.36 % (2980939)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2096768522:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.20/0.36 % (2980935) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2980902-2980935"...
% 0.20/0.36 % (2980934)Instruction limit reached!
% 0.20/0.36 % (2980934)------------------------------
% 0.20/0.36 % (2980934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980934)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980934)Termination reason: Instruction limit
% 0.20/0.36 % (2980934)Termination phase: Property scanning
% 0.20/0.36 % (2980934)Time elapsed: 0.017 s
% 0.20/0.36 % (2980934)Peak memory usage: 11 MB
% 0.20/0.36 % (2980934)Instructions burned: 38 (million)
% 0.20/0.36 % (2980935)...printing done.
% 0.20/0.36 % (2980935)Refutation found. Thanks to Tanya!
% 0.20/0.36 % SZS status Theorem for theBenchmark
% 0.20/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.36 % (2980935)------------------------------
% 0.20/0.36 % (2980935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (2980935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (2980935)CaDiCaL version: 2.1.3
% 0.20/0.36 % (2980935)Termination reason: Refutation
% 0.20/0.36 % (2980935)Time elapsed: 0.025 s
% 0.20/0.36 % (2980935)Peak memory usage: 14 MB
% 0.20/0.36 % (2980935)Instructions burned: 92 (million)
% 0.20/0.36 % (2980902)Success in time 0.111 s
% 0.20/0.36 % Vampire exiting
%------------------------------------------------------------------------------