%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM971_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 : Tue Sep 29 12:26:18 PM UTC 2026
% Result : ContradictoryAxioms 1.91s 0.83s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 25
% Syntax : Number of formulae : 125 ( 44 unt; 0 typ; 5 def)
% Number of atoms : 226 ( 47 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 187 ( 86 ~; 81 |; 2 &)
% ( 14 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 24 ( 22 usr; 6 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 90 ( 0 sgn 90 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(func_def_0,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
bit0: int > int ).
tff(func_def_4,type,
bit1: int > int ).
tff(func_def_5,type,
pls: int ).
tff(func_def_6,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_7,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_8,type,
fFalse: bool ).
tff(func_def_9,type,
fTrue: bool ).
tff(func_def_10,type,
s: int ).
tff(func_def_11,type,
t: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_16,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_17,type,
pp: bool > $o ).
tff(f2,axiom,
ord_less_eq(int,zero_zero(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__0960_A_060_061_As_A_094_A2_096) ).
tff(f3,axiom,
ord_less(int,t,one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096t_A_060_A1_096) ).
tff(f4,axiom,
( ( t = zero_zero(int) )
=> ( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = zero_zero(int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096t_A_061_A0_A_061_061_062_As_A_094_A2_A_L_A1_A_061_A0_096) ).
tff(f5,axiom,
( ord_less(int,t,zero_zero(int))
=> ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__096t_A_060_A0_A_061_061_062_As_A_094_A2_A_L_A1_A_060_A0_096) ).
tff(f54,axiom,
! [X0: int] :
( ( number_number_of(nat,X0) = zero_zero(nat) )
<=> ord_less_eq(int,X0,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_eq__number__of__0) ).
tff(f58,axiom,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
<=> ord_less_eq(int,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_zle__add1__eq__le) ).
tff(f68,axiom,
! [X0: int,X1: int] :
( ord_less(int,number_number_of(int,X1),number_number_of(int,X0))
<=> ord_less(int,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__number__of__int__code) ).
tff(f69,axiom,
! [X0: int,X1: int] :
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
<=> ord_less_eq(int,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__eq__number__of__int__code) ).
tff(f73,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_zero__is__num__zero) ).
tff(f75,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_add__Pls__right) ).
tff(f76,axiom,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__Pls) ).
tff(f77,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Bit0__def) ).
tff(f80,axiom,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
<=> ( ord_less_eq(int,X1,X0)
& ( X1 != X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_less__int__def) ).
tff(f85,axiom,
! [X0: int,X1: int] :
( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0)
<=> ord_less(int,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add1__zle__eq) ).
tff(f87,axiom,
! [X0: $tType] :
( ( number(X0)
& linorder(X0) )
=> ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_le__number__of__eq__not__less) ).
tff(f88,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__numeral__0) ).
tff(f94,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Bit1__def) ).
tff(f105,axiom,
linorder(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
tff(f110,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f112,axiom,
number(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(f127,plain,
( ( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = zero_zero(int) )
| ( t != zero_zero(int) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f128,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int))
| ~ ord_less(int,t,zero_zero(int)) ),
inference(ennf_transformation,[],[f5]) ).
tff(f172,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) )
| ~ number(X0)
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f87]) ).
tff(f173,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) )
| ~ number(X0)
| ~ linorder(X0) ),
inference(flattening,[],[f172]) ).
tff(f174,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f88]) ).
tff(f183,plain,
ord_less_eq(int,zero_zero(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f2]) ).
tff(f184,plain,
ord_less(int,t,one_one(int)),
inference(cnf_transformation,[],[f3]) ).
tff(f185,plain,
( ( t != zero_zero(int) )
| ( zero_zero(int) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) ) ),
inference(cnf_transformation,[],[f127]) ).
tff(f186,plain,
( ~ ord_less(int,t,zero_zero(int))
| ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)) ),
inference(cnf_transformation,[],[f128]) ).
tff(f267,plain,
! [X0: int] :
( ~ ord_less_eq(int,X0,pls)
| ( zero_zero(nat) = number_number_of(nat,X0) ) ),
inference(cnf_transformation,[],[f54]) ).
tff(f268,plain,
! [X0: int] :
( ord_less_eq(int,X0,pls)
| ( zero_zero(nat) != number_number_of(nat,X0) ) ),
inference(cnf_transformation,[],[f54]) ).
tff(f275,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,X1,X0)
| ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
inference(cnf_transformation,[],[f58]) ).
tff(f276,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
inference(cnf_transformation,[],[f58]) ).
tff(f291,plain,
! [X0: int,X1: int] :
( ord_less(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f68]) ).
tff(f293,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,X1,X0)
| ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ),
inference(cnf_transformation,[],[f69]) ).
tff(f301,plain,
zero_zero(int) = number_number_of(int,pls),
inference(cnf_transformation,[],[f73]) ).
tff(f303,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f75]) ).
tff(f304,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f76]) ).
tff(f305,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f77]) ).
tff(f310,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f80]) ).
tff(f311,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f80]) ).
tff(f312,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ~ ord_less_eq(int,X1,X0)
| ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f80]) ).
tff(f319,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0) ),
inference(cnf_transformation,[],[f85]) ).
tff(f321,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ linorder(X0)
| ~ number(X0)
| ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ),
inference(cnf_transformation,[],[f173]) ).
tff(f322,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 ) ),
inference(cnf_transformation,[],[f174]) ).
tff(f331,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f94]) ).
tff(f342,plain,
linorder(int),
inference(cnf_transformation,[],[f105]) ).
tff(f347,plain,
number_ring(int),
inference(cnf_transformation,[],[f110]) ).
tff(f349,plain,
number(int),
inference(cnf_transformation,[],[f112]) ).
tff(f362,plain,
ord_less_eq(int,zero_zero(int),power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))),
inference(definition_unfolding,[],[f183,f305,f331]) ).
tff(f363,plain,
( ( t != zero_zero(int) )
| ( zero_zero(int) = plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),one_one(int)) ) ),
inference(definition_unfolding,[],[f185,f305,f331]) ).
tff(f364,plain,
( ~ ord_less(int,t,zero_zero(int))
| ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),one_one(int)),zero_zero(int)) ),
inference(definition_unfolding,[],[f186,f305,f331]) ).
tff(f455,plain,
! [X1: int] : ~ ord_less(int,X1,X1),
inference(equality_resolution,[],[f310]) ).
tff(f457,plain,
~ ord_less_eq(int,zero_zero(int),power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))),
inference(consistent_polarity_flipping,[],[f362]) ).
tff(f503,plain,
! [X0: int] :
( ( zero_zero(nat) != number_number_of(nat,X0) )
| ~ ord_less_eq(int,X0,pls) ),
inference(consistent_polarity_flipping,[],[f268]) ).
tff(f504,plain,
! [X0: int] :
( ord_less_eq(int,X0,pls)
| ( zero_zero(nat) = number_number_of(nat,X0) ) ),
inference(consistent_polarity_flipping,[],[f267]) ).
tff(f511,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
inference(consistent_polarity_flipping,[],[f276]) ).
tff(f512,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ord_less_eq(int,X1,X0) ),
inference(consistent_polarity_flipping,[],[f275]) ).
tff(f525,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
| ord_less_eq(int,X1,X0) ),
inference(consistent_polarity_flipping,[],[f293]) ).
tff(f527,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ( X0 = X1 )
| ord_less(int,X1,X0) ),
inference(consistent_polarity_flipping,[],[f312]) ).
tff(f528,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,X1,X0)
| ~ ord_less(int,X1,X0) ),
inference(consistent_polarity_flipping,[],[f311]) ).
tff(f530,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0)
| ord_less(int,X1,X0) ),
inference(consistent_polarity_flipping,[],[f319]) ).
tff(f532,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ linorder(X0)
| number(X0)
| ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f321]) ).
tff(f534,plain,
! [X0: $tType,X1: X0] :
( number_ring(X0)
| ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 ) ),
inference(consistent_polarity_flipping,[],[f322]) ).
tff(f543,plain,
~ number_ring(int),
inference(consistent_polarity_flipping,[],[f347]) ).
tff(f545,plain,
~ number(int),
inference(consistent_polarity_flipping,[],[f349]) ).
tff(f552,definition,
( spl0_1
<=> ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),one_one(int)),zero_zero(int)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f554,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),one_one(int)),zero_zero(int))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f552]) ).
tff(f556,definition,
( spl0_2
<=> ord_less(int,t,zero_zero(int)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f558,plain,
( ~ ord_less(int,t,zero_zero(int))
| spl0_2 ),
inference(avatar_component_clause,[],[f556]) ).
tff(f559,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f364,f556,f552]) ).
tff(f561,definition,
( spl0_3
<=> ( zero_zero(int) = plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),one_one(int)) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f563,plain,
( ( zero_zero(int) = plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),one_one(int)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f561]) ).
tff(f565,definition,
( spl0_4
<=> ( t = zero_zero(int) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f567,plain,
( ( t != zero_zero(int) )
| spl0_4 ),
inference(avatar_component_clause,[],[f565]) ).
tff(f568,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f363,f565,f561]) ).
tff(f579,plain,
! [X0: int] : ( plus_plus(int,number_number_of(int,pls),X0) = X0 ),
inference(resolution,[],[f534,f543]) ).
tff(f580,plain,
! [X0: int] : ( plus_plus(int,zero_zero(int),X0) = X0 ),
inference(forward_demodulation,[],[f579,f301]) ).
tff(f589,plain,
zero_zero(int) = pls,
inference(superposition,[],[f580,f303]) ).
tff(f603,plain,
( ~ ord_less(int,t,pls)
| spl0_2 ),
inference(superposition,[],[f558,f589]) ).
tff(f605,plain,
( ( t != pls )
| spl0_4 ),
inference(superposition,[],[f567,f589]) ).
tff(f663,plain,
! [X0: int] :
( ~ ord_less(int,X0,plus_plus(int,pls,one_one(int)))
| ( zero_zero(nat) = number_number_of(nat,X0) ) ),
inference(resolution,[],[f511,f504]) ).
tff(f665,plain,
! [X0: int] :
( ~ ord_less(int,X0,one_one(int))
| ( zero_zero(nat) = number_number_of(nat,X0) ) ),
inference(forward_demodulation,[],[f663,f304]) ).
tff(f666,plain,
! [X0: int] : ord_less_eq(int,plus_plus(int,X0,one_one(int)),X0),
inference(resolution,[],[f512,f455]) ).
tff(f701,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,plus_plus(int,X0,one_one(int)),X1)
| ord_less(int,X0,X1) ),
inference(resolution,[],[f530,f528]) ).
tff(f1121,plain,
! [X0: int,X1: int] :
( number(int)
| ~ ord_less(int,number_number_of(int,X0),number_number_of(int,X1))
| ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ),
inference(resolution,[],[f532,f342]) ).
tff(f1133,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,number_number_of(int,X0),number_number_of(int,X1))
| ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ),
inference(forward_subsumption_resolution,[],[f1121,f545]) ).
tff(f1311,plain,
zero_zero(nat) = number_number_of(nat,t),
inference(resolution,[],[f665,f184]) ).
tff(f1320,plain,
( ( zero_zero(nat) != zero_zero(nat) )
| ~ ord_less_eq(int,t,pls) ),
inference(superposition,[],[f503,f1311]) ).
tff(f1323,plain,
~ ord_less_eq(int,t,pls),
inference(trivial_inequality_removal,[],[f1320]) ).
tff(f1330,definition,
( spl0_9
<=> ord_less_eq(int,t,pls) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
tff(f1332,plain,
( ~ ord_less_eq(int,t,pls)
| spl0_9 ),
inference(avatar_component_clause,[],[f1330]) ).
tff(f1334,plain,
~ spl0_9,
inference(avatar_split_clause,[],[f1323,f1330]) ).
tff(f1351,plain,
( ( t = pls )
| ord_less(int,t,pls)
| spl0_9 ),
inference(resolution,[],[f1332,f527]) ).
tff(f1352,plain,
( ord_less(int,t,pls)
| spl0_4
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f1351,f605]) ).
tff(f1353,plain,
( $false
| spl0_2
| spl0_4
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f1352,f603]) ).
tff(f1354,plain,
( spl0_2
| spl0_4
| spl0_9 ),
inference(avatar_contradiction_clause,[],[f1353]) ).
tff(f1355,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),one_one(int)),pls)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f554,f589]) ).
tff(f1357,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),one_one(int)),pls)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1355,f303]) ).
tff(f1358,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),one_one(int)),pls)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1357,f303]) ).
tff(f1443,plain,
~ ord_less_eq(int,zero_zero(int),power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))))),
inference(forward_demodulation,[],[f457,f303]) ).
tff(f1444,plain,
~ ord_less_eq(int,zero_zero(int),power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int))))),
inference(forward_demodulation,[],[f1443,f303]) ).
tff(f1445,plain,
~ ord_less_eq(int,pls,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int))))),
inference(forward_demodulation,[],[f1444,f589]) ).
tff(f1715,plain,
( ord_less(int,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),pls)
| ~ spl0_1 ),
inference(resolution,[],[f701,f1358]) ).
tff(f2519,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,number_number_of(int,X0),number_number_of(int,X1))
| ~ ord_less(int,X1,X0) ),
inference(resolution,[],[f1133,f291]) ).
tff(f3346,plain,
( ( zero_zero(int) = plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),one_one(int)) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f563,f303]) ).
tff(f3383,plain,
( ( zero_zero(int) = plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),one_one(int)) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f3346,f303]) ).
tff(f3385,plain,
( ( pls = plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),one_one(int)) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f3383,f589]) ).
tff(f3394,plain,
( ord_less_eq(int,pls,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))))
| ~ spl0_3 ),
inference(superposition,[],[f666,f3385]) ).
tff(f3400,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f3394,f1445]) ).
tff(f3401,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f3400]) ).
tff(f15442,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,X0,X1)
| ord_less_eq(int,X1,X0) ),
inference(resolution,[],[f2519,f525]) ).
tff(f17056,plain,
( ord_less_eq(int,pls,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))))
| ~ spl0_1 ),
inference(resolution,[],[f1715,f15442]) ).
tff(f17058,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f17056,f1445]) ).
tff(f17059,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f17058]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f559]) ).
cnf(s2,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f568]) ).
cnf(s6,plain,
~ spl0_9,
inference(sat_conversion,[],[f1334]) ).
cnf(s7,plain,
( spl0_2
| spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f1354]) ).
cnf(s37,plain,
~ spl0_3,
inference(sat_conversion,[],[f3401]) ).
cnf(s190,plain,
~ spl0_1,
inference(sat_conversion,[],[f17059]) ).
cnf(s192,plain,
~ spl0_4,
inference(rat,[],[s2,s37]) ).
cnf(s195,plain,
spl0_2,
inference(rat,[],[s7,s6,s192]) ).
cnf(s212,plain,
$false,
inference(rat,[],[s1,s195,s190]) ).
tff(f17063,plain,
$false,
inference(avatar_sat_refutation,[],[s212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM971_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n016.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 21:53:33 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.43 Running first-order model finding
% 0.14/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.91/0.83 % (3024292)Will run a generic schedule for satisfiability detection.
% 1.91/0.83 % (3024298)% WARNING: option uhcvi not known.
% 1.91/0.83 % (3024298)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2775439921:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.91/0.83 % (3024297)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=39450323_2999 on theBenchmark for (2999ds/0Mi)
% 1.91/0.83 % (3024303)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1289618:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.91/0.83 % (3024299)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2143677581:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.91/0.83 % (3024301)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=229648473:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.91/0.83 % (3024300)dis+10_1_sil=32000:sp=arity:random_seed=2869139273:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.91/0.83 % (3024302)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4223062560:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.91/0.83 % Exception at run slice level
% 1.91/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.91/0.83 % (3024312)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3565842930:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.91/0.83 % Exception at run slice level
% 1.91/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.91/0.83 % (3024314)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2624107319:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.91/0.83 % (3024300)Instruction limit reached!
% 1.91/0.83 % (3024300)------------------------------
% 1.91/0.83 % (3024300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.83 % (3024300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.83 % (3024300)CaDiCaL version: 2.1.3
% 1.91/0.83 % (3024300)Termination reason: Instruction limit
% 1.91/0.83 % (3024300)Termination phase: Saturation
% 1.91/0.83 % (3024300)Time elapsed: 0.104 s
% 1.91/0.83 % (3024300)Peak memory usage: 12 MB
% 1.91/0.83 % (3024300)Instructions burned: 103 (million)
% 1.91/0.83 % (3024301)Instruction limit reached!
% 1.91/0.83 % (3024301)------------------------------
% 1.91/0.83 % (3024301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.83 % (3024301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.83 % (3024301)CaDiCaL version: 2.1.3
% 1.91/0.83 % (3024301)Termination reason: Instruction limit
% 1.91/0.83 % (3024301)Termination phase: Saturation
% 1.91/0.83 % (3024301)Time elapsed: 0.114 s
% 1.91/0.83 % (3024301)Peak memory usage: 13 MB
% 1.91/0.83 % (3024301)Instructions burned: 116 (million)
% 1.91/0.83 % (3024302)Instruction limit reached!
% 1.91/0.83 % (3024302)------------------------------
% 1.91/0.83 % (3024302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.83 % (3024302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.83 % (3024302)CaDiCaL version: 2.1.3
% 1.91/0.83 % (3024302)Termination reason: Instruction limit
% 1.91/0.83 % (3024302)Termination phase: Saturation
% 1.91/0.83 % (3024302)Time elapsed: 0.124 s
% 1.91/0.83 % (3024302)Peak memory usage: 13 MB
% 1.91/0.83 % (3024302)Instructions burned: 131 (million)
% 1.91/0.83 % (3024316)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4084569907:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.91/0.83 % (3024317)ott-21_1_sil=16000:fs=off:random_seed=1004231933:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.91/0.83 % (3024303)Instruction limit reached!
% 1.91/0.83 % (3024303)------------------------------
% 1.91/0.83 % (3024303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.83 % (3024303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.83 % (3024303)CaDiCaL version: 2.1.3
% 1.91/0.83 % (3024303)Termination reason: Instruction limit
% 1.91/0.83 % (3024303)Termination phase: Saturation
% 1.91/0.83 % (3024303)Time elapsed: 0.142 s
% 1.91/0.83 % (3024303)Peak memory usage: 13 MB
% 1.91/0.83 % (3024303)Instructions burned: 159 (million)
% 1.91/0.83 % (3024318)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=228356338:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.91/0.83 % (3024321)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=164399881:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.91/0.83 % Exception at run slice level
% 1.91/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.91/0.83 % (3024314)Instruction limit reached!
% 1.91/0.83 % (3024314)------------------------------
% 1.91/0.83 % (3024314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.83 % (3024314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.83 % (3024314)CaDiCaL version: 2.1.3
% 1.91/0.83 % (3024314)Termination reason: Instruction limit
% 1.91/0.83 % (3024314)Termination phase: Saturation
% 1.91/0.83 % (3024314)Time elapsed: 0.097 s
% 1.91/0.83 % (3024314)Peak memory usage: 13 MB
% 1.91/0.83 % (3024314)Instructions burned: 133 (million)
% 1.91/0.83 % (3024324)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3783846615:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.91/0.83 % (3024325)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4189214053:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 1.91/0.83 % Exception at run slice level
% 1.91/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.91/0.83 % (3024328)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3412726134:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 1.91/0.83 % (3024317)Instruction limit reached!
% 1.91/0.83 % (3024317)------------------------------
% 1.91/0.83 % (3024317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.83 % (3024317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.83 % (3024317)CaDiCaL version: 2.1.3
% 1.91/0.83 % (3024317)Termination reason: Instruction limit
% 1.91/0.83 % (3024317)Termination phase: Saturation
% 1.91/0.83 % (3024317)Time elapsed: 0.143 s
% 1.91/0.83 % (3024317)Peak memory usage: 13 MB
% 1.91/0.83 % (3024317)Instructions burned: 180 (million)
% 1.91/0.83 % (3024330)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2953143051:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 1.91/0.83 % (3024298) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3024292-3024298"...
% 1.91/0.83 % (3024298)...printing done.
% 1.91/0.83 % (3024298)Refutation found. Thanks to Tanya!
% 1.91/0.83 % SZS status ContradictoryAxioms for theBenchmark
% 1.91/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 1.91/0.83 % (3024298)------------------------------
% 1.91/0.83 % (3024298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.83 % (3024298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.83 % (3024298)CaDiCaL version: 2.1.3
% 1.91/0.83 % (3024298)Termination reason: Refutation
% 1.91/0.83 % (3024298)Time elapsed: 0.358 s
% 1.91/0.83 % (3024298)Peak memory usage: 18 MB
% 1.91/0.83 % (3024298)Instructions burned: 1076 (million)
% 1.91/0.83 % (3024292)Success in time 0.389 s
% 1.91/0.83 % Vampire exiting
%------------------------------------------------------------------------------