%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM934_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 12:26:15 PM UTC 2026
% Result : Theorem 0.42s 0.53s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 37
% Syntax : Number of formulae : 222 ( 72 unt; 0 typ; 8 def)
% Number of atoms : 406 ( 69 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 345 ( 161 ~; 157 |; 2 &)
% ( 20 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 9 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 213 ( 0 sgn 213 !; 0 ?; 213 :)
% 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,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > 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,
fFalse: bool ).
tff(func_def_8,type,
fTrue: bool ).
tff(func_def_9,type,
m: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
semiring:
!>[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,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zprime: int > $o ).
tff(pred_def_9,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_10,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_11,type,
pp: bool > $o ).
tff(f1,axiom,
ord_less_eq(int,one_one(int),m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__0961_A_060_061_Am_096) ).
tff(f12,axiom,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
<=> ord_less(int,pls,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_rel__simps_I4_J) ).
tff(f13,axiom,
! [X0: int] :
( ord_less(int,bit0(X0),pls)
<=> ord_less(int,X0,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_rel__simps_I10_J) ).
tff(f22,axiom,
! [X0: int] :
( ( bit0(X0) = pls )
<=> ( X0 = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rel__simps_I44_J) ).
tff(f26,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_rel__simps_I2_J) ).
tff(f30,axiom,
! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit0(X0))
<=> ord_less_eq(int,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rel__simps_I31_J) ).
tff(f33,axiom,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_add__Bit0__Bit0) ).
tff(f40,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_add__number__of__left) ).
tff(f47,axiom,
! [X0: int] :
( ord_less_eq(int,bit1(X0),pls)
<=> ord_less(int,X0,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_rel__simps_I29_J) ).
tff(f51,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/sandbox/benchmark/theBenchmark.p',fact_50_zle__add1__eq__le) ).
tff(f56,axiom,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
<=> ( ord_less_eq(int,X1,X0)
& ( X1 != X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_less__int__def) ).
tff(f59,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/sandbox/benchmark/theBenchmark.p',fact_58_le__number__of__eq__not__less) ).
tff(f60,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_number__of__is__id) ).
tff(f64,axiom,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
=> ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_zless__imp__add1__zle) ).
tff(f65,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/sandbox/benchmark/theBenchmark.p',fact_64_add1__zle__eq) ).
tff(f68,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_add__Pls__right) ).
tff(f69,axiom,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_add__Pls) ).
tff(f70,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Bit0__def) ).
tff(f73,axiom,
! [X0: int,X1: int,X2: int] : ( times_times(int,plus_plus(int,X2,X1),X0) = plus_plus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_int__distrib_I1_J) ).
tff(f74,axiom,
! [X0: int,X1: int,X2: int] : ( times_times(int,X2,plus_plus(int,X1,X0)) = plus_plus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_int__distrib_I2_J) ).
tff(f81,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Bit1__def) ).
tff(f82,axiom,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
<=> ( ord_less(int,X1,X0)
| ( X1 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_zless__add1__eq) ).
tff(f85,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_mult__numeral__1__right) ).
tff(f89,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) = plus_plus(X0,X1,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_semiring__mult__2) ).
tff(f100,axiom,
number_semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
tff(f101,axiom,
linorder(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
tff(f103,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f105,axiom,
number(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(f113,conjecture,
ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f114,negated_conjecture,
~ ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(negated_conjecture,[status(cth)],[f113]) ).
tff(f115,plain,
~ ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(flattening,[],[f114]) ).
tff(f136,plain,
! [X0: $tType] :
( ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f40]) ).
tff(f143,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,[],[f59]) ).
tff(f144,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,[],[f143]) ).
tff(f145,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0)
| ~ ord_less(int,X1,X0) ),
inference(ennf_transformation,[],[f64]) ).
tff(f152,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f85]) ).
tff(f155,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) = plus_plus(X0,X1,X1) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f89]) ).
tff(f164,plain,
ord_less_eq(int,one_one(int),m),
inference(cnf_transformation,[],[f1]) ).
tff(f178,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,bit0(X0)) ),
inference(cnf_transformation,[],[f12]) ).
tff(f180,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit0(X0),pls) ),
inference(cnf_transformation,[],[f13]) ).
tff(f194,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != bit0(X0) ) ),
inference(cnf_transformation,[],[f22]) ).
tff(f200,plain,
~ ord_less(int,pls,pls),
inference(cnf_transformation,[],[f26]) ).
tff(f206,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,X1,X0)
| ord_less_eq(int,bit0(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f30]) ).
tff(f210,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f33]) ).
tff(f219,plain,
! [X0: $tType,X2: int,X3: int,X1: X0] :
( ~ number_ring(X0)
| ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) ) ),
inference(cnf_transformation,[],[f136]) ).
tff(f232,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less_eq(int,bit1(X0),pls) ),
inference(cnf_transformation,[],[f47]) ).
tff(f239,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,[],[f51]) ).
tff(f240,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,[],[f51]) ).
tff(f250,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f56]) ).
tff(f251,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ~ ord_less_eq(int,X1,X0)
| ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f56]) ).
tff(f254,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,[],[f144]) ).
tff(f255,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,[],[f144]) ).
tff(f256,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f60]) ).
tff(f263,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,[],[f145]) ).
tff(f265,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,[],[f65]) ).
tff(f270,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f68]) ).
tff(f271,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f69]) ).
tff(f272,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f70]) ).
tff(f276,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,plus_plus(int,X2,X1),X0) = plus_plus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
inference(cnf_transformation,[],[f73]) ).
tff(f277,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,X2,plus_plus(int,X1,X0)) = plus_plus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
inference(cnf_transformation,[],[f74]) ).
tff(f285,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f81]) ).
tff(f286,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ord_less(int,X1,X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f82]) ).
tff(f287,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
inference(cnf_transformation,[],[f82]) ).
tff(f288,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,X1,X0)
| ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
inference(cnf_transformation,[],[f82]) ).
tff(f291,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 ) ),
inference(cnf_transformation,[],[f152]) ).
tff(f295,plain,
! [X0: $tType,X1: X0] :
( ~ number_semiring(X0)
| ( times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) = plus_plus(X0,X1,X1) ) ),
inference(cnf_transformation,[],[f155]) ).
tff(f310,plain,
number_semiring(int),
inference(cnf_transformation,[],[f100]) ).
tff(f311,plain,
linorder(int),
inference(cnf_transformation,[],[f101]) ).
tff(f313,plain,
number_ring(int),
inference(cnf_transformation,[],[f103]) ).
tff(f315,plain,
number(int),
inference(cnf_transformation,[],[f105]) ).
tff(f323,plain,
~ ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f115]) ).
tff(f336,plain,
! [X0: int] :
( ~ ord_less(int,pls,plus_plus(int,X0,X0))
| ord_less(int,pls,X0) ),
inference(definition_unfolding,[],[f178,f272]) ).
tff(f338,plain,
! [X0: int] :
( ~ ord_less(int,plus_plus(int,X0,X0),pls)
| ord_less(int,X0,pls) ),
inference(definition_unfolding,[],[f180,f272]) ).
tff(f350,plain,
! [X0: int] :
( ( pls != plus_plus(int,X0,X0) )
| ( pls = X0 ) ),
inference(definition_unfolding,[],[f194,f272]) ).
tff(f362,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,X1,X0)
| ord_less_eq(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f206,f272,f272]) ).
tff(f364,plain,
! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) = plus_plus(int,plus_plus(int,X1,X0),plus_plus(int,X1,X0)) ),
inference(definition_unfolding,[],[f210,f272,f272,f272]) ).
tff(f375,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less_eq(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls) ),
inference(definition_unfolding,[],[f232,f285]) ).
tff(f405,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,X1,number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),pls))) = X1 ) ),
inference(definition_unfolding,[],[f291,f285]) ).
tff(f409,plain,
! [X0: $tType,X1: X0] :
( ~ number_semiring(X0)
| ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,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))),X1) ) ),
inference(definition_unfolding,[],[f295,f272,f285]) ).
tff(f417,plain,
~ ord_less(int,number_number_of(int,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))),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,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)),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)))),m),one_one(int))),
inference(definition_unfolding,[],[f323,f272,f285,f272,f272,f285]) ).
tff(f424,plain,
! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))),
inference(equality_resolution,[],[f287]) ).
tff(f425,plain,
~ ord_less_eq(int,one_one(int),m),
inference(consistent_polarity_flipping,[],[f164]) ).
tff(f431,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0))
| ord_less_eq(int,X1,X0) ),
inference(consistent_polarity_flipping,[],[f362]) ).
tff(f442,plain,
! [X0: int] :
( ord_less_eq(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls)
| ord_less(int,X0,pls) ),
inference(consistent_polarity_flipping,[],[f375]) ).
tff(f450,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,[],[f240]) ).
tff(f451,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,[],[f239]) ).
tff(f460,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ( X0 = X1 )
| ord_less(int,X1,X0) ),
inference(consistent_polarity_flipping,[],[f251]) ).
tff(f461,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,X1,X0)
| ~ ord_less(int,X1,X0) ),
inference(consistent_polarity_flipping,[],[f250]) ).
tff(f464,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ number(X0)
| linorder(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,[],[f255]) ).
tff(f465,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ number(X0)
| linorder(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,[],[f254]) ).
tff(f472,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,[],[f263]) ).
tff(f473,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,[],[f265]) ).
tff(f477,plain,
~ linorder(int),
inference(consistent_polarity_flipping,[],[f311]) ).
tff(f482,plain,
~ ord_less(int,number_number_of(int,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))),plus_plus(int,times_times(int,plus_plus(int,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)),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))),m),one_one(int))),
inference(forward_demodulation,[],[f417,f256]) ).
tff(f483,plain,
~ ord_less(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),m),one_one(int))),
inference(forward_demodulation,[],[f482,f270]) ).
tff(f484,plain,
~ ord_less(int,number_number_of(int,plus_plus(int,one_one(int),one_one(int))),plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int))),
inference(forward_demodulation,[],[f483,f270]) ).
tff(f485,plain,
~ ord_less(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int))),
inference(forward_demodulation,[],[f484,f256]) ).
tff(f486,plain,
ord_less(int,pls,one_one(int)),
inference(superposition,[],[f424,f271]) ).
tff(f509,plain,
( ( one_one(int) = m )
| ord_less(int,one_one(int),m) ),
inference(resolution,[],[f460,f425]) ).
tff(f515,definition,
( spl0_1
<=> ord_less(int,one_one(int),m) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f517,plain,
( ord_less(int,one_one(int),m)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f515]) ).
tff(f519,definition,
( spl0_2
<=> ( one_one(int) = m ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f521,plain,
( ( one_one(int) = m )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f519]) ).
tff(f522,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f509,f519,f515]) ).
tff(f531,plain,
( ! [X0: int] : ord_less(int,X0,plus_plus(int,X0,m))
| ~ spl0_2 ),
inference(superposition,[],[f424,f521]) ).
tff(f533,plain,
( ~ ord_less(int,plus_plus(int,m,m),plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),m),m))
| ~ spl0_2 ),
inference(superposition,[],[f485,f521]) ).
tff(f544,plain,
( ! [X0: int,X1: int] :
( ~ ord_less(int,X1,plus_plus(int,X0,m))
| ~ ord_less_eq(int,X1,X0) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f450,f521]) ).
tff(f549,plain,
( ! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,m))
| ord_less_eq(int,X1,X0) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f451,f521]) ).
tff(f555,plain,
( ord_less_eq(int,plus_plus(int,m,m),times_times(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),m))
| ~ spl0_2 ),
inference(resolution,[],[f549,f533]) ).
tff(f577,plain,
( ! [X0: int] : ord_less(int,X0,plus_plus(int,plus_plus(int,X0,m),one_one(int)))
| ~ spl0_2 ),
inference(resolution,[],[f531,f288]) ).
tff(f581,plain,
( ! [X0: int] : ord_less(int,X0,plus_plus(int,plus_plus(int,X0,m),m))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f577,f521]) ).
tff(f742,plain,
( ! [X0: int] : ~ ord_less_eq(int,X0,plus_plus(int,X0,m))
| ~ spl0_2 ),
inference(resolution,[],[f581,f544]) ).
tff(f811,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,number_number_of(X0,plus_plus(int,one_one(int),pls))) = X1 )
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f405,f270]) ).
tff(f812,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,X1,number_number_of(X0,one_one(int))) = X1 ) ),
inference(forward_demodulation,[],[f811,f270]) ).
tff(f813,plain,
( ! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,X1,number_number_of(X0,m)) = X1 ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f812,f521]) ).
tff(f814,plain,
( ! [X0: int] : ( times_times(int,X0,number_number_of(int,m)) = X0 )
| ~ spl0_2 ),
inference(resolution,[],[f813,f313]) ).
tff(f815,plain,
( ! [X0: int] : ( times_times(int,X0,m) = X0 )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f814,f256]) ).
tff(f826,plain,
! [X0: int,X1: int] :
( ( pls != times_times(int,plus_plus(int,X0,X0),X1) )
| ( pls = times_times(int,X0,X1) ) ),
inference(superposition,[],[f350,f276]) ).
tff(f829,plain,
! [X2: int,X0: int,X1: int] :
( ~ ord_less_eq(int,plus_plus(int,X2,X2),times_times(int,plus_plus(int,X0,X0),X1))
| ord_less_eq(int,X2,times_times(int,X0,X1)) ),
inference(superposition,[],[f431,f276]) ).
tff(f841,plain,
! [X0: int,X1: int] : ( times_times(int,plus_plus(int,X0,X0),X1) = times_times(int,X0,plus_plus(int,X1,X1)) ),
inference(superposition,[],[f277,f276]) ).
tff(f1007,plain,
! [X0: int,X1: int] :
( linorder(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,[],[f464,f315]) ).
tff(f1010,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,[],[f1007,f477]) ).
tff(f1011,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,number_number_of(int,X0),X1)
| ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ),
inference(forward_demodulation,[],[f1010,f256]) ).
tff(f1012,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,X0,X1)
| ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ),
inference(forward_demodulation,[],[f1011,f256]) ).
tff(f1013,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,number_number_of(int,X1),X0)
| ~ ord_less(int,X0,X1) ),
inference(forward_demodulation,[],[f1012,f256]) ).
tff(f1014,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,X0,X1)
| ord_less_eq(int,X1,X0) ),
inference(forward_demodulation,[],[f1013,f256]) ).
tff(f1018,plain,
! [X0: int,X1: int] :
( linorder(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,[],[f465,f315]) ).
tff(f1021,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,[],[f1018,f477]) ).
tff(f1022,plain,
! [X0: int,X1: int] :
( ord_less(int,number_number_of(int,X0),X1)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ),
inference(forward_demodulation,[],[f1021,f256]) ).
tff(f1023,plain,
! [X0: int,X1: int] :
( ord_less(int,X0,X1)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ),
inference(forward_demodulation,[],[f1022,f256]) ).
tff(f1024,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,number_number_of(int,X1),X0)
| ord_less(int,X0,X1) ),
inference(forward_demodulation,[],[f1023,f256]) ).
tff(f1025,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,X1,X0)
| ord_less(int,X0,X1) ),
inference(forward_demodulation,[],[f1024,f256]) ).
tff(f1041,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,pls,plus_plus(int,plus_plus(int,X0,X0),plus_plus(int,X1,X1)))
| ord_less(int,pls,plus_plus(int,X0,X1)) ),
inference(superposition,[],[f336,f364]) ).
tff(f1099,plain,
( ord_less_eq(int,plus_plus(int,m,m),plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)))
| ~ spl0_2 ),
inference(superposition,[],[f555,f815]) ).
tff(f1118,plain,
( ord_less_eq(int,m,plus_plus(int,m,m))
| ~ spl0_2 ),
inference(resolution,[],[f1099,f431]) ).
tff(f1122,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1118,f742]) ).
tff(f1123,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f1122]) ).
tff(f1146,plain,
ord_less_eq(int,plus_plus(int,one_one(int),one_one(int)),times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m)),
inference(resolution,[],[f451,f485]) ).
tff(f1152,plain,
! [X0: int] :
( ~ ord_less_eq(int,one_one(int),X0)
| ~ ord_less(int,pls,X0) ),
inference(superposition,[],[f472,f271]) ).
tff(f1154,plain,
! [X0: int] :
( ord_less(int,one_one(int),plus_plus(int,X0,X0))
| ord_less_eq(int,one_one(int),X0) ),
inference(resolution,[],[f473,f431]) ).
tff(f1162,definition,
( spl0_3
<=> ord_less_eq(int,one_one(int),pls) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f1164,plain,
( ord_less_eq(int,one_one(int),pls)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f1162]) ).
tff(f1166,definition,
( spl0_4
<=> ord_less(int,one_one(int),pls) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f1167,plain,
( ~ ord_less(int,one_one(int),pls)
| spl0_4 ),
inference(avatar_component_clause,[],[f1166]) ).
tff(f1185,plain,
! [X0: int] :
( ~ ord_less(int,X0,one_one(int))
| ord_less(int,X0,pls)
| ( pls = X0 ) ),
inference(superposition,[],[f286,f271]) ).
tff(f1212,plain,
( ord_less_eq(int,plus_plus(int,one_one(int),pls),pls)
| ord_less(int,pls,pls) ),
inference(superposition,[],[f442,f270]) ).
tff(f1213,plain,
ord_less_eq(int,plus_plus(int,one_one(int),pls),pls),
inference(forward_subsumption_resolution,[],[f1212,f200]) ).
tff(f1217,plain,
ord_less_eq(int,one_one(int),pls),
inference(forward_demodulation,[],[f1213,f270]) ).
tff(f1219,plain,
spl0_3,
inference(avatar_split_clause,[],[f1217,f1162]) ).
tff(f1223,plain,
( ~ ord_less(int,one_one(int),pls)
| ~ spl0_3 ),
inference(resolution,[],[f1164,f461]) ).
tff(f1224,plain,
( ~ spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f1223,f1162,f1166]) ).
tff(f1458,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X0),plus_plus(int,number_number_of(int,X1),X2)) = plus_plus(int,number_number_of(int,plus_plus(int,X0,X1)),X2) ),
inference(resolution,[],[f219,f313]) ).
tff(f1459,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,number_number_of(int,X0),plus_plus(int,number_number_of(int,X1),X2)) ),
inference(forward_demodulation,[],[f1458,f256]) ).
tff(f1460,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,number_number_of(int,X0),plus_plus(int,X1,X2)) ),
inference(forward_demodulation,[],[f1459,f256]) ).
tff(f1461,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,X0,plus_plus(int,X1,X2)) ),
inference(forward_demodulation,[],[f1460,f256]) ).
tff(f1527,plain,
( ord_less_eq(int,m,one_one(int))
| ~ spl0_1 ),
inference(resolution,[],[f1014,f517]) ).
tff(f1537,plain,
( ~ ord_less(int,m,one_one(int))
| ~ spl0_1 ),
inference(resolution,[],[f1527,f461]) ).
tff(f1565,definition,
( spl0_6
<=> ord_less(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
tff(f1566,plain,
( ~ ord_less(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int))
| spl0_6 ),
inference(avatar_component_clause,[],[f1565]) ).
tff(f1567,plain,
( ord_less(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f1565]) ).
tff(f1772,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),X1) )
| ~ number_semiring(X0) ),
inference(forward_demodulation,[],[f409,f270]) ).
tff(f1773,plain,
! [X0: $tType,X1: X0] :
( ~ number_semiring(X0)
| ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,one_one(int),one_one(int))),X1) ) ),
inference(forward_demodulation,[],[f1772,f270]) ).
tff(f1783,plain,
! [X0: int] : ( plus_plus(int,X0,X0) = times_times(int,number_number_of(int,plus_plus(int,one_one(int),one_one(int))),X0) ),
inference(resolution,[],[f1773,f310]) ).
tff(f1786,plain,
! [X0: int] : ( plus_plus(int,X0,X0) = times_times(int,plus_plus(int,one_one(int),one_one(int)),X0) ),
inference(forward_demodulation,[],[f1783,f256]) ).
tff(f1923,plain,
( ord_less(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),pls)
| ( pls = times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m) )
| ~ spl0_6 ),
inference(resolution,[],[f1185,f1567]) ).
tff(f1926,definition,
( spl0_7
<=> ( pls = times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
tff(f1928,plain,
( ( pls = times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f1926]) ).
tff(f1930,definition,
( spl0_8
<=> ord_less(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),pls) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
tff(f1932,plain,
( ord_less(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),pls)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f1930]) ).
tff(f1933,plain,
( spl0_7
| spl0_8
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f1923,f1565,f1930,f1926]) ).
tff(f2267,plain,
( ( pls != pls )
| ( pls = times_times(int,plus_plus(int,one_one(int),one_one(int)),m) )
| ~ spl0_7 ),
inference(superposition,[],[f826,f1928]) ).
tff(f2268,plain,
( ( pls = times_times(int,plus_plus(int,one_one(int),one_one(int)),m) )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f2267]) ).
tff(f2269,plain,
( ( pls = plus_plus(int,m,m) )
| ~ spl0_7 ),
inference(superposition,[],[f2268,f1786]) ).
tff(f2305,plain,
ord_less_eq(int,plus_plus(int,one_one(int),one_one(int)),times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,m))),
inference(superposition,[],[f1146,f841]) ).
tff(f2384,plain,
ord_less_eq(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m))),
inference(forward_demodulation,[],[f2305,f1786]) ).
tff(f2442,plain,
( ord_less(int,one_one(int),pls)
| ord_less_eq(int,one_one(int),m)
| ~ spl0_7 ),
inference(superposition,[],[f1154,f2269]) ).
tff(f2455,plain,
( ord_less_eq(int,one_one(int),m)
| spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f2442,f1167]) ).
tff(f2466,plain,
( $false
| spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f2455,f425]) ).
tff(f2467,plain,
( spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f2466]) ).
tff(f2475,definition,
( spl0_10
<=> ord_less(int,m,pls) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
tff(f2477,plain,
( ord_less(int,m,pls)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f2475]) ).
tff(f2479,plain,
( ord_less(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,m)),pls)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1932,f841]) ).
tff(f2480,plain,
( ord_less(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),pls)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2479,f1786]) ).
tff(f2481,plain,
( ord_less(int,plus_plus(int,m,m),pls)
| ~ spl0_8 ),
inference(resolution,[],[f2480,f338]) ).
tff(f2511,plain,
( ord_less(int,m,pls)
| ~ spl0_8 ),
inference(resolution,[],[f2481,f338]) ).
tff(f2530,plain,
( spl0_10
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f2511,f1930,f2475]) ).
tff(f3068,plain,
( ord_less(int,m,plus_plus(int,pls,one_one(int)))
| ~ spl0_10 ),
inference(resolution,[],[f2477,f288]) ).
tff(f3069,plain,
( ord_less(int,m,one_one(int))
| ~ spl0_10 ),
inference(forward_demodulation,[],[f3068,f271]) ).
tff(f3076,plain,
( $false
| ~ spl0_1
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f3069,f1537]) ).
tff(f3077,plain,
( ~ spl0_1
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f3076]) ).
tff(f3083,plain,
( ~ ord_less(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,m)),one_one(int))
| spl0_6 ),
inference(forward_demodulation,[],[f1566,f841]) ).
tff(f3085,plain,
( ~ ord_less(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int))
| spl0_6 ),
inference(forward_demodulation,[],[f3083,f1786]) ).
tff(f3087,plain,
( ~ ord_less(int,plus_plus(int,m,plus_plus(int,m,plus_plus(int,m,m))),one_one(int))
| spl0_6 ),
inference(forward_demodulation,[],[f3085,f1461]) ).
tff(f3511,plain,
ord_less_eq(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,plus_plus(int,m,plus_plus(int,m,m)))),
inference(forward_demodulation,[],[f2384,f1461]) ).
tff(f3582,plain,
ord_less(int,plus_plus(int,m,plus_plus(int,m,plus_plus(int,m,m))),plus_plus(int,one_one(int),one_one(int))),
inference(resolution,[],[f3511,f1025]) ).
tff(f3863,plain,
( ord_less(int,plus_plus(int,m,plus_plus(int,m,plus_plus(int,m,m))),one_one(int))
| ( one_one(int) = plus_plus(int,m,plus_plus(int,m,plus_plus(int,m,m))) ) ),
inference(resolution,[],[f3582,f286]) ).
tff(f3875,plain,
( ( one_one(int) = plus_plus(int,m,plus_plus(int,m,plus_plus(int,m,m))) )
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f3863,f3087]) ).
tff(f5247,plain,
ord_less_eq(int,one_one(int),times_times(int,plus_plus(int,one_one(int),one_one(int)),m)),
inference(resolution,[],[f829,f1146]) ).
tff(f5286,plain,
ord_less_eq(int,one_one(int),plus_plus(int,m,m)),
inference(forward_demodulation,[],[f5247,f1786]) ).
tff(f5292,plain,
~ ord_less(int,pls,plus_plus(int,m,m)),
inference(resolution,[],[f5286,f1152]) ).
tff(f5503,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,pls,plus_plus(int,X0,plus_plus(int,X0,plus_plus(int,X1,X1))))
| ord_less(int,pls,plus_plus(int,X0,X1)) ),
inference(forward_demodulation,[],[f1041,f1461]) ).
tff(f5566,plain,
( ~ ord_less(int,pls,one_one(int))
| ord_less(int,pls,plus_plus(int,m,m))
| spl0_6 ),
inference(superposition,[],[f5503,f3875]) ).
tff(f5567,plain,
( ord_less(int,pls,plus_plus(int,m,m))
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f5566,f486]) ).
tff(f5584,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f5567,f5292]) ).
tff(f5585,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f5584]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f522]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f1123]) ).
cnf(s6,plain,
spl0_3,
inference(sat_conversion,[],[f1219]) ).
cnf(s8,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f1224]) ).
cnf(s10,plain,
( ~ spl0_6
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f1933]) ).
cnf(s11,plain,
( spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f2467]) ).
cnf(s14,plain,
( ~ spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f2530]) ).
cnf(s15,plain,
( ~ spl0_1
| ~ spl0_10 ),
inference(sat_conversion,[],[f3077]) ).
cnf(s33,plain,
spl0_6,
inference(sat_conversion,[],[f5585]) ).
cnf(s35,plain,
( spl0_7
| spl0_8 ),
inference(rat,[],[s10,s33]) ).
cnf(s36,plain,
~ spl0_4,
inference(rat,[],[s8,s6]) ).
cnf(s37,plain,
~ spl0_7,
inference(rat,[],[s11,s36]) ).
cnf(s38,plain,
spl0_8,
inference(rat,[],[s35,s37]) ).
cnf(s39,plain,
spl0_10,
inference(rat,[],[s14,s38]) ).
cnf(s40,plain,
~ spl0_1,
inference(rat,[],[s15,s39]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s1,s2,s40]) ).
tff(f5613,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM934_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 21:44:49 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.37 Running first-order model finding
% 0.08/0.37 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.53 % (2777891)Will run a generic schedule for satisfiability detection.
% 0.42/0.53 % (2777897)% WARNING: option uhcvi not known.
% 0.42/0.53 % (2777901)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1360910142:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.42/0.53 % (2777896)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2005671568_2999 on theBenchmark for (2999ds/0Mi)
% 0.42/0.53 % (2777897)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=120093885:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.42/0.53 % (2777898)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=654697062:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.42/0.53 % (2777899)dis+10_1_sil=32000:sp=arity:random_seed=3956664917:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.42/0.53 % (2777900)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=349278753:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.42/0.53 % Exception at run slice level
% 0.42/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.42/0.53 % (2777902)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2959997090:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.42/0.53 % (2777910)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3686826922:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.42/0.53 % Exception at run slice level
% 0.42/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.42/0.53 % (2777901)Instruction limit reached!
% 0.42/0.53 % (2777901)------------------------------
% 0.42/0.53 % (2777901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.42/0.53 % (2777901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.53 % (2777901)CaDiCaL version: 2.1.3
% 0.42/0.53 % (2777901)Termination reason: Instruction limit
% 0.42/0.53 % (2777901)Termination phase: Saturation
% 0.42/0.53 % (2777901)Time elapsed: 0.049 s
% 0.42/0.53 % (2777901)Peak memory usage: 13 MB
% 0.42/0.53 % (2777901)Instructions burned: 132 (million)
% 0.42/0.53 % (2777899)Instruction limit reached!
% 0.42/0.53 % (2777899)------------------------------
% 0.42/0.53 % (2777899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.42/0.53 % (2777899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.53 % (2777899)CaDiCaL version: 2.1.3
% 0.42/0.53 % (2777899)Termination reason: Instruction limit
% 0.42/0.53 % (2777899)Termination phase: Saturation
% 0.42/0.53 % (2777899)Time elapsed: 0.048 s
% 0.42/0.53 % (2777899)Peak memory usage: 12 MB
% 0.42/0.53 % (2777899)Instructions burned: 105 (million)
% 0.42/0.53 % (2777912)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=187775179:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.42/0.53 % (2777900)Instruction limit reached!
% 0.42/0.53 % (2777900)------------------------------
% 0.42/0.53 % (2777900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.42/0.53 % (2777900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.53 % (2777900)CaDiCaL version: 2.1.3
% 0.42/0.53 % (2777900)Termination reason: Instruction limit
% 0.42/0.53 % (2777900)Termination phase: Saturation
% 0.42/0.53 % (2777900)Time elapsed: 0.058 s
% 0.42/0.53 % (2777900)Peak memory usage: 12 MB
% 0.42/0.53 % (2777900)Instructions burned: 116 (million)
% 0.42/0.53 % (2777913)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=775984942:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.42/0.53 % (2777914)ott-21_1_sil=16000:fs=off:random_seed=3399796609:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.42/0.53 % (2777917)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2529898581:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.42/0.53 % (2777902)Instruction limit reached!
% 0.42/0.53 % (2777902)------------------------------
% 0.42/0.53 % (2777902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.42/0.53 % (2777902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.53 % (2777902)CaDiCaL version: 2.1.3
% 0.42/0.53 % (2777902)Termination reason: Instruction limit
% 0.42/0.53 % (2777902)Termination phase: Saturation
% 0.42/0.53 % (2777902)Time elapsed: 0.083 s
% 0.42/0.53 % (2777902)Peak memory usage: 13 MB
% 0.42/0.53 % (2777902)Instructions burned: 161 (million)
% 0.42/0.53 % (2777921)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2150566906:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.42/0.53 % Exception at run slice level
% 0.42/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.42/0.53 % (2777923)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3126899781:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.42/0.53 % (2777912)Instruction limit reached!
% 0.42/0.53 % (2777912)------------------------------
% 0.42/0.53 % (2777912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.42/0.53 % (2777912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.53 % (2777912)CaDiCaL version: 2.1.3
% 0.42/0.53 % (2777912)Termination reason: Instruction limit
% 0.42/0.53 % (2777912)Termination phase: Saturation
% 0.42/0.53 % (2777912)Time elapsed: 0.071 s
% 0.42/0.53 % (2777912)Peak memory usage: 13 MB
% 0.42/0.53 % (2777912)Instructions burned: 132 (million)
% 0.42/0.53 % (2777897) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2777891-2777897"...
% 0.42/0.53 % (2777897)...printing done.
% 0.42/0.53 % (2777897)Refutation found. Thanks to Tanya!
% 0.42/0.53 % SZS status Theorem for theBenchmark
% 0.42/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.42/0.54 % (2777897)------------------------------
% 0.42/0.54 % (2777897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.42/0.54 % (2777897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.54 % (2777897)CaDiCaL version: 2.1.3
% 0.42/0.54 % (2777897)Termination reason: Refutation
% 0.42/0.54 % (2777897)Time elapsed: 0.135 s
% 0.42/0.54 % (2777897)Peak memory usage: 15 MB
% 0.42/0.54 % (2777897)Instructions burned: 265 (million)
% 0.42/0.54 % (2777891)Success in time 0.159 s
% 0.42/0.54 % Vampire exiting
%------------------------------------------------------------------------------