%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM989_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 : n002.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 12:26:20 PM UTC 2026
% Result : Theorem 4.05s 1.09s
% Output : Refutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 57
% Syntax : Number of formulae : 324 ( 92 unt; 0 typ; 15 def)
% Number of atoms : 745 ( 119 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 786 ( 365 ~; 358 |; 9 &)
% ( 41 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 28 ( 26 usr; 16 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 257 ( 0 sgn 257 !; 0 ?; 257 :)
% 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,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
bit0: int > int ).
tff(func_def_6,type,
bit1: int > int ).
tff(func_def_7,type,
pls: int ).
tff(func_def_8,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_9,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_10,type,
fFalse: bool ).
tff(func_def_11,type,
fTrue: bool ).
tff(func_def_12,type,
m1: int ).
tff(func_def_13,type,
n: nat ).
tff(func_def_14,type,
t: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linord219039673up_add:
!>[X0: $tType] : $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,minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1),zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__0961_A_L_Aint_An_A_N_Am1_A_060_061_A0_096) ).
tff(f4,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int] : ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_add__special_I3_J) ).
tff(f8,axiom,
! [X0: $tType] :
( ( number_ring(X0)
& linordered_idom(X0) )
=> ! [X1: int] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,pls,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_le__special_I1_J) ).
tff(f10,axiom,
! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,bit0(times_times(int,X1,X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_mult__Bit1) ).
tff(f11,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( number_number_of(X0,bit1(pls)) = one_one(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_numeral__1__eq__1) ).
tff(f12,axiom,
! [X0: int] : ( minus_minus(int,pls,bit0(X0)) = bit0(minus_minus(int,pls,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_diff__bin__simps_I3_J) ).
tff(f14,axiom,
! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit1(X0)) = bit0(minus_minus(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_diff__bin__simps_I10_J) ).
tff(f16,axiom,
! [X0: $tType] :
( ( number_ring(X0)
& ring_char_0(X0) )
=> ! [X1: int,X2: int] :
( ( number_number_of(X0,X2) = number_number_of(X0,X1) )
<=> ( X2 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_eq__number__of) ).
tff(f22,axiom,
! [X0: int] : ( bit1(X0) != pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rel__simps_I46_J) ).
tff(f28,axiom,
bit0(pls) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Bit0__Pls) ).
tff(f30,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rel__simps_I2_J) ).
tff(f35,axiom,
! [X0: int] : ( times_times(int,pls,X0) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_mult__Pls) ).
tff(f36,axiom,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_mult__Bit0) ).
tff(f37,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_36_add__Bit0__Bit0) ).
tff(f41,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( number_number_of(X0,pls) = zero_zero(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_number__of__Pls) ).
tff(f43,axiom,
! [X0: $tType] :
( ( number(X0)
& ring(X0) )
=> ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_right__diff__distrib__number__of) ).
tff(f45,axiom,
! [X0: $tType] :
( ( number_ring(X0)
& linordered_idom(X0) )
=> ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less_eq(int,X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_le__number__of) ).
tff(f47,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int,X2: int] : ( times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,times_times(int,X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_arith__simps_I32_J) ).
tff(f53,axiom,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
<=> ord_less(int,pls,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rel__simps_I4_J) ).
tff(f57,axiom,
! [X0: int] :
( ord_less_eq(int,pls,bit0(X0))
<=> ord_less_eq(int,pls,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_rel__simps_I21_J) ).
tff(f59,axiom,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit1(X0)) = bit1(plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_add__Bit0__Bit1) ).
tff(f61,axiom,
! [X0: int] :
( ord_less(int,pls,bit1(X0))
<=> ord_less_eq(int,pls,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_rel__simps_I5_J) ).
tff(f64,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_63_zle__add1__eq__le) ).
tff(f67,axiom,
! [X0: $tType] :
( ( number_ring(X0)
& linordered_idom(X0) )
=> ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_less__special_I1_J) ).
tff(f72,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_71_less__int__def) ).
tff(f73,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/sandbox/benchmark/theBenchmark.p',fact_72_less__number__of__int__code) ).
tff(f75,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_74_le__number__of__eq__not__less) ).
tff(f78,axiom,
~ ord_less(int,pls,zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_bin__less__0__simps_I1_J) ).
tff(f80,axiom,
! [X0: int,X1: int,X2: int] :
( ord_less(int,X2,X1)
=> ( ord_less(int,zero_zero(int),X0)
=> ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_zmult__zless__mono2) ).
tff(f81,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_80_zless__add1__eq) ).
tff(f82,axiom,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
<=> ord_less(int,minus_minus(int,X1,X0),zero_zero(int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_less__bin__lemma) ).
tff(f83,axiom,
! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_int__less__0__conv) ).
tff(f87,axiom,
semiring_1_of_nat(int,one_one(nat)) = one_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_int__1) ).
tff(f92,axiom,
! [X0: int] :
( ord_less_eq(int,one_one(int),X0)
<=> ord_less(int,zero_zero(int),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_int__one__le__iff__zero__less) ).
tff(f93,axiom,
! [X0: int,X1: int] :
( ord_less(int,zero_zero(int),X1)
=> ( ( times_times(int,X1,X0) = one_one(int) )
<=> ( ( X1 = one_one(int) )
& ( X0 = one_one(int) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_pos__zmult__eq__1__iff) ).
tff(f100,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f101,axiom,
linorder(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
tff(f102,axiom,
ring_char_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
tff(f103,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f105,axiom,
ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
tff(f106,axiom,
number(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(f113,conjecture,
ord_less_eq(int,minus_minus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f114,negated_conjecture,
~ ord_less_eq(int,minus_minus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),zero_zero(int)),
inference(negated_conjecture,[status(cth)],[f113]) ).
tff(f115,plain,
~ ord_less_eq(int,minus_minus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),zero_zero(int)),
inference(flattening,[],[f114]) ).
tff(f117,plain,
! [X0: $tType] :
( ! [X1: int] : ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f4]) ).
tff(f123,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,pls,X1) )
| ~ number_ring(X0)
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f8]) ).
tff(f124,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,pls,X1) )
| ~ number_ring(X0)
| ~ linordered_idom(X0) ),
inference(flattening,[],[f123]) ).
tff(f127,plain,
! [X0: $tType] :
( ( number_number_of(X0,bit1(pls)) = one_one(X0) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f11]) ).
tff(f128,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( number_number_of(X0,X2) = number_number_of(X0,X1) )
<=> ( X2 = X1 ) )
| ~ number_ring(X0)
| ~ ring_char_0(X0) ),
inference(ennf_transformation,[],[f16]) ).
tff(f129,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( number_number_of(X0,X2) = number_number_of(X0,X1) )
<=> ( X2 = X1 ) )
| ~ number_ring(X0)
| ~ ring_char_0(X0) ),
inference(flattening,[],[f128]) ).
tff(f135,plain,
! [X0: $tType] :
( ( number_number_of(X0,pls) = zero_zero(X0) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f41]) ).
tff(f138,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ number(X0)
| ~ ring(X0) ),
inference(ennf_transformation,[],[f43]) ).
tff(f139,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ number(X0)
| ~ ring(X0) ),
inference(flattening,[],[f138]) ).
tff(f142,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less_eq(int,X2,X1) )
| ~ number_ring(X0)
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f45]) ).
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_eq(int,X2,X1) )
| ~ number_ring(X0)
| ~ linordered_idom(X0) ),
inference(flattening,[],[f142]) ).
tff(f145,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] : ( times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,times_times(int,X2,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f47]) ).
tff(f150,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) )
| ~ number_ring(X0)
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f67]) ).
tff(f151,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) )
| ~ number_ring(X0)
| ~ linordered_idom(X0) ),
inference(flattening,[],[f150]) ).
tff(f157,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,[],[f75]) ).
tff(f158,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,[],[f157]) ).
tff(f159,plain,
! [X0: int,X1: int,X2: int] :
( ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1))
| ~ ord_less(int,zero_zero(int),X0)
| ~ ord_less(int,X2,X1) ),
inference(ennf_transformation,[],[f80]) ).
tff(f160,plain,
! [X0: int,X1: int,X2: int] :
( ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1))
| ~ ord_less(int,zero_zero(int),X0)
| ~ ord_less(int,X2,X1) ),
inference(flattening,[],[f159]) ).
tff(f161,plain,
! [X0: int,X1: int] :
( ( ( times_times(int,X1,X0) = one_one(int) )
<=> ( ( X1 = one_one(int) )
& ( X0 = one_one(int) ) ) )
| ~ ord_less(int,zero_zero(int),X1) ),
inference(ennf_transformation,[],[f93]) ).
tff(f164,plain,
ord_less_eq(int,minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1),zero_zero(int)),
inference(cnf_transformation,[],[f1]) ).
tff(f167,plain,
! [X0: $tType,X1: int] :
( ~ number_ring(X0)
| ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) ) ),
inference(cnf_transformation,[],[f117]) ).
tff(f174,plain,
! [X0: $tType,X1: int] :
( ~ linordered_idom(X0)
| ~ number_ring(X0)
| ord_less_eq(int,pls,X1)
| ~ ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1)) ),
inference(cnf_transformation,[],[f124]) ).
tff(f177,plain,
! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,bit0(times_times(int,X1,X0)),X0) ),
inference(cnf_transformation,[],[f10]) ).
tff(f178,plain,
! [X0: $tType] :
( ~ number_ring(X0)
| ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
inference(cnf_transformation,[],[f127]) ).
tff(f179,plain,
! [X0: int] : ( minus_minus(int,pls,bit0(X0)) = bit0(minus_minus(int,pls,X0)) ),
inference(cnf_transformation,[],[f12]) ).
tff(f181,plain,
! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit1(X0)) = bit0(minus_minus(int,X1,X0)) ),
inference(cnf_transformation,[],[f14]) ).
tff(f184,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ ring_char_0(X0)
| ~ number_ring(X0)
| ( X1 = X2 )
| ( number_number_of(X0,X1) != number_number_of(X0,X2) ) ),
inference(cnf_transformation,[],[f129]) ).
tff(f193,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(cnf_transformation,[],[f22]) ).
tff(f201,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f28]) ).
tff(f204,plain,
~ ord_less(int,pls,pls),
inference(cnf_transformation,[],[f30]) ).
tff(f212,plain,
! [X0: int] : ( pls = times_times(int,pls,X0) ),
inference(cnf_transformation,[],[f35]) ).
tff(f213,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(cnf_transformation,[],[f36]) ).
tff(f214,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f37]) ).
tff(f218,plain,
! [X0: $tType] :
( ~ number_ring(X0)
| ( zero_zero(X0) = number_number_of(X0,pls) ) ),
inference(cnf_transformation,[],[f135]) ).
tff(f220,plain,
! [X0: $tType,X2: X0,X3: int,X1: X0] :
( ~ ring(X0)
| ~ number(X0)
| ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) ) ),
inference(cnf_transformation,[],[f139]) ).
tff(f224,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ linordered_idom(X0)
| ~ number_ring(X0)
| ord_less_eq(int,X2,X1)
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ),
inference(cnf_transformation,[],[f143]) ).
tff(f226,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ number_ring(X0)
| ( times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,times_times(int,X2,X1)) ) ),
inference(cnf_transformation,[],[f145]) ).
tff(f235,plain,
! [X0: int] :
( ~ ord_less(int,pls,X0)
| ord_less(int,pls,bit0(X0)) ),
inference(cnf_transformation,[],[f53]) ).
tff(f236,plain,
! [X0: int] :
( ~ ord_less(int,pls,bit0(X0))
| ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f53]) ).
tff(f243,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit0(X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f57]) ).
tff(f246,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f59]) ).
tff(f250,plain,
! [X0: int] :
( ~ ord_less(int,pls,bit1(X0))
| ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f61]) ).
tff(f256,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f64]) ).
tff(f261,plain,
! [X0: $tType,X1: int] :
( ~ linordered_idom(X0)
| ~ number_ring(X0)
| ~ ord_less(int,pls,X1)
| ord_less(X0,zero_zero(X0),number_number_of(X0,X1)) ),
inference(cnf_transformation,[],[f151]) ).
tff(f262,plain,
! [X0: $tType,X1: int] :
( ~ linordered_idom(X0)
| ~ number_ring(X0)
| ord_less(int,pls,X1)
| ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1)) ),
inference(cnf_transformation,[],[f151]) ).
tff(f271,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f72]) ).
tff(f272,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,X1,X0)
| ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f72]) ).
tff(f273,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,X1,X0)
| ( X0 = X1 )
| ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f72]) ).
tff(f275,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,[],[f73]) ).
tff(f278,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(cnf_transformation,[],[f158]) ).
tff(f284,plain,
~ ord_less(int,pls,zero_zero(int)),
inference(cnf_transformation,[],[f78]) ).
tff(f287,plain,
! [X2: int,X0: int,X1: int] :
( ~ ord_less(int,zero_zero(int),X0)
| ~ ord_less(int,X2,X1)
| ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1)) ),
inference(cnf_transformation,[],[f160]) ).
tff(f288,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,[],[f81]) ).
tff(f289,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
inference(cnf_transformation,[],[f81]) ).
tff(f291,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,minus_minus(int,X1,X0),zero_zero(int))
| ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f82]) ).
tff(f292,plain,
! [X0: int,X1: int] :
( ord_less(int,minus_minus(int,X1,X0),zero_zero(int))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f82]) ).
tff(f293,plain,
! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
inference(cnf_transformation,[],[f83]) ).
tff(f298,plain,
one_one(int) = semiring_1_of_nat(int,one_one(nat)),
inference(cnf_transformation,[],[f87]) ).
tff(f306,plain,
! [X0: int] :
( ord_less_eq(int,one_one(int),X0)
| ~ ord_less(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f92]) ).
tff(f307,plain,
! [X0: int] :
( ~ ord_less_eq(int,one_one(int),X0)
| ord_less(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f92]) ).
tff(f309,plain,
! [X0: int,X1: int] :
( ( one_one(int) != times_times(int,X1,X0) )
| ( one_one(int) = X1 )
| ~ ord_less(int,zero_zero(int),X1) ),
inference(cnf_transformation,[],[f161]) ).
tff(f320,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f100]) ).
tff(f321,plain,
linorder(int),
inference(cnf_transformation,[],[f101]) ).
tff(f322,plain,
ring_char_0(int),
inference(cnf_transformation,[],[f102]) ).
tff(f323,plain,
number_ring(int),
inference(cnf_transformation,[],[f103]) ).
tff(f325,plain,
ring(int),
inference(cnf_transformation,[],[f105]) ).
tff(f326,plain,
number(int),
inference(cnf_transformation,[],[f106]) ).
tff(f333,plain,
~ ord_less_eq(int,minus_minus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),zero_zero(int)),
inference(cnf_transformation,[],[f115]) ).
tff(f340,plain,
! [X1: int] : ~ ord_less(int,X1,X1),
inference(equality_resolution,[],[f271]) ).
tff(f341,plain,
! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))),
inference(equality_resolution,[],[f289]) ).
tff(f350,plain,
! [X0: $tType,X1: int] :
( ~ number_ring(X0)
| linordered_idom(X0)
| ord_less_eq(int,pls,X1)
| ~ ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f174]) ).
tff(f354,plain,
! [X0: $tType,X2: int,X1: int] :
( ring_char_0(X0)
| ~ number_ring(X0)
| ( X1 = X2 )
| ( number_number_of(X0,X1) != number_number_of(X0,X2) ) ),
inference(consistent_polarity_flipping,[],[f184]) ).
tff(f361,plain,
! [X0: $tType,X2: X0,X3: int,X1: X0] :
( ring(X0)
| ~ number(X0)
| ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) ) ),
inference(consistent_polarity_flipping,[],[f220]) ).
tff(f364,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ number_ring(X0)
| linordered_idom(X0)
| ord_less_eq(int,X2,X1)
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f224]) ).
tff(f368,plain,
! [X0: $tType,X1: int] :
( ~ number_ring(X0)
| linordered_idom(X0)
| ord_less(int,pls,X1)
| ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f262]) ).
tff(f369,plain,
! [X0: $tType,X1: int] :
( ~ number_ring(X0)
| linordered_idom(X0)
| ~ ord_less(int,pls,X1)
| ord_less(X0,zero_zero(X0),number_number_of(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f261]) ).
tff(f377,plain,
~ linordered_idom(int),
inference(consistent_polarity_flipping,[],[f320]) ).
tff(f378,plain,
~ ring_char_0(int),
inference(consistent_polarity_flipping,[],[f322]) ).
tff(f380,plain,
~ ring(int),
inference(consistent_polarity_flipping,[],[f325]) ).
tff(f387,definition,
( spl0_2
<=> ord_less(int,zero_zero(int),one_one(int)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f388,plain,
( ord_less(int,zero_zero(int),one_one(int))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f387]) ).
tff(f391,plain,
~ ord_less(int,one_one(int),zero_zero(int)),
inference(superposition,[],[f293,f298]) ).
tff(f397,plain,
zero_zero(int) = number_number_of(int,pls),
inference(resolution,[],[f218,f323]) ).
tff(f401,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(resolution,[],[f178,f323]) ).
tff(f403,plain,
ord_less(int,pls,bit0(plus_plus(int,pls,one_one(int)))),
inference(resolution,[],[f235,f341]) ).
tff(f417,plain,
ord_less(int,pls,bit0(bit0(plus_plus(int,pls,one_one(int))))),
inference(resolution,[],[f403,f235]) ).
tff(f456,definition,
( spl0_4
<=> ( one_one(int) = zero_zero(int) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f470,plain,
! [X0: int] :
( ~ ord_less(int,zero_zero(int),X0)
| ord_less(int,one_one(int),X0)
| ( one_one(int) = X0 ) ),
inference(resolution,[],[f273,f306]) ).
tff(f481,plain,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
| ( pls = bit0(X0) )
| ~ ord_less_eq(int,pls,X0) ),
inference(resolution,[],[f273,f243]) ).
tff(f504,plain,
! [X0: int] : ( bit0(plus_plus(int,pls,X0)) = plus_plus(int,pls,bit0(X0)) ),
inference(superposition,[],[f214,f201]) ).
tff(f510,plain,
! [X0: int] : ( bit1(plus_plus(int,pls,X0)) = plus_plus(int,pls,bit1(X0)) ),
inference(superposition,[],[f246,f201]) ).
tff(f514,plain,
! [X0: int] : ord_less_eq(int,X0,X0),
inference(resolution,[],[f256,f341]) ).
tff(f517,plain,
ord_less(int,zero_zero(int),one_one(int)),
inference(resolution,[],[f514,f307]) ).
tff(f522,plain,
spl0_2,
inference(avatar_split_clause,[],[f517,f387]) ).
tff(f523,plain,
( ord_less_eq(int,zero_zero(int),one_one(int))
| ~ spl0_2 ),
inference(resolution,[],[f388,f272]) ).
tff(f556,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,bit0(minus_minus(int,X0,X1)),zero_zero(int))
| ord_less(int,bit1(X0),bit1(X1)) ),
inference(superposition,[],[f291,f181]) ).
tff(f560,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,minus_minus(int,X0,X1),zero_zero(int))
| ~ ord_less(int,X0,X1) ),
inference(resolution,[],[f292,f272]) ).
tff(f561,plain,
! [X0: int] :
( ord_less(int,bit0(minus_minus(int,pls,X0)),zero_zero(int))
| ~ ord_less(int,pls,bit0(X0)) ),
inference(superposition,[],[f292,f179]) ).
tff(f596,definition,
( spl0_6
<=> ord_less(int,minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1),zero_zero(int)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
tff(f598,plain,
( ord_less(int,minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1),zero_zero(int))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f596]) ).
tff(f600,definition,
( spl0_7
<=> ( minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1) = zero_zero(int) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
tff(f602,plain,
( ( minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1) = zero_zero(int) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f600]) ).
tff(f609,plain,
! [X0: int] : ( times_times(int,bit1(pls),X0) = plus_plus(int,bit0(pls),X0) ),
inference(superposition,[],[f177,f212]) ).
tff(f625,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = times_times(int,bit1(pls),X0) ),
inference(forward_demodulation,[],[f609,f201]) ).
tff(f628,plain,
! [X0: int,X1: int] :
( ~ number_ring(int)
| ( X0 = X1 )
| ( number_number_of(int,X1) != number_number_of(int,X0) ) ),
inference(resolution,[],[f354,f378]) ).
tff(f629,plain,
! [X0: int,X1: int] :
( ( number_number_of(int,X1) != number_number_of(int,X0) )
| ( X0 = X1 ) ),
inference(forward_subsumption_resolution,[],[f628,f323]) ).
tff(f640,plain,
! [X0: int] :
( linordered_idom(int)
| ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,zero_zero(int),number_number_of(int,X0)) ),
inference(resolution,[],[f350,f323]) ).
tff(f641,plain,
! [X0: int] :
( ~ ord_less_eq(int,zero_zero(int),number_number_of(int,X0))
| ord_less_eq(int,pls,X0) ),
inference(forward_subsumption_resolution,[],[f640,f377]) ).
tff(f688,plain,
! [X0: int] :
( ( zero_zero(int) != number_number_of(int,X0) )
| ( pls = X0 ) ),
inference(superposition,[],[f629,f397]) ).
tff(f689,plain,
! [X0: int] :
( ( one_one(int) != number_number_of(int,X0) )
| ( bit1(pls) = X0 ) ),
inference(superposition,[],[f629,f401]) ).
tff(f697,plain,
( ( one_one(int) != zero_zero(int) )
| ( pls = bit1(pls) ) ),
inference(superposition,[],[f688,f401]) ).
tff(f698,plain,
! [X0: int] :
( linordered_idom(int)
| ord_less(int,pls,X0)
| ~ ord_less(int,zero_zero(int),number_number_of(int,X0)) ),
inference(resolution,[],[f368,f323]) ).
tff(f699,plain,
! [X0: int] :
( ~ ord_less(int,zero_zero(int),number_number_of(int,X0))
| ord_less(int,pls,X0) ),
inference(forward_subsumption_resolution,[],[f698,f377]) ).
tff(f700,plain,
! [X0: int] :
( linordered_idom(int)
| ~ ord_less(int,pls,X0)
| ord_less(int,zero_zero(int),number_number_of(int,X0)) ),
inference(resolution,[],[f369,f323]) ).
tff(f701,plain,
! [X0: int] :
( ord_less(int,zero_zero(int),number_number_of(int,X0))
| ~ ord_less(int,pls,X0) ),
inference(forward_subsumption_resolution,[],[f700,f377]) ).
tff(f720,definition,
( spl0_8
<=> ord_less(int,zero_zero(int),pls) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
tff(f721,plain,
( ord_less(int,zero_zero(int),pls)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f720]) ).
tff(f732,definition,
( spl0_11
<=> ord_less(int,zero_zero(int),bit1(pls)) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
tff(f734,plain,
( ~ ord_less(int,zero_zero(int),bit1(pls))
| spl0_11 ),
inference(avatar_component_clause,[],[f732]) ).
tff(f740,plain,
! [X0: int] :
( ( one_one(int) != plus_plus(int,pls,X0) )
| ( one_one(int) = bit1(pls) )
| ~ ord_less(int,zero_zero(int),bit1(pls)) ),
inference(superposition,[],[f309,f625]) ).
tff(f743,definition,
( spl0_13
<=> ( one_one(int) = bit1(pls) ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
tff(f745,plain,
( ( one_one(int) = bit1(pls) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f743]) ).
tff(f747,definition,
( spl0_14
<=> ! [X0: int] : ( one_one(int) != plus_plus(int,pls,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
tff(f748,plain,
( ! [X0: int] : ( one_one(int) != plus_plus(int,pls,X0) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f747]) ).
tff(f749,plain,
( ~ spl0_11
| spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f740,f747,f743,f732]) ).
tff(f778,plain,
! [X0: int,X1: int] :
( linordered_idom(int)
| ord_less_eq(int,X0,X1)
| ~ ord_less_eq(int,number_number_of(int,X0),number_number_of(int,X1)) ),
inference(resolution,[],[f364,f323]) ).
tff(f779,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,number_number_of(int,X0),number_number_of(int,X1))
| ord_less_eq(int,X0,X1) ),
inference(forward_subsumption_resolution,[],[f778,f377]) ).
tff(f818,plain,
! [X0: int] : ( plus_plus(int,number_number_of(int,X0),one_one(int)) = number_number_of(int,plus_plus(int,X0,bit1(pls))) ),
inference(resolution,[],[f167,f323]) ).
tff(f821,plain,
! [X0: int,X1: int] : ( times_times(int,number_number_of(int,X0),number_number_of(int,X1)) = number_number_of(int,times_times(int,X0,X1)) ),
inference(resolution,[],[f226,f323]) ).
tff(f843,plain,
plus_plus(int,pls,pls) = bit0(plus_plus(int,pls,pls)),
inference(superposition,[],[f504,f201]) ).
tff(f845,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,[],[f278,f326]) ).
tff(f848,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
| ord_less(int,number_number_of(int,X0),number_number_of(int,X1)) ),
inference(forward_subsumption_resolution,[],[f845,f321]) ).
tff(f923,plain,
! [X2: int,X0: int,X1: int] :
( ~ number(int)
| ( times_times(int,number_number_of(int,X0),minus_minus(int,X1,X2)) = minus_minus(int,times_times(int,number_number_of(int,X0),X1),times_times(int,number_number_of(int,X0),X2)) ) ),
inference(resolution,[],[f361,f380]) ).
tff(f924,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,number_number_of(int,X0),minus_minus(int,X1,X2)) = minus_minus(int,times_times(int,number_number_of(int,X0),X1),times_times(int,number_number_of(int,X0),X2)) ),
inference(forward_subsumption_resolution,[],[f923,f326]) ).
tff(f928,plain,
( ~ ord_less_eq(int,zero_zero(int),one_one(int))
| ord_less_eq(int,pls,bit1(pls)) ),
inference(superposition,[],[f641,f401]) ).
tff(f929,plain,
( ord_less_eq(int,pls,bit1(pls))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f928,f523]) ).
tff(f931,plain,
( ( pls = bit1(pls) )
| ord_less(int,pls,bit1(pls))
| ~ spl0_2 ),
inference(resolution,[],[f929,f273]) ).
tff(f932,plain,
( ord_less(int,pls,bit1(pls))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f931,f193]) ).
tff(f975,plain,
! [X2: int,X0: int,X1: int] :
( ord_less(int,times_times(int,number_number_of(int,X0),X1),times_times(int,number_number_of(int,X0),X2))
| ~ ord_less(int,X1,X2)
| ~ ord_less(int,pls,X0) ),
inference(resolution,[],[f701,f287]) ).
tff(f999,plain,
~ ord_less(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),
inference(resolution,[],[f560,f333]) ).
tff(f1111,plain,
! [X0: int] :
( ~ ord_less_eq(int,pls,X0)
| ( pls = bit0(X0) )
| ord_less(int,pls,X0) ),
inference(resolution,[],[f481,f236]) ).
tff(f1179,definition,
( spl0_22
<=> ( one_one(int) = plus_plus(int,zero_zero(int),one_one(int)) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
tff(f1181,plain,
( ( one_one(int) = plus_plus(int,zero_zero(int),one_one(int)) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1179]) ).
tff(f1183,definition,
( spl0_23
<=> ord_less(int,one_one(int),plus_plus(int,zero_zero(int),one_one(int))) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
tff(f1185,plain,
( ord_less(int,one_one(int),plus_plus(int,zero_zero(int),one_one(int)))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1183]) ).
tff(f1251,definition,
( spl0_26
<=> ord_less_eq(int,pls,zero_zero(int)) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
tff(f1252,plain,
( ord_less_eq(int,pls,zero_zero(int))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1251]) ).
tff(f1253,plain,
( ~ ord_less_eq(int,pls,zero_zero(int))
| spl0_26 ),
inference(avatar_component_clause,[],[f1251]) ).
tff(f1295,plain,
! [X0: int] :
( ord_less(int,bit1(pls),bit1(X0))
| ~ ord_less(int,pls,bit0(X0)) ),
inference(resolution,[],[f556,f561]) ).
tff(f1429,plain,
plus_plus(int,zero_zero(int),one_one(int)) = number_number_of(int,plus_plus(int,pls,bit1(pls))),
inference(superposition,[],[f818,f397]) ).
tff(f1437,plain,
! [X0: int] : ord_less(int,number_number_of(int,X0),number_number_of(int,plus_plus(int,X0,bit1(pls)))),
inference(superposition,[],[f341,f818]) ).
tff(f1446,plain,
plus_plus(int,zero_zero(int),one_one(int)) = number_number_of(int,bit1(plus_plus(int,pls,pls))),
inference(forward_demodulation,[],[f1429,f510]) ).
tff(f1447,plain,
( ( one_one(int) = number_number_of(int,bit1(plus_plus(int,pls,pls))) )
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1446,f1181]) ).
tff(f1450,plain,
! [X0: int] : ( number_number_of(int,times_times(int,X0,pls)) = times_times(int,number_number_of(int,X0),zero_zero(int)) ),
inference(superposition,[],[f821,f397]) ).
tff(f1640,plain,
! [X0: int,X1: int] :
( ord_less(int,number_number_of(int,X0),number_number_of(int,X1))
| ord_less_eq(int,X1,X0) ),
inference(resolution,[],[f848,f779]) ).
tff(f2099,plain,
( ( one_one(int) != one_one(int) )
| ( bit1(pls) = bit1(plus_plus(int,pls,pls)) )
| ~ spl0_22 ),
inference(superposition,[],[f689,f1447]) ).
tff(f2130,plain,
( ( bit1(pls) = bit1(plus_plus(int,pls,pls)) )
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f2099]) ).
tff(f2192,plain,
~ ord_less_eq(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)),zero_zero(int)),
inference(superposition,[],[f333,f924]) ).
tff(f2331,plain,
( ~ ord_less(int,pls,bit1(pls))
| ord_less_eq(int,pls,plus_plus(int,pls,pls))
| ~ spl0_22 ),
inference(superposition,[],[f250,f2130]) ).
tff(f2374,plain,
( ord_less_eq(int,pls,plus_plus(int,pls,pls))
| ~ spl0_2
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f2331,f932]) ).
tff(f2391,definition,
( spl0_41
<=> ord_less(int,pls,plus_plus(int,pls,pls)) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
tff(f2395,definition,
( spl0_42
<=> ( pls = plus_plus(int,pls,pls) ) ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
tff(f2397,plain,
( ( pls = plus_plus(int,pls,pls) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f2395]) ).
tff(f2401,plain,
( ord_less(int,one_one(int),zero_zero(int))
| ( one_one(int) = zero_zero(int) )
| ~ spl0_23 ),
inference(resolution,[],[f1185,f288]) ).
tff(f2406,plain,
( ( one_one(int) = zero_zero(int) )
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f2401,f391]) ).
tff(f2729,plain,
( ord_less(int,bit1(pls),bit1(pls))
| ~ ord_less(int,pls,bit0(plus_plus(int,pls,pls)))
| ~ spl0_22 ),
inference(superposition,[],[f1295,f2130]) ).
tff(f2738,plain,
( ~ ord_less(int,pls,bit0(plus_plus(int,pls,pls)))
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f2729,f340]) ).
tff(f2752,plain,
( ~ ord_less(int,pls,plus_plus(int,pls,pls))
| ~ spl0_22 ),
inference(forward_demodulation,[],[f2738,f843]) ).
tff(f2757,plain,
( ~ spl0_41
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f2752,f1179,f2391]) ).
tff(f2772,plain,
( ( pls = bit0(plus_plus(int,pls,pls)) )
| ord_less(int,pls,plus_plus(int,pls,pls))
| ~ spl0_2
| ~ spl0_22 ),
inference(resolution,[],[f1111,f2374]) ).
tff(f2790,plain,
( ( pls = plus_plus(int,pls,pls) )
| ord_less(int,pls,plus_plus(int,pls,pls))
| ~ spl0_2
| ~ spl0_22 ),
inference(forward_demodulation,[],[f2772,f843]) ).
tff(f2791,plain,
( spl0_41
| spl0_42
| ~ spl0_2
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f2790,f1179,f387,f2395,f2391]) ).
tff(f2912,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X0,X1)
| ord_less(int,X1,X0) ),
inference(resolution,[],[f1640,f275]) ).
tff(f3800,plain,
ord_less(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1))),
inference(resolution,[],[f2912,f2192]) ).
tff(f3815,plain,
( ord_less(int,zero_zero(int),pls)
| spl0_26 ),
inference(resolution,[],[f2912,f1253]) ).
tff(f3845,plain,
( spl0_8
| spl0_26 ),
inference(avatar_split_clause,[],[f3815,f1251,f720]) ).
tff(f3850,plain,
( spl0_4
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f2406,f1183,f456]) ).
tff(f3905,plain,
one_one(int) != zero_zero(int),
inference(forward_subsumption_resolution,[],[f697,f193]) ).
tff(f3927,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f3905,f456]) ).
tff(f4200,plain,
( ! [X0: int,X1: int] :
( ~ ord_less(int,X0,X1)
| ord_less(int,times_times(int,pls,X0),times_times(int,pls,X1)) )
| ~ spl0_8 ),
inference(resolution,[],[f721,f287]) ).
tff(f4206,plain,
( ! [X0: int,X1: int] :
( ord_less(int,times_times(int,pls,X0),pls)
| ~ ord_less(int,X0,X1) )
| ~ spl0_8 ),
inference(forward_demodulation,[],[f4200,f212]) ).
tff(f4208,plain,
( ! [X0: int,X1: int] :
( ord_less(int,pls,pls)
| ~ ord_less(int,X0,X1) )
| ~ spl0_8 ),
inference(forward_demodulation,[],[f4206,f212]) ).
tff(f4210,plain,
( ! [X0: int,X1: int] : ~ ord_less(int,X0,X1)
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f4208,f204]) ).
tff(f4357,plain,
( $false
| ~ spl0_8 ),
inference(backward_subsumption_resolution,[],[f1437,f4210]) ).
tff(f4392,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f4357]) ).
tff(f4567,plain,
( ( minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1) = zero_zero(int) )
| ord_less(int,minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1),zero_zero(int)) ),
inference(resolution,[],[f273,f164]) ).
tff(f4654,definition,
( spl0_77
<=> ord_less(int,pls,bit0(bit0(bit1(pls)))) ),
introduced(definition,[new_symbols(definition,[spl0_77])],[avatar_definition]) ).
tff(f4715,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f4567,f600,f596]) ).
tff(f4778,definition,
( spl0_91
<=> ord_less(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1) ),
introduced(definition,[new_symbols(definition,[spl0_91])],[avatar_definition]) ).
tff(f4779,plain,
( ord_less(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f4778]) ).
tff(f5039,plain,
( ~ ord_less(int,zero_zero(int),one_one(int))
| ord_less(int,pls,bit1(pls)) ),
inference(superposition,[],[f699,f401]) ).
tff(f5046,plain,
( ord_less(int,pls,bit1(pls))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f5039,f388]) ).
tff(f5202,plain,
( ord_less(int,one_one(int),plus_plus(int,zero_zero(int),one_one(int)))
| ( one_one(int) = plus_plus(int,zero_zero(int),one_one(int)) ) ),
inference(resolution,[],[f470,f341]) ).
tff(f5205,plain,
( spl0_22
| spl0_23 ),
inference(avatar_split_clause,[],[f5202,f1183,f1179]) ).
tff(f5232,plain,
( ord_less(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)
| ~ spl0_6 ),
inference(resolution,[],[f598,f291]) ).
tff(f5239,plain,
( spl0_91
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f5232,f596,f4778]) ).
tff(f5258,plain,
( ( zero_zero(int) = pls )
| ord_less(int,pls,zero_zero(int))
| ~ spl0_26 ),
inference(resolution,[],[f1252,f273]) ).
tff(f5259,plain,
( ( zero_zero(int) = pls )
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f5258,f284]) ).
tff(f5342,plain,
( ~ ord_less(int,pls,bit1(pls))
| spl0_11
| ~ spl0_26 ),
inference(superposition,[],[f734,f5259]) ).
tff(f5379,plain,
( $false
| ~ spl0_2
| spl0_11
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f5342,f5046]) ).
tff(f5380,plain,
( ~ spl0_2
| spl0_11
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f5379]) ).
tff(f5961,plain,
( ord_less(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1)))
| ~ spl0_13 ),
inference(superposition,[],[f3800,f745]) ).
tff(f6014,plain,
( ord_less(int,pls,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1)))
| ~ spl0_13
| ~ spl0_26 ),
inference(forward_demodulation,[],[f5961,f5259]) ).
tff(f6137,plain,
( ord_less(int,pls,bit0(times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1))))
| ~ spl0_13
| ~ spl0_26 ),
inference(resolution,[],[f6014,f235]) ).
tff(f6153,plain,
( ord_less(int,pls,bit0(bit0(times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1)))))
| ~ spl0_13
| ~ spl0_26 ),
inference(resolution,[],[f6137,f235]) ).
tff(f6169,plain,
( ord_less(int,pls,bit0(bit0(plus_plus(int,pls,bit1(pls)))))
| ~ spl0_13 ),
inference(forward_demodulation,[],[f417,f745]) ).
tff(f6170,plain,
( ord_less(int,pls,bit0(bit0(bit1(plus_plus(int,pls,pls)))))
| ~ spl0_13 ),
inference(forward_demodulation,[],[f6169,f510]) ).
tff(f6171,plain,
( ord_less(int,pls,bit0(bit0(bit1(pls))))
| ~ spl0_13
| ~ spl0_42 ),
inference(forward_demodulation,[],[f6170,f2397]) ).
tff(f6172,plain,
( spl0_77
| ~ spl0_13
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f6171,f2395,f743,f4654]) ).
tff(f6317,plain,
( ( one_one(int) = plus_plus(int,pls,one_one(int)) )
| ~ spl0_22
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1181,f5259]) ).
tff(f6415,plain,
( $false
| ~ spl0_14
| ~ spl0_22
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f6317,f748]) ).
tff(f6416,plain,
( ~ spl0_14
| ~ spl0_22
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f6415]) ).
tff(f7848,plain,
( ! [X0: int] : ( number_number_of(int,times_times(int,X0,pls)) = times_times(int,number_number_of(int,X0),pls) )
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1450,f5259]) ).
tff(f8006,plain,
( ord_less(int,pls,bit0(bit0(bit0(times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1))))))
| ~ spl0_13
| ~ spl0_26 ),
inference(resolution,[],[f6153,f235]) ).
tff(f8030,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1)))))))
| ~ spl0_13
| ~ spl0_26 ),
inference(resolution,[],[f8006,f235]) ).
tff(f8221,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1))))))))
| ~ spl0_13
| ~ spl0_26 ),
inference(resolution,[],[f8030,f235]) ).
tff(f8325,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1)))))))))
| ~ spl0_13
| ~ spl0_26 ),
inference(resolution,[],[f8221,f235]) ).
tff(f8605,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1))))))))))
| ~ spl0_13
| ~ spl0_26 ),
inference(resolution,[],[f8325,f235]) ).
tff(f8681,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1)))))))))))
| ~ spl0_13
| ~ spl0_26 ),
inference(resolution,[],[f8605,f235]) ).
tff(f8812,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1))))))))))))
| ~ spl0_13
| ~ spl0_26 ),
inference(resolution,[],[f8681,f235]) ).
tff(f9474,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1)))))))))))))
| ~ spl0_13
| ~ spl0_26 ),
inference(resolution,[],[f8812,f235]) ).
tff(f22721,plain,
( ~ ord_less(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1)
| ~ ord_less(int,pls,bit0(bit0(bit1(pls)))) ),
inference(resolution,[],[f975,f999]) ).
tff(f22754,plain,
( ~ ord_less(int,pls,bit0(bit0(bit1(pls))))
| ~ spl0_91 ),
inference(forward_subsumption_resolution,[],[f22721,f4779]) ).
tff(f22759,plain,
( ~ spl0_77
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f22754,f4778,f4654]) ).
tff(f22770,plain,
( ( minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1) = pls )
| ~ spl0_7
| ~ spl0_26 ),
inference(forward_demodulation,[],[f602,f5259]) ).
tff(f22783,plain,
( ( pls = minus_minus(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),m1) )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26 ),
inference(forward_demodulation,[],[f22770,f745]) ).
tff(f22847,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),pls))))))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26 ),
inference(superposition,[],[f9474,f22783]) ).
tff(f22911,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(number_number_of(int,times_times(int,bit0(bit0(bit1(pls))),pls)))))))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26 ),
inference(forward_demodulation,[],[f22847,f7848]) ).
tff(f22947,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(number_number_of(int,bit0(times_times(int,bit0(bit1(pls)),pls))))))))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26 ),
inference(forward_demodulation,[],[f22911,f213]) ).
tff(f22990,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(number_number_of(int,bit0(bit0(times_times(int,bit1(pls),pls)))))))))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26 ),
inference(forward_demodulation,[],[f22947,f213]) ).
tff(f23017,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(number_number_of(int,bit0(bit0(plus_plus(int,pls,pls)))))))))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26 ),
inference(forward_demodulation,[],[f22990,f625]) ).
tff(f23044,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(number_number_of(int,bit0(plus_plus(int,pls,pls))))))))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26 ),
inference(forward_demodulation,[],[f23017,f843]) ).
tff(f23071,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(number_number_of(int,plus_plus(int,pls,pls)))))))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26 ),
inference(forward_demodulation,[],[f23044,f843]) ).
tff(f23098,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(number_number_of(int,pls))))))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23071,f2397]) ).
tff(f23125,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(zero_zero(int))))))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23098,f397]) ).
tff(f23152,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(pls)))))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23125,f5259]) ).
tff(f23180,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(pls))))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23152,f201]) ).
tff(f23207,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(bit0(pls)))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23180,f201]) ).
tff(f23227,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(bit0(pls))))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23207,f201]) ).
tff(f23245,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(bit0(pls)))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23227,f201]) ).
tff(f23261,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(bit0(pls))))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23245,f201]) ).
tff(f23275,plain,
( ord_less(int,pls,bit0(bit0(bit0(bit0(pls)))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23261,f201]) ).
tff(f23287,plain,
( ord_less(int,pls,bit0(bit0(bit0(pls))))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23275,f201]) ).
tff(f23297,plain,
( ord_less(int,pls,bit0(bit0(pls)))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23287,f201]) ).
tff(f23305,plain,
( ord_less(int,pls,bit0(pls))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23297,f201]) ).
tff(f23310,plain,
( ord_less(int,pls,pls)
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_demodulation,[],[f23305,f201]) ).
tff(f23313,plain,
( $false
| ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[],[f23310,f204]) ).
tff(f23314,plain,
( ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f23313]) ).
cnf(s5,plain,
spl0_2,
inference(sat_conversion,[],[f522]) ).
cnf(s9,plain,
( ~ spl0_11
| spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f749]) ).
cnf(s31,plain,
( ~ spl0_22
| ~ spl0_41 ),
inference(sat_conversion,[],[f2757]) ).
cnf(s32,plain,
( ~ spl0_2
| ~ spl0_22
| spl0_41
| spl0_42 ),
inference(sat_conversion,[],[f2791]) ).
cnf(s43,plain,
( spl0_8
| spl0_26 ),
inference(sat_conversion,[],[f3845]) ).
cnf(s46,plain,
( spl0_4
| ~ spl0_23 ),
inference(sat_conversion,[],[f3850]) ).
cnf(s62,plain,
~ spl0_4,
inference(sat_conversion,[],[f3927]) ).
cnf(s125,plain,
~ spl0_8,
inference(sat_conversion,[],[f4392]) ).
cnf(s143,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f4715]) ).
cnf(s168,plain,
( spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f5205]) ).
cnf(s171,plain,
( ~ spl0_6
| spl0_91 ),
inference(sat_conversion,[],[f5239]) ).
cnf(s172,plain,
( ~ spl0_2
| spl0_11
| ~ spl0_26 ),
inference(sat_conversion,[],[f5380]) ).
cnf(s195,plain,
( ~ spl0_13
| ~ spl0_42
| spl0_77 ),
inference(sat_conversion,[],[f6172]) ).
cnf(s225,plain,
( ~ spl0_14
| ~ spl0_22
| ~ spl0_26 ),
inference(sat_conversion,[],[f6416]) ).
cnf(s581,plain,
( ~ spl0_77
| ~ spl0_91 ),
inference(sat_conversion,[],[f22759]) ).
cnf(s609,plain,
( ~ spl0_7
| ~ spl0_13
| ~ spl0_26
| ~ spl0_42 ),
inference(sat_conversion,[],[f23314]) ).
cnf(s619,plain,
~ spl0_23,
inference(rat,[],[s46,s62]) ).
cnf(s620,plain,
spl0_22,
inference(rat,[],[s168,s619]) ).
cnf(s622,plain,
spl0_26,
inference(rat,[],[s43,s125]) ).
cnf(s631,plain,
~ spl0_14,
inference(rat,[],[s225,s620,s622]) ).
cnf(s641,plain,
( ~ spl0_2
| spl0_41
| spl0_42 ),
inference(rat,[],[s32,s620]) ).
cnf(s642,plain,
~ spl0_41,
inference(rat,[],[s31,s620]) ).
cnf(s646,plain,
( ~ spl0_11
| spl0_13 ),
inference(rat,[],[s9,s631]) ).
cnf(s647,plain,
spl0_11,
inference(rat,[],[s172,s622,s5]) ).
cnf(s649,plain,
spl0_42,
inference(rat,[],[s641,s642,s5]) ).
cnf(s650,plain,
spl0_13,
inference(rat,[],[s646,s647]) ).
cnf(s653,plain,
~ spl0_7,
inference(rat,[],[s609,s649,s622,s650]) ).
cnf(s664,plain,
spl0_77,
inference(rat,[],[s195,s649,s650]) ).
cnf(s665,plain,
spl0_6,
inference(rat,[],[s143,s653]) ).
cnf(s668,plain,
~ spl0_91,
inference(rat,[],[s581,s664]) ).
cnf(s670,plain,
$false,
inference(rat,[],[s171,s668,s665]) ).
tff(f23315,plain,
$false,
inference(avatar_sat_refutation,[],[s670]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM989_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 % Computer : n002.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 21:52:07 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.46 Running first-order model finding
% 0.13/0.46 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
% 4.05/1.09 % (3920857)Will run a generic schedule for satisfiability detection.
% 4.05/1.09 % (3920863)% WARNING: option uhcvi not known.
% 4.05/1.09 % (3920863)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2699223207:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.05/1.09 % (3920862)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=191511820_2999 on theBenchmark for (2999ds/0Mi)
% 4.05/1.09 % Exception at run slice level
% 4.05/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.05/1.09 % (3920867)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1542961741:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.05/1.09 % (3920865)dis+10_1_sil=32000:sp=arity:random_seed=2488892621:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.05/1.09 % (3920866)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=634275357:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.05/1.09 % (3920868)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1053923722:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.05/1.09 % (3920864)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4084905261:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.05/1.09 % (3920871)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=483530402:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.05/1.09 % Exception at run slice level
% 4.05/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.05/1.09 % (3920878)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1273010121:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.05/1.09 % (3920865)Instruction limit reached!
% 4.05/1.09 % (3920865)------------------------------
% 4.05/1.09 % (3920865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/1.09 % (3920865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.09 % (3920865)CaDiCaL version: 2.1.3
% 4.05/1.09 % (3920865)Termination reason: Instruction limit
% 4.05/1.09 % (3920865)Termination phase: Saturation
% 4.05/1.09 % (3920865)Time elapsed: 0.111 s
% 4.05/1.09 % (3920865)Peak memory usage: 12 MB
% 4.05/1.09 % (3920865)Instructions burned: 103 (million)
% 4.05/1.09 % (3920866)Instruction limit reached!
% 4.05/1.09 % (3920866)------------------------------
% 4.05/1.09 % (3920866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/1.09 % (3920866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.09 % (3920866)CaDiCaL version: 2.1.3
% 4.05/1.09 % (3920866)Termination reason: Instruction limit
% 4.05/1.09 % (3920866)Termination phase: Saturation
% 4.05/1.09 % (3920866)Time elapsed: 0.121 s
% 4.05/1.09 % (3920866)Peak memory usage: 13 MB
% 4.05/1.09 % (3920866)Instructions burned: 116 (million)
% 4.05/1.09 % (3920867)Instruction limit reached!
% 4.05/1.09 % (3920867)------------------------------
% 4.05/1.09 % (3920867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/1.09 % (3920867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.09 % (3920867)CaDiCaL version: 2.1.3
% 4.05/1.09 % (3920867)Termination reason: Instruction limit
% 4.05/1.09 % (3920867)Termination phase: Saturation
% 4.05/1.09 % (3920867)Time elapsed: 0.128 s
% 4.05/1.09 % (3920867)Peak memory usage: 13 MB
% 4.05/1.09 % (3920867)Instructions burned: 132 (million)
% 4.05/1.09 % (3920881)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=2637291781:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 4.05/1.09 % (3920868)Instruction limit reached!
% 4.05/1.09 % (3920868)------------------------------
% 4.05/1.09 % (3920868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/1.09 % (3920868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.09 % (3920868)CaDiCaL version: 2.1.3
% 4.05/1.09 % (3920868)Termination reason: Instruction limit
% 4.05/1.09 % (3920868)Termination phase: Saturation
% 4.05/1.09 % (3920868)Time elapsed: 0.147 s
% 4.05/1.09 % (3920868)Peak memory usage: 12 MB
% 4.05/1.09 % (3920868)Instructions burned: 160 (million)
% 4.05/1.09 % (3920883)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3542558784:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 4.05/1.09 % (3920882)ott-21_1_sil=16000:fs=off:random_seed=2539066345:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 4.05/1.09 % (3920885)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=945208370:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 4.05/1.09 % Exception at run slice level
% 4.05/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.05/1.09 % (3920889)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2301327307:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 4.05/1.09 % (3920878)Instruction limit reached!
% 4.05/1.09 % (3920878)------------------------------
% 4.05/1.09 % (3920878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/1.09 % (3920878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.09 % (3920878)CaDiCaL version: 2.1.3
% 4.05/1.09 % (3920878)Termination reason: Instruction limit
% 4.05/1.09 % (3920878)Termination phase: Saturation
% 4.05/1.09 % (3920878)Time elapsed: 0.141 s
% 4.05/1.09 % (3920878)Peak memory usage: 13 MB
% 4.05/1.09 % (3920878)Instructions burned: 131 (million)
% 4.05/1.09 % (3920892)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1239295568:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 4.05/1.09 % Exception at run slice level
% 4.05/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.05/1.09 % (3920882)Instruction limit reached!
% 4.05/1.09 % (3920882)------------------------------
% 4.05/1.09 % (3920882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/1.09 % (3920882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.09 % (3920882)CaDiCaL version: 2.1.3
% 4.05/1.09 % (3920882)Termination reason: Instruction limit
% 4.05/1.09 % (3920882)Termination phase: Saturation
% 4.05/1.09 % (3920882)Time elapsed: 0.164 s
% 4.05/1.09 % (3920882)Peak memory usage: 12 MB
% 4.05/1.09 % (3920882)Instructions burned: 180 (million)
% 4.05/1.09 % (3920894)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=3709423889:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 4.05/1.09 % (3920895)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4083398553:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 4.05/1.09 % (3920863) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3920857-3920863"...
% 4.05/1.09 % (3920863)...printing done.
% 4.05/1.09 % (3920863)Refutation found. Thanks to Tanya!
% 4.05/1.09 % SZS status Theorem for theBenchmark
% 4.05/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 4.05/1.10 % (3920863)------------------------------
% 4.05/1.10 % (3920863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/1.10 % (3920863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.10 % (3920863)CaDiCaL version: 2.1.3
% 4.05/1.10 % (3920863)Termination reason: Refutation
% 4.05/1.10 % (3920863)Time elapsed: 0.584 s
% 4.05/1.10 % (3920863)Peak memory usage: 22 MB
% 4.05/1.10 % (3920863)Instructions burned: 1177 (million)
% 4.05/1.10 % (3920857)Success in time 0.617 s
% 4.05/1.10 % Vampire exiting
%------------------------------------------------------------------------------