%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP317_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 11:33:35 AM UTC 2026
% Result : Theorem 8.91s 2.58s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 173 ( 53 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 205 ( 87 ~; 83 |; 15 &)
% ( 11 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 61 ( 21 atm; 0 fun; 0 num; 40 var)
% Number of types : 24 ( 21 usr; 2 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 27 ( 23 usr; 5 prp; 0-3 aty)
% Number of functors : 84 ( 84 usr; 22 con; 0-3 aty)
% Number of variables : 104 ( 100 !; 4 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Real_real_bool_fun_fun$': $tType ).
tff(type_def_6,type,
'Int_bool_fun$': $tType ).
tff(type_def_7,type,
'Real_a_fun$': $tType ).
tff(type_def_8,type,
'Bool_int_fun$': $tType ).
tff(type_def_9,type,
'Bool_real_fun$': $tType ).
tff(type_def_10,type,
'Int_real_fun$': $tType ).
tff(type_def_11,type,
'Nat_real_fun_bool_fun$': $tType ).
tff(type_def_12,type,
'Int_int_fun$': $tType ).
tff(type_def_13,type,
'Nat_nat_fun$': $tType ).
tff(type_def_14,type,
'Nat$': $tType ).
tff(type_def_15,type,
tlbool: $tType ).
tff(type_def_16,type,
'Real_real_fun$': $tType ).
tff(type_def_17,type,
'Nat_real_fun$': $tType ).
tff(type_def_18,type,
'Real_int_fun$': $tType ).
tff(type_def_19,type,
'Nat_real_fun_nat_nat_fun_fun$': $tType ).
tff(type_def_20,type,
'A$': $tType ).
tff(type_def_21,type,
'Nat_real_fun_nat_real_fun_fun$': $tType ).
tff(type_def_22,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_23,type,
'Nat_bool_fun$': $tType ).
tff(type_def_24,type,
'Real_bool_fun$': $tType ).
tff(type_def_25,type,
'Real_set$': $tType ).
tff(func_def_0,type,
'greatest$a': 'Int_bool_fun$' > $int ).
tff(func_def_1,type,
'n$a': 'Nat$' ).
tff(func_def_2,type,
'round$': 'Real_int_fun$' ).
tff(func_def_3,type,
'dbl_inc$': 'Int_int_fun$' ).
tff(func_def_4,type,
'a$a': $int ).
tff(func_def_5,type,
'eM_remainder_converges$': ( 'Nat$' * 'Real_a_fun$' ) > 'Int_bool_fun$' ).
tff(func_def_6,type,
'artanh$': 'Real_real_fun$' ).
tff(func_def_7,type,
'uub$': 'Int_int_bool_fun_fun$' ).
tff(func_def_8,type,
'dbl_inc$a': 'Real_real_fun$' ).
tff(func_def_9,type,
'arsinh$': 'Real_real_fun$' ).
tff(func_def_10,type,
'a$': $int ).
tff(func_def_11,type,
'n$': 'Nat$' ).
tff(func_def_12,type,
'fun_app$g': ( 'Real_real_fun$' * $real ) > $real ).
tff(func_def_13,type,
'fun_app$a': ( 'Real_real_bool_fun_fun$' * $real ) > 'Real_bool_fun$' ).
tff(func_def_14,type,
'of_nat$': 'Nat$' > $int ).
tff(func_def_15,type,
'g$': 'Real_a_fun$' ).
tff(func_def_16,type,
'f$': 'Real_a_fun$' ).
tff(func_def_17,type,
'times$': $int > 'Int_int_fun$' ).
tff(func_def_18,type,
tltrue: tlbool ).
tff(func_def_19,type,
'uu$': 'Real_set$' > 'Real_bool_fun$' ).
tff(func_def_20,type,
'of_int$': 'Int_real_fun$' ).
tff(func_def_21,type,
'of_int$a': 'Int_int_fun$' ).
tff(func_def_22,type,
'uud$': 'Int_int_bool_fun_fun$' ).
tff(func_def_23,type,
'greatest$': 'Real_bool_fun$' > $real ).
tff(func_def_24,type,
'uua$': 'Real_real_bool_fun_fun$' ).
tff(func_def_25,type,
'fun_app$n': ( 'Nat_real_fun$' * 'Nat$' ) > $real ).
tff(func_def_26,type,
'fun_app$l': ( 'Nat_real_fun_nat_real_fun_fun$' * 'Nat_real_fun$' ) > 'Nat_real_fun$' ).
tff(func_def_27,type,
'fun_app$h': ( 'Real_int_fun$' * $real ) > $int ).
tff(func_def_28,type,
'floor$': 'Real_int_fun$' ).
tff(func_def_29,type,
tlfalse: tlbool ).
tff(func_def_30,type,
'nat$': $int > 'Nat$' ).
tff(func_def_31,type,
'fun_app$c': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_32,type,
'fun_app$p': ( 'Nat_real_fun_nat_nat_fun_fun$' * 'Nat_real_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_33,type,
'fun_app$e': ( 'Real_a_fun$' * $real ) > 'A$' ).
tff(func_def_34,type,
'arcosh$': 'Real_real_fun$' ).
tff(func_def_35,type,
'power_int$': $real > 'Int_real_fun$' ).
tff(func_def_36,type,
'fun_app$o': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_37,type,
'fun_app$f': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_38,type,
'uuc$': 'Real_real_bool_fun_fun$' ).
tff(func_def_39,type,
'fun_app$j': ( 'Bool_int_fun$' * tlbool ) > $int ).
tff(func_def_40,type,
'fun_app$i': ( 'Bool_real_fun$' * tlbool ) > $real ).
tff(func_def_41,type,
'ceiling$': 'Real_int_fun$' ).
tff(func_def_42,type,
'collect$': 'Real_bool_fun$' > 'Real_set$' ).
tff(func_def_43,type,
'fun_app$d': ( 'Int_real_fun$' * $int ) > $real ).
tff(func_def_52,type,
sK6: 'Int_real_fun$' > $int ).
tff(func_def_53,type,
sK7: 'Int_real_fun$' > $int ).
tff(func_def_54,type,
sK8: 'Int_real_fun$' > $int ).
tff(func_def_55,type,
sK9: 'Int_real_fun$' > $int ).
tff(func_def_56,type,
sK10: 'Int_real_fun$' > $int ).
tff(func_def_57,type,
sK11: 'Int_real_fun$' > $int ).
tff(func_def_58,type,
sK12: 'Int_real_fun$' > $int ).
tff(func_def_59,type,
sK13: 'Int_real_fun$' > $int ).
tff(func_def_60,type,
sK14: 'Int_real_fun$' > $int ).
tff(func_def_61,type,
sK15: 'Int_real_fun$' > $int ).
tff(func_def_62,type,
sK16: $int > $int ).
tff(func_def_63,type,
sK17: 'Int_real_fun$' > $int ).
tff(func_def_64,type,
sK18: 'Int_real_fun$' > $int ).
tff(func_def_65,type,
sK19: ( $real * $real ) > $real ).
tff(func_def_66,type,
sK20: $real > $int ).
tff(func_def_67,type,
sK21: ( $real * $real ) > $real ).
tff(func_def_68,type,
sK22: 'Int_real_fun$' > $int ).
tff(func_def_69,type,
sK23: 'Int_real_fun$' > $int ).
tff(func_def_70,type,
sK24: $real > $int ).
tff(func_def_71,type,
sK25: ( $real * $real ) > $real ).
tff(func_def_72,type,
sK26: 'Int_real_fun$' > $int ).
tff(func_def_73,type,
sK27: 'Int_real_fun$' > $int ).
tff(func_def_74,type,
sK28: $int > $int ).
tff(func_def_75,type,
sK29: ( $real * $real * $real ) > $real ).
tff(func_def_76,type,
sK30: ( 'Real_a_fun$' * 'Real_a_fun$' * $int ) > $real ).
tff(func_def_77,type,
sK31: $real > $int ).
tff(func_def_78,type,
sK32: 'Int_real_fun$' > $int ).
tff(func_def_79,type,
sK33: 'Int_real_fun$' > $int ).
tff(func_def_80,type,
sK34: $real > $real ).
tff(func_def_81,type,
sK35: ( 'Int_bool_fun$' * $int ) > $int ).
tff(func_def_82,type,
sK36: 'Int_real_fun$' > $int ).
tff(func_def_83,type,
sK37: 'Int_real_fun$' > $int ).
tff(func_def_84,type,
sK38: 'Int_real_fun$' > $int ).
tff(func_def_85,type,
sK39: 'Int_real_fun$' > $int ).
tff(func_def_86,type,
sK40: ( $real * $real * $real ) > $real ).
tff(func_def_87,type,
sK41: ( $int * 'Int_bool_fun$' ) > $int ).
tff(func_def_88,type,
sK42: ( $real * $real ) > $real ).
tff(func_def_89,type,
sK43: 'Int_real_fun$' > $int ).
tff(func_def_90,type,
sK44: 'Int_real_fun$' > $int ).
tff(func_def_91,type,
sK45: $real > $real ).
tff(pred_def_1,type,
'antimono$c': 'Int_int_fun$' > $o ).
tff(pred_def_2,type,
'fun_app$m': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_3,type,
'antimono$b': 'Int_real_fun$' > $o ).
tff(pred_def_4,type,
'less_eq$a': ( 'Bool_int_fun$' * 'Bool_int_fun$' ) > $o ).
tff(pred_def_5,type,
'less_eq$': ( 'Bool_real_fun$' * 'Bool_real_fun$' ) > $o ).
tff(pred_def_6,type,
'fun_app$': ( 'Real_bool_fun$' * $real ) > $o ).
tff(pred_def_7,type,
'fun_app$k': ( 'Nat_real_fun_bool_fun$' * 'Nat_real_fun$' ) > $o ).
tff(pred_def_8,type,
'antimono$a': 'Real_int_fun$' > $o ).
tff(pred_def_9,type,
'partial_preordering$': 'Real_real_bool_fun_fun$' > $o ).
tff(pred_def_10,type,
'antimono$': 'Real_real_fun$' > $o ).
tff(pred_def_11,type,
'partial_preordering$a': 'Int_int_bool_fun_fun$' > $o ).
tff(pred_def_12,type,
'member$': ( $real * 'Real_set$' ) > $o ).
tff(pred_def_13,type,
'fun_app$b': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_18,type,
sP0: ( $int * $int * $int ) > $o ).
tff(pred_def_19,type,
sP1: ( $int * $int * $int ) > $o ).
tff(pred_def_20,type,
sP2: ( $int * $int * $int ) > $o ).
tff(pred_def_21,type,
sP3: ( $real * $real * $real ) > $o ).
tff(pred_def_22,type,
sP4: ( $real * $real * $real ) > $o ).
tff(pred_def_23,type,
sP5: ( $real * $real * $real ) > $o ).
tff(f6,conjecture,
( 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')
<=> 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture5) ).
tff(f7,negated_conjecture,
~ ( 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')
<=> 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$') ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,axiom,
'a$' = 'a$a',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).
tff(f9,axiom,
'of_nat$'('n$') = 'of_nat$'('n$a'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).
tff(f10,axiom,
! [X0: $real] :
( $lesseq('fun_app$d'('of_int$','a$'),X0)
=> ( 'fun_app$e'('f$',X0) = 'fun_app$e'('g$',X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).
tff(f11,axiom,
! [X5: $int,X1: 'Real_a_fun$',X0: $int,X4: 'Nat$',X3: 'Nat$',X2: 'Real_a_fun$'] :
( ( ( X0 = X5 )
& ! [X6: $real] :
( $lesseq('fun_app$d'('of_int$',X0),X6)
=> ( 'fun_app$e'(X1,X6) = 'fun_app$e'(X2,X6) ) )
& ( 'of_nat$'(X3) = 'of_nat$'(X4) ) )
=> ( 'fun_app$b'('eM_remainder_converges$'(X4,X2),X5)
<=> 'fun_app$b'('eM_remainder_converges$'(X3,X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
tff(f724,plain,
! [X0: $real] :
( ~ $less(X0,'fun_app$d'('of_int$','a$'))
=> ( 'fun_app$e'('f$',X0) = 'fun_app$e'('g$',X0) ) ),
inference(theory_normalization,[],[f10]) ).
tff(f902,plain,
! [X5: $int,X1: 'Real_a_fun$',X0: $int,X4: 'Nat$',X3: 'Nat$',X2: 'Real_a_fun$'] :
( ( ( X0 = X5 )
& ! [X6: $real] :
( ~ $less(X6,'fun_app$d'('of_int$',X0))
=> ( 'fun_app$e'(X1,X6) = 'fun_app$e'(X2,X6) ) )
& ( 'of_nat$'(X3) = 'of_nat$'(X4) ) )
=> ( 'fun_app$b'('eM_remainder_converges$'(X4,X2),X5)
<=> 'fun_app$b'('eM_remainder_converges$'(X3,X1),X0) ) ),
inference(theory_normalization,[],[f11]) ).
tff(f915,plain,
! [X2: $int,X1: 'Real_a_fun$',X3: 'Nat$',X4: 'Nat$',X0: $int,X5: 'Real_a_fun$'] :
( ( ( 'of_nat$'(X3) = 'of_nat$'(X4) )
& ( X0 = X2 )
& ! [X6: $real] :
( ~ $less(X6,'fun_app$d'('of_int$',X2))
=> ( 'fun_app$e'(X1,X6) = 'fun_app$e'(X5,X6) ) ) )
=> ( 'fun_app$b'('eM_remainder_converges$'(X3,X5),X0)
<=> 'fun_app$b'('eM_remainder_converges$'(X4,X1),X2) ) ),
inference(rectify,[],[f902]) ).
tff(f1184,plain,
! [X0: $real] :
( $less(X0,'fun_app$d'('of_int$','a$'))
| ( 'fun_app$e'('f$',X0) = 'fun_app$e'('g$',X0) ) ),
inference(ennf_transformation,[],[f724]) ).
tff(f1187,plain,
( 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')
<~> 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$') ),
inference(ennf_transformation,[],[f7]) ).
tff(f1239,plain,
! [X2: $int,X1: 'Real_a_fun$',X3: 'Nat$',X4: 'Nat$',X0: $int,X5: 'Real_a_fun$'] :
( ( 'fun_app$b'('eM_remainder_converges$'(X3,X5),X0)
<=> 'fun_app$b'('eM_remainder_converges$'(X4,X1),X2) )
| ( 'of_nat$'(X3) != 'of_nat$'(X4) )
| ( X0 != X2 )
| ? [X6: $real] :
( ( 'fun_app$e'(X1,X6) != 'fun_app$e'(X5,X6) )
& ~ $less(X6,'fun_app$d'('of_int$',X2)) ) ),
inference(ennf_transformation,[],[f915]) ).
tff(f1240,plain,
! [X5: 'Real_a_fun$',X3: 'Nat$',X1: 'Real_a_fun$',X4: 'Nat$',X0: $int,X2: $int] :
( ( X0 != X2 )
| ? [X6: $real] :
( ( 'fun_app$e'(X1,X6) != 'fun_app$e'(X5,X6) )
& ~ $less(X6,'fun_app$d'('of_int$',X2)) )
| ( 'of_nat$'(X3) != 'of_nat$'(X4) )
| ( 'fun_app$b'('eM_remainder_converges$'(X3,X5),X0)
<=> 'fun_app$b'('eM_remainder_converges$'(X4,X1),X2) ) ),
inference(flattening,[],[f1239]) ).
tff(f1639,plain,
! [X5: 'Real_a_fun$',X3: 'Nat$',X1: 'Real_a_fun$',X4: 'Nat$',X0: $int,X2: $int] :
( ( X0 != X2 )
| ? [X6: $real] :
( ( 'fun_app$e'(X1,X6) != 'fun_app$e'(X5,X6) )
& ~ $less(X6,'fun_app$d'('of_int$',X2)) )
| ( 'of_nat$'(X3) != 'of_nat$'(X4) )
| ( ( 'fun_app$b'('eM_remainder_converges$'(X3,X5),X0)
| ~ 'fun_app$b'('eM_remainder_converges$'(X4,X1),X2) )
& ( 'fun_app$b'('eM_remainder_converges$'(X4,X1),X2)
| ~ 'fun_app$b'('eM_remainder_converges$'(X3,X5),X0) ) ) ),
inference(nnf_transformation,[],[f1240]) ).
tff(f1640,plain,
! [X0: 'Real_a_fun$',X1: 'Nat$',X2: 'Real_a_fun$',X3: 'Nat$',X4: $int,X5: $int] :
( ( X4 != X5 )
| ? [X6: $real] :
( ( 'fun_app$e'(X2,X6) != 'fun_app$e'(X0,X6) )
& ~ $less(X6,'fun_app$d'('of_int$',X5)) )
| ( 'of_nat$'(X3) != 'of_nat$'(X1) )
| ( ( 'fun_app$b'('eM_remainder_converges$'(X1,X0),X4)
| ~ 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5) )
& ( 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5)
| ~ 'fun_app$b'('eM_remainder_converges$'(X1,X0),X4) ) ) ),
inference(rectify,[],[f1639]) ).
tff(f1641,plain,
! [X0: 'Real_a_fun$',X1: 'Nat$',X2: 'Real_a_fun$',X3: 'Nat$',X4: $int,X5: $int] :
( ( X4 != X5 )
| ( ( 'fun_app$e'(X2,sK30(X0,X2,X5)) != 'fun_app$e'(X0,sK30(X0,X2,X5)) )
& ~ $less(sK30(X0,X2,X5),'fun_app$d'('of_int$',X5)) )
| ( 'of_nat$'(X3) != 'of_nat$'(X1) )
| ( ( 'fun_app$b'('eM_remainder_converges$'(X1,X0),X4)
| ~ 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5) )
& ( 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5)
| ~ 'fun_app$b'('eM_remainder_converges$'(X1,X0),X4) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(X6,sK30(X0,X2,X5))],[f1640]) ).
tff(f1655,plain,
( ( ~ 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$')
| ~ 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') )
& ( 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$')
| 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') ) ),
inference(nnf_transformation,[],[f1187]) ).
tff(f2140,plain,
'of_nat$'('n$') = 'of_nat$'('n$a'),
inference(cnf_transformation,[],[f9]) ).
tff(f2244,plain,
! [X0: $real] :
( $less(X0,'fun_app$d'('of_int$','a$'))
| ( 'fun_app$e'('f$',X0) = 'fun_app$e'('g$',X0) ) ),
inference(cnf_transformation,[],[f1184]) ).
tff(f2266,plain,
! [X2: 'Real_a_fun$',X3: 'Nat$',X0: 'Real_a_fun$',X1: 'Nat$',X4: $int,X5: $int] :
( ( X4 != X5 )
| ~ $less(sK30(X0,X2,X5),'fun_app$d'('of_int$',X5))
| ( 'of_nat$'(X3) != 'of_nat$'(X1) )
| 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5)
| ~ 'fun_app$b'('eM_remainder_converges$'(X1,X0),X4) ),
inference(cnf_transformation,[],[f1641]) ).
tff(f2267,plain,
! [X2: 'Real_a_fun$',X3: 'Nat$',X0: 'Real_a_fun$',X1: 'Nat$',X4: $int,X5: $int] :
( ( X4 != X5 )
| ~ $less(sK30(X0,X2,X5),'fun_app$d'('of_int$',X5))
| ( 'of_nat$'(X3) != 'of_nat$'(X1) )
| 'fun_app$b'('eM_remainder_converges$'(X1,X0),X4)
| ~ 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5) ),
inference(cnf_transformation,[],[f1641]) ).
tff(f2268,plain,
! [X2: 'Real_a_fun$',X3: 'Nat$',X0: 'Real_a_fun$',X1: 'Nat$',X4: $int,X5: $int] :
( ( X4 != X5 )
| ( 'fun_app$e'(X2,sK30(X0,X2,X5)) != 'fun_app$e'(X0,sK30(X0,X2,X5)) )
| ( 'of_nat$'(X3) != 'of_nat$'(X1) )
| 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5)
| ~ 'fun_app$b'('eM_remainder_converges$'(X1,X0),X4) ),
inference(cnf_transformation,[],[f1641]) ).
tff(f2269,plain,
! [X2: 'Real_a_fun$',X3: 'Nat$',X0: 'Real_a_fun$',X1: 'Nat$',X4: $int,X5: $int] :
( ( X4 != X5 )
| ( 'fun_app$e'(X2,sK30(X0,X2,X5)) != 'fun_app$e'(X0,sK30(X0,X2,X5)) )
| ( 'of_nat$'(X3) != 'of_nat$'(X1) )
| 'fun_app$b'('eM_remainder_converges$'(X1,X0),X4)
| ~ 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5) ),
inference(cnf_transformation,[],[f1641]) ).
tff(f2291,plain,
( 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$')
| 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') ),
inference(cnf_transformation,[],[f1655]) ).
tff(f2292,plain,
( ~ 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$')
| ~ 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') ),
inference(cnf_transformation,[],[f1655]) ).
tff(f2378,plain,
'a$' = 'a$a',
inference(cnf_transformation,[],[f8]) ).
tff(f2511,plain,
! [X0: $real] :
( ( 'fun_app$e'('f$',X0) = 'fun_app$e'('g$',X0) )
| $less(X0,'fun_app$d'('of_int$','a$a')) ),
inference(definition_unfolding,[],[f2244,f2378]) ).
tff(f2512,plain,
( ~ 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')
| ~ 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') ),
inference(definition_unfolding,[],[f2292,f2378]) ).
tff(f2513,plain,
( 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')
| 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a') ),
inference(definition_unfolding,[],[f2291,f2378]) ).
tff(f2610,plain,
! [X2: 'Real_a_fun$',X3: 'Nat$',X0: 'Real_a_fun$',X1: 'Nat$',X5: $int] :
( ( 'fun_app$e'(X2,sK30(X0,X2,X5)) != 'fun_app$e'(X0,sK30(X0,X2,X5)) )
| ( 'of_nat$'(X3) != 'of_nat$'(X1) )
| ~ 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5)
| 'fun_app$b'('eM_remainder_converges$'(X1,X0),X5) ),
inference(equality_resolution,[],[f2269]) ).
tff(f2611,plain,
! [X2: 'Real_a_fun$',X3: 'Nat$',X0: 'Real_a_fun$',X1: 'Nat$',X5: $int] :
( ( 'fun_app$e'(X2,sK30(X0,X2,X5)) != 'fun_app$e'(X0,sK30(X0,X2,X5)) )
| ( 'of_nat$'(X3) != 'of_nat$'(X1) )
| 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5)
| ~ 'fun_app$b'('eM_remainder_converges$'(X1,X0),X5) ),
inference(equality_resolution,[],[f2268]) ).
tff(f2612,plain,
! [X2: 'Real_a_fun$',X3: 'Nat$',X0: 'Real_a_fun$',X1: 'Nat$',X5: $int] :
( ~ $less(sK30(X0,X2,X5),'fun_app$d'('of_int$',X5))
| ~ 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5)
| 'fun_app$b'('eM_remainder_converges$'(X1,X0),X5)
| ( 'of_nat$'(X3) != 'of_nat$'(X1) ) ),
inference(equality_resolution,[],[f2267]) ).
tff(f2613,plain,
! [X2: 'Real_a_fun$',X3: 'Nat$',X0: 'Real_a_fun$',X1: 'Nat$',X5: $int] :
( ~ $less(sK30(X0,X2,X5),'fun_app$d'('of_int$',X5))
| ( 'of_nat$'(X3) != 'of_nat$'(X1) )
| ~ 'fun_app$b'('eM_remainder_converges$'(X1,X0),X5)
| 'fun_app$b'('eM_remainder_converges$'(X3,X2),X5) ),
inference(equality_resolution,[],[f2266]) ).
tff(f2666,definition,
( spl46_1
<=> 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a') ),
introduced(definition,[new_symbols(definition,[spl46_1])],[avatar_definition]) ).
tff(f2667,plain,
( ~ 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')
| spl46_1 ),
inference(avatar_component_clause,[],[f2666]) ).
tff(f2668,plain,
( 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')
| ~ spl46_1 ),
inference(avatar_component_clause,[],[f2666]) ).
tff(f2670,definition,
( spl46_2
<=> 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') ),
introduced(definition,[new_symbols(definition,[spl46_2])],[avatar_definition]) ).
tff(f2671,plain,
( ~ 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')
| spl46_2 ),
inference(avatar_component_clause,[],[f2670]) ).
tff(f2672,plain,
( 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')
| ~ spl46_2 ),
inference(avatar_component_clause,[],[f2670]) ).
tff(f2673,plain,
( spl46_1
| spl46_2 ),
inference(avatar_split_clause,[],[f2513,f2670,f2666]) ).
tff(f2674,plain,
( ~ spl46_1
| ~ spl46_2 ),
inference(avatar_split_clause,[],[f2512,f2670,f2666]) ).
tff(f2676,plain,
( ( 'fun_app$e'('g$',sK30('f$','g$','a$a')) != 'fun_app$e'('f$',sK30('f$','g$','a$a')) )
| ~ spl46_1
| spl46_2 ),
inference(unit_resulting_resolution,[],[f2611,f2668,f2140,f2671]) ).
tff(f2677,plain,
( ~ $less(sK30('f$','g$','a$a'),'fun_app$d'('of_int$','a$a'))
| ~ spl46_1
| spl46_2 ),
inference(unit_resulting_resolution,[],[f2613,f2668,f2140,f2671]) ).
tff(f2680,definition,
( spl46_3
<=> $less(sK30('f$','g$','a$a'),'fun_app$d'('of_int$','a$a')) ),
introduced(definition,[new_symbols(definition,[spl46_3])],[avatar_definition]) ).
tff(f2682,plain,
( ~ $less(sK30('f$','g$','a$a'),'fun_app$d'('of_int$','a$a'))
| spl46_3 ),
inference(avatar_component_clause,[],[f2680]) ).
tff(f2683,plain,
( ~ spl46_3
| ~ spl46_1
| spl46_2 ),
inference(avatar_split_clause,[],[f2677,f2670,f2666,f2680]) ).
tff(f2685,definition,
( spl46_4
<=> ( 'fun_app$e'('g$',sK30('f$','g$','a$a')) = 'fun_app$e'('f$',sK30('f$','g$','a$a')) ) ),
introduced(definition,[new_symbols(definition,[spl46_4])],[avatar_definition]) ).
tff(f2688,plain,
( ~ spl46_4
| ~ spl46_1
| spl46_2 ),
inference(avatar_split_clause,[],[f2676,f2670,f2666,f2685]) ).
tff(f2699,plain,
( ( 'fun_app$e'('g$',sK30('f$','g$','a$a')) = 'fun_app$e'('f$',sK30('f$','g$','a$a')) )
| spl46_3 ),
inference(unit_resulting_resolution,[],[f2511,f2682]) ).
tff(f3684,plain,
( ( 'fun_app$e'('g$',sK30('f$','g$','a$a')) != 'fun_app$e'('f$',sK30('f$','g$','a$a')) )
| spl46_1
| ~ spl46_2 ),
inference(unit_resulting_resolution,[],[f2610,f2667,f2140,f2672]) ).
tff(f3687,plain,
( ~ $less(sK30('f$','g$','a$a'),'fun_app$d'('of_int$','a$a'))
| spl46_1
| ~ spl46_2 ),
inference(unit_resulting_resolution,[],[f2612,f2667,f2140,f2672]) ).
tff(f3691,plain,
( spl46_4
| spl46_3 ),
inference(avatar_split_clause,[],[f2699,f2680,f2685]) ).
tff(f3692,plain,
( ~ spl46_4
| spl46_1
| ~ spl46_2 ),
inference(avatar_split_clause,[],[f3684,f2670,f2666,f2685]) ).
tff(f3693,plain,
( ~ spl46_3
| spl46_1
| ~ spl46_2 ),
inference(avatar_split_clause,[],[f3687,f2670,f2666,f2680]) ).
tff(f3694,plain,
$false,
inference(avatar_smt_refutation,[],[f3693,f3692,f3691,f2688,f2683,f2674,f2673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP317_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 12:54:02 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 Running first-order theorem proving
% 0.23/0.48 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.64/1.95 % (3962031)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.64/1.95 % (3962037)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3689631542:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.64/1.95 % (3962042)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=532256981:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.64/1.95 % (3962037)Instruction limit reached!
% 5.64/1.95 % (3962037)------------------------------
% 5.64/1.95 % (3962037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.95 % (3962037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.95 % (3962037)CaDiCaL version: 2.1.3
% 5.64/1.95 % (3962037)Termination reason: Instruction limit
% 5.64/1.95 % (3962037)Termination phase: Property scanning
% 5.64/1.95 % (3962037)Time elapsed: 0.006 s
% 5.64/1.95 % (3962037)Peak memory usage: 86 MB
% 5.64/1.95 % (3962037)Instructions burned: 13 (million)
% 5.64/1.95 % (3962043)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=71065798:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.64/1.95 % (3962038)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4098764135:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.64/1.95 % (3962039)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2019656924:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.64/1.95 % (3962040)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3023353497:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.64/1.95 % (3962041)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2690789163:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.64/1.95 % (3962041)Instruction limit reached!
% 5.64/1.95 % (3962041)------------------------------
% 5.64/1.95 % (3962041)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.95 % (3962041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.95 % (3962041)CaDiCaL version: 2.1.3
% 5.64/1.95 % (3962041)Termination reason: Instruction limit
% 5.64/1.95 % (3962041)Termination phase: Property scanning
% 5.64/1.95 % (3962041)Time elapsed: 0.006 s
% 5.64/1.95 % (3962041)Peak memory usage: 85 MB
% 5.64/1.95 % (3962041)Instructions burned: 5 (million)
% 5.64/1.95 % (3962040)Instruction limit reached!
% 5.64/1.95 % (3962040)------------------------------
% 5.64/1.95 % (3962040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.95 % (3962040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.95 % (3962040)CaDiCaL version: 2.1.3
% 5.64/1.95 % (3962040)Termination reason: Instruction limit
% 5.64/1.95 % (3962040)Termination phase: Property scanning
% 5.64/1.95 % (3962040)Time elapsed: 0.007 s
% 5.64/1.95 % (3962040)Peak memory usage: 85 MB
% 5.64/1.95 % (3962040)Instructions burned: 7 (million)
% 5.64/1.95 % (3962042)Instruction limit reached!
% 5.64/1.95 % (3962042)------------------------------
% 5.64/1.95 % (3962042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.95 % (3962042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.95 % (3962042)CaDiCaL version: 2.1.3
% 5.64/1.95 % (3962042)Termination reason: Instruction limit
% 5.64/1.95 % (3962042)Termination phase: Saturation
% 5.64/1.95 % (3962042)Time elapsed: 0.073 s
% 5.64/1.95 % (3962042)Peak memory usage: 113 MB
% 5.64/1.95 % (3962042)Instructions burned: 46 (million)
% 5.64/1.95 % (3962043)Instruction limit reached!
% 5.64/1.95 % (3962043)------------------------------
% 5.64/1.95 % (3962043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.95 % (3962043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.95 % (3962043)CaDiCaL version: 2.1.3
% 5.64/1.95 % (3962043)Termination reason: Instruction limit
% 5.64/1.95 % (3962043)Termination phase: Function definition elimination
% 5.64/1.95 % (3962043)Time elapsed: 0.033 s
% 5.64/1.95 % (3962043)Peak memory usage: 87 MB
% 5.64/1.95 % (3962043)Instructions burned: 34 (million)
% 5.64/1.95 % (3962046)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2451426784:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 5.64/1.95 % (3962046)Instruction limit reached!
% 5.64/1.95 % (3962046)------------------------------
% 8.25/2.21 % (3962046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.25/2.21 % (3962046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/2.21 % (3962046)CaDiCaL version: 2.1.3
% 8.25/2.21 % (3962046)Termination reason: Instruction limit
% 8.25/2.21 % (3962046)Termination phase: shuffling
% 8.25/2.21 % (3962046)Time elapsed: 0.011 s
% 8.25/2.21 % (3962046)Peak memory usage: 86 MB
% 8.25/2.21 % (3962046)Instructions burned: 14 (million)
% 8.25/2.21 % (3962053)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2836549910:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/16Mi)
% 8.25/2.21 % (3962053)Instruction limit reached!
% 8.25/2.21 % (3962053)------------------------------
% 8.25/2.21 % (3962053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.25/2.21 % (3962053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/2.21 % (3962053)CaDiCaL version: 2.1.3
% 8.25/2.21 % (3962053)Termination reason: Instruction limit
% 8.25/2.21 % (3962053)Termination phase: Preprocessing 3
% 8.25/2.21 % (3962053)Time elapsed: 0.010 s
% 8.25/2.21 % (3962053)Peak memory usage: 87 MB
% 8.25/2.21 % (3962053)Instructions burned: 17 (million)
% 8.25/2.21 % (3962039)Instruction limit reached!
% 8.25/2.21 % (3962039)------------------------------
% 8.25/2.21 % (3962039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.25/2.21 % (3962039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/2.21 % (3962039)CaDiCaL version: 2.1.3
% 8.25/2.21 % (3962039)Termination reason: Instruction limit
% 8.25/2.21 % (3962039)Termination phase: Saturation
% 8.25/2.21 % (3962039)Time elapsed: 0.261 s
% 8.25/2.21 % (3962039)Peak memory usage: 118 MB
% 8.25/2.21 % (3962039)Instructions burned: 201 (million)
% 8.25/2.21 % (3962052)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=3897318821:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2996 on theBenchmark for (2996ds/29Mi)
% 8.25/2.21 % (3962055)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=1400662788:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 8.25/2.21 % (3962054)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=2813106762:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 8.25/2.21 % (3962052)Instruction limit reached!
% 8.25/2.21 % (3962052)------------------------------
% 8.25/2.21 % (3962052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.25/2.21 % (3962052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/2.21 % (3962052)CaDiCaL version: 2.1.3
% 8.25/2.21 % (3962052)Termination reason: Instruction limit
% 8.25/2.21 % (3962052)Termination phase: Property scanning
% 8.25/2.21 % (3962052)Time elapsed: 0.031 s
% 8.25/2.21 % (3962052)Peak memory usage: 87 MB
% 8.25/2.21 % (3962052)Instructions burned: 30 (million)
% 8.25/2.21 % (3962055)Instruction limit reached!
% 8.25/2.21 % (3962055)------------------------------
% 8.25/2.21 % (3962055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.25/2.21 % (3962055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/2.21 % (3962055)CaDiCaL version: 2.1.3
% 8.25/2.21 % (3962055)Termination reason: Instruction limit
% 8.25/2.21 % (3962055)Termination phase: Property scanning
% 8.25/2.21 % (3962055)Time elapsed: 0.015 s
% 8.25/2.21 % (3962055)Peak memory usage: 88 MB
% 8.25/2.21 % (3962055)Instructions burned: 27 (million)
% 8.25/2.21 % (3962054)Instruction limit reached!
% 8.25/2.21 % (3962054)------------------------------
% 8.25/2.21 % (3962054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.25/2.21 % (3962054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/2.21 % (3962054)CaDiCaL version: 2.1.3
% 8.25/2.21 % (3962054)Termination reason: Instruction limit
% 8.25/2.21 % (3962054)Termination phase: Preprocessing 3
% 8.25/2.21 % (3962054)Time elapsed: 0.025 s
% 8.25/2.21 % (3962054)Peak memory usage: 87 MB
% 8.25/2.21 % (3962054)Instructions burned: 24 (million)
% 8.25/2.21 % (3962057)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=1247784036:i=85:gtgl=4:rtra=on:gtg=exists_sym_2995 on theBenchmark for (2995ds/85Mi)
% 8.25/2.21 % (3962038)Instruction limit reached!
% 8.25/2.21 % (3962038)------------------------------
% 8.90/2.50 % (3962038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.50 % (3962038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.50 % (3962038)CaDiCaL version: 2.1.3
% 8.90/2.50 % (3962038)Termination reason: Instruction limit
% 8.90/2.50 % (3962038)Termination phase: Saturation
% 8.90/2.50 % (3962038)Time elapsed: 0.363 s
% 8.90/2.50 % (3962038)Peak memory usage: 119 MB
% 8.90/2.50 % (3962038)Instructions burned: 308 (million)
% 8.90/2.50 % (3962057)Instruction limit reached!
% 8.90/2.50 % (3962057)------------------------------
% 8.90/2.50 % (3962057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.50 % (3962057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.50 % (3962057)CaDiCaL version: 2.1.3
% 8.90/2.50 % (3962057)Termination reason: Instruction limit
% 8.90/2.50 % (3962057)Termination phase: Saturation
% 8.90/2.50 % (3962057)Time elapsed: 0.081 s
% 8.90/2.50 % (3962057)Peak memory usage: 90 MB
% 8.90/2.50 % (3962057)Instructions burned: 86 (million)
% 8.90/2.50 % (3962061)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=904019679:i=181:rtra=on:ss=axioms:ev=cautious_2994 on theBenchmark for (2994ds/181Mi)
% 8.90/2.50 % (3962059)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=4094025240:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2994 on theBenchmark for (2994ds/2Mi)
% 8.90/2.50 % (3962059)Instruction limit reached!
% 8.90/2.50 % (3962059)------------------------------
% 8.90/2.50 % (3962059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.50 % (3962059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.50 % (3962059)CaDiCaL version: 2.1.3
% 8.90/2.50 % (3962059)Termination reason: Instruction limit
% 8.90/2.50 % (3962059)Termination phase: Property scanning
% 8.90/2.50 % (3962059)Time elapsed: 0.004 s
% 8.90/2.50 % (3962059)Peak memory usage: 85 MB
% 8.90/2.50 % (3962059)Instructions burned: 3 (million)
% 8.90/2.50 % (3962065)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=3617677283:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2994 on theBenchmark for (2994ds/66Mi)
% 8.90/2.50 % (3962064)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=61403399:i=4:ep=RST:ins=2:rtra=on_2994 on theBenchmark for (2994ds/4Mi)
% 8.90/2.50 % (3962064)Instruction limit reached!
% 8.90/2.50 % (3962064)------------------------------
% 8.90/2.50 % (3962064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.50 % (3962064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.50 % (3962064)CaDiCaL version: 2.1.3
% 8.90/2.50 % (3962064)Termination reason: Instruction limit
% 8.90/2.50 % (3962064)Termination phase: Property scanning
% 8.90/2.50 % (3962064)Time elapsed: 0.005 s
% 8.90/2.50 % (3962064)Peak memory usage: 85 MB
% 8.90/2.50 % (3962064)Instructions burned: 4 (million)
% 8.90/2.50 % (3962065)Instruction limit reached!
% 8.90/2.50 % (3962065)------------------------------
% 8.90/2.50 % (3962065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.50 % (3962065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.50 % (3962065)CaDiCaL version: 2.1.3
% 8.90/2.50 % (3962065)Termination reason: Instruction limit
% 8.90/2.50 % (3962065)Termination phase: Saturation
% 8.90/2.50 % (3962065)Time elapsed: 0.066 s
% 8.90/2.50 % (3962065)Peak memory usage: 130 MB
% 8.90/2.50 % (3962065)Instructions burned: 66 (million)
% 8.90/2.50 % (3962066)lrs+10_1_thi=all:si=on:fd=off:random_seed=960315537:i=53:rtra=on:gtg=all_2993 on theBenchmark for (2993ds/53Mi)
% 8.90/2.50 % (3962068)ott+1011_1_to=kbo:plsq=on:drc=off:si=on:plsqr=32,1:sp=const_frequency:sos=all:uwa=one_side_interpreted:sac=on:random_seed=840576616:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2993 on theBenchmark for (2993ds/8Mi)
% 8.90/2.50 % (3962068)Instruction limit reached!
% 8.90/2.50 % (3962068)------------------------------
% 8.90/2.50 % (3962068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.50 % (3962068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.50 % (3962068)CaDiCaL version: 2.1.3
% 8.90/2.50 % (3962068)Termination reason: Instruction limit
% 8.90/2.50 % (3962068)Termination phase: Property scanning
% 8.90/2.50 % (3962068)Time elapsed: 0.009 s
% 8.90/2.50 % (3962068)Peak memory usage: 86 MB
% 8.91/2.58 % (3962068)Instructions burned: 9 (million)
% 8.91/2.58 % (3962066)Instruction limit reached!
% 8.91/2.58 % (3962066)------------------------------
% 8.91/2.58 % (3962066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962066)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962066)Termination reason: Instruction limit
% 8.91/2.58 % (3962066)Termination phase: Saturation
% 8.91/2.58 % (3962066)Time elapsed: 0.053 s
% 8.91/2.58 % (3962066)Peak memory usage: 90 MB
% 8.91/2.58 % (3962066)Instructions burned: 54 (million)
% 8.91/2.58 % (3962061)Instruction limit reached!
% 8.91/2.58 % (3962061)------------------------------
% 8.91/2.58 % (3962061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962061)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962061)Termination reason: Instruction limit
% 8.91/2.58 % (3962061)Termination phase: Saturation
% 8.91/2.58 % (3962061)Time elapsed: 0.196 s
% 8.91/2.58 % (3962061)Peak memory usage: 92 MB
% 8.91/2.58 % (3962061)Instructions burned: 181 (million)
% 8.91/2.58 % (3962073)dis+1002_1_to=lpo:sil=64000:si=on:flr=on:random_seed=552167223:i=2:doe=on:canc=force:asg=cautious:rtra=on_2992 on theBenchmark for (2992ds/2Mi)
% 8.91/2.58 % (3962071)lrs+10_1_to=lakbo:sil=128000:si=on:alasca=on:sp=occurrence:random_seed=3465039909:st=3:i=2:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/2Mi)
% 8.91/2.58 % (3962071)Instruction limit reached!
% 8.91/2.58 % (3962071)------------------------------
% 8.91/2.58 % (3962071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962071)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962071)Termination reason: Instruction limit
% 8.91/2.58 % (3962071)Termination phase: Property scanning
% 8.91/2.58 % (3962071)Time elapsed: 0.004 s
% 8.91/2.58 % (3962071)Peak memory usage: 85 MB
% 8.91/2.58 % (3962071)Instructions burned: 3 (million)
% 8.91/2.58 % (3962073)Instruction limit reached!
% 8.91/2.58 % (3962073)------------------------------
% 8.91/2.58 % (3962073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962073)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962073)Termination reason: Instruction limit
% 8.91/2.58 % (3962073)Termination phase: Property scanning
% 8.91/2.58 % (3962073)Time elapsed: 0.004 s
% 8.91/2.58 % (3962073)Peak memory usage: 85 MB
% 8.91/2.58 % (3962073)Instructions burned: 3 (million)
% 8.91/2.58 % (3962076)lrs+1011_16:1_to=kbo:sil=128000:sas=z3:si=on:sos=theory:erd=off:urr=full:random_seed=1225586879:i=127:doe=on:rtra=on_2991 on theBenchmark for (2991ds/127Mi)
% 8.91/2.58 % (3962077)dis+10_1_si=on:random_seed=1022944761:i=10:ep=R:rtra=on_2991 on theBenchmark for (2991ds/10Mi)
% 8.91/2.58 % (3962076)Instruction limit reached!
% 8.91/2.58 % (3962076)------------------------------
% 8.91/2.58 % (3962076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962076)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962076)Termination reason: Instruction limit
% 8.91/2.58 % (3962076)Termination phase: Saturation
% 8.91/2.58 % (3962076)Time elapsed: 0.062 s
% 8.91/2.58 % (3962076)Peak memory usage: 118 MB
% 8.91/2.58 % (3962076)Instructions burned: 129 (million)
% 8.91/2.58 % (3962077)Instruction limit reached!
% 8.91/2.58 % (3962077)------------------------------
% 8.91/2.58 % (3962077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962077)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962077)Termination reason: Instruction limit
% 8.91/2.58 % (3962077)Termination phase: Property scanning
% 8.91/2.58 % (3962077)Time elapsed: 0.011 s
% 8.91/2.58 % (3962077)Peak memory usage: 85 MB
% 8.91/2.58 % (3962077)Instructions burned: 11 (million)
% 8.91/2.58 % (3962080)lrs-1011_64_to=lpo:si=on:sp=unary_first:sos=on:br=off:random_seed=3367066259:i=26:canc=cautious:av=off:rtra=on_2990 on theBenchmark for (2990ds/26Mi)
% 8.91/2.58 % (3962082)ott+10_8:1_to=lpo:sil=128000:si=on:fs=off:spb=goal_then_units:uwa=alasca_main:random_seed=2440693243:i=2:fsr=off:rtra=on:inst=on_2990 on theBenchmark for (2990ds/2Mi)
% 8.91/2.58 % (3962082)Instruction limit reached!
% 8.91/2.58 % (3962082)------------------------------
% 8.91/2.58 % (3962082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962082)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962082)Termination reason: Instruction limit
% 8.91/2.58 % (3962082)Termination phase: Property scanning
% 8.91/2.58 % (3962082)Time elapsed: 0.004 s
% 8.91/2.58 % (3962082)Peak memory usage: 85 MB
% 8.91/2.58 % (3962082)Instructions burned: 3 (million)
% 8.91/2.58 % (3962081)dis+1011_5_anc=all:tgt=full:si=on:sp=const_frequency:spb=non_intro:fd=preordered:sac=on:random_seed=1724335764:avsq=on:i=35:doe=on:thsqd=64:nm=64:fsr=off:thsqc=32:rtra=on:tac=light:ss=included:thsq=on:ev=off:sgt=32_2990 on theBenchmark for (2990ds/35Mi)
% 8.91/2.58 % (3962080)Instruction limit reached!
% 8.91/2.58 % (3962080)------------------------------
% 8.91/2.58 % (3962080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962080)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962080)Termination reason: Instruction limit
% 8.91/2.58 % (3962080)Termination phase: Clausification
% 8.91/2.58 % (3962080)Time elapsed: 0.026 s
% 8.91/2.58 % (3962080)Peak memory usage: 87 MB
% 8.91/2.58 % (3962080)Instructions burned: 26 (million)
% 8.91/2.58 % (3962092)lrs+1002_1_to=lpo:sil=128000:sas=z3:si=on:sos=on:urr=on:tha=off:random_seed=1519079294:i=226:rtra=on:gtg=position:ss=axioms_2989 on theBenchmark for (2989ds/226Mi)
% 8.91/2.58 % (3962081)Instruction limit reached!
% 8.91/2.58 % (3962081)------------------------------
% 8.91/2.58 % (3962081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962081)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962081)Termination reason: Instruction limit
% 8.91/2.58 % (3962081)Termination phase: Property scanning
% 8.91/2.58 % (3962081)Time elapsed: 0.035 s
% 8.91/2.58 % (3962081)Peak memory usage: 88 MB
% 8.91/2.58 % (3962081)Instructions burned: 36 (million)
% 8.91/2.58 % (3962087)dis+21_1_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=off:s2agt=16:random_seed=1900164719:s2a=on:i=8:kws=inv_precedence:doe=on:rtra=on_2989 on theBenchmark for (2989ds/8Mi)
% 8.91/2.58 % (3962088)lrs-1011_1_to=kbo:sil=128000:prc=on:si=on:fs=off:tha=off:random_seed=1295882562:i=370:ep=RS:fsr=off:rtra=on_2989 on theBenchmark for (2989ds/370Mi)
% 8.91/2.58 % (3962087)Instruction limit reached!
% 8.91/2.58 % (3962087)------------------------------
% 8.91/2.58 % (3962087)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962087)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962087)Termination reason: Instruction limit
% 8.91/2.58 % (3962087)Termination phase: Property scanning
% 8.91/2.58 % (3962087)Time elapsed: 0.009 s
% 8.91/2.58 % (3962087)Peak memory usage: 85 MB
% 8.91/2.58 % (3962087)Instructions burned: 8 (million)
% 8.91/2.58 % (3962091)ott+1002_1_to=lpo:thi=overlap:prc=on:bsd=on:si=on:gve=cautious:thigen=on:tha=some:random_seed=2160890359:i=13:av=off:rtra=on:gtg=exists_sym:ev=force_2989 on theBenchmark for (2989ds/13Mi)
% 8.91/2.58 % (3962091)Instruction limit reached!
% 8.91/2.58 % (3962091)------------------------------
% 8.91/2.58 % (3962091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962091)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962091)Termination reason: Instruction limit
% 8.91/2.58 % (3962091)Termination phase: Property scanning
% 8.91/2.58 % (3962091)Time elapsed: 0.007 s
% 8.91/2.58 % (3962091)Peak memory usage: 86 MB
% 8.91/2.58 % (3962091)Instructions burned: 13 (million)
% 8.91/2.58 % (3962092)First to succeed.
% 8.91/2.58 % (3962092)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3962031"
% 8.91/2.58 % (3962096)lrs+1010_5_to=lpo:sil=128000:si=on:sp=const_frequency:sos=theory:tha=off:random_seed=16237949:i=10:rtra=on_2988 on theBenchmark for (2988ds/10Mi)
% 8.91/2.58 % (3962098)lrs+1002_1_to=lpo:thi=strong:sas=z3:si=on:sp=const_frequency:tha=off:random_seed=1390937300:i=71:rtra=on:gtg=exists_top_2987 on theBenchmark for (2987ds/71Mi)
% 8.91/2.58 % (3962096)Instruction limit reached!
% 8.91/2.58 % (3962096)------------------------------
% 8.91/2.58 % (3962096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.58 % (3962096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.58 % (3962096)CaDiCaL version: 2.1.3
% 8.91/2.58 % (3962096)Termination reason: Instruction limit
% 8.91/2.58 % (3962096)Termination phase: Unused predicate definition removal
% 8.91/2.58 % (3962096)Time elapsed: 0.011 s
% 8.91/2.58 % (3962096)Peak memory usage: 86 MB
% 8.91/2.58 % (3962096)Instructions burned: 10 (million)
% 8.91/2.58 % (3962105)ott+21_1_to=kbo:tgt=full:sas=z3:si=on:tha=off:random_seed=1195586784:i=130:kws=inv_frequency:nm=0:rtra=on:gtg=exists_all_2987 on theBenchmark for (2987ds/130Mi)
% 8.91/2.58 % (3962100)lrs+1010_1_to=lpo:prlc=on:sil=128000:prc=on:drc=off:si=on:sp=const_max:thsqr=8,1:tha=some:nwc=5:random_seed=274086124:i=75:doe=on:thsqd=64:canc=force:thsqc=64:rtra=on:thsq=on_2987 on theBenchmark for (2987ds/75Mi)
% 8.91/2.58 % (3962103)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=2052917459:i=294:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2987 on theBenchmark for (2987ds/294Mi)
% 8.91/2.58 % (3962092)Refutation found. Thanks to Tanya!
% 8.91/2.58 % SZS status Theorem for theBenchmark
% 8.91/2.58 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/2.80 % (3962092)------------------------------
% 0.24/2.80 % (3962092)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/2.80 % (3962092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/2.80 % (3962092)CaDiCaL version: 2.1.3
% 0.24/2.80 % (3962092)Termination reason: Refutation
% 0.24/2.80 % (3962092)Time elapsed: 0.074 s
% 0.24/2.80 % (3962092)Peak memory usage: 118 MB
% 0.24/2.80 % (3962092)Instructions burned: 98 (million)
% 0.24/2.80 % (3962092)------------------------------
% 0.24/2.80 % (3962092)------------------------------
% 0.24/2.80 % (3962031)Success in time 1.545 s
% 0.24/2.80 % Vampire exiting
%------------------------------------------------------------------------------