%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP328_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 11:33:37 AM UTC 2026
% Result : Theorem 10.23s 2.65s
% Output : Refutation 12.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 74 ( 21 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 76 ( 30 ~; 17 |; 10 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 87 ( 36 atm; 42 fun; 9 num; 0 var)
% Number of types : 29 ( 27 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 43 ( 39 usr; 2 prp; 0-3 aty)
% Number of functors : 91 ( 87 usr; 15 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Int_bool_fun$': $tType ).
tff(type_def_6,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_7,type,
'Int_set_set_set$': $tType ).
tff(type_def_8,type,
'Int_set$': $tType ).
tff(type_def_9,type,
'Int_int_fun$': $tType ).
tff(type_def_10,type,
'Int_set_set$': $tType ).
tff(type_def_11,type,
'N_set$': $tType ).
tff(type_def_12,type,
'Nat_n_fun$': $tType ).
tff(type_def_13,type,
'Int_set_int_fun$': $tType ).
tff(type_def_14,type,
'N_int_set_fun$': $tType ).
tff(type_def_15,type,
'Nat_nat_fun$': $tType ).
tff(type_def_16,type,
'Nat$': $tType ).
tff(type_def_17,type,
'N_int_fun$': $tType ).
tff(type_def_18,type,
'N$': $tType ).
tff(type_def_19,type,
tlbool: $tType ).
tff(type_def_20,type,
'Int_set_int_set_fun$': $tType ).
tff(type_def_21,type,
'Int_n_fun$': $tType ).
tff(type_def_22,type,
'Int_int_set_fun$': $tType ).
tff(type_def_23,type,
'Int_set_n_fun$': $tType ).
tff(type_def_24,type,
'N_n_fun$': $tType ).
tff(type_def_25,type,
'Int_set_bool_fun$': $tType ).
tff(type_def_26,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_27,type,
'Nat_bool_fun$': $tType ).
tff(type_def_28,type,
'N_set_set$': $tType ).
tff(type_def_29,type,
'N_n_bool_fun_fun$': $tType ).
tff(type_def_30,type,
'Nat_int_fun$': $tType ).
tff(type_def_31,type,
'N_bool_fun$': $tType ).
tff(func_def_0,type,
'fun_app$p': ( 'Int_n_fun$' * $int ) > 'N$' ).
tff(func_def_1,type,
'plus$e': ( 'Int_set_set_set$' * 'Int_set_set_set$' ) > 'Int_set_set_set$' ).
tff(func_def_2,type,
'fun_app$r': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_3,type,
'fun_app$l': ( 'Int_int_set_fun$' * $int ) > 'Int_set$' ).
tff(func_def_4,type,
'less$': 'N_n_bool_fun_fun$' ).
tff(func_def_5,type,
'uua$': 'Int_set_set$' > 'Int_set_bool_fun$' ).
tff(func_def_6,type,
'fun_app$g': ( 'N_n_bool_fun_fun$' * 'N$' ) > 'N_bool_fun$' ).
tff(func_def_7,type,
'triangle$': 'Nat_nat_fun$' ).
tff(func_def_8,type,
'from_nat$': 'Nat_n_fun$' ).
tff(func_def_9,type,
'collect$a': 'Int_set_bool_fun$' > 'Int_set_set$' ).
tff(func_def_10,type,
'fun_app$o': ( 'N_int_fun$' * 'N$' ) > $int ).
tff(func_def_11,type,
'fun_app$m': ( 'Int_set_n_fun$' * 'Int_set$' ) > 'N$' ).
tff(func_def_12,type,
'uuc$': 'Int_int_bool_fun_fun$' ).
tff(func_def_13,type,
'plus$c': ( 'N_set$' * 'N_set$' ) > 'N_set$' ).
tff(func_def_14,type,
'fun_app$e': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_15,type,
'fun_app$b': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_16,type,
'ja$': 'Nat$' ).
tff(func_def_17,type,
'uud$': $int > 'Int_int_fun$' ).
tff(func_def_18,type,
'a$': 'Nat$' ).
tff(func_def_19,type,
'i$': 'N$' ).
tff(func_def_20,type,
'zero$': 'Int_set$' ).
tff(func_def_21,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_22,type,
'fun_app$a': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_23,type,
'plus$a': ( 'Int_set_set$' * 'Int_set_set$' ) > 'Int_set_set$' ).
tff(func_def_24,type,
'member$a': $int > 'Int_set_bool_fun$' ).
tff(func_def_25,type,
tltrue: tlbool ).
tff(func_def_26,type,
'plus$': 'N$' > 'N_n_fun$' ).
tff(func_def_27,type,
'less_eq$': 'N_n_bool_fun_fun$' ).
tff(func_def_28,type,
'minus$': 'N$' > 'N_n_fun$' ).
tff(func_def_29,type,
'fun_app$f': ( 'N_n_fun$' * 'N$' ) > 'N$' ).
tff(func_def_30,type,
'fun_app$n': ( 'Int_set_int_fun$' * 'Int_set$' ) > $int ).
tff(func_def_31,type,
'fun_app$i': ( 'Nat_n_fun$' * 'Nat$' ) > 'N$' ).
tff(func_def_32,type,
'iterate_add$': 'Nat$' > 'Int_int_fun$' ).
tff(func_def_33,type,
'collect$b': 'Int_bool_fun$' > 'Int_set$' ).
tff(func_def_34,type,
'plus$d': ( 'N_set_set$' * 'N_set_set$' ) > 'N_set_set$' ).
tff(func_def_35,type,
'uu$': 'N_set$' > 'N_bool_fun$' ).
tff(func_def_36,type,
'collect$': 'N_bool_fun$' > 'N_set$' ).
tff(func_def_37,type,
tlfalse: tlbool ).
tff(func_def_38,type,
'nat$': $int > 'Nat$' ).
tff(func_def_39,type,
'zero$a': 'N$' ).
tff(func_def_40,type,
'plus$b': 'Int_set$' > 'Int_set_int_set_fun$' ).
tff(func_def_41,type,
'minus$a': 'Int_set$' > 'Int_set_int_set_fun$' ).
tff(func_def_42,type,
'fun_app$h': ( 'Int_set_int_set_fun$' * 'Int_set$' ) > 'Int_set$' ).
tff(func_def_43,type,
'less$a': 'Int_set$' > 'Int_set_bool_fun$' ).
tff(func_def_44,type,
'less_eq$a': 'Int_set$' > 'Int_set_bool_fun$' ).
tff(func_def_45,type,
'fun_app$k': ( 'N_int_set_fun$' * 'N$' ) > 'Int_set$' ).
tff(func_def_46,type,
'fun_app$q': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_47,type,
'uub$': 'Int_set$' > 'Int_bool_fun$' ).
tff(func_def_48,type,
'x$': 'N$' ).
tff(func_def_49,type,
'to_nat$': 'N$' > 'Nat$' ).
tff(func_def_55,type,
sK28: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_56,type,
sK29: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_57,type,
sK30: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_58,type,
sK31: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_59,type,
sK32: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_60,type,
sK33: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_61,type,
sK34: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_62,type,
sK35: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_63,type,
sK36: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_64,type,
sK37: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_65,type,
sK38: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_66,type,
sK39: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_67,type,
sK40: $int > $int ).
tff(func_def_68,type,
sK41: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_69,type,
sK42: 'N_bool_fun$' > 'N$' ).
tff(func_def_70,type,
sK43: 'N_bool_fun$' > 'N$' ).
tff(func_def_71,type,
sK44: 'N_bool_fun$' > 'N$' ).
tff(func_def_72,type,
sK45: ( 'N_bool_fun$' * 'N$' ) > 'N$' ).
tff(func_def_73,type,
sK46: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_74,type,
sK47: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_75,type,
sK48: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_76,type,
sK49: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_77,type,
sK50: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_78,type,
sK51: 'N_bool_fun$' > 'N$' ).
tff(func_def_79,type,
sK52: ( 'N_bool_fun$' * 'N$' ) > 'N$' ).
tff(func_def_80,type,
sK53: 'N_bool_fun$' > 'N$' ).
tff(func_def_81,type,
sK54: $int > $int ).
tff(func_def_82,type,
sK55: 'N_bool_fun$' > 'N$' ).
tff(func_def_83,type,
sK56: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_84,type,
sK57: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_85,type,
sK58: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_86,type,
sK59: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_87,type,
sK60: 'Nat$' > 'Nat$' ).
tff(func_def_88,type,
sK61: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_89,type,
sK62: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_90,type,
sK63: 'N_n_bool_fun_fun$' > 'N$' ).
tff(func_def_91,type,
sK64: 'N_n_bool_fun_fun$' > 'N$' ).
tff(pred_def_1,type,
'member$c': ( 'N_set$' * 'N_set_set$' ) > $o ).
tff(pred_def_2,type,
'member$b': ( 'N$' * 'N_set$' ) > $o ).
tff(pred_def_3,type,
'member$': ( 'Int_set$' * 'Int_set_set$' ) > $o ).
tff(pred_def_4,type,
'less_eq$c': ( 'Int_set_set$' * 'Int_set_set$' ) > $o ).
tff(pred_def_5,type,
'fun_app$c': ( 'Int_set_bool_fun$' * 'Int_set$' ) > $o ).
tff(pred_def_6,type,
'less_eq$b': ( 'N_set$' * 'N_set$' ) > $o ).
tff(pred_def_7,type,
'fun_app$': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_8,type,
'member$d': ( 'Int_set_set$' * 'Int_set_set_set$' ) > $o ).
tff(pred_def_9,type,
'fun_app$d': ( 'N_bool_fun$' * 'N$' ) > $o ).
tff(pred_def_10,type,
'fun_app$j': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_13,type,
sP0: ( 'N$' * 'N$' * 'N$' ) > $o ).
tff(pred_def_14,type,
sP1: ( 'N$' * 'N$' * 'N$' ) > $o ).
tff(pred_def_15,type,
sP2: ( 'N$' * 'N$' * 'N$' ) > $o ).
tff(pred_def_16,type,
sP3: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_17,type,
sP4: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_18,type,
sP5: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_19,type,
sP6: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_20,type,
sP7: ( 'N$' * 'N$' * 'N$' ) > $o ).
tff(pred_def_21,type,
sP8: ( 'N$' * 'N$' * 'N$' ) > $o ).
tff(pred_def_22,type,
sP9: ( 'N$' * 'N$' * 'N$' ) > $o ).
tff(pred_def_23,type,
sP10: ( $int * $int * $int ) > $o ).
tff(pred_def_24,type,
sP11: ( $int * $int * $int ) > $o ).
tff(pred_def_25,type,
sP12: ( $int * $int * $int ) > $o ).
tff(pred_def_26,type,
sP13: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_27,type,
sP14: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_28,type,
sP15: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_29,type,
sP16: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_30,type,
sP17: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_31,type,
sP18: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_32,type,
sP19: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_33,type,
sP20: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_34,type,
sP21: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_35,type,
sP22: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_36,type,
sP23: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_37,type,
sP24: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_38,type,
sP25: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_39,type,
sP26: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_40,type,
sP27: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(f6,conjecture,
( ( ~ $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$difference('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))) = 'fun_app$e'('of_nat$','to_nat$'('x$')) ) )
& ( $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) = 'fun_app$e'('of_nat$','to_nat$'('x$')) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture5) ).
tff(f7,negated_conjecture,
~ ( ( ~ $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$difference('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))) = 'fun_app$e'('of_nat$','to_nat$'('x$')) ) )
& ( $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) = 'fun_app$e'('of_nat$','to_nat$'('x$')) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f18,axiom,
'fun_app$d'('fun_app$g'('less_eq$','i$'),'x$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).
tff(f26,axiom,
! [X1: 'N$',X0: 'N$'] :
( 'fun_app$d'('fun_app$g'('less_eq$',X0),X1)
=> $lesseq('fun_app$e'('of_nat$','to_nat$'(X0)),'fun_app$e'('of_nat$','to_nat$'(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom24) ).
tff(f564,axiom,
! [X1: 'Nat$',X0: 'Nat$'] :
( ~ $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1))
=> ( ( $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1))
=> ( $sum('fun_app$e'('of_nat$',X1),0) = 'fun_app$e'('of_nat$',X0) ) )
& ( ~ $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1))
=> ( $sum('fun_app$e'('of_nat$',X1),$difference('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1))) = 'fun_app$e'('of_nat$',X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom562) ).
tff(f745,plain,
! [X1: 'Nat$',X0: 'Nat$'] :
( ~ $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1))
=> ( ( $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1))
=> ( $sum('fun_app$e'('of_nat$',X1),0) = 'fun_app$e'('of_nat$',X0) ) )
& ( ~ $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1))
=> ( 'fun_app$e'('of_nat$',X0) = $sum('fun_app$e'('of_nat$',X1),$sum('fun_app$e'('of_nat$',X0),$uminus('fun_app$e'('of_nat$',X1)))) ) ) ) ),
inference(theory_normalization,[],[f564]) ).
tff(f843,plain,
~ ( ( ~ $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( 'fun_app$e'('of_nat$','to_nat$'('x$')) = $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$'))))) ) )
& ( $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) = 'fun_app$e'('of_nat$','to_nat$'('x$')) ) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f851,plain,
! [X1: 'N$',X0: 'N$'] :
( 'fun_app$d'('fun_app$g'('less_eq$',X0),X1)
=> ~ $less('fun_app$e'('of_nat$','to_nat$'(X1)),'fun_app$e'('of_nat$','to_nat$'(X0))) ),
inference(theory_normalization,[],[f26]) ).
tff(f952,plain,
! [X0: 'N$',X1: 'N$'] :
( 'fun_app$d'('fun_app$g'('less_eq$',X1),X0)
=> ~ $less('fun_app$e'('of_nat$','to_nat$'(X0)),'fun_app$e'('of_nat$','to_nat$'(X1))) ),
inference(rectify,[],[f851]) ).
tff(f969,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$e'('of_nat$',X1),'fun_app$e'('of_nat$',X0))
=> ( ( $less('fun_app$e'('of_nat$',X1),'fun_app$e'('of_nat$',X0))
=> ( 'fun_app$e'('of_nat$',X1) = $sum('fun_app$e'('of_nat$',X0),0) ) )
& ( ~ $less('fun_app$e'('of_nat$',X1),'fun_app$e'('of_nat$',X0))
=> ( 'fun_app$e'('of_nat$',X1) = $sum('fun_app$e'('of_nat$',X0),$sum('fun_app$e'('of_nat$',X1),$uminus('fun_app$e'('of_nat$',X0)))) ) ) ) ),
inference(rectify,[],[f745]) ).
tff(f1322,plain,
! [X1: 'N$',X0: 'N$'] :
( ~ 'fun_app$d'('fun_app$g'('less_eq$',X1),X0)
| ~ $less('fun_app$e'('of_nat$','to_nat$'(X0)),'fun_app$e'('of_nat$','to_nat$'(X1))) ),
inference(ennf_transformation,[],[f952]) ).
tff(f1392,plain,
! [X1: 'Nat$',X0: 'Nat$'] :
( ( ( ( 'fun_app$e'('of_nat$',X1) = $sum('fun_app$e'('of_nat$',X0),$sum('fun_app$e'('of_nat$',X1),$uminus('fun_app$e'('of_nat$',X0)))) )
| $less('fun_app$e'('of_nat$',X1),'fun_app$e'('of_nat$',X0)) )
& ( ~ $less('fun_app$e'('of_nat$',X1),'fun_app$e'('of_nat$',X0))
| ( 'fun_app$e'('of_nat$',X1) = $sum('fun_app$e'('of_nat$',X0),0) ) ) )
| $less('fun_app$e'('of_nat$',X1),'fun_app$e'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f969]) ).
tff(f1454,plain,
( ( ( 'fun_app$e'('of_nat$','to_nat$'('x$')) != $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$'))))) )
& ~ $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) )
| ( ( 'fun_app$e'('of_nat$','to_nat$'('x$')) != $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) )
& $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) ) ),
inference(ennf_transformation,[],[f843]) ).
tff(f1806,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( ( 'fun_app$e'('of_nat$',X0) = $sum('fun_app$e'('of_nat$',X1),$sum('fun_app$e'('of_nat$',X0),$uminus('fun_app$e'('of_nat$',X1)))) )
| $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1)) )
& ( ~ $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1))
| ( 'fun_app$e'('of_nat$',X0) = $sum('fun_app$e'('of_nat$',X1),0) ) ) )
| $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1)) ),
inference(rectify,[],[f1392]) ).
tff(f1817,plain,
! [X0: 'N$',X1: 'N$'] :
( ~ 'fun_app$d'('fun_app$g'('less_eq$',X0),X1)
| ~ $less('fun_app$e'('of_nat$','to_nat$'(X1)),'fun_app$e'('of_nat$','to_nat$'(X0))) ),
inference(rectify,[],[f1322]) ).
tff(f2422,plain,
( ( 'fun_app$e'('of_nat$','to_nat$'('x$')) != $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$'))))) )
| $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) ),
inference(cnf_transformation,[],[f1454]) ).
tff(f2510,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1))
| ( 'fun_app$e'('of_nat$',X0) = $sum('fun_app$e'('of_nat$',X1),$sum('fun_app$e'('of_nat$',X0),$uminus('fun_app$e'('of_nat$',X1)))) )
| $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1806]) ).
tff(f2523,plain,
! [X0: 'N$',X1: 'N$'] :
( ~ $less('fun_app$e'('of_nat$','to_nat$'(X1)),'fun_app$e'('of_nat$','to_nat$'(X0)))
| ~ 'fun_app$d'('fun_app$g'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f1817]) ).
tff(f2831,plain,
'fun_app$d'('fun_app$g'('less_eq$','i$'),'x$'),
inference(cnf_transformation,[],[f18]) ).
tff(f3159,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$e'('of_nat$',X0) = $sum('fun_app$e'('of_nat$',X1),$sum('fun_app$e'('of_nat$',X0),$uminus('fun_app$e'('of_nat$',X1)))) )
| $less('fun_app$e'('of_nat$',X0),'fun_app$e'('of_nat$',X1)) ),
inference(duplicate_literal_removal,[],[f2510]) ).
tff(f3273,plain,
$less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))),
inference(forward_subsumption_resolution,[],[f2422,f3159]) ).
tff(f3275,definition,
( spl65_3
<=> $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) ),
introduced(definition,[new_symbols(definition,[spl65_3])],[avatar_definition]) ).
tff(f3277,plain,
( $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
| ~ spl65_3 ),
inference(avatar_component_clause,[],[f3275]) ).
tff(f3278,plain,
spl65_3,
inference(avatar_split_clause,[],[f3273,f3275]) ).
tff(f3317,plain,
( ~ 'fun_app$d'('fun_app$g'('less_eq$','i$'),'x$')
| ~ spl65_3 ),
inference(unit_resulting_resolution,[],[f2523,f3277]) ).
tff(f5097,plain,
( $false
| ~ spl65_3 ),
inference(forward_subsumption_resolution,[],[f3317,f2831]) ).
tff(f5098,plain,
~ spl65_3,
inference(avatar_contradiction_clause,[],[f5097]) ).
tff(f5401,plain,
$false,
inference(avatar_smt_refutation,[],[f5098,f3278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP328_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.45 % Computer : n005.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 27 12:54:17 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 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
% 4.95/1.88 % (3962519)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.95/1.88 % (3962534)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=254779162:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.95/1.88 % (3962534)Instruction limit reached!
% 4.95/1.88 % (3962534)------------------------------
% 4.95/1.88 % (3962534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.88 % (3962534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.88 % (3962534)CaDiCaL version: 2.1.3
% 4.95/1.88 % (3962534)Termination reason: Instruction limit
% 4.95/1.88 % (3962534)Termination phase: Preprocessing 1
% 4.95/1.88 % (3962534)Time elapsed: 0.016 s
% 4.95/1.88 % (3962534)Peak memory usage: 87 MB
% 4.95/1.88 % (3962534)Instructions burned: 34 (million)
% 4.95/1.88 % (3962532)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2799628471:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.95/1.88 % (3962529)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=347362077:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.95/1.88 % (3962530)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4188312576:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.95/1.88 % (3962531)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3550359249:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.95/1.88 % (3962528)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3220452511:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.95/1.88 % (3962533)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=699853744:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.95/1.88 % (3962532)Instruction limit reached!
% 4.95/1.88 % (3962532)------------------------------
% 4.95/1.88 % (3962532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.88 % (3962532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.88 % (3962532)CaDiCaL version: 2.1.3
% 4.95/1.88 % (3962532)Termination reason: Instruction limit
% 4.95/1.88 % (3962532)Termination phase: shuffling
% 4.95/1.88 % (3962532)Time elapsed: 0.005 s
% 4.95/1.88 % (3962532)Peak memory usage: 85 MB
% 4.95/1.88 % (3962532)Instructions burned: 4 (million)
% 4.95/1.88 % (3962531)Instruction limit reached!
% 4.95/1.88 % (3962531)------------------------------
% 4.95/1.88 % (3962531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.88 % (3962531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.88 % (3962531)CaDiCaL version: 2.1.3
% 4.95/1.88 % (3962531)Termination reason: Instruction limit
% 4.95/1.88 % (3962531)Termination phase: Property scanning
% 4.95/1.88 % (3962531)Time elapsed: 0.008 s
% 4.95/1.88 % (3962531)Peak memory usage: 85 MB
% 4.95/1.88 % (3962531)Instructions burned: 7 (million)
% 4.95/1.88 % (3962528)Instruction limit reached!
% 4.95/1.88 % (3962528)------------------------------
% 4.95/1.88 % (3962528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.88 % (3962528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.88 % (3962528)CaDiCaL version: 2.1.3
% 4.95/1.88 % (3962528)Termination reason: Instruction limit
% 4.95/1.88 % (3962528)Termination phase: Property scanning
% 4.95/1.88 % (3962528)Time elapsed: 0.011 s
% 4.95/1.88 % (3962528)Peak memory usage: 85 MB
% 4.95/1.88 % (3962528)Instructions burned: 12 (million)
% 4.95/1.88 % (3962533)Instruction limit reached!
% 4.95/1.88 % (3962533)------------------------------
% 4.95/1.88 % (3962533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.88 % (3962533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.88 % (3962533)CaDiCaL version: 2.1.3
% 4.95/1.88 % (3962533)Termination reason: Instruction limit
% 4.95/1.88 % (3962533)Termination phase: Property scanning
% 4.95/1.88 % (3962533)Time elapsed: 0.045 s
% 4.95/1.88 % (3962533)Peak memory usage: 88 MB
% 4.95/1.88 % (3962533)Instructions burned: 46 (million)
% 4.95/1.88 % (3962537)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1544233441:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.95/1.88 % (3962537)Instruction limit reached!
% 4.95/1.88 % (3962537)------------------------------
% 7.73/2.13 % (3962537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/2.13 % (3962537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/2.13 % (3962537)CaDiCaL version: 2.1.3
% 7.73/2.13 % (3962537)Termination reason: Instruction limit
% 7.73/2.13 % (3962537)Termination phase: Property scanning
% 7.73/2.13 % (3962537)Time elapsed: 0.008 s
% 7.73/2.13 % (3962537)Peak memory usage: 86 MB
% 7.73/2.13 % (3962537)Instructions burned: 16 (million)
% 7.73/2.13 % (3962544)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=3147947059:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 7.73/2.13 % (3962544)Instruction limit reached!
% 7.73/2.13 % (3962544)------------------------------
% 7.73/2.13 % (3962544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/2.13 % (3962544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/2.13 % (3962544)CaDiCaL version: 2.1.3
% 7.73/2.13 % (3962544)Termination reason: Instruction limit
% 7.73/2.13 % (3962544)Termination phase: Preprocessing 1
% 7.73/2.13 % (3962544)Time elapsed: 0.014 s
% 7.73/2.13 % (3962544)Peak memory usage: 86 MB
% 7.73/2.13 % (3962544)Instructions burned: 30 (million)
% 7.73/2.13 % (3962530)Instruction limit reached!
% 7.73/2.13 % (3962530)------------------------------
% 7.73/2.13 % (3962530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/2.13 % (3962530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/2.13 % (3962530)CaDiCaL version: 2.1.3
% 7.73/2.13 % (3962530)Termination reason: Instruction limit
% 7.73/2.13 % (3962530)Termination phase: Saturation
% 7.73/2.13 % (3962530)Time elapsed: 0.219 s
% 7.73/2.13 % (3962530)Peak memory usage: 118 MB
% 7.73/2.13 % (3962530)Instructions burned: 201 (million)
% 7.73/2.13 % (3962545)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2400952953:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 7.73/2.13 % (3962546)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1499675426:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 7.73/2.13 % (3962545)Instruction limit reached!
% 7.73/2.13 % (3962545)------------------------------
% 7.73/2.13 % (3962545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/2.13 % (3962545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/2.13 % (3962545)CaDiCaL version: 2.1.3
% 7.73/2.13 % (3962545)Termination reason: Instruction limit
% 7.73/2.13 % (3962545)Termination phase: Preprocessing 1
% 7.73/2.13 % (3962545)Time elapsed: 0.015 s
% 7.73/2.13 % (3962545)Peak memory usage: 86 MB
% 7.73/2.13 % (3962545)Instructions burned: 17 (million)
% 7.73/2.13 % (3962546)Instruction limit reached!
% 7.73/2.13 % (3962546)------------------------------
% 7.73/2.13 % (3962546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/2.13 % (3962546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/2.13 % (3962546)CaDiCaL version: 2.1.3
% 7.73/2.13 % (3962546)Termination reason: Instruction limit
% 7.73/2.13 % (3962546)Termination phase: Property scanning
% 7.73/2.13 % (3962546)Time elapsed: 0.022 s
% 7.73/2.13 % (3962546)Peak memory usage: 86 MB
% 7.73/2.13 % (3962546)Instructions burned: 24 (million)
% 7.73/2.13 % (3962547)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=441519087:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 7.73/2.13 % (3962549)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=3278379937:i=85:gtgl=4:rtra=on:gtg=exists_sym_2996 on theBenchmark for (2996ds/85Mi)
% 7.73/2.13 % (3962529)Instruction limit reached!
% 7.73/2.13 % (3962529)------------------------------
% 7.73/2.13 % (3962529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/2.13 % (3962529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/2.13 % (3962529)CaDiCaL version: 2.1.3
% 7.73/2.13 % (3962529)Termination reason: Instruction limit
% 7.73/2.13 % (3962529)Termination phase: Saturation
% 7.73/2.13 % (3962529)Time elapsed: 0.336 s
% 7.73/2.13 % (3962529)Peak memory usage: 119 MB
% 7.73/2.13 % (3962529)Instructions burned: 307 (million)
% 7.73/2.13 % (3962547)Instruction limit reached!
% 7.73/2.13 % (3962547)------------------------------
% 9.14/2.41 % (3962547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.14/2.41 % (3962547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.14/2.41 % (3962547)CaDiCaL version: 2.1.3
% 9.14/2.41 % (3962547)Termination reason: Instruction limit
% 9.14/2.41 % (3962547)Termination phase: Property scanning
% 9.14/2.41 % (3962547)Time elapsed: 0.025 s
% 9.14/2.41 % (3962547)Peak memory usage: 86 MB
% 9.14/2.41 % (3962547)Instructions burned: 28 (million)
% 9.14/2.41 % (3962549)Instruction limit reached!
% 9.14/2.41 % (3962549)------------------------------
% 9.14/2.41 % (3962549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.14/2.41 % (3962549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.14/2.41 % (3962549)CaDiCaL version: 2.1.3
% 9.14/2.41 % (3962549)Termination reason: Instruction limit
% 9.14/2.41 % (3962549)Termination phase: Property scanning
% 9.14/2.41 % (3962549)Time elapsed: 0.076 s
% 9.14/2.41 % (3962549)Peak memory usage: 88 MB
% 9.14/2.41 % (3962549)Instructions burned: 85 (million)
% 9.14/2.41 % (3962551)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=3186741782:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2994 on theBenchmark for (2994ds/2Mi)
% 9.14/2.42 % (3962551)Instruction limit reached!
% 9.14/2.42 % (3962551)------------------------------
% 9.14/2.42 % (3962551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.14/2.42 % (3962551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.14/2.42 % (3962551)CaDiCaL version: 2.1.3
% 9.14/2.42 % (3962551)Termination reason: Instruction limit
% 9.14/2.42 % (3962551)Termination phase: shuffling
% 9.14/2.42 % (3962551)Time elapsed: 0.003 s
% 9.14/2.42 % (3962551)Peak memory usage: 85 MB
% 9.14/2.42 % (3962551)Instructions burned: 2 (million)
% 9.14/2.42 % (3962552)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=2210940357:i=181:rtra=on:ss=axioms:ev=cautious_2994 on theBenchmark for (2994ds/181Mi)
% 9.14/2.42 % (3962552)Instruction limit reached!
% 9.14/2.42 % (3962552)------------------------------
% 9.14/2.42 % (3962552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.14/2.42 % (3962552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.14/2.42 % (3962552)CaDiCaL version: 2.1.3
% 9.14/2.42 % (3962552)Termination reason: Instruction limit
% 9.14/2.42 % (3962552)Termination phase: Saturation
% 9.14/2.42 % (3962552)Time elapsed: 0.099 s
% 9.14/2.42 % (3962552)Peak memory usage: 92 MB
% 9.14/2.42 % (3962552)Instructions burned: 182 (million)
% 9.14/2.42 % (3962555)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=1052153826:i=4:ep=RST:ins=2:rtra=on_2994 on theBenchmark for (2994ds/4Mi)
% 9.14/2.42 % (3962555)Instruction limit reached!
% 9.14/2.42 % (3962555)------------------------------
% 9.14/2.42 % (3962555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.14/2.42 % (3962555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.14/2.42 % (3962555)CaDiCaL version: 2.1.3
% 9.14/2.42 % (3962555)Termination reason: Instruction limit
% 9.14/2.42 % (3962555)Termination phase: Property scanning
% 9.14/2.42 % (3962555)Time elapsed: 0.006 s
% 9.14/2.42 % (3962555)Peak memory usage: 86 MB
% 9.14/2.42 % (3962555)Instructions burned: 5 (million)
% 9.14/2.42 % (3962556)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=1193988544:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2994 on theBenchmark for (2994ds/66Mi)
% 9.14/2.42 % (3962563)dis+1002_1_to=lpo:sil=64000:si=on:flr=on:random_seed=1329700485:i=2:doe=on:canc=force:asg=cautious:rtra=on_2992 on theBenchmark for (2992ds/2Mi)
% 9.14/2.42 % (3962563)Instruction limit reached!
% 9.14/2.42 % (3962563)------------------------------
% 9.14/2.42 % (3962563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.14/2.42 % (3962563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.14/2.42 % (3962563)CaDiCaL version: 2.1.3
% 9.14/2.42 % (3962563)Termination reason: Instruction limit
% 9.14/2.42 % (3962563)Termination phase: shuffling
% 9.14/2.42 % (3962563)Time elapsed: 0.002 s
% 9.14/2.42 % (3962563)Peak memory usage: 85 MB
% 9.14/2.42 % (3962563)Instructions burned: 3 (million)
% 9.14/2.42 % (3962559)lrs+10_1_thi=all:si=on:fd=off:random_seed=2268826033:i=53:rtra=on:gtg=all_2993 on theBenchmark for (2993ds/53Mi)
% 9.14/2.42 % (3962560)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=332589970:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2993 on theBenchmark for (2993ds/8Mi)
% 10.23/2.64 % (3962560)Instruction limit reached!
% 10.23/2.64 % (3962560)------------------------------
% 10.23/2.64 % (3962560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.64 % (3962560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.64 % (3962560)CaDiCaL version: 2.1.3
% 10.23/2.64 % (3962560)Termination reason: Instruction limit
% 10.23/2.64 % (3962560)Termination phase: Property scanning
% 10.23/2.64 % (3962560)Time elapsed: 0.008 s
% 10.23/2.64 % (3962560)Peak memory usage: 85 MB
% 10.23/2.64 % (3962560)Instructions burned: 8 (million)
% 10.23/2.64 % (3962556)Instruction limit reached!
% 10.23/2.64 % (3962556)------------------------------
% 10.23/2.64 % (3962556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.64 % (3962556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.64 % (3962556)CaDiCaL version: 2.1.3
% 10.23/2.64 % (3962556)Termination reason: Instruction limit
% 10.23/2.64 % (3962556)Termination phase: Property scanning
% 10.23/2.64 % (3962556)Time elapsed: 0.062 s
% 10.23/2.64 % (3962556)Peak memory usage: 89 MB
% 10.23/2.64 % (3962556)Instructions burned: 66 (million)
% 10.23/2.64 % (3962559)Instruction limit reached!
% 10.23/2.64 % (3962559)------------------------------
% 10.23/2.64 % (3962559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.64 % (3962559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.64 % (3962559)CaDiCaL version: 2.1.3
% 10.23/2.64 % (3962559)Termination reason: Instruction limit
% 10.23/2.64 % (3962559)Termination phase: Property scanning
% 10.23/2.64 % (3962559)Time elapsed: 0.045 s
% 10.23/2.64 % (3962559)Peak memory usage: 86 MB
% 10.23/2.64 % (3962559)Instructions burned: 54 (million)
% 10.23/2.64 % (3962562)lrs+10_1_to=lakbo:sil=128000:si=on:alasca=on:sp=occurrence:random_seed=435381287:st=3:i=2:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/2Mi)
% 10.23/2.64 % (3962562)Instruction limit reached!
% 10.23/2.64 % (3962562)------------------------------
% 10.23/2.64 % (3962562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.64 % (3962562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.64 % (3962562)CaDiCaL version: 2.1.3
% 10.23/2.64 % (3962562)Termination reason: Instruction limit
% 10.23/2.64 % (3962562)Termination phase: shuffling
% 10.23/2.64 % (3962562)Time elapsed: 0.004 s
% 10.23/2.64 % (3962562)Peak memory usage: 85 MB
% 10.23/2.64 % (3962562)Instructions burned: 2 (million)
% 10.23/2.64 % (3962567)dis+10_1_si=on:random_seed=3204073549:i=10:ep=R:rtra=on_2991 on theBenchmark for (2991ds/10Mi)
% 10.23/2.64 % (3962566)lrs+1011_16:1_to=kbo:sil=128000:sas=z3:si=on:sos=theory:erd=off:urr=full:random_seed=1801405280:i=127:doe=on:rtra=on_2991 on theBenchmark for (2991ds/127Mi)
% 10.23/2.64 % (3962567)Instruction limit reached!
% 10.23/2.64 % (3962567)------------------------------
% 10.23/2.64 % (3962567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.64 % (3962567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.64 % (3962567)CaDiCaL version: 2.1.3
% 10.23/2.64 % (3962567)Termination reason: Instruction limit
% 10.23/2.64 % (3962567)Termination phase: Property scanning
% 10.23/2.64 % (3962567)Time elapsed: 0.011 s
% 10.23/2.64 % (3962567)Peak memory usage: 85 MB
% 10.23/2.64 % (3962567)Instructions burned: 11 (million)
% 10.23/2.64 % (3962572)lrs-1011_64_to=lpo:si=on:sp=unary_first:sos=on:br=off:random_seed=270167371:i=26:canc=cautious:av=off:rtra=on_2991 on theBenchmark for (2991ds/26Mi)
% 10.23/2.64 % (3962572)Instruction limit reached!
% 10.23/2.64 % (3962572)------------------------------
% 10.23/2.64 % (3962572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.64 % (3962572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.64 % (3962572)CaDiCaL version: 2.1.3
% 10.23/2.64 % (3962572)Termination reason: Instruction limit
% 10.23/2.64 % (3962572)Termination phase: Property scanning
% 10.23/2.64 % (3962572)Time elapsed: 0.012 s
% 10.23/2.64 % (3962572)Peak memory usage: 86 MB
% 10.23/2.64 % (3962572)Instructions burned: 27 (million)
% 10.23/2.64 % (3962573)dis+1011_5_anc=all:tgt=full:si=on:sp=const_frequency:spb=non_intro:fd=preordered:sac=on:random_seed=2140416555: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_2991 on theBenchmark for (2991ds/35Mi)
% 10.23/2.64 % (3962575)dis+21_1_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=off:s2agt=16:random_seed=381073931:s2a=on:i=8:kws=inv_precedence:doe=on:rtra=on_2990 on theBenchmark for (2990ds/8Mi)
% 10.23/2.64 % (3962573)Instruction limit reached!
% 10.23/2.64 % (3962573)------------------------------
% 10.23/2.64 % (3962573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.64 % (3962573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.64 % (3962573)CaDiCaL version: 2.1.3
% 10.23/2.64 % (3962573)Termination reason: Instruction limit
% 10.23/2.64 % (3962573)Termination phase: Preprocessing 1
% 10.23/2.64 % (3962573)Time elapsed: 0.032 s
% 10.23/2.64 % (3962573)Peak memory usage: 86 MB
% 10.23/2.64 % (3962573)Instructions burned: 36 (million)
% 10.23/2.64 % (3962575)Instruction limit reached!
% 10.23/2.64 % (3962575)------------------------------
% 10.23/2.64 % (3962575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.64 % (3962575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.65 % (3962575)CaDiCaL version: 2.1.3
% 10.23/2.65 % (3962575)Termination reason: Instruction limit
% 10.23/2.65 % (3962575)Termination phase: Property scanning
% 10.23/2.65 % (3962575)Time elapsed: 0.009 s
% 10.23/2.65 % (3962575)Peak memory usage: 86 MB
% 10.23/2.65 % (3962575)Instructions burned: 8 (million)
% 10.23/2.65 % (3962574)ott+10_8:1_to=lpo:sil=128000:si=on:fs=off:spb=goal_then_units:uwa=alasca_main:random_seed=1565820574:i=2:fsr=off:rtra=on:inst=on_2990 on theBenchmark for (2990ds/2Mi)
% 10.23/2.65 % (3962574)Instruction limit reached!
% 10.23/2.65 % (3962574)------------------------------
% 10.23/2.65 % (3962574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.65 % (3962574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.65 % (3962574)CaDiCaL version: 2.1.3
% 10.23/2.65 % (3962574)Termination reason: Instruction limit
% 10.23/2.65 % (3962574)Termination phase: shuffling
% 10.23/2.65 % (3962574)Time elapsed: 0.003 s
% 10.23/2.65 % (3962574)Peak memory usage: 85 MB
% 10.23/2.65 % (3962574)Instructions burned: 2 (million)
% 10.23/2.65 % (3962566)Instruction limit reached!
% 10.23/2.65 % (3962566)------------------------------
% 10.23/2.65 % (3962566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.65 % (3962566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.65 % (3962566)CaDiCaL version: 2.1.3
% 10.23/2.65 % (3962566)Termination reason: Instruction limit
% 10.23/2.65 % (3962566)Termination phase: Saturation
% 10.23/2.65 % (3962566)Time elapsed: 0.152 s
% 10.23/2.65 % (3962566)Peak memory usage: 115 MB
% 10.23/2.65 % (3962566)Instructions burned: 127 (million)
% 10.23/2.65 % (3962577)lrs-1011_1_to=kbo:sil=128000:prc=on:si=on:fs=off:tha=off:random_seed=4164577337:i=370:ep=RS:fsr=off:rtra=on_2990 on theBenchmark for (2990ds/370Mi)
% 10.23/2.65 % (3962582)lrs+1002_1_to=lpo:sil=128000:sas=z3:si=on:sos=on:urr=on:tha=off:random_seed=111580287:i=226:rtra=on:gtg=position:ss=axioms_2989 on theBenchmark for (2989ds/226Mi)
% 10.23/2.65 % (3962581)ott+1002_1_to=lpo:thi=overlap:prc=on:bsd=on:si=on:gve=cautious:thigen=on:tha=some:random_seed=1168569861:i=13:av=off:rtra=on:gtg=exists_sym:ev=force_2989 on theBenchmark for (2989ds/13Mi)
% 10.23/2.65 % (3962581)Instruction limit reached!
% 10.23/2.65 % (3962581)------------------------------
% 10.23/2.65 % (3962581)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.65 % (3962581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.65 % (3962581)CaDiCaL version: 2.1.3
% 10.23/2.65 % (3962581)Termination reason: Instruction limit
% 10.23/2.65 % (3962581)Termination phase: shuffling
% 10.23/2.65 % (3962581)Time elapsed: 0.012 s
% 10.23/2.65 % (3962581)Peak memory usage: 85 MB
% 10.23/2.65 % (3962581)Instructions burned: 14 (million)
% 10.23/2.65 % (3962582)First to succeed.
% 10.23/2.65 % (3962582)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3962519"
% 10.23/2.65 % (3962588)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=3755155054:i=75:doe=on:thsqd=64:canc=force:thsqc=64:rtra=on:thsq=on_2988 on theBenchmark for (2988ds/75Mi)
% 10.23/2.65 % (3962585)lrs+1010_5_to=lpo:sil=128000:si=on:sp=const_frequency:sos=theory:tha=off:random_seed=461784002:i=10:rtra=on_2988 on theBenchmark for (2988ds/10Mi)
% 10.23/2.65 % (3962587)lrs+1002_1_to=lpo:thi=strong:sas=z3:si=on:sp=const_frequency:tha=off:random_seed=2466580669:i=71:rtra=on:gtg=exists_top_2988 on theBenchmark for (2988ds/71Mi)
% 10.23/2.65 % (3962590)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=1224542178:i=294:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2987 on theBenchmark for (2987ds/294Mi)
% 10.23/2.65 % (3962585)Instruction limit reached!
% 10.23/2.65 % (3962585)------------------------------
% 10.23/2.65 % (3962585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.65 % (3962585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.65 % (3962585)CaDiCaL version: 2.1.3
% 10.23/2.65 % (3962585)Termination reason: Instruction limit
% 10.23/2.65 % (3962585)Termination phase: Property scanning
% 10.23/2.65 % (3962585)Time elapsed: 0.010 s
% 10.23/2.65 % (3962585)Peak memory usage: 85 MB
% 10.23/2.65 % (3962585)Instructions burned: 11 (million)
% 10.23/2.65 % (3962577)Also succeeded, but the first one will report.
% 10.23/2.65 % (3962587)Instruction limit reached!
% 10.23/2.65 % (3962587)------------------------------
% 10.23/2.65 % (3962587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.65 % (3962587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.65 % (3962587)CaDiCaL version: 2.1.3
% 10.23/2.65 % (3962587)Termination reason: Instruction limit
% 10.23/2.65 % (3962587)Termination phase: Property scanning
% 10.23/2.65 % (3962587)Time elapsed: 0.064 s
% 10.23/2.65 % (3962587)Peak memory usage: 88 MB
% 10.23/2.65 % (3962587)Instructions burned: 71 (million)
% 10.23/2.65 % (3962588)Instruction limit reached!
% 10.23/2.65 % (3962588)------------------------------
% 10.23/2.65 % (3962588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.65 % (3962588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.65 % (3962588)CaDiCaL version: 2.1.3
% 10.23/2.65 % (3962588)Termination reason: Instruction limit
% 10.23/2.65 % (3962588)Termination phase: Property scanning
% 10.23/2.65 % (3962588)Time elapsed: 0.068 s
% 10.23/2.65 % (3962588)Peak memory usage: 88 MB
% 10.23/2.65 % (3962588)Instructions burned: 76 (million)
% 10.23/2.65 % (3962593)ott+21_1_to=kbo:tgt=full:sas=z3:si=on:tha=off:random_seed=3852691436:i=130:kws=inv_frequency:nm=0:rtra=on:gtg=exists_all_2986 on theBenchmark for (2986ds/130Mi)
% 10.23/2.65 % (3962593)Instruction limit reached!
% 10.23/2.65 % (3962593)------------------------------
% 10.23/2.65 % (3962593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.23/2.65 % (3962593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.23/2.65 % (3962593)CaDiCaL version: 2.1.3
% 10.23/2.65 % (3962593)Termination reason: Instruction limit
% 10.23/2.65 % (3962593)Termination phase: Property scanning
% 10.23/2.65 % (3962593)Time elapsed: 0.109 s
% 10.23/2.65 % (3962593)Peak memory usage: 89 MB
% 10.23/2.65 % (3962593)Instructions burned: 130 (million)
% 10.23/2.65 % (3962582)Refutation found. Thanks to Tanya!
% 10.23/2.65 % SZS status Theorem for theBenchmark
% 10.23/2.65 % SZS output start Proof for theBenchmark
% See solution above
% 12.19/2.84 % (3962582)------------------------------
% 12.19/2.84 % (3962582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.19/2.84 % (3962582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.19/2.84 % (3962582)CaDiCaL version: 2.1.3
% 12.19/2.84 % (3962582)Termination reason: Refutation
% 12.19/2.84 % (3962582)Time elapsed: 0.118 s
% 12.19/2.84 % (3962582)Peak memory usage: 119 MB
% 12.19/2.84 % (3962582)Instructions burned: 206 (million)
% 12.19/2.84 % (3962582)------------------------------
% 12.19/2.84 % (3962582)------------------------------
% 12.19/2.84 % (3962519)Success in time 1.648 s
% 12.19/2.84 % Vampire exiting
%------------------------------------------------------------------------------