%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP352_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 : n011.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 11:33:40 AM UTC 2026
% Result : Theorem 4.61s 1.69s
% Output : Refutation 6.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 31
% Syntax : Number of formulae : 131 ( 47 unt; 0 typ; 16 def)
% Number of atoms : 260 ( 82 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 233 ( 104 ~; 92 |; 16 &)
% ( 17 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 352 ( 105 atm; 0 fun; 195 num; 52 var)
% Number of types : 13 ( 10 usr; 2 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 23 ( 19 usr; 10 prp; 0-3 aty)
% Number of functors : 62 ( 57 usr; 22 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Int_int_fun$': $tType ).
tff(type_def_6,type,
'Num_bool_fun$': $tType ).
tff(type_def_7,type,
'Nat_nat_fun$': $tType ).
tff(type_def_8,type,
'Nat$': $tType ).
tff(type_def_9,type,
'Num$': $tType ).
tff(type_def_10,type,
'Real_real_fun$': $tType ).
tff(type_def_11,type,
'Nat_real_fun$': $tType ).
tff(type_def_12,type,
'A$': $tType ).
tff(type_def_13,type,
'Nat_bool_fun$': $tType ).
tff(type_def_14,type,
'Nat_int_fun$': $tType ).
tff(func_def_0,type,
'times$b': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_1,type,
'norm$': $real > $real ).
tff(func_def_2,type,
'bit0$': 'Num$' > 'Num$' ).
tff(func_def_3,type,
'zero$': 'Nat$' ).
tff(func_def_4,type,
'one$a': 'A$' ).
tff(func_def_5,type,
'c$a': $real ).
tff(func_def_6,type,
'f$': 'Nat$' > 'A$' ).
tff(func_def_7,type,
'zero$a': 'A$' ).
tff(func_def_8,type,
'power$a': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_9,type,
'fun_app$e': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_10,type,
'n$': 'Nat$' ).
tff(func_def_11,type,
'u$': $real ).
tff(func_def_12,type,
'fun_app$': ( 'Real_real_fun$' * $real ) > $real ).
tff(func_def_13,type,
'of_nat$': 'Nat$' > $int ).
tff(func_def_14,type,
'power$': $real > 'Nat_real_fun$' ).
tff(func_def_15,type,
'c$': $real ).
tff(func_def_16,type,
'inverse$a': 'A$' > 'A$' ).
tff(func_def_17,type,
'power$c': ( 'A$' * 'Nat$' ) > 'A$' ).
tff(func_def_18,type,
'divide$': $real > 'Real_real_fun$' ).
tff(func_def_19,type,
'numeral$a': 'Num$' > $int ).
tff(func_def_20,type,
'numeral$c': 'Num$' > 'Nat$' ).
tff(func_def_21,type,
'divide$a': $int > 'Int_int_fun$' ).
tff(func_def_22,type,
'times$a': ( 'Num$' * 'Num$' ) > 'Num$' ).
tff(func_def_23,type,
'fun_app$d': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_24,type,
'times$d': ( 'A$' * 'A$' ) > 'A$' ).
tff(func_def_25,type,
'one$b': 'Nat$' ).
tff(func_def_26,type,
'numeral$': 'Num$' > $real ).
tff(func_def_27,type,
'times$c': ( $int * $int ) > $int ).
tff(func_def_28,type,
'one$': 'Num$' ).
tff(func_def_29,type,
'times$': ( $real * $real ) > $real ).
tff(func_def_30,type,
'less_eq$a': 'Nat$' > 'Nat_bool_fun$' ).
tff(func_def_31,type,
'less_eq$': 'Num$' > 'Num_bool_fun$' ).
tff(func_def_32,type,
'nat$': $int > 'Nat$' ).
tff(func_def_33,type,
'numeral$b': 'Num$' > 'A$' ).
tff(func_def_34,type,
'less$': 'Num$' > 'Num_bool_fun$' ).
tff(func_def_35,type,
'fun_app$a': ( 'Nat_real_fun$' * 'Nat$' ) > $real ).
tff(func_def_36,type,
'less$a': 'Nat$' > 'Nat_bool_fun$' ).
tff(func_def_37,type,
'l$': $real ).
tff(func_def_38,type,
'fun_app$f': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_39,type,
'norm$a': 'A$' > $real ).
tff(func_def_40,type,
'power$b': $int > 'Nat_int_fun$' ).
tff(func_def_41,type,
'inverse$': $real > $real ).
tff(func_def_42,type,
'divide$b': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_53,type,
sK8: $real > $real ).
tff(func_def_54,type,
sK9: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_55,type,
sK10: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_56,type,
sK11: ( $real * 'Nat$' ) > $real ).
tff(func_def_57,type,
sK12: $real > $real ).
tff(func_def_58,type,
sK13: ( $real * $real ) > $real ).
tff(func_def_59,type,
sK14: ( $real * 'Nat$' ) > $real ).
tff(func_def_60,type,
sF15: 'Real_real_fun$' ).
tff(func_def_61,type,
sF16: $real ).
tff(func_def_62,type,
sF17: $real ).
tff(func_def_63,type,
sF18: 'Nat_real_fun$' ).
tff(func_def_64,type,
sF19: $real ).
tff(func_def_65,type,
sF20: $real ).
tff(func_def_66,type,
sF21: $real ).
tff(pred_def_1,type,
'fun_app$c': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_2,type,
'fun_app$b': ( 'Num_bool_fun$' * 'Num$' ) > $o ).
tff(pred_def_7,type,
sP0: ( $real * $real * $real ) > $o ).
tff(pred_def_8,type,
sP1: ( $real * 'Num$' * $real ) > $o ).
tff(pred_def_9,type,
sP2: ( $real * $real * $real ) > $o ).
tff(pred_def_10,type,
sP3: ( $real * 'Num$' * $real ) > $o ).
tff(pred_def_11,type,
sP4: ( $real * $real * $real ) > $o ).
tff(pred_def_12,type,
sP5: ( $real * $real * 'Num$' ) > $o ).
tff(pred_def_13,type,
sP6: ( $real * $real * $real ) > $o ).
tff(pred_def_14,type,
sP7: ( $real * $real * 'Num$' ) > $o ).
tff(f1,conjecture,
$less('times$'('fun_app$'('divide$'(1/1),2/1),'norm$'('fun_app$a'('power$'('inverse$'('c$')),'n$'))),'norm$'('fun_app$a'('power$'('inverse$'('c$')),'n$'))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture0) ).
tff(f2,negated_conjecture,
~ $less('times$'('fun_app$'('divide$'(1/1),2/1),'norm$'('fun_app$a'('power$'('inverse$'('c$')),'n$'))),'norm$'('fun_app$a'('power$'('inverse$'('c$')),'n$'))),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,axiom,
$less(0/1,'c$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
tff(f49,axiom,
! [X1: 'Nat$',X0: $int] :
( ( 'fun_app$e'('power$b'(X0),X1) = 0 )
<=> ( $less(0,'of_nat$'(X1))
& ( X0 = 0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom47) ).
tff(f60,axiom,
! [X0: $real] :
( ( X0 = 0/1 )
<=> ( 'norm$'(X0) = 0/1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom58) ).
tff(f74,axiom,
! [X0: $real] :
( $less(0/1,'norm$'(X0))
<=> ( X0 != 0/1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom72) ).
tff(f79,axiom,
! [X0: 'Nat$'] :
( $less(0,'of_nat$'(X0))
=> ( 'fun_app$a'('power$'(0/1),X0) = 0/1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom77) ).
tff(f96,axiom,
! [X0: $real,X1: 'Nat$'] :
( ( X0 != 0/1 )
=> ( 'fun_app$a'('power$'(X0),X1) != 0/1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).
tff(f101,axiom,
'fun_app$e'('power$b'(0),'nat$'(2)) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom99) ).
tff(f195,axiom,
! [X0: $real] :
( $less(0/1,'fun_app$'('divide$'(1/1),X0))
<=> $less(0/1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom193) ).
tff(f198,axiom,
! [X0: $real,X1: $real] :
( $less(0/1,X0)
=> ( $less('fun_app$'('divide$'(X1),X0),1/1)
<=> $less(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom196) ).
tff(f203,axiom,
! [X0: $real] : ( 'inverse$'('inverse$'(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom201) ).
tff(f310,axiom,
! [X0: $real] : ( 'inverse$'(X0) = 'fun_app$'('divide$'(1/1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom308) ).
tff(f440,axiom,
! [X0: $real] :
( $lesseq('inverse$'(X0),1/1)
<=> ( $lesseq(1/1,X0)
| $lesseq(X0,0/1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom438) ).
tff(f493,axiom,
! [X0: $real] : $lesseq(0/1,'fun_app$a'('power$'(X0),'nat$'(2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom491) ).
tff(f527,axiom,
! [X0: $real,X1: $real] :
( ( X0 != 0/1 )
=> ( 'fun_app$'('divide$'('times$'(X1,X0)),X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom525) ).
tff(f771,plain,
! [X0: $real] :
( ( ~ $less(X0,1/1)
| ~ $less(0/1,X0) )
<=> ~ $less(1/1,'inverse$'(X0)) ),
inference(theory_normalization,[],[f440]) ).
tff(f808,plain,
! [X0: $real] : ~ $less('fun_app$a'('power$'(X0),'nat$'(2)),0/1),
inference(theory_normalization,[],[f493]) ).
tff(f826,plain,
~ $less('times$'('fun_app$'('divide$'(1/1),2/1),'norm$'('fun_app$a'('power$'('inverse$'('c$')),'n$'))),'norm$'('fun_app$a'('power$'('inverse$'('c$')),'n$'))),
inference(flattening,[],[f2]) ).
tff(f1057,plain,
! [X0: $real,X1: 'Nat$'] :
( ( 'fun_app$a'('power$'(X0),X1) != 0/1 )
| ( 0/1 = X0 ) ),
inference(ennf_transformation,[],[f96]) ).
tff(f1190,plain,
! [X0: 'Nat$'] :
( ~ $less(0,'of_nat$'(X0))
| ( 'fun_app$a'('power$'(0/1),X0) = 0/1 ) ),
inference(ennf_transformation,[],[f79]) ).
tff(f1215,plain,
! [X1: $real,X0: $real] :
( ( 'fun_app$'('divide$'('times$'(X1,X0)),X0) = X1 )
| ( 0/1 = X0 ) ),
inference(ennf_transformation,[],[f527]) ).
tff(f1258,plain,
! [X1: $real,X0: $real] :
( ~ $less(0/1,X0)
| ( $less('fun_app$'('divide$'(X1),X0),1/1)
<=> $less(X1,X0) ) ),
inference(ennf_transformation,[],[f198]) ).
tff(f1450,plain,
! [X1: $real,X0: $real] :
( ~ $less(0/1,X0)
| ( ( $less('fun_app$'('divide$'(X1),X0),1/1)
| ~ $less(X1,X0) )
& ( $less(X1,X0)
| ~ $less('fun_app$'('divide$'(X1),X0),1/1) ) ) ),
inference(nnf_transformation,[],[f1258]) ).
tff(f1451,plain,
! [X0: $real,X1: $real] :
( ~ $less(0/1,X1)
| ( ( $less('fun_app$'('divide$'(X0),X1),1/1)
| ~ $less(X0,X1) )
& ( $less(X0,X1)
| ~ $less('fun_app$'('divide$'(X0),X1),1/1) ) ) ),
inference(rectify,[],[f1450]) ).
tff(f1461,plain,
! [X0: $real] :
( ( $less(0/1,'norm$'(X0))
| ( 0/1 = X0 ) )
& ( ( X0 != 0/1 )
| ~ $less(0/1,'norm$'(X0)) ) ),
inference(nnf_transformation,[],[f74]) ).
tff(f1482,plain,
! [X0: $real] :
( ( ( X0 = 0/1 )
| ( 0/1 != 'norm$'(X0) ) )
& ( ( 'norm$'(X0) = 0/1 )
| ( 0/1 != X0 ) ) ),
inference(nnf_transformation,[],[f60]) ).
tff(f1513,plain,
! [X1: 'Nat$',X0: $int] :
( ( ( 'fun_app$e'('power$b'(X0),X1) = 0 )
| ~ $less(0,'of_nat$'(X1))
| ( 0 != X0 ) )
& ( ( $less(0,'of_nat$'(X1))
& ( X0 = 0 ) )
| ( 'fun_app$e'('power$b'(X0),X1) != 0 ) ) ),
inference(nnf_transformation,[],[f49]) ).
tff(f1514,plain,
! [X1: 'Nat$',X0: $int] :
( ( ( 'fun_app$e'('power$b'(X0),X1) = 0 )
| ~ $less(0,'of_nat$'(X1))
| ( 0 != X0 ) )
& ( ( $less(0,'of_nat$'(X1))
& ( X0 = 0 ) )
| ( 'fun_app$e'('power$b'(X0),X1) != 0 ) ) ),
inference(flattening,[],[f1513]) ).
tff(f1515,plain,
! [X0: 'Nat$',X1: $int] :
( ( ( 0 = 'fun_app$e'('power$b'(X1),X0) )
| ~ $less(0,'of_nat$'(X0))
| ( 0 != X1 ) )
& ( ( $less(0,'of_nat$'(X0))
& ( 0 = X1 ) )
| ( 0 != 'fun_app$e'('power$b'(X1),X0) ) ) ),
inference(rectify,[],[f1514]) ).
tff(f1546,plain,
! [X0: $real] :
( ( ~ $less(X0,1/1)
| ~ $less(0/1,X0)
| $less(1/1,'inverse$'(X0)) )
& ( ~ $less(1/1,'inverse$'(X0))
| ( $less(X0,1/1)
& $less(0/1,X0) ) ) ),
inference(nnf_transformation,[],[f771]) ).
tff(f1547,plain,
! [X0: $real] :
( ( ~ $less(X0,1/1)
| ~ $less(0/1,X0)
| $less(1/1,'inverse$'(X0)) )
& ( ~ $less(1/1,'inverse$'(X0))
| ( $less(X0,1/1)
& $less(0/1,X0) ) ) ),
inference(flattening,[],[f1546]) ).
tff(f1561,plain,
! [X0: $real] :
( ( $less(0/1,'fun_app$'('divide$'(1/1),X0))
| ~ $less(0/1,X0) )
& ( $less(0/1,X0)
| ~ $less(0/1,'fun_app$'('divide$'(1/1),X0)) ) ),
inference(nnf_transformation,[],[f195]) ).
tff(f1776,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$'('divide$'('times$'(X0,X1)),X1) = X0 )
| ( 0/1 = X1 ) ),
inference(rectify,[],[f1215]) ).
tff(f1941,plain,
! [X0: $real,X1: $real] :
( ~ $less('fun_app$'('divide$'(X0),X1),1/1)
| $less(X0,X1)
| ~ $less(0/1,X1) ),
inference(cnf_transformation,[],[f1451]) ).
tff(f1960,plain,
! [X0: $real] :
( $less(0/1,'norm$'(X0))
| ( 0/1 = X0 ) ),
inference(cnf_transformation,[],[f1461]) ).
tff(f1965,plain,
~ $less('times$'('fun_app$'('divide$'(1/1),2/1),'norm$'('fun_app$a'('power$'('inverse$'('c$')),'n$'))),'norm$'('fun_app$a'('power$'('inverse$'('c$')),'n$'))),
inference(cnf_transformation,[],[f826]) ).
tff(f2006,plain,
! [X0: $real] :
( ( 0/1 != 'norm$'(X0) )
| ( 0/1 = X0 ) ),
inference(cnf_transformation,[],[f1482]) ).
tff(f2052,plain,
! [X0: 'Nat$',X1: $int] :
( ( 0 != 'fun_app$e'('power$b'(X1),X0) )
| $less(0,'of_nat$'(X0)) ),
inference(cnf_transformation,[],[f1515]) ).
tff(f2064,plain,
! [X0: $real,X1: 'Nat$'] :
( ( 0/1 != 'fun_app$a'('power$'(X0),X1) )
| ( 0/1 = X0 ) ),
inference(cnf_transformation,[],[f1057]) ).
tff(f2105,plain,
! [X0: $real] :
( ~ $less(1/1,'inverse$'(X0))
| $less(X0,1/1) ),
inference(cnf_transformation,[],[f1547]) ).
tff(f2127,plain,
! [X0: $real] :
( $less(0/1,'fun_app$'('divide$'(1/1),X0))
| ~ $less(0/1,X0) ),
inference(cnf_transformation,[],[f1561]) ).
tff(f2143,plain,
! [X0: $real] : ( 'inverse$'('inverse$'(X0)) = X0 ),
inference(cnf_transformation,[],[f203]) ).
tff(f2311,plain,
$less(0/1,'c$'),
inference(cnf_transformation,[],[f3]) ).
tff(f2336,plain,
0 = 'fun_app$e'('power$b'(0),'nat$'(2)),
inference(cnf_transformation,[],[f101]) ).
tff(f2453,plain,
! [X0: $real] : ~ $less('fun_app$a'('power$'(X0),'nat$'(2)),0/1),
inference(cnf_transformation,[],[f808]) ).
tff(f2492,plain,
! [X0: 'Nat$'] :
( ( 0/1 = 'fun_app$a'('power$'(0/1),X0) )
| ~ $less(0,'of_nat$'(X0)) ),
inference(cnf_transformation,[],[f1190]) ).
tff(f2505,plain,
! [X0: $real] : ( 'inverse$'(X0) = 'fun_app$'('divide$'(1/1),X0) ),
inference(cnf_transformation,[],[f310]) ).
tff(f2520,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$'('divide$'('times$'(X0,X1)),X1) = X0 )
| ( 0/1 = X1 ) ),
inference(cnf_transformation,[],[f1776]) ).
tff(f2779,plain,
~ $less('times$'('fun_app$'('divide$'(1/1),2/1),'norm$'('fun_app$a'('power$'('fun_app$'('divide$'(1/1),'c$')),'n$'))),'norm$'('fun_app$a'('power$'('fun_app$'('divide$'(1/1),'c$')),'n$'))),
inference(definition_unfolding,[],[f1965,f2505,f2505]) ).
tff(f2791,plain,
! [X0: $real] :
( ~ $less(1/1,'fun_app$'('divide$'(1/1),X0))
| $less(X0,1/1) ),
inference(definition_unfolding,[],[f2105,f2505]) ).
tff(f2794,plain,
! [X0: $real] : ( 'fun_app$'('divide$'(1/1),'fun_app$'('divide$'(1/1),X0)) = X0 ),
inference(definition_unfolding,[],[f2143,f2505,f2505]) ).
tff(f2992,definition,
sF15 = 'divide$'(1/1),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
tff(f2993,plain,
'divide$'(1/1) = sF15,
inference(reorient_equations,[],[f2992]) ).
tff(f2994,definition,
sF16 = 'fun_app$'(sF15,2/1),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
tff(f2995,definition,
sF17 = 'fun_app$'(sF15,'c$'),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
tff(f2996,plain,
'fun_app$'(sF15,'c$') = sF17,
inference(reorient_equations,[],[f2995]) ).
tff(f2997,definition,
sF18 = 'power$'(sF17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
tff(f2998,plain,
'power$'(sF17) = sF18,
inference(reorient_equations,[],[f2997]) ).
tff(f2999,definition,
sF19 = 'fun_app$a'(sF18,'n$'),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
tff(f3000,plain,
'fun_app$a'(sF18,'n$') = sF19,
inference(reorient_equations,[],[f2999]) ).
tff(f3001,definition,
sF20 = 'norm$'(sF19),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
tff(f3002,definition,
sF21 = 'times$'(sF16,sF20),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
tff(f3003,plain,
'times$'(sF16,sF20) = sF21,
inference(reorient_equations,[],[f3002]) ).
tff(f3004,plain,
~ $less(sF21,sF20),
inference(definition_folding,[],[f2779,f3001,f3000,f2998,f2996,f2993,f3003,f3001,f3000,f2998,f2996,f2993,f2994,f2993]) ).
tff(f3029,plain,
( ( 0/1 = sF19 )
| $less(0/1,sF20) ),
inference(superposition,[],[f1960,f3001]) ).
tff(f3031,definition,
( spl22_1
<=> ( 0/1 = sF19 ) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
tff(f3035,definition,
( spl22_2
<=> $less(0/1,sF20) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
tff(f3037,plain,
( $less(0/1,sF20)
| ~ spl22_2 ),
inference(avatar_component_clause,[],[f3035]) ).
tff(f3038,plain,
( spl22_1
| spl22_2 ),
inference(avatar_split_clause,[],[f3029,f3035,f3031]) ).
tff(f3051,plain,
( ( 0/1 = sF19 )
| ( 0/1 != sF20 ) ),
inference(superposition,[],[f2006,f3001]) ).
tff(f3053,definition,
( spl22_5
<=> ( 0/1 = sF20 ) ),
introduced(definition,[new_symbols(definition,[spl22_5])],[avatar_definition]) ).
tff(f3055,plain,
( ( 0/1 != sF20 )
| spl22_5 ),
inference(avatar_component_clause,[],[f3053]) ).
tff(f3056,plain,
( spl22_1
| ~ spl22_5 ),
inference(avatar_split_clause,[],[f3051,f3053,f3031]) ).
tff(f3174,definition,
( spl22_15
<=> $less(0/1,0/1) ),
introduced(definition,[new_symbols(definition,[spl22_15])],[avatar_definition]) ).
tff(f3185,plain,
! [X0: 'Nat$'] :
( ( 0/1 = sF17 )
| ( 0/1 != 'fun_app$a'(sF18,X0) ) ),
inference(superposition,[],[f2064,f2998]) ).
tff(f3190,definition,
( spl22_18
<=> ! [X0: 'Nat$'] : ( 0/1 != 'fun_app$a'(sF18,X0) ) ),
introduced(definition,[new_symbols(definition,[spl22_18])],[avatar_definition]) ).
tff(f3191,plain,
( ! [X0: 'Nat$'] : ( 0/1 != 'fun_app$a'(sF18,X0) )
| ~ spl22_18 ),
inference(avatar_component_clause,[],[f3190]) ).
tff(f3193,definition,
( spl22_19
<=> ( 0/1 = sF17 ) ),
introduced(definition,[new_symbols(definition,[spl22_19])],[avatar_definition]) ).
tff(f3195,plain,
( ( 0/1 = sF17 )
| ~ spl22_19 ),
inference(avatar_component_clause,[],[f3193]) ).
tff(f3196,plain,
( spl22_18
| spl22_19 ),
inference(avatar_split_clause,[],[f3185,f3193,f3190]) ).
tff(f3213,plain,
( ( 0/1 != sF19 )
| ~ spl22_18 ),
inference(superposition,[],[f3191,f3000]) ).
tff(f3217,plain,
( ~ spl22_1
| ~ spl22_18 ),
inference(avatar_split_clause,[],[f3213,f3190,f3031]) ).
tff(f3224,plain,
! [X0: $real] :
( $less(0/1,'fun_app$'(sF15,X0))
| ~ $less(0/1,X0) ),
inference(forward_demodulation,[],[f2127,f2993]) ).
tff(f3226,plain,
( $less(0/1,sF17)
| ~ $less(0/1,'c$') ),
inference(superposition,[],[f3224,f2996]) ).
tff(f3230,plain,
$less(0/1,sF17),
inference(forward_subsumption_resolution,[],[f3226,f2311]) ).
tff(f3445,plain,
! [X0: $real] :
( ~ $less(1/1,'fun_app$'(sF15,X0))
| $less(X0,1/1) ),
inference(forward_demodulation,[],[f2791,f2993]) ).
tff(f3487,definition,
( spl22_41
<=> $less(sF16,1/1) ),
introduced(definition,[new_symbols(definition,[spl22_41])],[avatar_definition]) ).
tff(f3495,plain,
! [X0: $real] : ( 'fun_app$'(sF15,'fun_app$'(sF15,X0)) = X0 ),
inference(forward_demodulation,[],[f2794,f2993]) ).
tff(f3500,plain,
2/1 = 'fun_app$'(sF15,sF16),
inference(superposition,[],[f3495,f2994]) ).
tff(f3519,definition,
( spl22_43
<=> $less(1/1,2/1) ),
introduced(definition,[new_symbols(definition,[spl22_43])],[avatar_definition]) ).
tff(f3521,plain,
( ~ $less(1/1,2/1)
| spl22_43 ),
inference(avatar_component_clause,[],[f3519]) ).
tff(f3549,plain,
( $less(sF16,1/1)
| ~ $less(1/1,2/1) ),
inference(superposition,[],[f3445,f3500]) ).
tff(f3704,plain,
( ( 0 != 0 )
| $less(0,'of_nat$'('nat$'(2))) ),
inference(superposition,[],[f2052,f2336]) ).
tff(f3708,plain,
$less(0,'of_nat$'('nat$'(2))),
inference(trivial_inequality_removal,[],[f3704]) ).
tff(f3715,definition,
( spl22_50
<=> $less(0,'of_nat$'('nat$'(2))) ),
introduced(definition,[new_symbols(definition,[spl22_50])],[avatar_definition]) ).
tff(f3717,plain,
( $less(0,'of_nat$'('nat$'(2)))
| ~ spl22_50 ),
inference(avatar_component_clause,[],[f3715]) ).
tff(f3734,plain,
spl22_50,
inference(avatar_split_clause,[],[f3708,f3715]) ).
tff(f4124,plain,
( $less(0/1,0/1)
| ~ spl22_19 ),
inference(superposition,[],[f3230,f3195]) ).
tff(f4132,plain,
( spl22_15
| ~ spl22_19 ),
inference(avatar_split_clause,[],[f4124,f3193,f3174]) ).
tff(f4212,plain,
( ~ $less(0,'of_nat$'('nat$'(2)))
| ~ $less(0/1,0/1) ),
inference(superposition,[],[f2453,f2492]) ).
tff(f4217,plain,
( ~ $less(0/1,0/1)
| ~ spl22_50 ),
inference(forward_subsumption_resolution,[],[f4212,f3717]) ).
tff(f4218,plain,
( ~ spl22_15
| ~ spl22_50 ),
inference(avatar_split_clause,[],[f4217,f3715,f3174]) ).
tff(f4665,plain,
( ( 0/1 = sF20 )
| ( sF16 = 'fun_app$'('divide$'(sF21),sF20) ) ),
inference(superposition,[],[f2520,f3003]) ).
tff(f4685,plain,
( ( sF16 = 'fun_app$'('divide$'(sF21),sF20) )
| spl22_5 ),
inference(forward_subsumption_resolution,[],[f4665,f3055]) ).
tff(f5183,plain,
( ~ $less(0/1,sF20)
| $less(sF21,sF20)
| ~ $less(sF16,1/1)
| spl22_5 ),
inference(superposition,[],[f1941,f4685]) ).
tff(f5184,plain,
( $less(sF21,sF20)
| ~ $less(sF16,1/1)
| ~ spl22_2
| spl22_5 ),
inference(forward_subsumption_resolution,[],[f5183,f3037]) ).
tff(f5191,plain,
( ~ $less(sF16,1/1)
| ~ spl22_2
| spl22_5 ),
inference(forward_subsumption_resolution,[],[f5184,f3004]) ).
tff(f5200,plain,
( ~ spl22_43
| spl22_41 ),
inference(avatar_split_clause,[],[f3549,f3487,f3519]) ).
tff(f5206,plain,
( ~ spl22_41
| ~ spl22_2
| spl22_5 ),
inference(avatar_split_clause,[],[f5191,f3053,f3035,f3487]) ).
tff(f5865,plain,
( $false
| spl22_43 ),
inference(evaluation,[],[f3521]) ).
tff(f5867,plain,
spl22_43,
inference(avatar_contradiction_clause,[],[f5865]) ).
cnf(s1,plain,
( spl22_1
| spl22_2 ),
inference(sat_conversion,[],[f3038]) ).
cnf(s3,plain,
( spl22_1
| ~ spl22_5 ),
inference(sat_conversion,[],[f3056]) ).
cnf(s23,plain,
( spl22_18
| spl22_19 ),
inference(sat_conversion,[],[f3196]) ).
cnf(s28,plain,
( ~ spl22_1
| ~ spl22_18 ),
inference(sat_conversion,[],[f3217]) ).
cnf(s78,plain,
spl22_50,
inference(sat_conversion,[],[f3734]) ).
cnf(s172,plain,
( spl22_15
| ~ spl22_19 ),
inference(sat_conversion,[],[f4132]) ).
cnf(s191,plain,
( ~ spl22_15
| ~ spl22_50 ),
inference(sat_conversion,[],[f4218]) ).
cnf(s263,plain,
( spl22_41
| ~ spl22_43 ),
inference(sat_conversion,[],[f5200]) ).
cnf(s267,plain,
( ~ spl22_2
| spl22_5
| ~ spl22_41 ),
inference(sat_conversion,[],[f5206]) ).
cnf(s341,plain,
spl22_43,
inference(sat_conversion,[],[f5867]) ).
cnf(s343,plain,
spl22_41,
inference(rat,[],[s263,s341]) ).
cnf(s351,plain,
~ spl22_15,
inference(rat,[],[s191,s78]) ).
cnf(s353,plain,
~ spl22_19,
inference(rat,[],[s172,s351]) ).
cnf(s362,plain,
spl22_18,
inference(rat,[],[s23,s353]) ).
cnf(s363,plain,
~ spl22_1,
inference(rat,[],[s28,s362]) ).
cnf(s373,plain,
~ spl22_5,
inference(rat,[],[s3,s363]) ).
cnf(s374,plain,
~ spl22_2,
inference(rat,[],[s267,s343,s373]) ).
cnf(s377,plain,
$false,
inference(rat,[],[s1,s374,s363]) ).
tff(f5869,plain,
$false,
inference(avatar_sat_refutation,[],[s377]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP352_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 12:55:30 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 2.80/1.33 % (2375553)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.80/1.33 % (2375562)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2784989282:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.80/1.33 % (2375562)Instruction limit reached!
% 2.80/1.33 % (2375562)------------------------------
% 2.80/1.33 % (2375562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.33 % (2375562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.33 % (2375562)CaDiCaL version: 2.1.3
% 2.80/1.33 % (2375562)Termination reason: Instruction limit
% 2.80/1.33 % (2375562)Termination phase: Property scanning
% 2.80/1.33 % (2375562)Time elapsed: 0.002 s
% 2.80/1.33 % (2375562)Peak memory usage: 86 MB
% 2.80/1.33 % (2375562)Instructions burned: 6 (million)
% 2.80/1.33 % (2375558)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2160105906:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.80/1.33 % (2375561)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2988070712:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.80/1.33 % (2375559)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1020108:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.80/1.33 % (2375560)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2594397773:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.80/1.33 % (2375561)Instruction limit reached!
% 2.80/1.33 % (2375561)------------------------------
% 2.80/1.33 % (2375561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.33 % (2375561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.33 % (2375561)CaDiCaL version: 2.1.3
% 2.80/1.33 % (2375561)Termination reason: Instruction limit
% 2.80/1.33 % (2375561)Termination phase: Property scanning
% 2.80/1.33 % (2375561)Time elapsed: 0.004 s
% 2.80/1.33 % (2375561)Peak memory usage: 85 MB
% 2.80/1.33 % (2375561)Instructions burned: 7 (million)
% 2.80/1.33 % (2375564)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2687174927:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.80/1.33 % (2375558)Instruction limit reached!
% 2.80/1.33 % (2375558)------------------------------
% 2.80/1.33 % (2375558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.33 % (2375558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.33 % (2375558)CaDiCaL version: 2.1.3
% 2.80/1.33 % (2375558)Termination reason: Instruction limit
% 2.80/1.33 % (2375558)Termination phase: Property scanning
% 2.80/1.33 % (2375558)Time elapsed: 0.008 s
% 2.80/1.33 % (2375558)Peak memory usage: 85 MB
% 2.80/1.33 % (2375558)Instructions burned: 14 (million)
% 2.80/1.33 % (2375563)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2361792008:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.80/1.33 % (2375564)Instruction limit reached!
% 2.80/1.33 % (2375564)------------------------------
% 2.80/1.33 % (2375564)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.33 % (2375564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.33 % (2375564)CaDiCaL version: 2.1.3
% 2.80/1.33 % (2375564)Termination reason: Instruction limit
% 2.80/1.33 % (2375564)Termination phase: Property scanning
% 2.80/1.33 % (2375564)Time elapsed: 0.019 s
% 2.80/1.33 % (2375564)Peak memory usage: 87 MB
% 2.80/1.33 % (2375564)Instructions burned: 35 (million)
% 2.80/1.33 % (2375563)Instruction limit reached!
% 2.80/1.33 % (2375563)------------------------------
% 2.80/1.33 % (2375563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.33 % (2375563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.33 % (2375563)CaDiCaL version: 2.1.3
% 2.80/1.33 % (2375563)Termination reason: Instruction limit
% 2.80/1.33 % (2375563)Termination phase: Property scanning
% 2.80/1.33 % (2375563)Time elapsed: 0.025 s
% 2.80/1.33 % (2375563)Peak memory usage: 88 MB
% 2.80/1.33 % (2375563)Instructions burned: 48 (million)
% 2.80/1.33 % (2375566)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3920839799:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.80/1.33 % (2375566)Instruction limit reached!
% 2.80/1.33 % (2375566)------------------------------
% 3.64/1.50 % (2375566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.50 % (2375566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.50 % (2375566)CaDiCaL version: 2.1.3
% 3.64/1.50 % (2375566)Termination reason: Instruction limit
% 3.64/1.50 % (2375566)Termination phase: Preprocessing 1
% 3.64/1.50 % (2375566)Time elapsed: 0.005 s
% 3.64/1.50 % (2375566)Peak memory usage: 86 MB
% 3.64/1.50 % (2375566)Instructions burned: 16 (million)
% 3.64/1.50 % (2375574)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=117303941:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.64/1.50 % (2375573)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=3383473876:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.64/1.50 % (2375574)Instruction limit reached!
% 3.64/1.50 % (2375574)------------------------------
% 3.64/1.50 % (2375574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.50 % (2375574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.50 % (2375574)CaDiCaL version: 2.1.3
% 3.64/1.50 % (2375574)Termination reason: Instruction limit
% 3.64/1.50 % (2375574)Termination phase: Preprocessing 3
% 3.64/1.50 % (2375574)Time elapsed: 0.011 s
% 3.64/1.50 % (2375574)Peak memory usage: 87 MB
% 3.64/1.50 % (2375574)Instructions burned: 16 (million)
% 3.64/1.50 % (2375578)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=3969438630:i=85:gtgl=4:rtra=on:gtg=exists_sym_2997 on theBenchmark for (2997ds/85Mi)
% 3.64/1.50 % (2375575)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1218477717:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.64/1.50 % (2375573)Instruction limit reached!
% 3.64/1.50 % (2375573)------------------------------
% 3.64/1.50 % (2375573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.50 % (2375573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.50 % (2375573)CaDiCaL version: 2.1.3
% 3.64/1.50 % (2375573)Termination reason: Instruction limit
% 3.64/1.50 % (2375573)Termination phase: Property scanning
% 3.64/1.50 % (2375573)Time elapsed: 0.017 s
% 3.64/1.50 % (2375573)Peak memory usage: 87 MB
% 3.64/1.50 % (2375573)Instructions burned: 30 (million)
% 3.64/1.50 % (2375576)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=366364609:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.64/1.50 % (2375560)Instruction limit reached!
% 3.64/1.50 % (2375560)------------------------------
% 3.64/1.50 % (2375560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.50 % (2375560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.50 % (2375560)CaDiCaL version: 2.1.3
% 3.64/1.50 % (2375560)Termination reason: Instruction limit
% 3.64/1.50 % (2375560)Termination phase: Saturation
% 3.64/1.50 % (2375560)Time elapsed: 0.159 s
% 3.64/1.50 % (2375560)Peak memory usage: 118 MB
% 3.64/1.50 % (2375560)Instructions burned: 201 (million)
% 3.64/1.50 % (2375575)Instruction limit reached!
% 3.64/1.50 % (2375575)------------------------------
% 3.64/1.50 % (2375575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.50 % (2375575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.50 % (2375575)CaDiCaL version: 2.1.3
% 3.64/1.50 % (2375575)Termination reason: Instruction limit
% 3.64/1.50 % (2375575)Termination phase: Preprocessing 3
% 3.64/1.50 % (2375575)Time elapsed: 0.014 s
% 3.64/1.50 % (2375575)Peak memory usage: 87 MB
% 3.64/1.50 % (2375575)Instructions burned: 25 (million)
% 3.64/1.50 % (2375578)Instruction limit reached!
% 3.64/1.50 % (2375578)------------------------------
% 3.64/1.50 % (2375578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.50 % (2375578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.50 % (2375578)CaDiCaL version: 2.1.3
% 3.64/1.50 % (2375578)Termination reason: Instruction limit
% 3.64/1.50 % (2375578)Termination phase: Saturation
% 3.64/1.50 % (2375578)Time elapsed: 0.023 s
% 3.64/1.50 % (2375578)Peak memory usage: 90 MB
% 3.64/1.50 % (2375578)Instructions burned: 87 (million)
% 3.64/1.50 % (2375576)Instruction limit reached!
% 3.64/1.50 % (2375576)------------------------------
% 4.61/1.65 % (2375576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.65 % (2375576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.65 % (2375576)CaDiCaL version: 2.1.3
% 4.61/1.65 % (2375576)Termination reason: Instruction limit
% 4.61/1.65 % (2375576)Termination phase: Preprocessing 3
% 4.61/1.65 % (2375576)Time elapsed: 0.015 s
% 4.61/1.65 % (2375576)Peak memory usage: 87 MB
% 4.61/1.65 % (2375576)Instructions burned: 27 (million)
% 4.61/1.65 % (2375559)Instruction limit reached!
% 4.61/1.65 % (2375559)------------------------------
% 4.61/1.65 % (2375559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.65 % (2375559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.65 % (2375559)CaDiCaL version: 2.1.3
% 4.61/1.65 % (2375559)Termination reason: Instruction limit
% 4.61/1.65 % (2375559)Termination phase: Saturation
% 4.61/1.65 % (2375559)Time elapsed: 0.222 s
% 4.61/1.65 % (2375559)Peak memory usage: 119 MB
% 4.61/1.65 % (2375559)Instructions burned: 307 (million)
% 4.61/1.65 % (2375587)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=2584730402:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2996 on theBenchmark for (2996ds/66Mi)
% 4.61/1.65 % (2375582)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=3772633189:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2996 on theBenchmark for (2996ds/2Mi)
% 4.61/1.65 % (2375582)Instruction limit reached!
% 4.61/1.65 % (2375582)------------------------------
% 4.61/1.65 % (2375582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.65 % (2375582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.65 % (2375582)CaDiCaL version: 2.1.3
% 4.61/1.65 % (2375582)Termination reason: Instruction limit
% 4.61/1.65 % (2375582)Termination phase: shuffling
% 4.61/1.65 % (2375582)Time elapsed: 0.002 s
% 4.61/1.65 % (2375582)Peak memory usage: 85 MB
% 4.61/1.65 % (2375582)Instructions burned: 2 (million)
% 4.61/1.65 % (2375586)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=365066355:i=4:ep=RST:ins=2:rtra=on_2996 on theBenchmark for (2996ds/4Mi)
% 4.61/1.65 % (2375588)lrs+10_1_thi=all:si=on:fd=off:random_seed=1549889824:i=53:rtra=on:gtg=all_2996 on theBenchmark for (2996ds/53Mi)
% 4.61/1.65 % (2375586)Instruction limit reached!
% 4.61/1.65 % (2375586)------------------------------
% 4.61/1.65 % (2375586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.65 % (2375586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.65 % (2375586)CaDiCaL version: 2.1.3
% 4.61/1.65 % (2375586)Termination reason: Instruction limit
% 4.61/1.65 % (2375586)Termination phase: Property scanning
% 4.61/1.65 % (2375586)Time elapsed: 0.003 s
% 4.61/1.65 % (2375586)Peak memory usage: 85 MB
% 4.61/1.65 % (2375586)Instructions burned: 4 (million)
% 4.61/1.65 % (2375585)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=4078979009:i=181:rtra=on:ss=axioms:ev=cautious_2996 on theBenchmark for (2996ds/181Mi)
% 4.61/1.65 % (2375587)Instruction limit reached!
% 4.61/1.65 % (2375587)------------------------------
% 4.61/1.65 % (2375587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.65 % (2375587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.65 % (2375587)CaDiCaL version: 2.1.3
% 4.61/1.65 % (2375587)Termination reason: Instruction limit
% 4.61/1.65 % (2375587)Termination phase: Saturation
% 4.61/1.65 % (2375587)Time elapsed: 0.046 s
% 4.61/1.65 % (2375587)Peak memory usage: 130 MB
% 4.61/1.65 % (2375587)Instructions burned: 67 (million)
% 4.61/1.65 % (2375589)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=3264437998:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2996 on theBenchmark for (2996ds/8Mi)
% 4.61/1.65 % (2375588)Instruction limit reached!
% 4.61/1.65 % (2375588)------------------------------
% 4.61/1.65 % (2375588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.65 % (2375588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.65 % (2375588)CaDiCaL version: 2.1.3
% 4.61/1.65 % (2375588)Termination reason: Instruction limit
% 4.61/1.65 % (2375588)Termination phase: Property scanning
% 4.61/1.65 % (2375588)Time elapsed: 0.028 s
% 4.61/1.65 % (2375588)Peak memory usage: 87 MB
% 4.61/1.65 % (2375588)Instructions burned: 55 (million)
% 4.61/1.69 % (2375589)Instruction limit reached!
% 4.61/1.69 % (2375589)------------------------------
% 4.61/1.69 % (2375589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.69 % (2375589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.69 % (2375589)CaDiCaL version: 2.1.3
% 4.61/1.69 % (2375589)Termination reason: Instruction limit
% 4.61/1.69 % (2375589)Termination phase: shuffling
% 4.61/1.69 % (2375589)Time elapsed: 0.005 s
% 4.61/1.69 % (2375589)Peak memory usage: 86 MB
% 4.61/1.69 % (2375589)Instructions burned: 9 (million)
% 4.61/1.69 % (2375590)lrs+10_1_to=lakbo:sil=128000:si=on:alasca=on:sp=occurrence:random_seed=2390639316:st=3:i=2:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/2Mi)
% 4.61/1.69 % (2375590)Instruction limit reached!
% 4.61/1.69 % (2375590)------------------------------
% 4.61/1.69 % (2375590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.69 % (2375590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.69 % (2375590)CaDiCaL version: 2.1.3
% 4.61/1.69 % (2375590)Termination reason: Instruction limit
% 4.61/1.69 % (2375590)Termination phase: shuffling
% 4.61/1.69 % (2375590)Time elapsed: 0.002 s
% 4.61/1.69 % (2375590)Peak memory usage: 85 MB
% 4.61/1.69 % (2375590)Instructions burned: 2 (million)
% 4.61/1.69 % (2375599)dis+10_1_si=on:random_seed=1992253373:i=10:ep=R:rtra=on_2995 on theBenchmark for (2995ds/10Mi)
% 4.61/1.69 % (2375599)Instruction limit reached!
% 4.61/1.69 % (2375599)------------------------------
% 4.61/1.69 % (2375599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.69 % (2375599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.69 % (2375599)CaDiCaL version: 2.1.3
% 4.61/1.69 % (2375599)Termination reason: Instruction limit
% 4.61/1.69 % (2375599)Termination phase: Property scanning
% 4.61/1.69 % (2375599)Time elapsed: 0.004 s
% 4.61/1.69 % (2375599)Peak memory usage: 86 MB
% 4.61/1.69 % (2375599)Instructions burned: 15 (million)
% 4.61/1.69 % (2375595)dis+1002_1_to=lpo:sil=64000:si=on:flr=on:random_seed=3112784315:i=2:doe=on:canc=force:asg=cautious:rtra=on_2995 on theBenchmark for (2995ds/2Mi)
% 4.61/1.69 % (2375585)First to succeed.
% 4.61/1.69 % (2375595)Instruction limit reached!
% 4.61/1.69 % (2375595)------------------------------
% 4.61/1.69 % (2375595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.69 % (2375595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.69 % (2375595)CaDiCaL version: 2.1.3
% 4.61/1.69 % (2375595)Termination reason: Instruction limit
% 4.61/1.69 % (2375595)Termination phase: shuffling
% 4.61/1.69 % (2375595)Time elapsed: 0.002 s
% 4.61/1.69 % (2375595)Peak memory usage: 85 MB
% 4.61/1.69 % (2375595)Instructions burned: 2 (million)
% 4.61/1.69 % (2375585)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2375553"
% 4.61/1.69 % (2375597)lrs+1011_16:1_to=kbo:sil=128000:sas=z3:si=on:sos=theory:erd=off:urr=full:random_seed=3302100811:i=127:doe=on:rtra=on_2995 on theBenchmark for (2995ds/127Mi)
% 4.61/1.69 % (2375600)lrs-1011_64_to=lpo:si=on:sp=unary_first:sos=on:br=off:random_seed=407464940:i=26:canc=cautious:av=off:rtra=on_2995 on theBenchmark for (2995ds/26Mi)
% 4.61/1.69 % (2375600)Instruction limit reached!
% 4.61/1.69 % (2375600)------------------------------
% 4.61/1.69 % (2375600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.69 % (2375600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.69 % (2375600)CaDiCaL version: 2.1.3
% 4.61/1.69 % (2375600)Termination reason: Instruction limit
% 4.61/1.69 % (2375600)Termination phase: Preprocessing 3
% 4.61/1.69 % (2375600)Time elapsed: 0.015 s
% 4.61/1.69 % (2375600)Peak memory usage: 87 MB
% 4.61/1.69 % (2375600)Instructions burned: 26 (million)
% 4.61/1.69 % (2375601)dis+1011_5_anc=all:tgt=full:si=on:sp=const_frequency:spb=non_intro:fd=preordered:sac=on:random_seed=3869506162: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_2995 on theBenchmark for (2995ds/35Mi)
% 4.61/1.69 % (2375601)Instruction limit reached!
% 4.61/1.69 % (2375601)------------------------------
% 4.61/1.69 % (2375601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.69 % (2375601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.69 % (2375601)CaDiCaL version: 2.1.3
% 4.61/1.69 % (2375601)Termination reason: Instruction limit
% 4.61/1.69 % (2375601)Termination phase: Property scanning
% 4.61/1.69 % (2375601)Time elapsed: 0.022 s
% 4.61/1.69 % (2375601)Peak memory usage: 87 MB
% 4.61/1.69 % (2375601)Instructions burned: 37 (million)
% 4.61/1.69 % (2375606)dis+21_1_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=off:s2agt=16:random_seed=2231384741:s2a=on:i=8:kws=inv_precedence:doe=on:rtra=on_2994 on theBenchmark for (2994ds/8Mi)
% 4.61/1.69 % (2375606)Instruction limit reached!
% 4.61/1.69 % (2375606)------------------------------
% 4.61/1.69 % (2375606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.69 % (2375606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.69 % (2375606)CaDiCaL version: 2.1.3
% 4.61/1.69 % (2375606)Termination reason: Instruction limit
% 4.61/1.69 % (2375606)Termination phase: Property scanning
% 4.61/1.69 % (2375606)Time elapsed: 0.003 s
% 4.61/1.69 % (2375606)Peak memory usage: 86 MB
% 4.61/1.69 % (2375606)Instructions burned: 10 (million)
% 4.61/1.69 % (2375603)ott+10_8:1_to=lpo:sil=128000:si=on:fs=off:spb=goal_then_units:uwa=alasca_main:random_seed=2370897140:i=2:fsr=off:rtra=on:inst=on_2994 on theBenchmark for (2994ds/2Mi)
% 4.61/1.69 % (2375603)Instruction limit reached!
% 4.61/1.69 % (2375603)------------------------------
% 4.61/1.69 % (2375603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.69 % (2375603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.69 % (2375603)CaDiCaL version: 2.1.3
% 4.61/1.69 % (2375603)Termination reason: Instruction limit
% 4.61/1.69 % (2375603)Termination phase: shuffling
% 4.61/1.69 % (2375603)Time elapsed: 0.002 s
% 4.61/1.69 % (2375603)Peak memory usage: 85 MB
% 4.61/1.69 % (2375603)Instructions burned: 2 (million)
% 4.61/1.69 % (2375597)Instruction limit reached!
% 4.61/1.69 % (2375597)------------------------------
% 4.61/1.69 % (2375597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.69 % (2375597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.69 % (2375597)CaDiCaL version: 2.1.3
% 4.61/1.69 % (2375597)Termination reason: Instruction limit
% 4.61/1.69 % (2375597)Termination phase: Saturation
% 4.61/1.69 % (2375597)Time elapsed: 0.103 s
% 4.61/1.69 % (2375597)Peak memory usage: 118 MB
% 4.61/1.69 % (2375597)Instructions burned: 129 (million)
% 4.61/1.69 % (2375607)lrs-1011_1_to=kbo:sil=128000:prc=on:si=on:fs=off:tha=off:random_seed=1409403112:i=370:ep=RS:fsr=off:rtra=on_2994 on theBenchmark for (2994ds/370Mi)
% 4.61/1.69 % (2375610)ott+1002_1_to=lpo:thi=overlap:prc=on:bsd=on:si=on:gve=cautious:thigen=on:tha=some:random_seed=3451150951:i=13:av=off:rtra=on:gtg=exists_sym:ev=force_2993 on theBenchmark for (2993ds/13Mi)
% 4.61/1.69 % (2375610)Instruction limit reached!
% 4.61/1.69 % (2375610)------------------------------
% 4.61/1.69 % (2375610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.69 % (2375610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.69 % (2375610)CaDiCaL version: 2.1.3
% 4.61/1.69 % (2375610)Termination reason: Instruction limit
% 4.61/1.69 % (2375610)Termination phase: Property scanning
% 4.61/1.69 % (2375610)Time elapsed: 0.007 s
% 4.61/1.69 % (2375610)Peak memory usage: 85 MB
% 4.61/1.69 % (2375614)lrs+1010_5_to=lpo:sil=128000:si=on:sp=const_frequency:sos=theory:tha=off:random_seed=2206779445:i=10:rtra=on_2993 on theBenchmark for (2993ds/10Mi)
% 4.61/1.69 % (2375610)Instructions burned: 15 (million)
% 4.61/1.69 % (2375614)Instruction limit reached!
% 4.61/1.69 % (2375614)------------------------------
% 4.61/1.69 % (2375614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.69 % (2375614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.69 % (2375614)CaDiCaL version: 2.1.3
% 4.61/1.69 % (2375614)Termination reason: Instruction limit
% 4.61/1.69 % (2375614)Termination phase: Preprocessing 1
% 4.61/1.69 % (2375614)Time elapsed: 0.003 s
% 4.61/1.69 % (2375614)Peak memory usage: 86 MB
% 4.61/1.69 % (2375614)Instructions burned: 10 (million)
% 4.61/1.69 % (2375613)lrs+1002_1_to=lpo:sil=128000:sas=z3:si=on:sos=on:urr=on:tha=off:random_seed=3513844340:i=226:rtra=on:gtg=position:ss=axioms_2993 on theBenchmark for (2993ds/226Mi)
% 4.61/1.69 % (2375616)lrs+1002_1_to=lpo:thi=strong:sas=z3:si=on:sp=const_frequency:tha=off:random_seed=2102736725:i=71:rtra=on:gtg=exists_top_2993 on theBenchmark for (2993ds/71Mi)
% 4.61/1.69 % (2375617)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=2859875252:i=75:doe=on:thsqd=64:canc=force:thsqc=64:rtra=on:thsq=on_2993 on theBenchmark for (2993ds/75Mi)
% 4.61/1.69 % (2375585)Refutation found. Thanks to Tanya!
% 4.61/1.69 % SZS status Theorem for theBenchmark
% 4.61/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 6.26/1.79 % (2375585)------------------------------
% 6.26/1.79 % (2375585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.26/1.79 % (2375585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.79 % (2375585)CaDiCaL version: 2.1.3
% 6.26/1.79 % (2375585)Termination reason: Refutation
% 6.26/1.79 % (2375585)Time elapsed: 0.111 s
% 6.26/1.79 % (2375585)Peak memory usage: 93 MB
% 6.26/1.79 % (2375585)Instructions burned: 152 (million)
% 6.26/1.79 % (2375585)------------------------------
% 6.26/1.79 % (2375585)------------------------------
% 6.26/1.79 % (2375553)Success in time 0.846 s
% 6.26/1.79 % Vampire exiting
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