%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW506_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 01:30:42 PM UTC 2026
% Result : Theorem 4.17s 1.23s
% Output : Refutation 4.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 4 unt; 0 typ; 2 def)
% Number of atoms : 150 ( 14 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 147 ( 56 ~; 65 |; 13 &)
% ( 7 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 3 prp; 0-4 aty)
% Number of functors : 46 ( 46 usr; 6 con; 0-6 aty)
% Number of variables : 109 ( 0 sgn 102 !; 7 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
com: $tType ).
tff(type_def_7,type,
pname: $tType ).
tff(type_def_8,type,
state: $tType ).
tff(type_def_9,type,
bool: $tType ).
tff(type_def_10,type,
hoare_28830079triple: $tType > $tType ).
tff(type_def_11,type,
int: $tType ).
tff(type_def_12,type,
nat: $tType ).
tff(type_def_13,type,
option: $tType > $tType ).
tff(type_def_14,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
body1: pname > option(com) ).
tff(func_def_1,type,
body: pname > com ).
tff(func_def_2,type,
com_size: com > nat ).
tff(func_def_3,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
sgn_sgn:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_5,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_6,type,
hoare_1841697145triple:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(X0,fun(state,bool)) ) > hoare_28830079triple(X0) ) ).
tff(func_def_7,type,
hoare_376461865e_case:
!>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),X1))) * hoare_28830079triple(X0) ) > X1 ) ).
tff(func_def_8,type,
hoare_678420151le_rec:
!>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),X1))) * hoare_28830079triple(X0) ) > X1 ) ).
tff(func_def_9,type,
hoare_47506394e_size:
!>[X0: $tType] : ( ( fun(X0,nat) * hoare_28830079triple(X0) ) > nat ) ).
tff(func_def_10,type,
suc: nat > nat ).
tff(func_def_11,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_12,type,
semiri532925092at_aux:
!>[X0: $tType] : ( ( fun(X0,X0) * nat * X0 ) > X0 ) ).
tff(func_def_13,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_14,type,
the:
!>[X0: $tType] : ( option(X0) > X0 ) ).
tff(func_def_15,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_16,type,
fFalse: bool ).
tff(func_def_17,type,
fTrue: bool ).
tff(func_def_18,type,
p: fun(a,fun(state,bool)) ).
tff(func_def_19,type,
q: fun(a,fun(state,bool)) ).
tff(func_def_20,type,
n: nat ).
tff(func_def_21,type,
pn: pname ).
tff(func_def_22,type,
sK0:
!>[X0: $tType] : ( hoare_28830079triple(X0) > fun(X0,fun(state,bool)) ) ).
tff(func_def_23,type,
sK1:
!>[X0: $tType] : ( hoare_28830079triple(X0) > com ) ).
tff(func_def_24,type,
sK2:
!>[X0: $tType] : ( hoare_28830079triple(X0) > fun(X0,fun(state,bool)) ) ).
tff(func_def_25,type,
sK3: ( state * nat * state * pname ) > nat ).
tff(func_def_26,type,
sK4: ( state * state * com ) > nat ).
tff(func_def_27,type,
sK5:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(X0,fun(state,bool)) * nat ) > X0 ) ).
tff(func_def_28,type,
sK6:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(X0,fun(state,bool)) * nat ) > state ) ).
tff(func_def_29,type,
sK7:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(X0,fun(state,bool)) * nat ) > state ) ).
tff(func_def_30,type,
sK8: ( state * state * com ) > nat ).
tff(func_def_31,type,
sK9: nat > nat ).
tff(func_def_32,type,
sK10: fun(nat,bool) > nat ).
tff(func_def_33,type,
sK11: fun(nat,bool) > nat ).
tff(func_def_34,type,
sK12: nat > nat ).
tff(func_def_35,type,
sK13: ( state * state * com * state * state * com ) > nat ).
tff(func_def_36,type,
sK14: nat > nat ).
tff(func_def_37,type,
sK15: ( nat * nat ) > nat ).
tff(func_def_38,type,
sK16: nat > nat ).
tff(func_def_39,type,
sK17:
!>[X0: $tType] : ( fun(nat,X0) > nat ) ).
tff(func_def_40,type,
sK18:
!>[X0: $tType] : ( fun(nat,X0) > nat ) ).
tff(func_def_41,type,
sK19: ( nat * nat ) > nat ).
tff(func_def_42,type,
sK20: ( nat * nat ) > nat ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
sgn_if:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
hoare_1633586161_valid:
!>[X0: $tType] : ( ( nat * hoare_28830079triple(X0) ) > $o ) ).
tff(pred_def_11,type,
evalc: ( com * state * state ) > $o ).
tff(pred_def_12,type,
evaln: ( com * state * nat * state ) > $o ).
tff(pred_def_13,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(f3,axiom,
! [X0: nat,X1: nat] :
( ( suc(X1) = suc(X0) )
<=> ( X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_nat_Oinject) ).
tff(f7,axiom,
! [X0: state,X1: nat,X2: state,X3: pname] :
( evaln(the(com,body1(X3)),X2,X1,X0)
=> evaln(body(X3),X2,suc(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_evaln_OBody) ).
tff(f11,axiom,
! [X0: state,X1: nat,X2: state,X3: pname] :
( evaln(body(X3),X2,X1,X0)
=> ~ ! [X4: nat] :
( ( X1 = suc(X4) )
=> ~ evaln(the(com,body1(X3)),X2,X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_evaln__elim__cases_I6_J) ).
tff(f23,axiom,
! [X0: $tType,X1: fun(X0,fun(state,bool)),X2: com,X3: fun(X0,fun(state,bool)),X4: nat] :
( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
<=> ! [X5: X0,X6: state] :
( pp(aa(state,bool,aa(X0,fun(state,bool),X3,X5),X6))
=> ! [X7: state] :
( evaln(X2,X6,X4,X7)
=> pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_triple__valid__def2) ).
tff(f118,conjecture,
( hoare_1633586161_valid(a,n,hoare_1841697145triple(a,p,the(com,body1(pn)),q))
<=> hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,p,body(pn),q)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f119,negated_conjecture,
~ ( hoare_1633586161_valid(a,n,hoare_1841697145triple(a,p,the(com,body1(pn)),q))
<=> hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,p,body(pn),q)) ),
inference(negated_conjecture,[status(cth)],[f118]) ).
tff(f122,plain,
! [X0: state,X1: nat,X2: state,X3: pname] :
( evaln(body(X3),X2,suc(X1),X0)
| ~ evaln(the(com,body1(X3)),X2,X1,X0) ),
inference(ennf_transformation,[],[f7]) ).
tff(f125,plain,
! [X0: state,X1: nat,X2: state,X3: pname] :
( ? [X4: nat] :
( evaln(the(com,body1(X3)),X2,X4,X0)
& ( X1 = suc(X4) ) )
| ~ evaln(body(X3),X2,X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
tff(f130,plain,
! [X0: $tType,X1: fun(X0,fun(state,bool)),X2: com,X3: fun(X0,fun(state,bool)),X4: nat] :
( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
<=> ! [X5: X0,X6: state] :
( ! [X7: state] :
( pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X7))
| ~ evaln(X2,X6,X4,X7) )
| ~ pp(aa(state,bool,aa(X0,fun(state,bool),X3,X5),X6)) ) ),
inference(ennf_transformation,[],[f23]) ).
tff(f195,plain,
( hoare_1633586161_valid(a,n,hoare_1841697145triple(a,p,the(com,body1(pn)),q))
<~> hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,p,body(pn),q)) ),
inference(ennf_transformation,[],[f119]) ).
tff(f199,plain,
! [X0: nat,X1: nat] :
( ( ( suc(X1) = suc(X0) )
| ( X0 != X1 ) )
& ( ( X1 = X0 )
| ( suc(X1) != suc(X0) ) ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f201,plain,
! [X0: state,X1: nat,X2: state,X3: pname] :
( ( evaln(the(com,body1(X3)),X2,sK3(X0,X1,X2,X3),X0)
& ( suc(sK3(X0,X1,X2,X3)) = X1 ) )
| ~ evaln(body(X3),X2,X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X1,X2,X3))],[f125]) ).
tff(f205,plain,
! [X0: $tType,X1: fun(X0,fun(state,bool)),X2: com,X3: fun(X0,fun(state,bool)),X4: nat] :
( ( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
| ? [X5: X0,X6: state] :
( ? [X7: state] :
( ~ pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X7))
& evaln(X2,X6,X4,X7) )
& pp(aa(state,bool,aa(X0,fun(state,bool),X3,X5),X6)) ) )
& ( ! [X5: X0,X6: state] :
( ! [X7: state] :
( pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X7))
| ~ evaln(X2,X6,X4,X7) )
| ~ pp(aa(state,bool,aa(X0,fun(state,bool),X3,X5),X6)) )
| ~ hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1)) ) ),
inference(nnf_transformation,[],[f130]) ).
tff(f206,plain,
! [X0: $tType,X1: fun(X0,fun(state,bool)),X2: com,X3: fun(X0,fun(state,bool)),X4: nat] :
( ( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
| ? [X5: X0,X6: state] :
( ? [X7: state] :
( ~ pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X7))
& evaln(X2,X6,X4,X7) )
& pp(aa(state,bool,aa(X0,fun(state,bool),X3,X5),X6)) ) )
& ( ! [X8: X0,X9: state] :
( ! [X10: state] :
( pp(aa(state,bool,aa(X0,fun(state,bool),X1,X8),X10))
| ~ evaln(X2,X9,X4,X10) )
| ~ pp(aa(state,bool,aa(X0,fun(state,bool),X3,X8),X9)) )
| ~ hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1)) ) ),
inference(rectify,[],[f205]) ).
tff(f207,plain,
! [X0: $tType,X1: fun(X0,fun(state,bool)),X2: com,X3: fun(X0,fun(state,bool)),X4: nat] :
( ( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
| ( ~ pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK5(X0,X1,X2,X3,X4)),sK7(X0,X1,X2,X3,X4)))
& evaln(X2,sK6(X0,X1,X2,X3,X4),X4,sK7(X0,X1,X2,X3,X4))
& pp(aa(state,bool,aa(X0,fun(state,bool),X3,sK5(X0,X1,X2,X3,X4)),sK6(X0,X1,X2,X3,X4))) ) )
& ( ! [X8: X0,X9: state] :
( ! [X10: state] :
( pp(aa(state,bool,aa(X0,fun(state,bool),X1,X8),X10))
| ~ evaln(X2,X9,X4,X10) )
| ~ pp(aa(state,bool,aa(X0,fun(state,bool),X3,X8),X9)) )
| ~ hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X5,sK5(X0,X1,X2,X3,X4)),skolemize(X6,sK6(X0,X1,X2,X3,X4)),skolemize(X7,sK7(X0,X1,X2,X3,X4))],[f206]) ).
tff(f246,plain,
( ( ~ hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,p,body(pn),q))
| ~ hoare_1633586161_valid(a,n,hoare_1841697145triple(a,p,the(com,body1(pn)),q)) )
& ( hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,p,body(pn),q))
| hoare_1633586161_valid(a,n,hoare_1841697145triple(a,p,the(com,body1(pn)),q)) ) ),
inference(nnf_transformation,[],[f195]) ).
tff(f253,plain,
! [X0: nat,X1: nat] :
( ( suc(X1) != suc(X0) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f199]) ).
tff(f258,plain,
! [X2: state,X3: pname,X0: state,X1: nat] :
( ~ evaln(the(com,body1(X3)),X2,X1,X0)
| evaln(body(X3),X2,suc(X1),X0) ),
inference(cnf_transformation,[],[f122]) ).
tff(f262,plain,
! [X2: state,X3: pname,X0: state,X1: nat] :
( ~ evaln(body(X3),X2,X1,X0)
| ( suc(sK3(X0,X1,X2,X3)) = X1 ) ),
inference(cnf_transformation,[],[f201]) ).
tff(f263,plain,
! [X2: state,X3: pname,X0: state,X1: nat] :
( evaln(the(com,body1(X3)),X2,sK3(X0,X1,X2,X3),X0)
| ~ evaln(body(X3),X2,X1,X0) ),
inference(cnf_transformation,[],[f201]) ).
tff(f276,plain,
! [X0: $tType,X2: com,X3: fun(X0,fun(state,bool)),X10: state,X1: fun(X0,fun(state,bool)),X8: X0,X9: state,X4: nat] :
( ~ pp(aa(state,bool,aa(X0,fun(state,bool),X3,X8),X9))
| ~ evaln(X2,X9,X4,X10)
| pp(aa(state,bool,aa(X0,fun(state,bool),X1,X8),X10))
| ~ hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1)) ),
inference(cnf_transformation,[],[f207]) ).
tff(f277,plain,
! [X0: $tType,X2: com,X3: fun(X0,fun(state,bool)),X1: fun(X0,fun(state,bool)),X4: nat] :
( pp(aa(state,bool,aa(X0,fun(state,bool),X3,sK5(X0,X1,X2,X3,X4)),sK6(X0,X1,X2,X3,X4)))
| hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1)) ),
inference(cnf_transformation,[],[f207]) ).
tff(f278,plain,
! [X0: $tType,X2: com,X3: fun(X0,fun(state,bool)),X1: fun(X0,fun(state,bool)),X4: nat] :
( evaln(X2,sK6(X0,X1,X2,X3,X4),X4,sK7(X0,X1,X2,X3,X4))
| hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1)) ),
inference(cnf_transformation,[],[f207]) ).
tff(f279,plain,
! [X0: $tType,X2: com,X3: fun(X0,fun(state,bool)),X1: fun(X0,fun(state,bool)),X4: nat] :
( ~ pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK5(X0,X1,X2,X3,X4)),sK7(X0,X1,X2,X3,X4)))
| hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1)) ),
inference(cnf_transformation,[],[f207]) ).
tff(f410,plain,
( hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,p,body(pn),q))
| hoare_1633586161_valid(a,n,hoare_1841697145triple(a,p,the(com,body1(pn)),q)) ),
inference(cnf_transformation,[],[f246]) ).
tff(f411,plain,
( ~ hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,p,body(pn),q))
| ~ hoare_1633586161_valid(a,n,hoare_1841697145triple(a,p,the(com,body1(pn)),q)) ),
inference(cnf_transformation,[],[f246]) ).
tff(f417,definition,
( spl21_1
<=> hoare_1633586161_valid(a,n,hoare_1841697145triple(a,p,the(com,body1(pn)),q)) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
tff(f418,plain,
( ~ hoare_1633586161_valid(a,n,hoare_1841697145triple(a,p,the(com,body1(pn)),q))
| spl21_1 ),
inference(avatar_component_clause,[],[f417]) ).
tff(f419,plain,
( hoare_1633586161_valid(a,n,hoare_1841697145triple(a,p,the(com,body1(pn)),q))
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f417]) ).
tff(f421,definition,
( spl21_2
<=> hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,p,body(pn),q)) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
tff(f422,plain,
( ~ hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,p,body(pn),q))
| spl21_2 ),
inference(avatar_component_clause,[],[f421]) ).
tff(f423,plain,
( hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,p,body(pn),q))
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f421]) ).
tff(f424,plain,
( spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f410,f421,f417]) ).
tff(f425,plain,
( ~ spl21_1
| ~ spl21_2 ),
inference(avatar_split_clause,[],[f411,f421,f417]) ).
tff(f547,plain,
( evaln(the(com,body1(pn)),sK6(a,q,the(com,body1(pn)),p,n),n,sK7(a,q,the(com,body1(pn)),p,n))
| spl21_1 ),
inference(unit_resulting_resolution,[],[f278,f418]) ).
tff(f549,plain,
( evaln(body(pn),sK6(a,q,the(com,body1(pn)),p,n),suc(n),sK7(a,q,the(com,body1(pn)),p,n))
| spl21_1 ),
inference(unit_resulting_resolution,[],[f258,f547]) ).
tff(f550,plain,
( pp(aa(state,bool,aa(a,fun(state,bool),p,sK5(a,q,the(com,body1(pn)),p,n)),sK6(a,q,the(com,body1(pn)),p,n)))
| spl21_1 ),
inference(unit_resulting_resolution,[],[f277,f418]) ).
tff(f551,plain,
( ~ pp(aa(state,bool,aa(a,fun(state,bool),q,sK5(a,q,the(com,body1(pn)),p,n)),sK7(a,q,the(com,body1(pn)),p,n)))
| spl21_1 ),
inference(unit_resulting_resolution,[],[f279,f418]) ).
tff(f722,plain,
( ~ hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,p,body(pn),q))
| spl21_1 ),
inference(unit_resulting_resolution,[],[f276,f551,f550,f549]) ).
tff(f729,plain,
( $false
| spl21_1
| ~ spl21_2 ),
inference(forward_subsumption_resolution,[],[f722,f423]) ).
tff(f730,plain,
( spl21_1
| ~ spl21_2 ),
inference(avatar_contradiction_clause,[],[f729]) ).
tff(f731,plain,
( ~ pp(aa(state,bool,aa(a,fun(state,bool),q,sK5(a,q,body(pn),p,suc(n))),sK7(a,q,body(pn),p,suc(n))))
| spl21_2 ),
inference(unit_resulting_resolution,[],[f279,f422]) ).
tff(f732,plain,
( pp(aa(state,bool,aa(a,fun(state,bool),p,sK5(a,q,body(pn),p,suc(n))),sK6(a,q,body(pn),p,suc(n))))
| spl21_2 ),
inference(unit_resulting_resolution,[],[f277,f422]) ).
tff(f733,plain,
( evaln(body(pn),sK6(a,q,body(pn),p,suc(n)),suc(n),sK7(a,q,body(pn),p,suc(n)))
| spl21_2 ),
inference(unit_resulting_resolution,[],[f278,f422]) ).
tff(f735,plain,
( ( suc(n) = suc(sK3(sK7(a,q,body(pn),p,suc(n)),suc(n),sK6(a,q,body(pn),p,suc(n)),pn)) )
| spl21_2 ),
inference(unit_resulting_resolution,[],[f262,f733]) ).
tff(f737,plain,
( ~ evaln(the(com,body1(pn)),sK6(a,q,body(pn),p,suc(n)),n,sK7(a,q,body(pn),p,suc(n)))
| ~ spl21_1
| spl21_2 ),
inference(unit_resulting_resolution,[],[f276,f419,f731,f732]) ).
tff(f789,plain,
( ( n = sK3(sK7(a,q,body(pn),p,suc(n)),suc(n),sK6(a,q,body(pn),p,suc(n)),pn) )
| spl21_2 ),
inference(unit_resulting_resolution,[],[f253,f735]) ).
tff(f845,plain,
( evaln(the(com,body1(pn)),sK6(a,q,body(pn),p,suc(n)),n,sK7(a,q,body(pn),p,suc(n)))
| ~ evaln(body(pn),sK6(a,q,body(pn),p,suc(n)),suc(n),sK7(a,q,body(pn),p,suc(n)))
| spl21_2 ),
inference(superposition,[],[f263,f789]) ).
tff(f846,plain,
( ~ evaln(body(pn),sK6(a,q,body(pn),p,suc(n)),suc(n),sK7(a,q,body(pn),p,suc(n)))
| ~ spl21_1
| spl21_2 ),
inference(forward_subsumption_resolution,[],[f845,f737]) ).
tff(f849,plain,
( $false
| ~ spl21_1
| spl21_2 ),
inference(forward_subsumption_resolution,[],[f846,f733]) ).
tff(f850,plain,
( ~ spl21_1
| spl21_2 ),
inference(avatar_contradiction_clause,[],[f849]) ).
cnf(s1,plain,
( spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f424]) ).
cnf(s2,plain,
( ~ spl21_1
| ~ spl21_2 ),
inference(sat_conversion,[],[f425]) ).
cnf(s6,plain,
( spl21_1
| ~ spl21_2 ),
inference(sat_conversion,[],[f730]) ).
cnf(s8,plain,
( ~ spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f850]) ).
cnf(s9,plain,
spl21_1,
inference(rat,[],[s1,s6]) ).
cnf(s10,plain,
spl21_2,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s10,s9]) ).
tff(f851,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW506_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 14:15:25 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.17/1.23 % (3991470)Detected formulas, will run a generic FOF schedule.
% 4.17/1.23 % (3991478)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1518537181:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.17/1.23 % (3991478)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.17/1.23 % (3991478)Refutation not found, incomplete strategy
% 4.17/1.23 % (3991478)------------------------------
% 4.17/1.23 % (3991478)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.23 % (3991478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.23 % (3991478)CaDiCaL version: 2.1.3
% 4.17/1.23 % (3991478)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.23 % (3991478)Time elapsed: 0.002 s
% 4.17/1.23 % (3991478)Peak memory usage: 88 MB
% 4.17/1.23 % (3991478)Instructions burned: 5 (million)
% 4.17/1.23 % (3991481)dis-21_1_sil=8000:lcm=predicate:random_seed=3712036351:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.17/1.23 % (3991475)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=991784424:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.17/1.23 % (3991480)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1344121079:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.17/1.23 % (3991479)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=619527440:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.17/1.23 % (3991477)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3687985599:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.17/1.23 % (3991476)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3820043325:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.17/1.23 % (3991477)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.17/1.23 % (3991479)Instruction limit reached!
% 4.17/1.23 % (3991479)------------------------------
% 4.17/1.23 % (3991479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.23 % (3991479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.23 % (3991479)CaDiCaL version: 2.1.3
% 4.17/1.23 % (3991479)Termination reason: Instruction limit
% 4.17/1.23 % (3991479)Termination phase: Saturation
% 4.17/1.23 % (3991479)Time elapsed: 0.070 s
% 4.17/1.23 % (3991479)Peak memory usage: 88 MB
% 4.17/1.23 % (3991479)Instructions burned: 120 (million)
% 4.17/1.23 % (3991481)Instruction limit reached!
% 4.17/1.23 % (3991481)------------------------------
% 4.17/1.23 % (3991481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.23 % (3991481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.23 % (3991481)CaDiCaL version: 2.1.3
% 4.17/1.23 % (3991481)Termination reason: Instruction limit
% 4.17/1.23 % (3991481)Termination phase: Saturation
% 4.17/1.23 % (3991481)Time elapsed: 0.073 s
% 4.17/1.23 % (3991481)Peak memory usage: 89 MB
% 4.17/1.23 % (3991481)Instructions burned: 131 (million)
% 4.17/1.23 % (3991480)Instruction limit reached!
% 4.17/1.23 % (3991480)------------------------------
% 4.17/1.23 % (3991480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.23 % (3991480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.23 % (3991480)CaDiCaL version: 2.1.3
% 4.17/1.23 % (3991480)Termination reason: Instruction limit
% 4.17/1.23 % (3991480)Termination phase: Saturation
% 4.17/1.23 % (3991480)Time elapsed: 0.085 s
% 4.17/1.23 % (3991480)Peak memory usage: 89 MB
% 4.17/1.23 % (3991480)Instructions burned: 139 (million)
% 4.17/1.23 % (3991478)------------------------------
% 4.17/1.23 % (3991478)------------------------------
% 4.17/1.23 % (3991490)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4073307727:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.17/1.23 % (3991489)lrs+10_1_sil=8000:sp=occurrence:random_seed=2937694378:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.17/1.23 % (3991492)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3891044142:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.17/1.23 % (3991491)lrs+1011_1_sil=32000:sp=occurrence:random_seed=143371239:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.17/1.23 % (3991492)First to succeed.
% 4.17/1.23 % (3991492)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3991470"
% 4.17/1.23 % (3991490)Also succeeded, but the first one will report.
% 4.17/1.23 % Exception at run slice level% Exception at run slice level
% 4.17/1.23
% 4.17/1.23 User error: User error: GNN currently only supports monomorphic FOL.GNN currently only supports monomorphic FOL.
% 4.17/1.23
% 4.17/1.23 % Exception at run slice level
% 4.17/1.23 User error: GNN currently only supports monomorphic FOL.
% 4.17/1.23 % (3991489)Instruction limit reached!
% 4.17/1.23 % (3991489)------------------------------
% 4.17/1.23 % (3991489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.23 % (3991489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.23 % (3991489)CaDiCaL version: 2.1.3
% 4.17/1.23 % (3991489)Termination reason: Instruction limit
% 4.17/1.23 % (3991489)Termination phase: Saturation
% 4.17/1.23 % (3991489)Time elapsed: 0.170 s
% 4.17/1.23 % (3991489)Peak memory usage: 90 MB
% 4.17/1.23 % (3991489)Instructions burned: 285 (million)
% 4.17/1.23 % (3991492)Refutation found. Thanks to Tanya!
% 4.17/1.23 % SZS status Theorem for theBenchmark
% 4.17/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 4.60/1.42 % (3991492)------------------------------
% 4.60/1.42 % (3991492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.42 % (3991492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.42 % (3991492)CaDiCaL version: 2.1.3
% 4.60/1.42 % (3991492)Termination reason: Refutation
% 4.60/1.42 % (3991492)Time elapsed: 0.014 s
% 4.60/1.42 % (3991492)Peak memory usage: 90 MB
% 4.60/1.42 % (3991492)Instructions burned: 40 (million)
% 4.60/1.42 % (3991492)------------------------------
% 4.60/1.42 % (3991492)------------------------------
% 4.60/1.42 % (3991470)Success in time 0.564 s
% 4.60/1.42 % Vampire exiting
%------------------------------------------------------------------------------