%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW515_5 : TPTP v9.3.1. Released v6.0.0.
% 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 01:30:43 PM UTC 2026
% Result : Theorem 4.39s 1.34s
% Output : Refutation 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 21 ~; 15 |; 1 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-4 aty)
% Number of functors : 45 ( 45 usr; 15 con; 0-5 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
b: $tType ).
tff(type_def_7,type,
com: $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,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,X1) > fun(fun(X2,X0),fun(X2,X1)) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_4,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).
tff(func_def_5,type,
skip: com ).
tff(func_def_6,type,
semi: ( com * com ) > com ).
tff(func_def_7,type,
while: ( fun(state,bool) * com ) > com ).
tff(func_def_8,type,
the:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_9,type,
hoare_1841697145triple:
!>[X0: $tType] : fun(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),hoare_28830079triple(X0)))) ).
tff(func_def_10,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_11,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_12,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_13,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_14,type,
image:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fun(X0,bool) ) > fun(X1,bool) ) ).
tff(func_def_15,type,
insert:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),fun(X0,bool))) ).
tff(func_def_16,type,
the_elem:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_17,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_18,type,
fFalse: bool ).
tff(func_def_19,type,
fNot: fun(bool,bool) ).
tff(func_def_20,type,
fTrue: bool ).
tff(func_def_21,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_22,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(func_def_23,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_24,type,
fimplies: fun(bool,fun(bool,bool)) ).
tff(func_def_25,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_26,type,
f: fun(a,bool) ).
tff(func_def_27,type,
g: fun(hoare_28830079triple(b),bool) ).
tff(func_def_28,type,
p: fun(a,fun(b,fun(state,bool))) ).
tff(func_def_29,type,
p1: fun(a,fun(b,fun(state,bool))) ).
tff(func_def_30,type,
q: fun(a,fun(b,fun(state,bool))) ).
tff(func_def_31,type,
q1: fun(a,fun(b,fun(state,bool))) ).
tff(func_def_32,type,
c0: fun(a,com) ).
tff(func_def_33,type,
x: a ).
tff(func_def_34,type,
sK0:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > X0 ) ).
tff(func_def_35,type,
sK1:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_36,type,
sK2:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_37,type,
sK3:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > X0 ) ).
tff(func_def_38,type,
sK4:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_39,type,
sK5:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > X0 ) ).
tff(func_def_40,type,
sK6:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_41,type,
sK7:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,bool) * fun(X1,X0) * X0 ) > X1 ) ).
tff(func_def_42,type,
sK8:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,bool) * fun(X1,X0) * X0 ) > X1 ) ).
tff(pred_def_1,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
finite_finite1:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
finite_finite:
!>[X0: $tType] : ( fun(X0,bool) > $o ) ).
tff(pred_def_4,type,
finite_fold1Set:
!>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * fun(X0,bool) * X0 ) > $o ) ).
tff(pred_def_5,type,
finite_folding_one:
!>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * fun(fun(X0,bool),X0) ) > $o ) ).
tff(pred_def_6,type,
finite2073411215e_idem:
!>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * fun(fun(X0,bool),X0) ) > $o ) ).
tff(pred_def_7,type,
hoare_992312373derivs:
!>[X0: $tType] : ( ( fun(hoare_28830079triple(X0),bool) * fun(hoare_28830079triple(X0),bool) ) > $o ) ).
tff(pred_def_8,type,
pp: bool > $o ).
tff(f4,axiom,
! [X0: $tType,X1: fun(hoare_28830079triple(X0),bool),X2: hoare_28830079triple(X0),X3: fun(hoare_28830079triple(X0),bool)] :
( hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),bot_bot(fun(hoare_28830079triple(X0),bool))))
=> ( hoare_992312373derivs(X0,X3,X1)
=> hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert) ).
tff(f127,axiom,
! [X0: a] :
( hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p1,X0)),aa(a,com,c0,X0)),aa(a,fun(b,fun(state,bool)),q1,X0))),bot_bot(fun(hoare_28830079triple(b),bool))))
=> hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p,X0)),aa(a,com,c0,X0)),aa(a,fun(b,fun(state,bool)),q,X0))),bot_bot(fun(hoare_28830079triple(b),bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f130,axiom,
( hoare_992312373derivs(b,g,image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p1)),c0)),q1),f))
=> hoare_992312373derivs(b,g,image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p)),c0)),q),f)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
tff(f131,axiom,
( hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p1,x)),aa(a,com,c0,x)),aa(a,fun(b,fun(state,bool)),q1,x))),bot_bot(fun(hoare_28830079triple(b),bool))))
& hoare_992312373derivs(b,g,image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p1)),c0)),q1),f)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
tff(f132,conjecture,
hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p,x)),aa(a,com,c0,x)),aa(a,fun(b,fun(state,bool)),q,x))),image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p)),c0)),q),f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
tff(f133,negated_conjecture,
~ hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p,x)),aa(a,com,c0,x)),aa(a,fun(b,fun(state,bool)),q,x))),image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p)),c0)),q),f))),
inference(negated_conjecture,[status(cth)],[f132]) ).
tff(f134,plain,
~ hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p,x)),aa(a,com,c0,x)),aa(a,fun(b,fun(state,bool)),q,x))),image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p)),c0)),q),f))),
inference(flattening,[],[f133]) ).
tff(f137,plain,
( hoare_992312373derivs(b,g,image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p)),c0)),q),f))
| ~ hoare_992312373derivs(b,g,image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p1)),c0)),q1),f)) ),
inference(ennf_transformation,[],[f130]) ).
tff(f138,plain,
! [X0: a] :
( hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p,X0)),aa(a,com,c0,X0)),aa(a,fun(b,fun(state,bool)),q,X0))),bot_bot(fun(hoare_28830079triple(b),bool))))
| ~ hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p1,X0)),aa(a,com,c0,X0)),aa(a,fun(b,fun(state,bool)),q1,X0))),bot_bot(fun(hoare_28830079triple(b),bool)))) ),
inference(ennf_transformation,[],[f127]) ).
tff(f140,plain,
! [X0: $tType,X1: fun(hoare_28830079triple(X0),bool),X2: hoare_28830079triple(X0),X3: fun(hoare_28830079triple(X0),bool)] :
( hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),X1))
| ~ hoare_992312373derivs(X0,X3,X1)
| ~ hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),bot_bot(fun(hoare_28830079triple(X0),bool)))) ),
inference(ennf_transformation,[],[f4]) ).
tff(f141,plain,
! [X0: $tType,X1: fun(hoare_28830079triple(X0),bool),X2: hoare_28830079triple(X0),X3: fun(hoare_28830079triple(X0),bool)] :
( hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),X1))
| ~ hoare_992312373derivs(X0,X3,X1)
| ~ hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),bot_bot(fun(hoare_28830079triple(X0),bool)))) ),
inference(flattening,[],[f140]) ).
tff(f173,plain,
~ hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p,x)),aa(a,com,c0,x)),aa(a,fun(b,fun(state,bool)),q,x))),image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p)),c0)),q),f))),
inference(cnf_transformation,[],[f134]) ).
tff(f177,plain,
hoare_992312373derivs(b,g,image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p1)),c0)),q1),f)),
inference(cnf_transformation,[],[f131]) ).
tff(f178,plain,
hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p1,x)),aa(a,com,c0,x)),aa(a,fun(b,fun(state,bool)),q1,x))),bot_bot(fun(hoare_28830079triple(b),bool)))),
inference(cnf_transformation,[],[f131]) ).
tff(f179,plain,
( hoare_992312373derivs(b,g,image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p)),c0)),q),f))
| ~ hoare_992312373derivs(b,g,image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p1)),c0)),q1),f)) ),
inference(cnf_transformation,[],[f137]) ).
tff(f181,plain,
! [X0: a] :
( ~ hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p1,X0)),aa(a,com,c0,X0)),aa(a,fun(b,fun(state,bool)),q1,X0))),bot_bot(fun(hoare_28830079triple(b),bool))))
| hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p,X0)),aa(a,com,c0,X0)),aa(a,fun(b,fun(state,bool)),q,X0))),bot_bot(fun(hoare_28830079triple(b),bool)))) ),
inference(cnf_transformation,[],[f138]) ).
tff(f184,plain,
! [X0: $tType,X2: hoare_28830079triple(X0),X3: fun(hoare_28830079triple(X0),bool),X1: fun(hoare_28830079triple(X0),bool)] :
( ~ hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),bot_bot(fun(hoare_28830079triple(X0),bool))))
| ~ hoare_992312373derivs(X0,X3,X1)
| hoare_992312373derivs(X0,X3,aa(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool),aa(hoare_28830079triple(X0),fun(fun(hoare_28830079triple(X0),bool),fun(hoare_28830079triple(X0),bool)),insert(hoare_28830079triple(X0)),X2),X1)) ),
inference(cnf_transformation,[],[f141]) ).
tff(f241,definition,
( spl9_1
<=> hoare_992312373derivs(b,g,image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p1)),c0)),q1),f)) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
tff(f245,definition,
( spl9_2
<=> hoare_992312373derivs(b,g,image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p)),c0)),q),f)) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
tff(f247,plain,
( hoare_992312373derivs(b,g,image(a,hoare_28830079triple(b),aa(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b)),aa(fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),fun(fun(a,fun(b,fun(state,bool))),fun(a,hoare_28830079triple(b))),combs(a,fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),fun(fun(a,com),fun(a,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combs(a,com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),aa(fun(a,fun(b,fun(state,bool))),fun(a,fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)))),combb(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),a,hoare_1841697145triple(b)),p)),c0)),q),f))
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f245]) ).
tff(f248,plain,
( ~ spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f179,f245,f241]) ).
tff(f249,plain,
spl9_1,
inference(avatar_split_clause,[],[f177,f241]) ).
tff(f640,plain,
( ~ hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p,x)),aa(a,com,c0,x)),aa(a,fun(b,fun(state,bool)),q,x))),bot_bot(fun(hoare_28830079triple(b),bool))))
| ~ spl9_2 ),
inference(unit_resulting_resolution,[],[f184,f173,f247]) ).
tff(f734,plain,
hoare_992312373derivs(b,g,aa(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool),aa(hoare_28830079triple(b),fun(fun(hoare_28830079triple(b),bool),fun(hoare_28830079triple(b),bool)),insert(hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),hoare_28830079triple(b),aa(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b)),aa(fun(b,fun(state,bool)),fun(com,fun(fun(b,fun(state,bool)),hoare_28830079triple(b))),hoare_1841697145triple(b),aa(a,fun(b,fun(state,bool)),p,x)),aa(a,com,c0,x)),aa(a,fun(b,fun(state,bool)),q,x))),bot_bot(fun(hoare_28830079triple(b),bool)))),
inference(unit_resulting_resolution,[],[f181,f178]) ).
tff(f741,plain,
( $false
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f734,f640]) ).
tff(f742,plain,
~ spl9_2,
inference(avatar_contradiction_clause,[],[f741]) ).
cnf(s1,plain,
( ~ spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f248]) ).
cnf(s2,plain,
spl9_1,
inference(sat_conversion,[],[f249]) ).
cnf(s6,plain,
~ spl9_2,
inference(sat_conversion,[],[f742]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s2]) ).
tff(f743,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW515_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 14:17:00 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 4.39/1.34 % (807867)Detected formulas, will run a generic FOF schedule.
% 4.39/1.34 % (807878)dis-21_1_sil=8000:lcm=predicate:random_seed=2095755123: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)
% 4.39/1.34 % (807878)Instruction limit reached!
% 4.39/1.34 % (807878)------------------------------
% 4.39/1.34 % (807878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.34 % (807878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.34 % (807878)CaDiCaL version: 2.1.3
% 4.39/1.34 % (807878)Termination reason: Instruction limit
% 4.39/1.34 % (807878)Termination phase: Saturation
% 4.39/1.34 % (807878)Time elapsed: 0.028 s
% 4.39/1.34 % (807878)Peak memory usage: 88 MB
% 4.39/1.34 % (807878)Instructions burned: 131 (million)
% 4.39/1.34 % (807876)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=954485144:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.39/1.34 % (807877)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2835239204:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.39/1.34 % (807874)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=1578299652:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.39/1.34 % (807872)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=858231712:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.39/1.34 % (807875)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3503892970:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.39/1.34 % (807873)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=2779895713:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.39/1.34 % (807875)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.39/1.34 % (807874)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.39/1.34 % (807876)Instruction limit reached!
% 4.39/1.34 % (807876)------------------------------
% 4.39/1.34 % (807876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.34 % (807876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.34 % (807876)CaDiCaL version: 2.1.3
% 4.39/1.34 % (807876)Termination reason: Instruction limit
% 4.39/1.34 % (807876)Termination phase: Saturation
% 4.39/1.34 % (807876)Time elapsed: 0.059 s
% 4.39/1.34 % (807876)Peak memory usage: 88 MB
% 4.39/1.34 % (807876)Instructions burned: 119 (million)
% 4.39/1.34 % (807875)Instruction limit reached!
% 4.39/1.34 % (807875)------------------------------
% 4.39/1.34 % (807875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.34 % (807875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.34 % (807875)CaDiCaL version: 2.1.3
% 4.39/1.34 % (807875)Termination reason: Instruction limit
% 4.39/1.34 % (807875)Termination phase: Saturation
% 4.39/1.34 % (807875)Time elapsed: 0.059 s
% 4.39/1.34 % (807875)Peak memory usage: 89 MB
% 4.39/1.34 % (807875)Instructions burned: 110 (million)
% 4.39/1.34 % (807877)Instruction limit reached!
% 4.39/1.34 % (807877)------------------------------
% 4.39/1.34 % (807877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.34 % (807877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.34 % (807877)CaDiCaL version: 2.1.3
% 4.39/1.34 % (807877)Termination reason: Instruction limit
% 4.39/1.34 % (807877)Termination phase: Saturation
% 4.39/1.34 % (807877)Time elapsed: 0.088 s
% 4.39/1.34 % (807877)Peak memory usage: 89 MB
% 4.39/1.34 % (807877)Instructions burned: 141 (million)
% 4.39/1.34 % (807880)lrs+10_1_sil=8000:sp=occurrence:random_seed=1334197917:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.39/1.34 % (807888)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1725717281:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.39/1.34 % (807887)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3623779203:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.39/1.34 % (807880)Instruction limit reached!
% 4.39/1.34 % (807880)------------------------------
% 4.39/1.34 % (807880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.34 % (807880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.34 % (807880)CaDiCaL version: 2.1.3
% 4.39/1.34 % (807880)Termination reason: Instruction limit
% 4.39/1.34 % (807880)Termination phase: Saturation
% 4.39/1.34 % (807880)Time elapsed: 0.093 s
% 4.39/1.34 % (807880)Peak memory usage: 91 MB
% 4.39/1.34 % (807880)Instructions burned: 287 (million)
% 4.39/1.34 % (807890)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=542497862:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.39/1.34 % (807887)First to succeed.
% 4.39/1.34 % (807887)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-807867"
% 4.39/1.34 % (807893)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=849787319:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.39/1.34 % (807890)Also succeeded, but the first one will report.
% 4.39/1.34 % Exception at run slice level
% 4.39/1.34 User error: GNN currently only supports monomorphic FOL.
% 4.39/1.34 % Exception at run slice level
% 4.39/1.34 User error: GNN currently only supports monomorphic FOL.
% 4.39/1.34 % (807893)Instruction limit reached!
% 4.39/1.34 % (807893)------------------------------
% 4.39/1.34 % (807893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.34 % (807893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.34 % (807893)CaDiCaL version: 2.1.3
% 4.39/1.34 % (807893)Termination reason: Instruction limit
% 4.39/1.34 % (807893)Termination phase: Saturation
% 4.39/1.34 % (807893)Time elapsed: 0.087 s
% 4.39/1.34 % (807893)Peak memory usage: 90 MB
% 4.39/1.34 % (807893)Instructions burned: 300 (million)
% 4.39/1.34 % Exception at run slice level
% 4.39/1.34 User error: GNN currently only supports monomorphic FOL.
% 4.39/1.34 % (807888)Instruction limit reached!
% 4.39/1.34 % (807888)------------------------------
% 4.39/1.34 % (807888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.34 % (807888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.34 % (807888)CaDiCaL version: 2.1.3
% 4.39/1.34 % (807888)Termination reason: Instruction limit
% 4.39/1.34 % (807888)Termination phase: Saturation
% 4.39/1.34 % (807888)Time elapsed: 0.201 s
% 4.39/1.34 % (807888)Peak memory usage: 91 MB
% 4.39/1.34 % (807888)Instructions burned: 325 (million)
% 4.39/1.34 % (807897)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3058210038:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.39/1.34 % (807897)Also succeeded, but the first one will report.
% 4.39/1.34 % (807899)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=108806948:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 4.39/1.34 % (807887)Refutation found. Thanks to Tanya!
% 4.39/1.34 % SZS status Theorem for theBenchmark
% 4.39/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 5.29/1.54 % (807887)------------------------------
% 5.29/1.54 % (807887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.29/1.54 % (807887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.29/1.54 % (807887)CaDiCaL version: 2.1.3
% 5.29/1.54 % (807887)Termination reason: Refutation
% 5.29/1.54 % (807887)Time elapsed: 0.069 s
% 5.29/1.54 % (807887)Peak memory usage: 91 MB
% 5.29/1.54 % (807887)Instructions burned: 120 (million)
% 5.29/1.54 % (807887)------------------------------
% 5.29/1.54 % (807887)------------------------------
% 5.29/1.54 % (807867)Success in time 0.673 s
% 5.29/1.54 % Vampire exiting
%------------------------------------------------------------------------------