%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n015.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 01:40:22 PM UTC 2026
% Result : Theorem 4.50s 0.94s
% Output : Refutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 21 ~; 15 |; 1 &)
% ( 0 <=>; 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 : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 64 ( 64 usr; 15 con; 0-5 aty)
% Number of variables : 35 ( 35 !; 0 ?; 35 :)
% 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)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool)) ) > X0 ) ).
tff(func_def_35,type,
sK1:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),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)) ) > X0 ) ).
tff(func_def_37,type,
sK3:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_38,type,
sK4:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > X0 ) ).
tff(func_def_39,type,
sK5:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_40,type,
sK6:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_41,type,
sK7:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_42,type,
sK8:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_43,type,
sK9:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_44,type,
sK10:
!>[X0: $tType] : ( ( fun(X0,bool) * X0 * fun(X0,bool) * X0 ) > fun(X0,bool) ) ).
tff(func_def_45,type,
sK11:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,bool) * fun(X1,X0) * X0 ) > X1 ) ).
tff(func_def_46,type,
sK12:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,bool) * fun(X1,X0) * X0 ) > X1 ) ).
tff(func_def_47,type,
sK13:
!>[X0: $tType] : ( fun(fun(X0,bool),bool) > X0 ) ).
tff(func_def_48,type,
sK14:
!>[X0: $tType] : ( fun(fun(X0,bool),bool) > fun(X0,bool) ) ).
tff(func_def_49,type,
sK15:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_50,type,
sK16:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_51,type,
sK17:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,bool) ) > X1 ) ).
tff(func_def_52,type,
sK18:
!>[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_53,type,
sK19:
!>[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_54,type,
sK20:
!>[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_55,type,
sK21:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_56,type,
sK22:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_57,type,
sK23:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_58,type,
sK24:
!>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * fun(X0,bool) ) > X0 ) ).
tff(func_def_59,type,
sK25:
!>[X0: $tType] : ( fun(fun(X0,bool),bool) > X0 ) ).
tff(func_def_60,type,
sK26:
!>[X0: $tType] : ( fun(fun(X0,bool),bool) > X0 ) ).
tff(func_def_61,type,
sK27:
!>[X0: $tType] : ( fun(fun(X0,bool),bool) > fun(X0,bool) ) ).
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(f7,axiom,
! [X0: $tType,X1: X0] : ( collect(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_singleton__conv2) ).
tff(f78,axiom,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
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(f136,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(f146,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(f147,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,[],[f146]) ).
tff(f202,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(f203,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(f210,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,[],[f147]) ).
tff(f215,plain,
! [X0: $tType,X1: X0] : ( collect(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) ),
inference(cnf_transformation,[],[f7]) ).
tff(f335,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f78]) ).
tff(f387,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,[],[f202]) ).
tff(f390,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))
| 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)) ),
inference(cnf_transformation,[],[f203]) ).
tff(f391,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(f392,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(f393,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,[],[f136]) ).
tff(f1544,plain,
! [X0: $tType,X1: X0] : ( aa(X0,fun(X0,bool),fequal(X0),X1) = aa(fun(X0,bool),fun(X0,bool),aa(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) ),
inference(forward_demodulation,[],[f215,f335]) ).
tff(f5037,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),X1))
| ~ hoare_992312373derivs(X0,X3,X1)
| ~ hoare_992312373derivs(X0,X3,aa(hoare_28830079triple(X0),fun(hoare_28830079triple(X0),bool),fequal(hoare_28830079triple(X0)),X2)) ),
inference(forward_demodulation,[],[f210,f1544]) ).
tff(f5038,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,aa(hoare_28830079triple(b),fun(hoare_28830079triple(b),bool),fequal(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)))) ),
inference(resolution,[],[f5037,f393]) ).
tff(f8744,plain,
hoare_992312373derivs(b,g,aa(hoare_28830079triple(b),fun(hoare_28830079triple(b),bool),fequal(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)))),
inference(forward_demodulation,[],[f392,f1544]) ).
tff(f12799,plain,
! [X0: a] :
( ~ hoare_992312373derivs(b,g,aa(hoare_28830079triple(b),fun(hoare_28830079triple(b),bool),fequal(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))))
| 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(forward_demodulation,[],[f387,f1544]) ).
tff(f12800,plain,
! [X0: a] :
( hoare_992312373derivs(b,g,aa(hoare_28830079triple(b),fun(hoare_28830079triple(b),bool),fequal(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))))
| ~ hoare_992312373derivs(b,g,aa(hoare_28830079triple(b),fun(hoare_28830079triple(b),bool),fequal(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)))) ),
inference(forward_demodulation,[],[f12799,f1544]) ).
tff(f14292,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)),
inference(forward_subsumption_resolution,[],[f390,f391]) ).
tff(f19372,plain,
~ hoare_992312373derivs(b,g,aa(hoare_28830079triple(b),fun(hoare_28830079triple(b),bool),fequal(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)))),
inference(forward_subsumption_resolution,[],[f5038,f14292]) ).
tff(f19448,plain,
~ hoare_992312373derivs(b,g,aa(hoare_28830079triple(b),fun(hoare_28830079triple(b),bool),fequal(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)))),
inference(resolution,[],[f19372,f12800]) ).
tff(f19455,plain,
$false,
inference(forward_subsumption_resolution,[],[f19448,f8744]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % 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 SAT
% 0.09/0.17 % Computer : n015.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 14:20:30 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.50/0.94 % (2654096)Will run a generic schedule for satisfiability detection.
% 4.50/0.94 % (2654107)% WARNING: option uhcvi not known.
% 4.50/0.94 % (2654108)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=53749859:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.50/0.94 % (2654109)dis+10_1_sil=32000:sp=arity:random_seed=2322171961:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.50/0.94 % (2654106)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2384649785_2999 on theBenchmark for (2999ds/0Mi)
% 4.50/0.94 % (2654107)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3971178476:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.50/0.94 % (2654110)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2521026125:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.50/0.94 % (2654112)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3637886456:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.50/0.94 % (2654111)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3142682464:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.50/0.94 % Exception at run slice level
% 4.50/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.50/0.94 % (2654127)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=167039185:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.50/0.94 % Exception at run slice level
% 4.50/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.50/0.94 % (2654111)Instruction limit reached!
% 4.50/0.94 % (2654111)------------------------------
% 4.50/0.94 % (2654111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.50/0.94 % (2654111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/0.94 % (2654111)CaDiCaL version: 2.1.3
% 4.50/0.94 % (2654111)Termination reason: Instruction limit
% 4.50/0.94 % (2654111)Termination phase: Saturation
% 4.50/0.94 % (2654111)Time elapsed: 0.042 s
% 4.50/0.94 % (2654111)Peak memory usage: 12 MB
% 4.50/0.94 % (2654111)Instructions burned: 134 (million)
% 4.50/0.94 % (2654109)Instruction limit reached!
% 4.50/0.94 % (2654109)------------------------------
% 4.50/0.94 % (2654109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.50/0.94 % (2654109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/0.94 % (2654109)CaDiCaL version: 2.1.3
% 4.50/0.94 % (2654109)Termination reason: Instruction limit
% 4.50/0.94 % (2654109)Termination phase: Saturation
% 4.50/0.94 % (2654109)Time elapsed: 0.052 s
% 4.50/0.94 % (2654109)Peak memory usage: 12 MB
% 4.50/0.94 % (2654109)Instructions burned: 103 (million)
% 4.50/0.94 % (2654136)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3246119728:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.50/0.94 % (2654134)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3902509231:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.50/0.94 % (2654110)Instruction limit reached!
% 4.50/0.94 % (2654110)------------------------------
% 4.50/0.94 % (2654110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.50/0.94 % (2654110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/0.94 % (2654110)CaDiCaL version: 2.1.3
% 4.50/0.94 % (2654110)Termination reason: Instruction limit
% 4.50/0.94 % (2654110)Termination phase: Saturation
% 4.50/0.94 % (2654110)Time elapsed: 0.067 s
% 4.50/0.94 % (2654110)Peak memory usage: 12 MB
% 4.50/0.94 % (2654110)Instructions burned: 116 (million)
% 4.50/0.94 % (2654137)ott-21_1_sil=16000:fs=off:random_seed=2658069832:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.50/0.94 % (2654142)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2009907993:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 4.50/0.94 % (2654112)Instruction limit reached!
% 4.50/0.94 % (2654112)------------------------------
% 4.50/0.94 % (2654112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.50/0.94 % (2654112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/0.94 % (2654112)CaDiCaL version: 2.1.3
% 4.50/0.94 % (2654112)Termination reason: Instruction limit
% 4.50/0.94 % (2654112)Termination phase: Saturation
% 4.50/0.94 % (2654112)Time elapsed: 0.088 s
% 4.50/0.94 % (2654112)Peak memory usage: 12 MB
% 4.50/0.94 % (2654112)Instructions burned: 160 (million)
% 4.50/0.94 % (2654146)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=562963240:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 4.50/0.94 % Exception at run slice level
% 4.50/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.50/0.94 % (2654155)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=461327686:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 4.50/0.94 % (2654134)Instruction limit reached!
% 4.50/0.94 % (2654134)------------------------------
% 4.50/0.94 % (2654134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.50/0.94 % (2654134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/0.94 % (2654134)CaDiCaL version: 2.1.3
% 4.50/0.94 % (2654134)Termination reason: Instruction limit
% 4.50/0.94 % (2654134)Termination phase: Saturation
% 4.50/0.94 % (2654134)Time elapsed: 0.074 s
% 4.50/0.94 % (2654134)Peak memory usage: 12 MB
% 4.50/0.94 % (2654134)Instructions burned: 131 (million)
% 4.50/0.94 % (2654160)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2294307625:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 4.50/0.94 % (2654137)Instruction limit reached!
% 4.50/0.94 % (2654137)------------------------------
% 4.50/0.94 % (2654137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.50/0.94 % (2654137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/0.94 % (2654137)CaDiCaL version: 2.1.3
% 4.50/0.94 % (2654137)Termination reason: Instruction limit
% 4.50/0.94 % (2654137)Termination phase: Saturation
% 4.50/0.94 % (2654137)Time elapsed: 0.088 s
% 4.50/0.94 % (2654137)Peak memory usage: 12 MB
% 4.50/0.94 % (2654137)Instructions burned: 181 (million)
% 4.50/0.94 % Exception at run slice level
% 4.50/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.50/0.94 % (2654167)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1640056045:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 4.50/0.94 % (2654169)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3323436556:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 4.50/0.94 % (2654136)Instruction limit reached!
% 4.50/0.94 % (2654136)------------------------------
% 4.50/0.94 % (2654136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.50/0.94 % (2654136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/0.94 % (2654136)CaDiCaL version: 2.1.3
% 4.50/0.94 % (2654136)Termination reason: Instruction limit
% 4.50/0.94 % (2654136)Termination phase: Saturation
% 4.50/0.94 % (2654136)Time elapsed: 0.175 s
% 4.50/0.94 % (2654136)Peak memory usage: 14 MB
% 4.50/0.94 % (2654136)Instructions burned: 686 (million)
% 4.50/0.94 % (2654197)fmb+10_1_sil=64000:random_seed=3794361516:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 4.50/0.94 % (2654197)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.50/0.94 % Exception at run slice level
% 4.50/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.50/0.94 % (2654202)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1075478794:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 4.50/0.94 % Exception at run slice level
% 4.50/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.50/0.94 % (2654205)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=232469361:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 4.50/0.94 % Exception at run slice level
% 4.50/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.50/0.94 % (2654213)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2962269972:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 4.50/0.94 % (2654142)Instruction limit reached!
% 4.50/0.94 % (2654142)------------------------------
% 4.50/0.94 % (2654142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.50/0.94 % (2654142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/0.94 % (2654142)CaDiCaL version: 2.1.3
% 4.50/0.94 % (2654142)Termination reason: Instruction limit
% 4.50/0.94 % (2654142)Termination phase: Saturation
% 4.50/0.94 % (2654142)Time elapsed: 0.243 s
% 4.50/0.94 % (2654142)Peak memory usage: 13 MB
% 4.50/0.94 % (2654142)Instructions burned: 478 (million)
% 4.50/0.94 % (2654230)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3517223909:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 4.50/0.94 % (2654230)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.50/0.94 % (2654167)Instruction limit reached!
% 4.50/0.94 % (2654167)------------------------------
% 4.50/0.94 % (2654167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.50/0.94 % (2654167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/0.94 % (2654167)CaDiCaL version: 2.1.3
% 4.50/0.94 % (2654167)Termination reason: Instruction limit
% 4.50/0.94 % (2654167)Termination phase: Saturation
% 4.50/0.94 % (2654167)Time elapsed: 0.359 s
% 4.50/0.94 % (2654167)Peak memory usage: 18 MB
% 4.50/0.94 % (2654167)Instructions burned: 693 (million)
% 4.50/0.94 % (2654233)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2764173359:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 4.50/0.94 % Exception at run slice level
% 4.50/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.50/0.94 % (2654235)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3016030152:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 4.50/0.94 % Exception at run slice level
% 4.50/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.50/0.94 % (2654237)ott-2_1_sil=16000:newcnf=on:random_seed=1812740937:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 4.50/0.94 % (2654169)Instruction limit reached!
% 4.50/0.94 % (2654169)------------------------------
% 4.50/0.94 % (2654169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.50/0.94 % (2654169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/0.94 % (2654169)CaDiCaL version: 2.1.3
% 4.50/0.94 % (2654169)Termination reason: Instruction limit
% 4.50/0.94 % (2654169)Termination phase: Saturation
% 4.50/0.94 % (2654169)Time elapsed: 0.492 s
% 4.50/0.94 % (2654169)Peak memory usage: 18 MB
% 4.50/0.94 % (2654169)Instructions burned: 879 (million)
% 4.50/0.94 % (2654239)ott+10_1_sil=32000:tgt=ground:random_seed=2727350563:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 4.50/0.94 % (2654213) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2654096-2654213"...
% 4.50/0.94 % (2654213)...printing done.
% 4.50/0.94 % (2654213)Refutation found. Thanks to Tanya!
% 4.50/0.94 % SZS status Theorem for theBenchmark
% 4.50/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 4.50/0.95 % (2654213)------------------------------
% 4.50/0.95 % (2654213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.50/0.95 % (2654213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/0.95 % (2654213)CaDiCaL version: 2.1.3
% 4.50/0.95 % (2654213)Termination reason: Refutation
% 4.50/0.95 % (2654213)Time elapsed: 0.404 s
% 4.50/0.95 % (2654213)Peak memory usage: 16 MB
% 4.50/0.95 % (2654213)Instructions burned: 1531 (million)
% 4.50/0.95 % (2654096)Success in time 0.737 s
% 4.50/0.95 % Vampire exiting
%------------------------------------------------------------------------------