%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW510_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 : n010.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 4.01s 1.34s
% Output : Refutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 85 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 100 ( 52 ~; 38 |; 8 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 2 prp; 0-6 aty)
% Number of functors : 82 ( 82 usr; 11 con; 0-7 aty)
% Number of variables : 84 ( 0 sgn 75 !; 9 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
com: $tType ).
tff(type_def_7,type,
state: $tType ).
tff(type_def_8,type,
bool: $tType ).
tff(type_def_9,type,
hoare_28830079triple: $tType > $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
skip: com ).
tff(func_def_5,type,
semi: ( com * com ) > com ).
tff(func_def_6,type,
finite_fold1:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > fun(fun(X0,bool),X0) ) ).
tff(func_def_7,type,
finite_fold1Set:
!>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * fun(X0,bool) ) > fun(X0,bool) ) ).
tff(func_def_8,type,
the:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_9,type,
hoare_1841697145triple:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * 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,
insert:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),fun(X0,bool))) ).
tff(func_def_15,type,
the_elem:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_16,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_17,type,
fFalse: bool ).
tff(func_def_18,type,
fNot: fun(bool,bool) ).
tff(func_def_19,type,
fTrue: bool ).
tff(func_def_20,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_21,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(func_def_22,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_23,type,
fimplies: fun(bool,fun(bool,bool)) ).
tff(func_def_24,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_25,type,
g: fun(hoare_28830079triple(a),bool) ).
tff(func_def_26,type,
q: a > fun(state,bool) ).
tff(func_def_27,type,
c: com ).
tff(func_def_28,type,
sK3: a ).
tff(func_def_29,type,
sK4: state ).
tff(func_def_30,type,
sK5: ( fun(a,fun(state,bool)) * fun(a,fun(state,bool)) ) > state ).
tff(func_def_31,type,
sK6:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool)) ) > X0 ) ).
tff(func_def_32,type,
sK7:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_33,type,
sK8:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_34,type,
sK9:
!>[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,
sK10:
!>[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,
sK11:
!>[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,
sK12:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > X0 ) ).
tff(func_def_38,type,
sK13:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_39,type,
sK14:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > X0 ) ).
tff(func_def_40,type,
sK15:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_41,type,
sK16:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_42,type,
sK17:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_43,type,
sK18:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_44,type,
sK19:
!>[X0: $tType] : ( ( fun(X0,bool) * X0 ) > fun(X0,bool) ) ).
tff(func_def_45,type,
sK20:
!>[X0: $tType] : ( ( fun(X0,bool) * X0 ) > fun(X0,bool) ) ).
tff(func_def_46,type,
sK21:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) * X0 * X0 ) > fun(X0,bool) ) ).
tff(func_def_47,type,
sK22:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_48,type,
sK23:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_49,type,
sK24:
!>[X0: $tType] : ( hoare_28830079triple(X0) > fun(X0,fun(state,bool)) ) ).
tff(func_def_50,type,
sK25:
!>[X0: $tType] : ( hoare_28830079triple(X0) > com ) ).
tff(func_def_51,type,
sK26:
!>[X0: $tType] : ( hoare_28830079triple(X0) > fun(X0,fun(state,bool)) ) ).
tff(func_def_52,type,
sK27:
!>[X0: $tType] : ( fun(fun(X0,bool),bool) > X0 ) ).
tff(func_def_53,type,
sK28:
!>[X0: $tType] : ( fun(fun(X0,bool),bool) > fun(X0,bool) ) ).
tff(func_def_54,type,
sK29:
!>[X0: $tType] : ( fun(fun(X0,bool),bool) > X0 ) ).
tff(func_def_55,type,
sK30:
!>[X0: $tType] : ( fun(fun(X0,bool),bool) > X0 ) ).
tff(func_def_56,type,
sK31:
!>[X0: $tType] : ( fun(fun(X0,bool),bool) > fun(X0,bool) ) ).
tff(func_def_57,type,
sK32:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_58,type,
sK33:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_59,type,
sK34:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_60,type,
sK35:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_61,type,
sK36:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_62,type,
sK37:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_63,type,
sK38:
!>[X0: $tType] : ( ( fun(X0,bool) * X0 ) > X0 ) ).
tff(func_def_64,type,
sK39:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_65,type,
sK40:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > X0 ) ).
tff(func_def_66,type,
sK41:
!>[X0: $tType] : ( ( fun(X0,bool) * X0 ) > X0 ) ).
tff(func_def_67,type,
sK42:
!>[X0: $tType] : ( ( fun(X0,bool) * X0 ) > X0 ) ).
tff(func_def_68,type,
sK43:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > X0 ) ).
tff(func_def_69,type,
sK44:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > X0 ) ).
tff(func_def_70,type,
sK45:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,bool) * X1 * X1 * fun(X0,fun(X1,X1)) ) > X0 ) ).
tff(func_def_71,type,
sK46:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,bool) * X1 * X1 * fun(X0,fun(X1,X1)) ) > fun(X0,bool) ) ).
tff(func_def_72,type,
sK47:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,bool) * X1 * X1 * fun(X0,fun(X1,X1)) ) > X1 ) ).
tff(func_def_73,type,
sK48:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) * fun(X0,fun(X0,X0)) ) > X0 ) ).
tff(func_def_74,type,
sK49:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) * fun(X0,fun(X0,X0)) ) > fun(X0,bool) ) ).
tff(func_def_75,type,
sK50:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) * fun(X0,fun(X0,X0)) ) > X0 ) ).
tff(func_def_76,type,
sK51:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) * X0 * fun(X0,fun(X0,X0)) ) > X0 ) ).
tff(func_def_77,type,
sK52:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) * X0 * fun(X0,fun(X0,X0)) ) > fun(X0,bool) ) ).
tff(func_def_78,type,
sK53:
!>[X0: $tType,X1: $tType] : ( ( X1 * fun(X0,fun(X1,X1)) * fun(X0,bool) ) > X1 ) ).
tff(func_def_79,type,
sK54:
!>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * fun(X0,bool) ) > X0 ) ).
tff(pred_def_1,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
finite_finite:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
finite_finite1:
!>[X0: $tType] : ( fun(X0,bool) > $o ) ).
tff(pred_def_4,type,
finite_fold_graph:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * X1 * fun(X0,bool) * X1 ) > $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(pred_def_9,type,
p: ( a * state ) > $o ).
tff(pred_def_10,type,
sP0:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) * X0 * X0 ) > $o ) ).
tff(pred_def_11,type,
sP1:
!>[X0: $tType] : ( ( X0 * X0 * fun(X0,bool) * fun(X0,bool) ) > $o ) ).
tff(pred_def_12,type,
sP2:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,bool) * X1 * X1 * fun(X0,fun(X1,X1)) ) > $o ) ).
tff(f110,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f111,axiom,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
tff(f122,axiom,
! [X0: $tType,X1: X0,X2: X0] :
( ( X2 != X1 )
| pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
tff(f126,axiom,
! [X0: a,X1: state] :
( p(X0,X1)
=> hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),c,combk(fun(state,bool),a,q(X0)))),bot_bot(fun(hoare_28830079triple(a),bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f127,conjecture,
! [X0: a,X1: state] :
( ~ p(X0,X1)
| ? [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
( hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool))))
& ! [X4: state] :
( ? [X5: a] :
( pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1))
& ~ pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4)) )
| pp(aa(state,bool,q(X0),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f128,negated_conjecture,
~ ! [X0: a,X1: state] :
( ~ p(X0,X1)
| ? [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
( hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool))))
& ! [X4: state] :
( ? [X5: a] :
( pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1))
& ~ pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4)) )
| pp(aa(state,bool,q(X0),X4)) ) ) ),
inference(negated_conjecture,[status(cth)],[f127]) ).
tff(f137,plain,
! [X0: a,X1: state] :
( hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),c,combk(fun(state,bool),a,q(X0)))),bot_bot(fun(hoare_28830079triple(a),bool))))
| ~ p(X0,X1) ),
inference(ennf_transformation,[],[f126]) ).
tff(f138,plain,
? [X0: a,X1: state] :
( p(X0,X1)
& ! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
( ~ hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool))))
| ? [X4: state] :
( ! [X5: a] :
( ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1))
| pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4)) )
& ~ pp(aa(state,bool,q(X0),X4)) ) ) ),
inference(ennf_transformation,[],[f128]) ).
tff(f203,plain,
( p(sK3,sK4)
& ! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
( ~ hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool))))
| ( ! [X5: a] :
( ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4))
| pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK5(X2,X3))) )
& ~ pp(aa(state,bool,q(sK3),sK5(X2,X3))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X4,sK5(X2,X3))],[f138]) ).
tff(f277,plain,
! [X0: a,X1: state] :
( hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),c,combk(fun(state,bool),a,q(X0)))),bot_bot(fun(hoare_28830079triple(a),bool))))
| ~ p(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tff(f278,plain,
! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
( ~ hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool))))
| ~ pp(aa(state,bool,q(sK3),sK5(X2,X3))) ),
inference(cnf_transformation,[],[f203]) ).
tff(f279,plain,
! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool)),X5: a] :
( ~ hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool))))
| ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4))
| pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK5(X2,X3))) ),
inference(cnf_transformation,[],[f203]) ).
tff(f280,plain,
p(sK3,sK4),
inference(cnf_transformation,[],[f203]) ).
tff(f281,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f110]) ).
tff(f291,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(cnf_transformation,[],[f111]) ).
tff(f395,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 != X2 )
| pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(cnf_transformation,[],[f122]) ).
tff(f494,plain,
! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
inference(equality_resolution,[],[f395]) ).
tff(f504,plain,
! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
( ~ hoare_992312373derivs(a,g,aa(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),insert(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool))),hoare_1841697145triple(a,X2,c,X3)))
| ~ pp(aa(state,bool,q(sK3),sK5(X2,X3))) ),
inference(forward_demodulation,[],[f278,f281]) ).
tff(f505,plain,
! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool)),X5: a] :
( ~ hoare_992312373derivs(a,g,aa(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),insert(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool))),hoare_1841697145triple(a,X2,c,X3)))
| ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK4))
| pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK5(X2,X3))) ),
inference(forward_demodulation,[],[f279,f281]) ).
tff(f506,plain,
! [X0: a,X1: state] :
( hoare_992312373derivs(a,g,aa(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),insert(hoare_28830079triple(a)),bot_bot(fun(hoare_28830079triple(a),bool))),hoare_1841697145triple(a,combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),c,combk(fun(state,bool),a,q(X0)))))
| ~ p(X0,X1) ),
inference(forward_demodulation,[],[f277,f281]) ).
tff(f515,plain,
! [X2: a,X0: a,X1: state] :
( ~ p(X0,X1)
| ~ pp(aa(state,bool,aa(a,fun(state,bool),combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),X2),sK4))
| pp(aa(state,bool,aa(a,fun(state,bool),combk(fun(state,bool),a,q(X0)),X2),sK5(combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),combk(fun(state,bool),a,q(X0))))) ),
inference(resolution,[],[f506,f505]) ).
tff(f516,plain,
! [X0: a,X1: state] :
( ~ p(X0,X1)
| ~ pp(aa(state,bool,q(sK3),sK5(combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),combk(fun(state,bool),a,q(X0))))) ),
inference(resolution,[],[f506,f504]) ).
tff(f526,definition,
( spl55_2
<=> ! [X0: a,X1: state] :
( ~ p(X0,X1)
| ~ pp(aa(state,bool,q(sK3),sK5(combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),combk(fun(state,bool),a,q(X0))))) ) ),
introduced(definition,[new_symbols(definition,[spl55_2])],[avatar_definition]) ).
tff(f527,plain,
( ! [X0: a,X1: state] :
( ~ pp(aa(state,bool,q(sK3),sK5(combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),combk(fun(state,bool),a,q(X0)))))
| ~ p(X0,X1) )
| ~ spl55_2 ),
inference(avatar_component_clause,[],[f526]) ).
tff(f529,plain,
spl55_2,
inference(avatar_split_clause,[],[f516,f526]) ).
tff(f530,plain,
! [X2: a,X0: a,X1: state] :
( ~ pp(aa(state,bool,combc(state,state,bool,fequal(state),X1),sK4))
| ~ p(X0,X1)
| pp(aa(state,bool,aa(a,fun(state,bool),combk(fun(state,bool),a,q(X0)),X2),sK5(combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),combk(fun(state,bool),a,q(X0))))) ),
inference(forward_demodulation,[],[f515,f291]) ).
tff(f536,plain,
! [X0: a,X1: state] :
( pp(aa(state,bool,q(X0),sK5(combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),combk(fun(state,bool),a,q(X0)))))
| ~ pp(aa(state,bool,combc(state,state,bool,fequal(state),X1),sK4))
| ~ p(X0,X1) ),
inference(forward_demodulation,[],[f530,f291]) ).
tff(f640,plain,
( ! [X0: state] :
( ~ p(sK3,X0)
| ~ pp(aa(state,bool,combc(state,state,bool,fequal(state),X0),sK4))
| ~ p(sK3,X0) )
| ~ spl55_2 ),
inference(resolution,[],[f527,f536]) ).
tff(f642,plain,
( ! [X0: state] :
( ~ pp(aa(state,bool,combc(state,state,bool,fequal(state),X0),sK4))
| ~ p(sK3,X0) )
| ~ spl55_2 ),
inference(duplicate_literal_removal,[],[f640]) ).
tff(f1164,plain,
( ! [X0: state] :
( ~ pp(aa(state,bool,aa(state,fun(state,bool),fequal(state),sK4),X0))
| ~ p(sK3,X0) )
| ~ spl55_2 ),
inference(superposition,[],[f642,f281]) ).
tff(f1693,plain,
( ~ p(sK3,sK4)
| ~ spl55_2 ),
inference(resolution,[],[f1164,f494]) ).
tff(f1724,plain,
( $false
| ~ spl55_2 ),
inference(forward_subsumption_resolution,[],[f1693,f280]) ).
tff(f1725,plain,
~ spl55_2,
inference(avatar_contradiction_clause,[],[f1724]) ).
cnf(s2,plain,
spl55_2,
inference(sat_conversion,[],[f529]) ).
cnf(s52,plain,
~ spl55_2,
inference(sat_conversion,[],[f1725]) ).
cnf(s91,plain,
$false,
inference(rat,[],[s2,s52]) ).
tff(f1764,plain,
$false,
inference(avatar_sat_refutation,[],[s91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW510_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n010.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 14:16:02 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 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
% 4.01/1.33 % (1945530)Detected formulas, will run a generic FOF schedule.
% 4.01/1.33 % (1945539)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2678260784:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.01/1.33 % (1945540)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2598664577:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.01/1.33 % (1945536)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=4170874692:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.01/1.33 % (1945541)dis-21_1_sil=8000:lcm=predicate:random_seed=84174775: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)
% 4.01/1.33 % (1945535)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=519466757:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.01/1.33 % (1945537)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=1171976659:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.01/1.33 % (1945538)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1491926489:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.01/1.33 % (1945538)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.01/1.33 % (1945539)Instruction limit reached!
% 4.01/1.33 % (1945539)------------------------------
% 4.01/1.33 % (1945539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.33 % (1945539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.33 % (1945539)CaDiCaL version: 2.1.3
% 4.01/1.33 % (1945539)Termination reason: Instruction limit
% 4.01/1.33 % (1945539)Termination phase: Saturation
% 4.01/1.33 % (1945539)Time elapsed: 0.035 s
% 4.01/1.33 % (1945539)Peak memory usage: 88 MB
% 4.01/1.33 % (1945539)Instructions burned: 120 (million)
% 4.01/1.33 % (1945537)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.01/1.33 % (1945538)Instruction limit reached!
% 4.01/1.33 % (1945538)------------------------------
% 4.01/1.33 % (1945538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.33 % (1945538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.33 % (1945538)CaDiCaL version: 2.1.3
% 4.01/1.33 % (1945538)Termination reason: Instruction limit
% 4.01/1.33 % (1945538)Termination phase: Saturation
% 4.01/1.33 % (1945538)Time elapsed: 0.046 s
% 4.01/1.33 % (1945538)Peak memory usage: 88 MB
% 4.01/1.33 % (1945538)Instructions burned: 109 (million)
% 4.01/1.33 % (1945541)Instruction limit reached!
% 4.01/1.33 % (1945541)------------------------------
% 4.01/1.33 % (1945541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.33 % (1945541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.33 % (1945541)CaDiCaL version: 2.1.3
% 4.01/1.33 % (1945541)Termination reason: Instruction limit
% 4.01/1.33 % (1945541)Termination phase: Saturation
% 4.01/1.33 % (1945541)Time elapsed: 0.051 s
% 4.01/1.33 % (1945541)Peak memory usage: 88 MB
% 4.01/1.33 % (1945541)Instructions burned: 131 (million)
% 4.01/1.33 % (1945540)Instruction limit reached!
% 4.01/1.33 % (1945540)------------------------------
% 4.01/1.33 % (1945540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.33 % (1945540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.33 % (1945540)CaDiCaL version: 2.1.3
% 4.01/1.33 % (1945540)Termination reason: Instruction limit
% 4.01/1.33 % (1945540)Termination phase: Saturation
% 4.01/1.33 % (1945540)Time elapsed: 0.081 s
% 4.01/1.33 % (1945540)Peak memory usage: 89 MB
% 4.01/1.33 % (1945540)Instructions burned: 140 (million)
% 4.01/1.33 % (1945549)lrs+10_1_sil=8000:sp=occurrence:random_seed=1911586319:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.01/1.33 % (1945549)Instruction limit reached!
% 4.01/1.33 % (1945549)------------------------------
% 4.01/1.33 % (1945549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.33 % (1945549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.33 % (1945549)CaDiCaL version: 2.1.3
% 4.01/1.33 % (1945549)Termination reason: Instruction limit
% 4.01/1.33 % (1945549)Termination phase: Saturation
% 4.01/1.33 % (1945549)Time elapsed: 0.072 s
% 4.01/1.33 % (1945549)Peak memory usage: 89 MB
% 4.01/1.33 % (1945549)Instructions burned: 287 (million)
% 4.01/1.33 % (1945550)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3835778921:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.01/1.33 % (1945551)lrs+1011_1_sil=32000:sp=occurrence:random_seed=95997834:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.01/1.33 % (1945552)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=4251125449:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.01/1.33 % (1945550)Instruction limit reached!
% 4.01/1.33 % (1945550)------------------------------
% 4.01/1.33 % (1945550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.33 % (1945550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.33 % (1945550)CaDiCaL version: 2.1.3
% 4.01/1.33 % (1945550)Termination reason: Instruction limit
% 4.01/1.33 % (1945550)Termination phase: Saturation
% 4.01/1.33 % (1945550)Time elapsed: 0.084 s
% 4.01/1.33 % (1945550)Peak memory usage: 89 MB
% 4.01/1.33 % (1945550)Instructions burned: 159 (million)
% 4.01/1.33 % (1945556)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3960543881:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.01/1.33 % (1945551)Instruction limit reached!
% 4.01/1.33 % (1945551)------------------------------
% 4.01/1.33 % (1945551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.33 % (1945551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.33 % (1945551)CaDiCaL version: 2.1.3
% 4.01/1.33 % (1945551)Termination reason: Instruction limit
% 4.01/1.33 % (1945551)Termination phase: Saturation
% 4.01/1.33 % (1945551)Time elapsed: 0.128 s
% 4.01/1.33 % (1945551)Peak memory usage: 89 MB
% 4.01/1.33 % (1945551)Instructions burned: 326 (million)
% 4.01/1.33 % (1945556)First to succeed.
% 4.01/1.33 % (1945556)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1945530"
% 4.01/1.33 % (1945552)Instruction limit reached!
% 4.01/1.33 % (1945552)------------------------------
% 4.01/1.33 % (1945552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.33 % (1945552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.33 % (1945552)CaDiCaL version: 2.1.3
% 4.01/1.33 % (1945552)Termination reason: Instruction limit
% 4.01/1.33 % (1945552)Termination phase: Saturation
% 4.01/1.33 % (1945552)Time elapsed: 0.121 s
% 4.01/1.33 % (1945552)Peak memory usage: 89 MB
% 4.01/1.33 % (1945552)Instructions burned: 249 (million)
% 4.01/1.33 % Exception at run slice level
% 4.01/1.33 User error: GNN currently only supports monomorphic FOL.
% 4.01/1.33 % Exception at run slice level
% 4.01/1.33 User error: GNN currently only supports monomorphic FOL.
% 4.01/1.33 % Exception at run slice level
% 4.01/1.33 User error: GNN currently only supports monomorphic FOL.
% 4.01/1.33 % (1945558)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2303960978:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.01/1.33 % (1945560)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2655821009:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.01/1.34 % (1945556)Refutation found. Thanks to Tanya!
% 4.01/1.34 % SZS status Theorem for theBenchmark
% 4.01/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 5.34/1.46 % (1945556)------------------------------
% 5.34/1.46 % (1945556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.34/1.46 % (1945556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.34/1.46 % (1945556)CaDiCaL version: 2.1.3
% 5.34/1.46 % (1945556)Termination reason: Refutation
% 5.34/1.46 % (1945556)Time elapsed: 0.040 s
% 5.34/1.46 % (1945556)Peak memory usage: 91 MB
% 5.34/1.46 % (1945556)Instructions burned: 125 (million)
% 5.34/1.46 % (1945556)------------------------------
% 5.34/1.46 % (1945556)------------------------------
% 5.34/1.46 % (1945530)Success in time 0.685 s
% 5.34/1.46 % Vampire exiting
%------------------------------------------------------------------------------