%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP023_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:35:56 AM UTC 2026
% Result : Theorem 0.16s 0.51s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 9 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 11 con; 0-4 aty)
% Number of variables : 35 ( 33 !; 2 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
tyop_2Emin_2Ebool: $tType ).
tff(type_def_6,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(type_def_7,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(type_def_8,type,
tyop_2Erealax_2Ereal: $tType ).
tff(func_def_0,type,
app_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_1,type,
combin_i_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,X0) ).
tff(func_def_2,type,
combin_k_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X0)) ).
tff(func_def_3,type,
combin_s_2E0:
!>[X0: $tType,X1: $tType,X2: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2))) ).
tff(func_def_4,type,
c_2Ebool_2E_21_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_5,type,
c_2Ebool_2E_21_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_6,type,
c_2Epair_2E_2C_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Epair_2Eprod(X0,X1))) ).
tff(func_def_7,type,
c_2Epair_2E_2C_2E2:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > tyop_2Epair_2Eprod(X0,X1) ) ).
tff(func_def_8,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_9,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_10,type,
c_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_11,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_12,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_13,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_14,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_15,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_16,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_17,type,
c_2Epred__set_2ESUBSET_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(func_def_18,type,
c_2Epred__set_2ESUBSET_2E2:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_19,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_20,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_21,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_22,type,
c_2Ereal__topology_2Eball_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(func_def_23,type,
c_2Ereal__topology_2Eball_2E1: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) > tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool) ).
tff(func_def_24,type,
c_2Ereal__topology_2Ebounded__def_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_25,type,
c_2Ereal__topology_2Ebounded__def_2E1: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ).
tff(func_def_26,type,
c_2Ereal__topology_2Ecball_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(func_def_27,type,
c_2Ereal__topology_2Ecball_2E1: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) > tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool) ).
tff(func_def_28,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_29,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_30,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_31,type,
sK1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_32,type,
sK2:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_33,type,
sK3:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_34,type,
sK4:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_35,type,
sK11: tyop_2Erealax_2Ereal ).
tff(func_def_36,type,
sK12: tyop_2Erealax_2Ereal ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP5: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_3,type,
sP6: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_4,type,
sP7: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_5,type,
sP8: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_6,type,
sP9: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_7,type,
sP10: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(f24,axiom,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] : ( c_2Ereal__topology_2Eball_2E1(X0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ereal__topology_2Eball_2E1) ).
tff(f25,axiom,
! [X0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] : ( c_2Ereal__topology_2Ebounded__def_2E1(X0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ereal__topology_2Ebounded__def_2E1) ).
tff(f26,axiom,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] : ( c_2Ereal__topology_2Ecball_2E1(X0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ereal__topology_2Ecball_2E1) ).
tff(f40,axiom,
! [X0: tyop_2Erealax_2Ereal,X1: tyop_2Erealax_2Ereal] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,c_2Ereal__topology_2Eball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)),c_2Ereal__topology_2Ecball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
tff(f41,axiom,
! [X0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
( ( p(c_2Ereal__topology_2Ebounded__def_2E1(X1))
& p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,X0,X1)) )
=> p(c_2Ereal__topology_2Ebounded__def_2E1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
tff(f42,axiom,
! [X0: tyop_2Erealax_2Ereal,X1: tyop_2Erealax_2Ereal] : p(c_2Ereal__topology_2Ebounded__def_2E1(c_2Ereal__topology_2Ecball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
tff(f53,conjecture,
! [X0: tyop_2Erealax_2Ereal,X1: tyop_2Erealax_2Ereal] : p(c_2Ereal__topology_2Ebounded__def_2E1(c_2Ereal__topology_2Eball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
tff(f54,negated_conjecture,
~ ! [X0: tyop_2Erealax_2Ereal,X1: tyop_2Erealax_2Ereal] : p(c_2Ereal__topology_2Ebounded__def_2E1(c_2Ereal__topology_2Eball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)))),
inference(negated_conjecture,[status(cth)],[f53]) ).
tff(f68,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
( p(c_2Ereal__topology_2Ebounded__def_2E1(X0))
| ~ p(c_2Ereal__topology_2Ebounded__def_2E1(X1))
| ~ p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,X0,X1)) ),
inference(ennf_transformation,[],[f41]) ).
tff(f69,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
( p(c_2Ereal__topology_2Ebounded__def_2E1(X0))
| ~ p(c_2Ereal__topology_2Ebounded__def_2E1(X1))
| ~ p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,X0,X1)) ),
inference(flattening,[],[f68]) ).
tff(f79,plain,
? [X0: tyop_2Erealax_2Ereal,X1: tyop_2Erealax_2Ereal] : ~ p(c_2Ereal__topology_2Ebounded__def_2E1(c_2Ereal__topology_2Eball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)))),
inference(ennf_transformation,[],[f54]) ).
tff(f121,plain,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] : ( c_2Ereal__topology_2Eball_2E1(X0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E0,X0) ),
inference(cnf_transformation,[],[f24]) ).
tff(f122,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] : ( c_2Ereal__topology_2Ebounded__def_2E1(X0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E0,X0) ),
inference(cnf_transformation,[],[f25]) ).
tff(f123,plain,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] : ( c_2Ereal__topology_2Ecball_2E1(X0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E0,X0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f152,plain,
! [X0: tyop_2Erealax_2Ereal,X1: tyop_2Erealax_2Ereal] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,c_2Ereal__topology_2Eball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)),c_2Ereal__topology_2Ecball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)))),
inference(cnf_transformation,[],[f40]) ).
tff(f153,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,X0,X1))
| ~ p(c_2Ereal__topology_2Ebounded__def_2E1(X1))
| p(c_2Ereal__topology_2Ebounded__def_2E1(X0)) ),
inference(cnf_transformation,[],[f69]) ).
tff(f154,plain,
! [X0: tyop_2Erealax_2Ereal,X1: tyop_2Erealax_2Ereal] : p(c_2Ereal__topology_2Ebounded__def_2E1(c_2Ereal__topology_2Ecball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)))),
inference(cnf_transformation,[],[f42]) ).
tff(f214,plain,
~ p(c_2Ereal__topology_2Ebounded__def_2E1(c_2Ereal__topology_2Eball_2E1(c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,sK11,sK12)))),
inference(cnf_transformation,[],[f79]) ).
tff(f219,plain,
! [X0: tyop_2Erealax_2Ereal,X1: tyop_2Erealax_2Ereal] : p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E0,c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)),app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E0,c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)))),
inference(definition_unfolding,[],[f152,f121,f123]) ).
tff(f220,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,X0,X1))
| ~ p(app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E0,X1))
| p(app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E0,X0)) ),
inference(definition_unfolding,[],[f153,f122,f122]) ).
tff(f221,plain,
! [X0: tyop_2Erealax_2Ereal,X1: tyop_2Erealax_2Ereal] : p(app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E0,app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E0,c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0,X1)))),
inference(definition_unfolding,[],[f154,f122,f123]) ).
tff(f222,plain,
~ p(app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E0,app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E0,c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,sK11,sK12)))),
inference(definition_unfolding,[],[f214,f122,f121]) ).
tff(f1164,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2ESUBSET_2E2(tyop_2Erealax_2Ereal,app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E0,c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,sK11,sK12)),X0))
| ~ p(app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E0,X0)) ),
inference(resolution,[],[f220,f222]) ).
tff(f1322,plain,
~ p(app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E0,app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E0,c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,sK11,sK12)))),
inference(resolution,[],[f1164,f219]) ).
tff(f1332,plain,
$false,
inference(forward_subsumption_resolution,[],[f1322,f221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP023_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 12:11:41 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.42 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
% 0.16/0.51 % (421916)Will run a generic schedule for satisfiability detection.
% 0.16/0.51 % (421921)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3466505334_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.51 % Exception at run slice level
% 0.16/0.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.51 % (421922)% WARNING: option uhcvi not known.
% 0.16/0.51 % (421922)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3912793470:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.51 % (421923)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=227137017:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.51 % (421924)dis+10_1_sil=32000:sp=arity:random_seed=4165133661:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.51 % (421925)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3248184982:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.51 % (421926)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2009127453:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.51 % (421927)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1351213162:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.51 % (421929)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1645225945:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.51 % Exception at run slice level
% 0.16/0.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.51 % (421937)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2982128080:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.51 % (421925) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-421916-421925"...
% 0.16/0.51 % (421925)...printing done.
% 0.16/0.51 % (421925)Refutation found. Thanks to Tanya!
% 0.16/0.51 % SZS status Theorem for theBenchmark
% 0.16/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (421925)------------------------------
% 0.16/0.52 % (421925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (421925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (421925)CaDiCaL version: 2.1.3
% 0.16/0.52 % (421925)Termination reason: Refutation
% 0.16/0.52 % (421925)Time elapsed: 0.044 s
% 0.16/0.52 % (421925)Peak memory usage: 13 MB
% 0.16/0.52 % (421925)Instructions burned: 69 (million)
% 0.16/0.52 % (421916)Success in time 0.091 s
% 0.16/0.52 % Vampire exiting
%------------------------------------------------------------------------------