%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP020_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 11:28:37 AM UTC 2026
% Result : Theorem 2.74s 1.23s
% Output : Refutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 7 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 55 ( 55 usr; 7 con; 0-5 aty)
% Number of variables : 38 ( 29 !; 9 ?; 38 :)
% 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_2Enum_2Enum: $tType ).
tff(type_def_8,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $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_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_7,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_8,type,
c_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_9,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_10,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_11,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_12,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_13,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_14,type,
c_2Epred__set_2EBIJ_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(func_def_15,type,
c_2Epred__set_2EBIJ_2E3:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_16,type,
c_2Epred__set_2ECROSS_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool))) ).
tff(func_def_17,type,
c_2Epred__set_2ECROSS_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool) ) ).
tff(func_def_18,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_19,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_20,type,
c_2Epred__set_2EUNIV_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ).
tff(func_def_21,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_22,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_23,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_24,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_25,type,
sK12:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_26,type,
sK13:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_27,type,
sK14:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_28,type,
sK15:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_29,type,
sK16:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_30,type,
sK17:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Ebool ) > X0 ) ).
tff(func_def_31,type,
sK18:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_32,type,
sK19:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_33,type,
sK20:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_34,type,
sK21:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_35,type,
sK22:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Ebool ) > X0 ) ).
tff(func_def_36,type,
sK23:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_37,type,
sK24:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_38,type,
sK25:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Ebool ) > X0 ) ).
tff(func_def_39,type,
sK26:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_40,type,
sK27:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_41,type,
sK28:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_42,type,
sK29:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_43,type,
sK30:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_44,type,
sK31:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_45,type,
sK32:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_46,type,
sK33:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) * X0 ) > X1 ) ).
tff(func_def_47,type,
sK34:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_48,type,
sK35:
!>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(X0,X1) ) ).
tff(func_def_49,type,
sK36:
!>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) > X0 ) ).
tff(func_def_50,type,
sK37:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(X0,X1) ) ).
tff(func_def_51,type,
sK38:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(X1,X0) ) ).
tff(func_def_52,type,
sK39: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP0: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_3,type,
sP1: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_4,type,
sP2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_5,type,
sP3: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_6,type,
sP4: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_7,type,
sP5: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_8,type,
sP6: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_9,type,
sP7: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_10,type,
sP8: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_11,type,
sP9: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_12,type,
sP10: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_13,type,
sP11: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(f47,axiom,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ? [X4: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3))
<=> ? [X5: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EBIJ__SYM) ).
tff(f58,axiom,
? [X0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,X0,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ) ).
tff(f59,conjecture,
? [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).
tff(f60,negated_conjecture,
~ ? [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
inference(negated_conjecture,[status(cth)],[f59]) ).
tff(f82,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
inference(ennf_transformation,[],[f60]) ).
tff(f172,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( ? [X4: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3))
| ! [X5: tyop_2Emin_2Efun(X1,X0)] : ~ p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) )
& ( ? [X5: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2))
| ! [X4: tyop_2Emin_2Efun(X0,X1)] : ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3)) ) ),
inference(nnf_transformation,[],[f47]) ).
tff(f173,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( ? [X4: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3))
| ! [X5: tyop_2Emin_2Efun(X1,X0)] : ~ p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) )
& ( ? [X6: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X6,X3,X2))
| ! [X7: tyop_2Emin_2Efun(X0,X1)] : ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X7,X2,X3)) ) ),
inference(rectify,[],[f172]) ).
tff(f174,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EBIJ_2E3(X0,X1,sK37(X0,X1,X2,X3),X2,X3))
| ! [X5: tyop_2Emin_2Efun(X1,X0)] : ~ p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) )
& ( p(c_2Epred__set_2EBIJ_2E3(X1,X0,sK38(X0,X1,X2,X3),X3,X2))
| ! [X7: tyop_2Emin_2Efun(X0,X1)] : ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X7,X2,X3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37,sK38]),skolemize(X4,sK37(X0,X1,X2,X3)),skolemize(X6,sK38(X0,X1,X2,X3))],[f173]) ).
tff(f222,plain,
p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,sK39,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X0,sK39)],[f58]) ).
tff(f348,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X7: tyop_2Emin_2Efun(X0,X1)] :
( ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X7,X2,X3))
| p(c_2Epred__set_2EBIJ_2E3(X1,X0,sK38(X0,X1,X2,X3),X3,X2)) ),
inference(cnf_transformation,[],[f174]) ).
tff(f456,plain,
p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,sK39,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
inference(cnf_transformation,[],[f222]) ).
tff(f457,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
inference(cnf_transformation,[],[f82]) ).
tff(f1669,plain,
p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK38(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
inference(resolution,[],[f348,f456]) ).
tff(f1680,plain,
$false,
inference(forward_subsumption_resolution,[],[f1669,f457]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP020_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n010.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 12:06:46 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.74/1.23 % (855631)Detected formulas, will run a generic FOF schedule.
% 2.74/1.23 % (855710)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1653623189:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.23 % (855702)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=704433035:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.23 % (855710)First to succeed.
% 2.74/1.23 % (855710)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-855631"
% 2.74/1.23 % (855706)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=486455509:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.23 % (855703)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=3491001959:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.23 % (855707)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3895010417:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.23 % (855707)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.74/1.23 % (855706)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.74/1.23 % (855707)Also succeeded, but the first one will report.
% 2.74/1.23 % (855709)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3462509176:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.23 % (855709)Also succeeded, but the first one will report.
% 2.74/1.23 % (855712)dis-21_1_sil=8000:lcm=predicate:random_seed=1886229281: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)
% 2.74/1.23 % (855712)Also succeeded, but the first one will report.
% 2.74/1.23 % (855710)Refutation found. Thanks to Tanya!
% 2.74/1.23 % SZS status Theorem for theBenchmark
% 2.74/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.15/1.41 % (855710)------------------------------
% 3.15/1.41 % (855710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.41 % (855710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.41 % (855710)CaDiCaL version: 2.1.3
% 3.15/1.41 % (855710)Termination reason: Refutation
% 3.15/1.41 % (855710)Time elapsed: 0.021 s
% 3.15/1.41 % (855710)Peak memory usage: 89 MB
% 3.15/1.41 % (855710)Instructions burned: 56 (million)
% 3.15/1.41 % (855710)------------------------------
% 3.15/1.41 % (855710)------------------------------
% 3.15/1.41 % (855631)Success in time 0.351 s
% 3.15/1.41 % Vampire exiting
%------------------------------------------------------------------------------