%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP001_7 : 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 : n014.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 11:33:52 AM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 21 ( 10 ~; 7 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 91 ( 91 usr; 10 con; 0-4 aty)
% Number of variables : 6 ( 4 !; 2 ?; 6 :)
% 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_2Emin_2Eind: $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_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_15,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_16,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_17,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_18,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_19,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_20,type,
c_2Ebool_2E_3F_21_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_21,type,
c_2Ebool_2E_3F_21_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_22,type,
c_2Emin_2E_40_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X0) ).
tff(func_def_23,type,
c_2Emin_2E_40_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_24,type,
c_2Ebool_2EBOUNDED_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_25,type,
c_2Ebool_2EBOUNDED_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_26,type,
c_2Ebool_2ECOND_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0))) ).
tff(func_def_27,type,
c_2Ebool_2ECOND_2E3:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * X0 * X0 ) > X0 ) ).
tff(func_def_28,type,
c_2Ebool_2EDATATYPE_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ).
tff(func_def_29,type,
c_2Ebool_2EDATATYPE_2E1:
!>[X0: $tType] : ( X0 > tyop_2Emin_2Ebool ) ).
tff(func_def_30,type,
c_2Ebool_2EIN_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(func_def_31,type,
c_2Ebool_2EIN_2E2:
!>[X0: $tType] : ( ( X0 * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_32,type,
c_2Ebool_2ELET_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X1)) ).
tff(func_def_33,type,
c_2Ebool_2ELET_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_34,type,
c_2Ebool_2EONE__ONE_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Ebool) ).
tff(func_def_35,type,
c_2Ebool_2EONE__ONE_2E1:
!>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X0,X1) > tyop_2Emin_2Ebool ) ).
tff(func_def_36,type,
c_2Ebool_2EONTO_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Ebool) ).
tff(func_def_37,type,
c_2Ebool_2EONTO_2E1:
!>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X0,X1) > tyop_2Emin_2Ebool ) ).
tff(func_def_38,type,
c_2Ebool_2ERES__EXISTS_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_39,type,
c_2Ebool_2ERES__EXISTS_2E2:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_40,type,
c_2Ebool_2ERES__EXISTS__UNIQUE_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_41,type,
c_2Ebool_2ERES__EXISTS__UNIQUE_2E2:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_42,type,
c_2Ebool_2ERES__FORALL_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_43,type,
c_2Ebool_2ERES__FORALL_2E2:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_44,type,
c_2Ebool_2ERES__SELECT_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X0)) ).
tff(func_def_45,type,
c_2Ebool_2ERES__SELECT_2E2:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_46,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,X0),tyop_2Emin_2Ebool)) ).
tff(func_def_47,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,X0) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_48,type,
c_2Ebool_2Eliteral__case_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X1)) ).
tff(func_def_49,type,
c_2Ebool_2Eliteral__case_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_50,type,
sK2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_51,type,
sK3:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_52,type,
sK4:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_53,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_54,type,
sK6:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_55,type,
sK7:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_56,type,
sK8: tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind) ).
tff(func_def_57,type,
sK9: tyop_2Emin_2Ebool ).
tff(func_def_58,type,
sK10:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_59,type,
sK11: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_60,type,
sK12: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_61,type,
sK13: tyop_2Emin_2Ebool ).
tff(func_def_62,type,
sK14:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_63,type,
sK15:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_64,type,
sK16:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)))) > tyop_2Emin_2Ebool ) ).
tff(func_def_65,type,
sK17:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)))) > X0 ) ).
tff(func_def_66,type,
sK18:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)))) > X0 ) ).
tff(func_def_67,type,
sK19:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)))) > X0 ) ).
tff(func_def_68,type,
sK20:
!>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X0,X1) > X0 ) ).
tff(func_def_69,type,
sK21:
!>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X0,X1) > X0 ) ).
tff(func_def_70,type,
sK22:
!>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X0,X1) > X1 ) ).
tff(func_def_71,type,
sK23:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X1 ) > X0 ) ).
tff(func_def_72,type,
sK24:
!>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X1,X0) > X1 ) ).
tff(func_def_73,type,
sK25:
!>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X1,X0) > X1 ) ).
tff(func_def_74,type,
sK26:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,X0) ) > X0 ) ).
tff(func_def_75,type,
sK27:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,X0) ) > X1 ) ).
tff(func_def_76,type,
sK28:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X1,X0) * X0 ) > X1 ) ).
tff(func_def_77,type,
sK29:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_78,type,
sK30:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_79,type,
sK31:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) > tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) ).
tff(func_def_80,type,
sK32:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) > X0 ) ).
tff(func_def_81,type,
sK33:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) > X0 ) ).
tff(func_def_82,type,
sK34:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) ).
tff(func_def_83,type,
sK35:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) > X0 ) ).
tff(func_def_84,type,
sK36:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) ) > tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) ).
tff(func_def_85,type,
sK37:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) ) > tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) ).
tff(func_def_86,type,
sK38:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) ) > X0 ) ).
tff(func_def_87,type,
sK39:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) > tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) ).
tff(func_def_88,type,
sK40:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) > tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) ).
tff(func_def_89,type,
sK41:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) > X0 ) ).
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:
!>[X0: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) > $o ) ).
tff(f66,axiom,
( p(c_2Ebool_2ET_2E0)
<=> ! [X0: tyop_2Emin_2Ebool] : ( X0 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF) ).
tff(f87,conjecture,
p(c_2Ebool_2ET_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
tff(f88,negated_conjecture,
~ p(c_2Ebool_2ET_2E0),
inference(negated_conjecture,[status(cth)],[f87]) ).
tff(f94,plain,
~ p(c_2Ebool_2ET_2E0),
inference(flattening,[],[f88]) ).
tff(f171,plain,
( ( p(c_2Ebool_2ET_2E0)
| ? [X0: tyop_2Emin_2Ebool] : ( X0 != X0 ) )
& ( ! [X0: tyop_2Emin_2Ebool] : ( X0 = X0 )
| ~ p(c_2Ebool_2ET_2E0) ) ),
inference(nnf_transformation,[],[f66]) ).
tff(f172,plain,
( ( p(c_2Ebool_2ET_2E0)
| ? [X0: tyop_2Emin_2Ebool] : ( X0 != X0 ) )
& ( ! [X1: tyop_2Emin_2Ebool] : ( X1 = X1 )
| ~ p(c_2Ebool_2ET_2E0) ) ),
inference(rectify,[],[f171]) ).
tff(f173,plain,
( ( p(c_2Ebool_2ET_2E0)
| ( sK9 != sK9 ) )
& ( ! [X1: tyop_2Emin_2Ebool] : ( X1 = X1 )
| ~ p(c_2Ebool_2ET_2E0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f172]) ).
tff(f332,plain,
( p(c_2Ebool_2ET_2E0)
| ( sK9 != sK9 ) ),
inference(cnf_transformation,[],[f173]) ).
tff(f402,plain,
~ p(c_2Ebool_2ET_2E0),
inference(cnf_transformation,[],[f94]) ).
tff(f474,plain,
p(c_2Ebool_2ET_2E0),
inference(trivial_inequality_removal,[],[f332]) ).
tff(f493,plain,
$false,
inference(resolution,[],[f474,f402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP001_7 : 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 : n014.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 11:47:32 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 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
% 0.10/0.45 % (665430)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (665441)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1703077472:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (665436)% WARNING: option uhcvi not known.
% 0.10/0.45 % (665441) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-665430-665441"...
% 0.10/0.45 % (665441)...printing done.
% 0.10/0.45 % (665435)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1988891064_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (665437)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3095550849:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (665436)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3897250389:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (665440)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3516772735:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (665438)dis+10_1_sil=32000:sp=arity:random_seed=1725990102:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (665439)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=306029760:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (665441)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (665441)------------------------------
% 0.10/0.46 % (665441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (665441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (665441)CaDiCaL version: 2.1.3
% 0.10/0.46 % (665441)Termination reason: Refutation
% 0.10/0.46 % (665441)Time elapsed: 0.005 s
% 0.10/0.46 % (665441)Peak memory usage: 12 MB
% 0.10/0.46 % (665441)Instructions burned: 16 (million)
% 0.10/0.46 % (665430)Success in time 0.032 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------