%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP012_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 11:28:05 AM UTC 2026
% Result : Theorem 2.50s 1.28s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 3 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 75 ( 75 usr; 31 con; 0-2 aty)
% Number of variables : 26 ( 23 !; 3 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
u: $tType ).
tff(type_def_6,type,
d: $tType ).
tff(type_def_7,type,
du: $tType ).
tff(type_def_8,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
tff(type_def_9,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(type_def_10,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(type_def_11,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(type_def_12,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(type_def_13,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: $tType ).
tff(type_def_14,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: $tType ).
tff(type_def_15,type,
mono_2Etyop_2Einteger_2Eint: $tType ).
tff(func_def_0,type,
tyop_2Einteger_2Eint: d ).
tff(func_def_1,type,
tyop_2Emin_2Ebool: d ).
tff(func_def_2,type,
tyop_2Emin_2Efun: ( d * d ) > d ).
tff(func_def_3,type,
s: ( d * u ) > du ).
tff(func_def_4,type,
app_2E2: ( du * du ) > u ).
tff(func_def_5,type,
combin_i_2E0: u ).
tff(func_def_6,type,
combin_k_2E0: u ).
tff(func_def_7,type,
combin_s_2E0: u ).
tff(func_def_8,type,
c_2Ebool_2E_21_2E0: u ).
tff(func_def_9,type,
c_2Ebool_2E_21_2E1: du > u ).
tff(func_def_10,type,
c_2Ebool_2E_2F_5C_2E0: u ).
tff(func_def_11,type,
c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).
tff(func_def_12,type,
c_2Emin_2E_3D_2E0: u ).
tff(func_def_13,type,
c_2Emin_2E_3D_2E2: ( du * du ) > u ).
tff(func_def_14,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
tff(func_def_15,type,
c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).
tff(func_def_16,type,
c_2Ebool_2E_3F_2E0: u ).
tff(func_def_17,type,
c_2Ebool_2E_3F_2E1: du > u ).
tff(func_def_18,type,
c_2Ebool_2EF_2E0: u ).
tff(func_def_19,type,
c_2Ebool_2ET_2E0: u ).
tff(func_def_20,type,
c_2Ebool_2E_5C_2F_2E0: u ).
tff(func_def_21,type,
c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).
tff(func_def_22,type,
c_2Einteger_2Eint__add_2E0: u ).
tff(func_def_23,type,
c_2Einteger_2Eint__add_2E2: ( du * du ) > u ).
tff(func_def_24,type,
c_2Einteger_2Eint__divides_2E0: u ).
tff(func_def_25,type,
c_2Einteger_2Eint__divides_2E2: ( du * du ) > u ).
tff(func_def_26,type,
c_2Einteger_2Eint__neg_2E0: u ).
tff(func_def_27,type,
c_2Einteger_2Eint__neg_2E1: du > u ).
tff(func_def_28,type,
c_2Einteger_2Eint__sub_2E0: u ).
tff(func_def_29,type,
c_2Einteger_2Eint__sub_2E2: ( du * du ) > u ).
tff(func_def_30,type,
c_2Ebool_2E_7E_2E0: u ).
tff(func_def_31,type,
c_2Ebool_2E_7E_2E1: du > u ).
tff(func_def_32,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_33,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_34,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_35,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_36,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 * mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
tff(func_def_37,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 * mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint ).
tff(func_def_38,type,
mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_39,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_40,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_41,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_42,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_43,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_44,type,
mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_45,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_46,type,
mono_2Ec_2Einteger_2Eint__add_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 ).
tff(func_def_47,type,
mono_2Ec_2Einteger_2Eint__add_2E2: ( mono_2Etyop_2Einteger_2Eint * mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint ).
tff(func_def_48,type,
mono_2Ec_2Einteger_2Eint__divides_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_49,type,
mono_2Ec_2Einteger_2Eint__divides_2E2: ( mono_2Etyop_2Einteger_2Eint * mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_50,type,
mono_2Ec_2Einteger_2Eint__neg_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
tff(func_def_51,type,
mono_2Ec_2Einteger_2Eint__neg_2E1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
tff(func_def_52,type,
mono_2Ec_2Einteger_2Eint__sub_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 ).
tff(func_def_53,type,
mono_2Ec_2Einteger_2Eint__sub_2E2: ( mono_2Etyop_2Einteger_2Eint * mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint ).
tff(func_def_54,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_55,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_56,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(func_def_57,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).
tff(func_def_58,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(func_def_59,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 > u ).
tff(func_def_60,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(func_def_61,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 > u ).
tff(func_def_62,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > u ).
tff(func_def_63,type,
i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).
tff(func_def_64,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_65,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_66,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_67,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_68,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_69,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 ).
tff(func_def_70,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
tff(func_def_71,type,
j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint ).
tff(func_def_72,type,
sK11: mono_2Etyop_2Einteger_2Eint ).
tff(func_def_73,type,
sK12: mono_2Etyop_2Einteger_2Eint ).
tff(func_def_74,type,
sK13: mono_2Etyop_2Einteger_2Eint ).
tff(pred_def_1,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP0: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_3,type,
sP1: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_4,type,
sP2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_5,type,
sP3: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_6,type,
sP4: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_7,type,
sP5: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_8,type,
sP6: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_9,type,
sP7: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_10,type,
sP8: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_11,type,
sP9: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_12,type,
sP10: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(f61,axiom,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__sub_2E2(X0,X1) = mono_2Ec_2Einteger_2Eint__add_2E2(X0,mono_2Ec_2Einteger_2Eint__neg_2E1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__sub) ).
tff(f62,axiom,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( p(mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X1))
=> ( mono_2Ec_2Einteger_2Eint__divides_2E2(X0,mono_2Ec_2Einteger_2Eint__add_2E2(X2,X1)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RADD) ).
tff(f63,axiom,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides_2E2(X0,mono_2Ec_2Einteger_2Eint__neg_2E1(X1)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X1) )
& ( mono_2Ec_2Einteger_2Eint__divides_2E2(mono_2Ec_2Einteger_2Eint__neg_2E1(X0),X1) = mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__NEG) ).
tff(f74,conjecture,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( p(mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X1))
=> ( mono_2Ec_2Einteger_2Eint__divides_2E2(X0,mono_2Ec_2Einteger_2Eint__sub_2E2(X2,X1)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RSUB) ).
tff(f75,negated_conjecture,
~ ! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( p(mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X1))
=> ( mono_2Ec_2Einteger_2Eint__divides_2E2(X0,mono_2Ec_2Einteger_2Eint__sub_2E2(X2,X1)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f74]) ).
tff(f76,plain,
? [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X2) != mono_2Ec_2Einteger_2Eint__divides_2E2(X0,mono_2Ec_2Einteger_2Eint__sub_2E2(X2,X1)) )
& p(mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X1)) ),
inference(ennf_transformation,[],[f75]) ).
tff(f82,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides_2E2(X0,mono_2Ec_2Einteger_2Eint__add_2E2(X2,X1)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X2) )
| ~ p(mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X1)) ),
inference(ennf_transformation,[],[f62]) ).
tff(f99,plain,
( ( mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,sK13) != mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,mono_2Ec_2Einteger_2Eint__sub_2E2(sK13,sK12)) )
& p(mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f76]) ).
tff(f147,plain,
p(mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,sK12)),
inference(cnf_transformation,[],[f99]) ).
tff(f148,plain,
mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,sK13) != mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,mono_2Ec_2Einteger_2Eint__sub_2E2(sK13,sK12)),
inference(cnf_transformation,[],[f99]) ).
tff(f259,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__sub_2E2(X0,X1) = mono_2Ec_2Einteger_2Eint__add_2E2(X0,mono_2Ec_2Einteger_2Eint__neg_2E1(X1)) ),
inference(cnf_transformation,[],[f61]) ).
tff(f260,plain,
! [X2: mono_2Etyop_2Einteger_2Eint,X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides_2E2(X0,mono_2Ec_2Einteger_2Eint__add_2E2(X2,X1)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X2) )
| ~ p(mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f82]) ).
tff(f262,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__divides_2E2(X0,X1) = mono_2Ec_2Einteger_2Eint__divides_2E2(X0,mono_2Ec_2Einteger_2Eint__neg_2E1(X1)) ),
inference(cnf_transformation,[],[f63]) ).
tff(f263,plain,
mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,sK13) != mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,mono_2Ec_2Einteger_2Eint__add_2E2(sK13,mono_2Ec_2Einteger_2Eint__neg_2E1(sK12))),
inference(definition_unfolding,[],[f148,f259]) ).
tff(f402,plain,
( ( mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,sK13) != mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,sK13) )
| ~ p(mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,mono_2Ec_2Einteger_2Eint__neg_2E1(sK12))) ),
inference(superposition,[],[f263,f260]) ).
tff(f404,plain,
~ p(mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,mono_2Ec_2Einteger_2Eint__neg_2E1(sK12))),
inference(trivial_inequality_removal,[],[f402]) ).
tff(f406,plain,
~ p(mono_2Ec_2Einteger_2Eint__divides_2E2(sK11,sK12)),
inference(forward_demodulation,[],[f404,f262]) ).
tff(f409,plain,
$false,
inference(forward_subsumption_resolution,[],[f406,f147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP012_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n019.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 11:58:34 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 2.50/1.28 % (2953542)Detected formulas, will run a generic FOF schedule.
% 2.50/1.28 % (2953549)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=3909217916:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.50/1.28 % (2953552)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2356099011:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.50/1.28 % (2953547)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=2403717136:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.50/1.28 % (2953548)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=4085090607:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.50/1.28 % (2953551)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4274372795:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.50/1.28 % (2953550)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2194100623:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.50/1.28 % (2953550)Refutation not found, incomplete strategy
% 2.50/1.28 % (2953550)------------------------------
% 2.50/1.28 % (2953550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.28 % (2953550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.28 % (2953550)CaDiCaL version: 2.1.3
% 2.50/1.28 % (2953550)Termination reason: Refutation not found, incomplete strategy
% 2.50/1.28 % (2953550)Time elapsed: 0.004 s
% 2.50/1.28 % (2953550)Peak memory usage: 88 MB
% 2.50/1.28 % (2953550)Instructions burned: 7 (million)
% 2.50/1.28 % (2953551)First to succeed.
% 2.50/1.28 % (2953551)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2953542"
% 2.50/1.28 % (2953553)dis-21_1_sil=8000:lcm=predicate:random_seed=3361589515: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)
% 2.50/1.28 % (2953552)Instruction limit reached!
% 2.50/1.28 % (2953552)------------------------------
% 2.50/1.28 % (2953552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.28 % (2953552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.28 % (2953552)CaDiCaL version: 2.1.3
% 2.50/1.28 % (2953552)Termination reason: Instruction limit
% 2.50/1.28 % (2953552)Termination phase: Saturation
% 2.50/1.28 % (2953552)Time elapsed: 0.085 s
% 2.50/1.28 % (2953552)Peak memory usage: 90 MB
% 2.50/1.28 % (2953552)Instructions burned: 139 (million)
% 2.50/1.28 % (2953553)Instruction limit reached!
% 2.50/1.28 % (2953553)------------------------------
% 2.50/1.28 % (2953553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.28 % (2953553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.28 % (2953553)CaDiCaL version: 2.1.3
% 2.50/1.28 % (2953553)Termination reason: Instruction limit
% 2.50/1.28 % (2953553)Termination phase: Saturation
% 2.50/1.28 % (2953553)Time elapsed: 0.070 s
% 2.50/1.28 % (2953553)Peak memory usage: 89 MB
% 2.50/1.28 % (2953553)Instructions burned: 129 (million)
% 2.50/1.28 % (2953561)lrs+10_1_sil=8000:sp=occurrence:random_seed=3545784819:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.50/1.28 % (2953562)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3856489867:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.50/1.28 % (2953562)Also succeeded, but the first one will report.
% 2.50/1.28 % (2953550)------------------------------
% 2.50/1.28 % (2953550)------------------------------
% 2.50/1.28 % (2953551)Refutation found. Thanks to Tanya!
% 2.50/1.28 % SZS status Theorem for theBenchmark
% 2.50/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/1.43 % (2953551)------------------------------
% 3.43/1.43 % (2953551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.43 % (2953551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.43 % (2953551)CaDiCaL version: 2.1.3
% 3.43/1.43 % (2953551)Termination reason: Refutation
% 3.43/1.43 % (2953551)Time elapsed: 0.006 s
% 3.43/1.43 % (2953551)Peak memory usage: 88 MB
% 3.43/1.43 % (2953551)Instructions burned: 7 (million)
% 3.43/1.43 % (2953551)------------------------------
% 3.43/1.44 % (2953551)------------------------------
% 3.43/1.44 % (2953542)Success in time 0.406 s
% 3.43/1.44 % Vampire exiting
%------------------------------------------------------------------------------