%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP019_1 : 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 : n017.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 11:35:26 AM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 5 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 68 ( 68 usr; 28 con; 0-4 aty)
% Number of variables : 11 ( 10 !; 1 ?; 11 :)
% 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_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: $tType ).
tff(type_def_12,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: $tType ).
tff(type_def_13,type,
mono_2Etyop_2Enum_2Enum: $tType ).
tff(type_def_14,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
tff(func_def_0,type,
tyop_2Emin_2Ebool: d ).
tff(func_def_1,type,
tyop_2Emin_2Efun: ( d * d ) > d ).
tff(func_def_2,type,
tyop_2Enum_2Enum: d ).
tff(func_def_3,type,
tyop_2Epair_2Eprod: ( d * d ) > d ).
tff(func_def_4,type,
tyop_2Erealax_2Ereal: d ).
tff(func_def_5,type,
s: ( d * u ) > du ).
tff(func_def_6,type,
app_2E2: ( du * du ) > u ).
tff(func_def_7,type,
combin_i_2E0: u ).
tff(func_def_8,type,
combin_k_2E0: u ).
tff(func_def_9,type,
combin_s_2E0: u ).
tff(func_def_10,type,
c_2Ebool_2E_21_2E0: u ).
tff(func_def_11,type,
c_2Ebool_2E_21_2E1: du > u ).
tff(func_def_12,type,
c_2Ebool_2E_2F_5C_2E0: u ).
tff(func_def_13,type,
c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).
tff(func_def_14,type,
c_2Enum_2E0_2E0: u ).
tff(func_def_15,type,
c_2Emin_2E_3D_2E0: u ).
tff(func_def_16,type,
c_2Emin_2E_3D_2E2: ( du * du ) > u ).
tff(func_def_17,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
tff(func_def_18,type,
c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).
tff(func_def_19,type,
c_2Ebool_2E_3F_2E0: u ).
tff(func_def_20,type,
c_2Ebool_2E_3F_2E1: du > u ).
tff(func_def_21,type,
c_2Ebool_2EF_2E0: u ).
tff(func_def_22,type,
c_2Ebool_2ET_2E0: u ).
tff(func_def_23,type,
c_2Ebool_2E_5C_2F_2E0: u ).
tff(func_def_24,type,
c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).
tff(func_def_25,type,
c_2Ecomplex_2Ecomplex__inv_2E0: u ).
tff(func_def_26,type,
c_2Ecomplex_2Ecomplex__inv_2E1: du > u ).
tff(func_def_27,type,
c_2Ecomplex_2Ecomplex__of__num_2E0: u ).
tff(func_def_28,type,
c_2Ecomplex_2Ecomplex__of__num_2E1: du > u ).
tff(func_def_29,type,
c_2Ebool_2E_7E_2E0: u ).
tff(func_def_30,type,
c_2Ebool_2E_7E_2E1: du > u ).
tff(func_def_31,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_32,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_33,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
tff(func_def_34,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 * mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
tff(func_def_35,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_36,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_37,type,
mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).
tff(func_def_38,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_39,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_40,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_41,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_42,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_43,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_44,type,
mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).
tff(func_def_45,type,
mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
tff(func_def_46,type,
mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).
tff(func_def_47,type,
mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
tff(func_def_48,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_49,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_50,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(func_def_51,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_52,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_53,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 > u ).
tff(func_def_54,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 > u ).
tff(func_def_55,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
tff(func_def_56,type,
i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).
tff(func_def_57,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_58,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_59,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_60,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).
tff(func_def_61,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).
tff(func_def_62,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
tff(func_def_63,type,
j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
tff(func_def_64,type,
sK0: ( d * d * u * u ) > u ).
tff(func_def_65,type,
sK1: ( d * u ) > u ).
tff(func_def_66,type,
sK2: ( d * u ) > u ).
tff(func_def_67,type,
sK3: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
tff(pred_def_1,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(f36,axiom,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ecomplex_2Ecomplex__inv_2E1) ).
tff(f37,axiom,
! [X0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ecomplex_2Ecomplex__of__num_2E1) ).
tff(f46,axiom,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(X0) = mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) )
<=> ( X0 = mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
tff(f47,conjecture,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( X0 != mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) )
=> ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(X0) != mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
tff(f48,negated_conjecture,
~ ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( X0 != mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) )
=> ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(X0) != mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
tff(f55,plain,
? [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(X0) = mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) )
& ( X0 != mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) ) ),
inference(ennf_transformation,[],[f48]) ).
tff(f84,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(X0) = mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) )
| ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) != X0 ) )
& ( ( X0 = mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) )
| ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(X0) != mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) ) ) ),
inference(nnf_transformation,[],[f46]) ).
tff(f85,plain,
( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(sK3) )
& ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) != sK3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f55]) ).
tff(f139,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0,X0) ),
inference(cnf_transformation,[],[f36]) ).
tff(f140,plain,
! [X0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0,X0) ),
inference(cnf_transformation,[],[f37]) ).
tff(f165,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = X0 )
| ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(X0) != mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) ) ),
inference(cnf_transformation,[],[f84]) ).
tff(f167,plain,
mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) != sK3,
inference(cnf_transformation,[],[f85]) ).
tff(f168,plain,
mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(sK3),
inference(cnf_transformation,[],[f85]) ).
tff(f170,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0,X0) != mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0,mono_2Ec_2Enum_2E0_2E0) )
| ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0,mono_2Ec_2Enum_2E0_2E0) = X0 ) ),
inference(definition_unfolding,[],[f165,f140,f139,f140]) ).
tff(f171,plain,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0,mono_2Ec_2Enum_2E0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0,sK3),
inference(definition_unfolding,[],[f168,f140,f139]) ).
tff(f172,plain,
sK3 != mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0,mono_2Ec_2Enum_2E0_2E0),
inference(definition_unfolding,[],[f167,f140]) ).
tff(f502,plain,
( ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0,mono_2Ec_2Enum_2E0_2E0) != mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0,mono_2Ec_2Enum_2E0_2E0) )
| ( sK3 = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0,mono_2Ec_2Enum_2E0_2E0) ) ),
inference(superposition,[],[f170,f171]) ).
tff(f503,plain,
sK3 = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0,mono_2Ec_2Enum_2E0_2E0),
inference(trivial_inequality_removal,[],[f502]) ).
tff(f504,plain,
$false,
inference(forward_subsumption_resolution,[],[f503,f172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n017.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 12:00:51 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.44 Running first-order model finding
% 0.13/0.44 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
% 0.19/0.49 % (2430680)Will run a generic schedule for satisfiability detection.
% 0.19/0.49 % (2430688)dis+10_1_sil=32000:sp=arity:random_seed=155095850:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.49 % (2430686)% WARNING: option uhcvi not known.
% 0.19/0.49 % (2430688) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2430680-2430688"...
% 0.19/0.49 % (2430685)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4290271258_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.49 % (2430686)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1765957599:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.49 % (2430687)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1640523600:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.49 % (2430691)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1331460118:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.49 % (2430689)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3175886702:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.49 % (2430688)...printing done.
% 0.19/0.49 % (2430690)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=981451862:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.49 % (2430688)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (2430688)------------------------------
% 0.19/0.49 % (2430688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.49 % (2430688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.49 % (2430688)CaDiCaL version: 2.1.3
% 0.19/0.49 % (2430688)Termination reason: Refutation
% 0.19/0.49 % (2430688)Time elapsed: 0.007 s
% 0.19/0.49 % (2430688)Peak memory usage: 12 MB
% 0.19/0.49 % (2430688)Instructions burned: 18 (million)
% 0.19/0.49 % (2430680)Success in time 0.036 s
% 0.19/0.49 % Vampire exiting
%------------------------------------------------------------------------------