%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP019_1 : 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 : n007.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 11:28:30 AM UTC 2026
% Result : Theorem 1.97s 1.15s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 29 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 6 |; 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 65 ( 65 usr; 28 con; 0-2 aty)
% Number of variables : 8 ( 7 !; 1 ?; 8 :)
% 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: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
tff(pred_def_1,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > $o ).
tff(pred_def_3,type,
sP2: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > $o ).
tff(pred_def_4,type,
sP3: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > $o ).
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/sandbox2/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/sandbox2/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(f49,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(f50,plain,
( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(sK0) )
& ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) != sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f49]) ).
tff(f51,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(f52,plain,
mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) != sK0,
inference(cnf_transformation,[],[f50]) ).
tff(f53,plain,
mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(sK0),
inference(cnf_transformation,[],[f50]) ).
tff(f54,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,[],[f51]) ).
tff(f56,definition,
~ sP1(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0)),
introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction]) ).
tff(f57,plain,
sP1(sK0),
inference(inequality_splitting,[],[f52,f56]) ).
tff(f60,definition,
~ sP3(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0)),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
tff(f61,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 )
| sP3(mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(X0)) ),
inference(inequality_splitting,[],[f54,f60]) ).
tff(f62,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( sP3(mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(X0))
| ~ sP1(X0) ),
inference(superposition,[],[f56,f61]) ).
tff(f64,plain,
( sP3(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0))
| ~ sP1(sK0) ),
inference(superposition,[],[f62,f53]) ).
tff(f65,plain,
~ sP1(sK0),
inference(forward_subsumption_resolution,[],[f64,f60]) ).
tff(f67,plain,
$false,
inference(forward_subsumption_resolution,[],[f65,f57]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n007.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 27 12:02:56 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 1.97/1.15 % (1288238)Detected formulas, will run a generic FOF schedule.
% 1.97/1.15 % (1288246)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2289276721:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.97/1.15 % (1288246)First to succeed.
% 1.97/1.15 % (1288246)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1288238"
% 1.97/1.15 % (1288245)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=2766366525:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.97/1.15 % (1288248)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1162721594:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.97/1.15 % (1288249)dis-21_1_sil=8000:lcm=predicate:random_seed=4025227015: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)
% 1.97/1.15 % (1288243)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=3486710085:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.97/1.15 % (1288244)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=703072606:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.97/1.15 % (1288247)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=749719907:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.97/1.15 % (1288247)Also succeeded, but the first one will report.
% 1.97/1.15 % (1288249)Also succeeded, but the first one will report.
% 1.97/1.15 % (1288248)Also succeeded, but the first one will report.
% 1.97/1.15 % (1288246)Refutation found. Thanks to Tanya!
% 1.97/1.15 % SZS status Theorem for theBenchmark
% 1.97/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/1.33 % (1288246)------------------------------
% 2.50/1.33 % (1288246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.33 % (1288246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.33 % (1288246)CaDiCaL version: 2.1.3
% 2.50/1.33 % (1288246)Termination reason: Refutation
% 2.50/1.33 % (1288246)Time elapsed: 0.001 s
% 2.50/1.33 % (1288246)Peak memory usage: 88 MB
% 2.50/1.33 % (1288246)Instructions burned: 1 (million)
% 2.50/1.33 % (1288246)------------------------------
% 2.50/1.33 % (1288246)------------------------------
% 2.50/1.33 % (1288238)Success in time 0.268 s
% 2.50/1.33 % Vampire exiting
%------------------------------------------------------------------------------