%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP019_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p 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 : Fri Sep 25 01:47:51 PM UTC 2026
% Result : Theorem 2.41s 1.27s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 18 unt; 0 typ; 2 def)
% Number of atoms : 51 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 6 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 67 ( 67 usr; 28 con; 0-4 aty)
% Number of variables : 13 ( 0 sgn 12 !; 1 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
tyop_2Emin_2Ebool: d ).
tff(pred_def_1,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
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: ( u * d ) > 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_2Ebool * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) > 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_2Ebool * 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_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_2Enum_2Enum * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ) > 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_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 ).
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: ( u * ( u * ( d * d ) ) ) > u ).
tff(func_def_65,type,
sK1: ( u * d ) > u ).
tff(func_def_66,type,
sK2: ( u * d ) > u ).
tff(func_def_67,type,
sK3: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
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/sandbox2/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/sandbox2/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/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(f55,plain,
? [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(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) )
| ( 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 )
| ( 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) != sK3 )
& ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(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__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 ) ),
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]) ).
tcf(c_118,plain,
! [X0_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( 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_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_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) != 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(cnf_transformation,[],[f170]) ).
tcf(c_119,negated_conjecture,
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(cnf_transformation,[],[f171]) ).
tcf(c_120,negated_conjecture,
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,
inference(cnf_transformation,[],[f172]) ).
tcf(c_1260,definition,
iPr_def_10 = 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),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1261,definition,
iPr_def_11 = 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),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1262,negated_conjecture,
iPr_def_10 != sK3,
inference(demodulation,[status(thm)],[c_120,c_1260]) ).
tcf(c_1263,negated_conjecture,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_119,c_1261]) ).
tcf(c_2049,plain,
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) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1261,c_1263]) ).
tcf(c_9520,plain,
! [X0_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( X0_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 = iPr_def_10 )
| ( 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_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_118,c_1260]) ).
tcf(c_9527,plain,
sK3 = iPr_def_10,
inference(superposition,[status(thm)],[c_2049,c_9520]) ).
tcf(c_9530,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_1262,c_9527]) ).
tcf(c_9531,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_9530]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 17:42:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 2.41/1.27 % SZS status Started for theBenchmark.p
% 2.41/1.27 % SZS status Theorem for theBenchmark.p
% 2.41/1.27
% 2.41/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.41/1.27
% 2.41/1.27 % ------ iProver source info
% 2.41/1.27
% 2.41/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.41/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.41/1.27 % git: non_committed_changes: false
% 2.41/1.27
% 2.41/1.27 % ------ Parsing...
% 2.41/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 2.41/1.27 %
% 2.41/1.27
% 2.41/1.27 % ------ Preprocessing... sup_sim: 0 pe_s pe_e sup_sim: 0 pe_s pe_e %
% 2.41/1.27
% 2.41/1.27 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 2.41/1.27 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 2.41/1.27 %
% 2.41/1.27
% 2.41/1.27 % ------ Preprocessing...
% 2.41/1.27 % ------ Proving...
% 2.41/1.27 % ------ Problem Properties
% 2.41/1.27
% 2.41/1.27 %
% 2.41/1.27 % clauses 65
% 2.41/1.27 % conjectures 2
% 2.41/1.27 % EPR 7
% 2.41/1.27 % Horn 57
% 2.41/1.27 % unary 30
% 2.41/1.27 % binary 27
% 2.41/1.27 % lits 108
% 2.41/1.27 % lits eq 38
% 2.41/1.27 % fd_pure 1
% 2.41/1.27 % fd_pseudo 0
% 2.41/1.27 % fd_cond 1
% 2.41/1.27 % fd_pseudo_cond 2
% 2.41/1.27 % AC symbols 0
% 2.41/1.27
% 2.41/1.27 % ------ Schedule dynamic 5 is on
% 2.41/1.27
% 2.41/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.41/1.27
% 2.41/1.27
% 2.41/1.27 % ------
% 2.41/1.27 % Current options:
% 2.41/1.27 % ------
% 2.41/1.27
% 2.41/1.27
% 2.41/1.27 %
% 2.41/1.27
% 2.41/1.27 % ------ Proving...
% 2.41/1.27 %
% 2.41/1.27
% 2.41/1.27 % SZS status Theorem for theBenchmark.p
% 2.41/1.27
% 2.41/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.41/1.27
% 2.41/1.27
%------------------------------------------------------------------------------