TSTP Solution File: ITP019^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP019^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:44:29 EDT 2024
% Result : Theorem 0.18s 0.37s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 83
% Syntax : Number of formulae : 100 ( 8 unt; 80 typ; 0 def)
% Number of atoms : 180 ( 35 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 29 ( 13 ~; 4 |; 5 &; 0 @)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 94 ( 93 >; 1 *; 0 +; 0 <<)
% Number of symbols : 75 ( 72 usr; 24 con; 0-6 aty)
% Number of variables : 16 ( 0 ^ 8 !; 2 ?; 16 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
d: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
u: $tType ).
thf(type_def_8,type,
du: $tType ).
thf(type_def_9,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(type_def_10,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(func_def_0,type,
u: $tType ).
thf(func_def_1,type,
d: $tType ).
thf(func_def_2,type,
du: $tType ).
thf(func_def_3,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(func_def_4,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(func_def_5,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_6,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_7,type,
tyop_2Enum_2Enum: d ).
thf(func_def_8,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(func_def_9,type,
tyop_2Erealax_2Ereal: d ).
thf(func_def_10,type,
s: d > u > du ).
thf(func_def_11,type,
app_2E2: du > du > u ).
thf(func_def_12,type,
combin_i_2E0: u ).
thf(func_def_13,type,
combin_k_2E0: u ).
thf(func_def_14,type,
combin_s_2E0: u ).
thf(func_def_15,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_16,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_17,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_18,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_19,type,
c_2Enum_2E0_2E0: u ).
thf(func_def_20,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_21,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_22,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_23,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_24,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_25,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_26,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_27,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_28,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_29,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_30,type,
c_2Ecomplex_2Ecomplex__inv_2E0: u ).
thf(func_def_31,type,
c_2Ecomplex_2Ecomplex__inv_2E1: du > u ).
thf(func_def_32,type,
c_2Ecomplex_2Ecomplex__of__num_2E0: u ).
thf(func_def_33,type,
c_2Ecomplex_2Ecomplex__of__num_2E1: du > u ).
thf(func_def_34,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_35,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_36,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_37,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(func_def_38,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_39,type,
mono_2Eapp_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_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_40,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_41,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(func_def_42,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_43,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(func_def_44,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(func_def_45,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_46,type,
mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_47,type,
mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_48,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_49,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_50,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_51,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(func_def_52,type,
i_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 ) > u ).
thf(func_def_53,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_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).
thf(func_def_54,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(func_def_55,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 ).
thf(func_def_56,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_57,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_58,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(func_def_59,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_60,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_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_61,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(func_def_62,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 ).
thf(func_def_64,type,
vNOT: $o > $o ).
thf(func_def_67,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_68,type,
sK0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_69,type,
sK1: u > d > u ).
thf(func_def_70,type,
sK2: u > d > u ).
thf(func_def_71,type,
sK3: u > u > d > d > u ).
thf(func_def_73,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_74,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_75,type,
vAND: $o > $o > $o ).
thf(func_def_76,type,
vOR: $o > $o > $o ).
thf(func_def_77,type,
vIMP: $o > $o > $o ).
thf(f350,plain,
$false,
inference(subsumption_resolution,[],[f349,f220]) ).
thf(f220,plain,
vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) != sK0,
inference(equality_proxy_clausification,[],[f219]) ).
thf(f219,plain,
$false = vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),sK0),
inference(not_proxy_clausification,[],[f125]) ).
thf(f125,plain,
$true = vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),sK0)),
inference(cnf_transformation,[],[f103]) ).
thf(f103,plain,
( ( $true != vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,sK0))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),sK0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f98,f102]) ).
thf(f102,plain,
( ? [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( $true != vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,X0))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),X0)) ) )
=> ( ( $true != vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,sK0))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),sK0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f98,plain,
? [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( $true != vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,X0))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),X0)) ) ),
inference(ennf_transformation,[],[f46]) ).
thf(f46,plain,
~ ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( $true = vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),X0)) )
=> ( $true = vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,X0))) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f45,plain,
~ ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = X0)
=> vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,X0)) ),
inference(rectify,[],[f42]) ).
thf(f42,negated_conjecture,
~ ! [X16: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = X16)
=> vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,X16) = vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)) ),
inference(negated_conjecture,[],[f41]) ).
thf(f41,conjecture,
! [X16: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = X16)
=> vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,X16) = vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(f349,plain,
vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = sK0,
inference(trivial_inequality_removal,[],[f347]) ).
thf(f347,plain,
( ( vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) != vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) )
| ( vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = sK0 ) ),
inference(superposition,[],[f156,f222]) ).
thf(f222,plain,
vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,sK0),
inference(equality_proxy_clausification,[],[f221]) ).
thf(f221,plain,
$true = vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,sK0)),
inference(not_proxy_clausification,[],[f126]) ).
thf(f126,plain,
$true != vAPP($o,$o,vNOT,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,$o),vEQ(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0)),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,sK0))),
inference(cnf_transformation,[],[f103]) ).
thf(f156,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) != vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,X0) )
| ( vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = X0 ) ),
inference(cnf_transformation,[],[f106]) ).
thf(f106,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,X0) )
| ( vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) != X0 ) )
& ( ( vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = X0 )
| ( vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) != vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,X0) ) ) ),
inference(nnf_transformation,[],[f83]) ).
thf(f83,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,X0) )
<=> ( vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = X0 ) ),
inference(rectify,[],[f40]) ).
thf(f40,axiom,
! [X16: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__inv,X16) = vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) )
<=> ( vAPP(mono_2Etyop_2Enum_2Enum,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,mono_2Ec_2Ecomplex_2Ecomplex__of__num,mono_2Ec_2Enum_2E0) = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ITP019^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.12/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sat May 18 18:31:38 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (23499)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.35 % (23502)WARNING: value z3 for option sas not known
% 0.18/0.35 % (23501)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.35 % (23503)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.35 % (23502)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.18/0.35 % (23504)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.18/0.35 % (23506)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.18/0.36 % (23506)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.36 % Exception at run slice level
% 0.18/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.36 % Exception at run slice level
% 0.18/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.36 % (23500)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.36 % (23505)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.18/0.36 % (23502)First to succeed.
% 0.18/0.36 % (23504)Also succeeded, but the first one will report.
% 0.18/0.36 % (23502)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23499"
% 0.18/0.37 % (23502)Refutation found. Thanks to Tanya!
% 0.18/0.37 % SZS status Theorem for theBenchmark
% 0.18/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.37 % (23502)------------------------------
% 0.18/0.37 % (23502)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.37 % (23502)Termination reason: Refutation
% 0.18/0.37
% 0.18/0.37 % (23502)Memory used [KB]: 958
% 0.18/0.37 % (23502)Time elapsed: 0.015 s
% 0.18/0.37 % (23502)Instructions burned: 26 (million)
% 0.18/0.37 % (23499)Success in time 0.038 s
%------------------------------------------------------------------------------