%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP001^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n031.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 : Wed Feb 25 08:53:00 AM UTC 2026
% Result : Theorem 0.26s 2.96s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 24 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 28 ( 14 ~; 7 |; 3 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 48 ( 30 fml; 18 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 35 con; 0-0 aty)
% Number of variables : 9 ( 6 !; 3 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
d: $tType ).
tff(type_def_7,type,
u: $tType ).
tff(type_def_8,type,
du: $tType ).
tff(func_def_0,type,
u: $tType ).
tff(func_def_1,type,
d: $tType ).
tff(func_def_2,type,
du: $tType ).
tff(func_def_3,type,
tyop_2Emin_2Ebool: d ).
tff(func_def_4,type,
tyop_2Emin_2Efun: sTfun(d,sTfun(d,d)) ).
tff(func_def_5,type,
s: sTfun(d,sTfun(u,du)) ).
tff(func_def_6,type,
app_2E2: sTfun(du,sTfun(du,u)) ).
tff(func_def_7,type,
combin_i_2E0: u ).
tff(func_def_8,type,
combin_k_2E0: u ).
tff(func_def_9,type,
combin_s_2E0: u ).
tff(func_def_10,type,
c_2Ebool_2E_21_2E0: u ).
tff(func_def_11,type,
c_2Ebool_2E_21_2E1: sTfun(du,u) ).
tff(func_def_12,type,
c_2Ebool_2E_2F_5C_2E0: u ).
tff(func_def_13,type,
c_2Ebool_2E_2F_5C_2E2: sTfun(du,sTfun(du,u)) ).
tff(func_def_14,type,
c_2Emin_2E_3D_2E0: u ).
tff(func_def_15,type,
c_2Emin_2E_3D_2E2: sTfun(du,sTfun(du,u)) ).
tff(func_def_16,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
tff(func_def_17,type,
c_2Emin_2E_3D_3D_3E_2E2: sTfun(du,sTfun(du,u)) ).
tff(func_def_18,type,
c_2Ebool_2E_3F_2E0: u ).
tff(func_def_19,type,
c_2Ebool_2E_3F_2E1: sTfun(du,u) ).
tff(func_def_20,type,
c_2Ebool_2EF_2E0: u ).
tff(func_def_21,type,
c_2Ebool_2ET_2E0: u ).
tff(func_def_22,type,
c_2Ebool_2E_5C_2F_2E0: u ).
tff(func_def_23,type,
c_2Ebool_2E_5C_2F_2E2: sTfun(du,sTfun(du,u)) ).
tff(func_def_24,type,
c_2Ebool_2E_7E_2E0: u ).
tff(func_def_25,type,
c_2Ebool_2E_7E_2E1: sTfun(du,u) ).
tff(func_def_26,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: sTfun(sTfun($o,$o),sTfun($o,$o)) ).
tff(func_def_27,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: sTfun(sTfun($o,sTfun($o,$o)),sTfun($o,sTfun($o,$o))) ).
tff(func_def_28,type,
mono_2Ec_2Ebool_2E_2F_5C: sTfun($o,sTfun($o,$o)) ).
tff(func_def_29,type,
mono_2Ec_2Emin_2E_3D_3D_3E: sTfun($o,sTfun($o,$o)) ).
tff(func_def_32,type,
mono_2Ec_2Ebool_2E_5C_2F: sTfun($o,sTfun($o,$o)) ).
tff(func_def_33,type,
mono_2Ec_2Ebool_2E_7E: sTfun($o,$o) ).
tff(func_def_34,type,
i_mono_2Etyop_2Emin_2Ebool: sTfun($o,u) ).
tff(func_def_35,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: sTfun(sTfun($o,$o),u) ).
tff(func_def_36,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: sTfun(sTfun($o,sTfun($o,$o)),u) ).
tff(func_def_37,type,
j_mono_2Etyop_2Emin_2Ebool: sTfun(du,$o) ).
tff(func_def_38,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: sTfun(du,sTfun($o,$o)) ).
tff(func_def_39,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: sTfun(du,sTfun($o,sTfun($o,$o))) ).
tff(f58,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f54,f57]) ).
tff(f57,plain,
mono_2Ec_2Ebool_2ET = $true,
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
tff(f55,plain,
( ( mono_2Ec_2Ebool_2ET = $true )
| ( sK0 != sK0 ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
tff(f53,plain,
( ( ! [X0: $o] : ( (X0) = (X0) )
| ( mono_2Ec_2Ebool_2ET != $true ) )
& ( ( mono_2Ec_2Ebool_2ET = $true )
| ( sK0 != sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f51,f52]) ).
tff(f52,plain,
( ? [X1: $o] : ( (X1) != (X1) )
=> ( sK0 != sK0 ) ),
introduced(definition,[],[choice_axiom]) ).
tff(f51,plain,
( ( ! [X0: $o] : ( (X0) = (X0) )
| ( mono_2Ec_2Ebool_2ET != $true ) )
& ( ( mono_2Ec_2Ebool_2ET = $true )
| ? [X1: $o] : ( (X1) != (X1) ) ) ),
inference(rectify,[status(thm)],[f50]) ).
tff(f50,plain,
( ( ! [X0: $o] : ( (X0) = (X0) )
| ( mono_2Ec_2Ebool_2ET != $true ) )
& ( ( mono_2Ec_2Ebool_2ET = $true )
| ? [X0: $o] : ( (X0) != (X0) ) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
tff(f32,plain,
( ! [X0: $o] : ( (X0) = (X0) )
<=> ( mono_2Ec_2Ebool_2ET = $true ) ),
inference(fool_elimination,[status(thm)],[f31]) ).
tff(f31,plain,
( mono_2Ec_2Ebool_2ET
<=> ! [X0: $o] : ( (X0) = (X0) ) ),
inference(rectify,[status(thm)],[f25]) ).
tff(f25,axiom,
( mono_2Ec_2Ebool_2ET
<=> ! [X15: $o] : ( (X15) = (X15) ) ),
file('/export/starexec/sandbox/tmp/tmp.7HGaHfDLGw/DTF2THF_2875.p',thm_2Ebool_2ET__DEF) ).
tff(f54,plain,
mono_2Ec_2Ebool_2ET != $true,
inference(cnf_transformation,[status(thm)],[f49]) ).
tff(f49,plain,
mono_2Ec_2Ebool_2ET != $true,
inference(flattening,[status(thm)],[f40]) ).
tff(f40,plain,
mono_2Ec_2Ebool_2ET != $true,
inference(fool_elimination,[status(thm)],[f39]) ).
tff(f39,plain,
~ mono_2Ec_2Ebool_2ET,
inference(rectify,[status(thm)],[f27]) ).
tff(f27,negated_conjecture,
~ mono_2Ec_2Ebool_2ET,
inference(negated_conjecture,[status(cth)],[f26]) ).
tff(f26,conjecture,
mono_2Ec_2Ebool_2ET,
file('/export/starexec/sandbox/tmp/tmp.7HGaHfDLGw/DTF2THF_2875.p',thm_2Ebool_2ETRUTH) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.21 % Problem : ITP001^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.08/0.22 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.58 % Computer : n031.cluster.edu
% 0.13/0.58 % Model : x86_64 x86_64
% 0.13/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.58 % Memory : 8042.1875MB
% 0.13/0.58 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.58 % CPULimit : 300
% 0.13/0.58 % WCLimit : 300
% 0.13/0.58 % DateTime : Tue Feb 24 08:17:03 EST 2026
% 0.13/0.58 % CPUTime :
% 0.13/0.58 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.92 ---- Original DTF file ---
% 0.17/0.92 thf(spec,logic,$$dhol).
% 0.17/0.92 %------------------------------------------------------------------------------
% 0.17/0.92 % File : ITP001^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.17/0.92 % Domain : Interactive Theorem Proving
% 0.17/0.92 % Problem : HOL4 syntactic export of thm_2Ebool_2ETRUTH.p, bushy mode
% 0.17/0.92 % Version : [BG+19] axioms.
% 0.17/0.92 % English :
% 0.17/0.92
% 0.17/0.92 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.17/0.92 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.17/0.92 % Source : [BG+19]
% 0.17/0.92 % Names : thm_2Ebool_2ETRUTH.p [Gau19]
% 0.17/0.92 % : HL400001^1.p [TPAP]
% 0.17/0.92
% 0.17/0.92 % Status : Theorem
% 0.17/0.92 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0
% 0.17/0.92 % Syntax : Number of formulae : 66 ( 19 unt; 40 typ; 0 def)
% 0.17/0.92 % Number of atoms : 43 ( 20 equ; 1 cnn)
% 0.17/0.92 % Maximal formula atoms : 2 ( 1 avg)
% 0.17/0.92 % Number of connectives : 382 ( 1 ~; 1 |; 1 &; 368 @)
% 0.17/0.92 % ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% 0.17/0.92 % Maximal formula depth : 17 ( 5 avg)
% 0.17/0.92 % Number of types : 4 ( 3 usr)
% 0.17/0.92 % Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% 0.17/0.92 % Number of symbols : 39 ( 37 usr; 16 con; 0-3 aty)
% 0.17/0.92 % Number of variables : 55 ( 0 ^; 54 !; 1 ?; 55 :)
% 0.17/0.92 % SPC : TH0_THM_EQU_NAR
% 0.17/0.92
% 0.17/0.92 % Comments :
% 0.17/0.92 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.17/0.92 %------------------------------------------------------------------------------
% 0.17/0.92 thf(u,type,
% 0.17/0.92 u: $tType ).
% 0.17/0.92
% 0.17/0.92 thf(d,type,
% 0.17/0.92 d: $tType ).
% 0.17/0.92
% 0.17/0.92 thf(du,type,
% 0.17/0.92 du: $tType ).
% 0.17/0.92
% 0.17/0.92 thf(tyop_2Emin_2Ebool,type,
% 0.17/0.92 tyop_2Emin_2Ebool: d ).
% 0.17/0.92
% 0.17/0.92 thf(tyop_2Emin_2Efun,type,
% 0.17/0.92 tyop_2Emin_2Efun: d > d > d ).
% 0.17/0.92
% 0.17/0.92 thf(s,type,
% 0.17/0.92 s: d > u > du ).
% 0.17/0.92
% 0.17/0.92 thf(app_2E2,type,
% 0.17/0.92 app_2E2: du > du > u ).
% 0.17/0.92
% 0.17/0.92 thf(combin_i_2E0,type,
% 0.17/0.92 combin_i_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(combin_k_2E0,type,
% 0.17/0.92 combin_k_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(combin_s_2E0,type,
% 0.17/0.92 combin_s_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2E_21_2E0,type,
% 0.17/0.92 c_2Ebool_2E_21_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2E_21_2E1,type,
% 0.17/0.92 c_2Ebool_2E_21_2E1: du > u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.17/0.92 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.17/0.92 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Emin_2E_3D_2E0,type,
% 0.17/0.92 c_2Emin_2E_3D_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Emin_2E_3D_2E2,type,
% 0.17/0.92 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.17/0.92 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.17/0.92 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2E_3F_2E0,type,
% 0.17/0.92 c_2Ebool_2E_3F_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2E_3F_2E1,type,
% 0.17/0.92 c_2Ebool_2E_3F_2E1: du > u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2EF_2E0,type,
% 0.17/0.92 c_2Ebool_2EF_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2ET_2E0,type,
% 0.17/0.92 c_2Ebool_2ET_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.17/0.92 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.17/0.92 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2E_7E_2E0,type,
% 0.17/0.92 c_2Ebool_2E_7E_2E0: u ).
% 0.17/0.92
% 0.17/0.92 thf(c_2Ebool_2E_7E_2E1,type,
% 0.17/0.92 c_2Ebool_2E_7E_2E1: du > u ).
% 0.17/0.92
% 0.17/0.92 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.17/0.92 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.17/0.92
% 0.17/0.92 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.17/0.92 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.17/0.92
% 0.17/0.92 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.17/0.92 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.17/0.92
% 0.17/0.92 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.17/0.92 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.17/0.92
% 0.17/0.92 thf(mono_2Ec_2Ebool_2EF,type,
% 0.17/0.92 mono_2Ec_2Ebool_2EF: $o ).
% 0.17/0.92
% 0.17/0.92 thf(mono_2Ec_2Ebool_2ET,type,
% 0.17/0.92 mono_2Ec_2Ebool_2ET: $o ).
% 0.17/0.92
% 0.17/0.92 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.17/0.92 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.17/0.92
% 0.17/0.92 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.17/0.92 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.17/0.92
% 0.17/0.92 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.17/0.92 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.17/0.92
% 0.17/0.92 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.17/0.92 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.17/0.92
% 0.17/0.92 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.17/0.92 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.17/0.92
% 0.17/0.92 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.17/0.92 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.17/0.92
% 0.17/0.92 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.17/0.92 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.17/0.92
% 0.17/0.92 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.17/0.92 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.17/0.92
% 0.17/0.92 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.17/0.92 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.17/0.92 ( ! [V2x_2E0: u] :
% 0.17/0.92 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.17/0.92 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.17/0.92 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.17/0.92 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.17/0.92 ! [A_27a: d,V0x_2E0: u] :
% 0.17/0.92 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.17/0.92 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.17/0.92 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.17/0.92 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 0.17/0.92 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(reserved_2Eho_2Es__thm,axiom,
% 0.17/0.92 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.17/0.92 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.17/0.92 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.17/0.92 ! [V0: $o,V1: $o] :
% 0.17/0.92 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.17/0.92 <=> ( V0
% 0.17/0.92 & V1 ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.17/0.92 ! [V0: $o,V1: $o] :
% 0.17/0.92 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.17/0.92 <=> ( V0
% 0.17/0.92 | V1 ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(reserved_2Elogic_2E_7E,axiom,
% 0.17/0.92 ! [V0: $o] :
% 0.17/0.92 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.17/0.92 <=> ( (~) @ V0 ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.17/0.92 ! [V0: $o,V1: $o] :
% 0.17/0.92 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.17/0.92 <=> ( V0
% 0.17/0.92 => V1 ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(reserved_2Elogic_2E_3D,axiom,
% 0.17/0.92 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.17/0.92 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.17/0.92 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.17/0.92 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(reserved_2Equant_2E_21,axiom,
% 0.17/0.92 ! [A_27a: d,V0f_2E0: u] :
% 0.17/0.92 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.17/0.92 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(reserved_2Equant_2E_3F,axiom,
% 0.17/0.92 ! [A_27a: d,V0f_2E0: u] :
% 0.17/0.92 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.17/0.92 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.17/0.92 ! [V0_2E0: u] :
% 0.17/0.92 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.17/0.92 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.17/0.92 ! [V0_2E0: u] :
% 0.17/0.92 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.17/0.92 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.17/0.92 ! [V0_2E0: u] :
% 0.17/0.92 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.17/0.92 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.17/0.92 ! [V0: $o] :
% 0.17/0.92 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.17/0.92 = V0 ) ).
% 0.17/0.92
% 0.17/0.92 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.17/0.92 ! [V0: $o > $o] :
% 0.17/0.92 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.17/0.92 = V0 ) ).
% 0.17/0.92
% 0.17/0.92 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.17/0.92 ! [V0: $o > $o > $o] :
% 0.17/0.92 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 0.17/0.92 = V0 ) ).
% 0.17/0.92
% 0.17/0.92 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.17/0.92 ! [A_27a: d,X0_2E0: u] :
% 0.17/0.92 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.17/0.92 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.17/0.92 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.17/0.92 ( ( ( s @ A_27a @ X0_2E0 )
% 0.17/0.92 = ( s @ A_27a @ X1_2E0 ) )
% 0.17/0.92 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.17/0.92 ! [A_27a: d,X0_2E0: u] :
% 0.17/0.92 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.17/0.92 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.17/0.92 ! [V0: $o > $o,V1: $o] :
% 0.17/0.92 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.17/0.92 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.17/0.92 ! [V0: $o > $o > $o,V1: $o] :
% 0.17/0.92 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.17/0.92 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.17/0.92 ! [V0: $o > $o,V1: $o] :
% 0.17/0.92 ( ( V0 @ V1 )
% 0.17/0.92 = ( V0 @ V1 ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.17/0.92 ! [V0: $o > $o > $o,V1: $o] :
% 0.17/0.92 ( ( V0 @ V1 )
% 0.17/0.92 = ( V0 @ V1 ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(thm_2Ebool_2ET__DEF,axiom,
% 0.17/0.92 ( mono_2Ec_2Ebool_2ET
% 0.17/0.92 <=> ! [V0x: $o] : ( V0x = V0x ) ) ).
% 0.17/0.92
% 0.17/0.92 thf(thm_2Ebool_2ETRUTH,conjecture,
% 0.17/0.92 mono_2Ec_2Ebool_2ET ).
% 0.17/0.92
% 0.17/0.92 %------------------------------------------------------------------------------
% 0.17/0.92 ------------------------
% 0.26/2.91 ---- Embedded in THF ---
% 0.26/2.91 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.26/2.91 %%% Generated on Tue Feb 24 08:17:05 EST 2026
% 0.26/2.91 %%% using '$$dhol' embedding, version 1.3.0.
% 0.26/2.91 %%% Logic specification used:
% 0.26/2.91 %%% thf(spec, logic, $$dhol).
% 0.26/2.91
% 0.26/2.91 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.7HGaHfDLGw/DTF2DTF2875.p
% See solution above
% 0.26/2.91 ------------------------
% 0.26/2.93 ---- Cleaned THF ---
% 0.26/2.93 thf(u,type,
% 0.26/2.93 u: $tType ).
% 0.26/2.93
% 0.26/2.93 thf(d,type,
% 0.26/2.93 d: $tType ).
% 0.26/2.93
% 0.26/2.93 thf(du,type,
% 0.26/2.93 du: $tType ).
% 0.26/2.93
% 0.26/2.93 thf(tyop_2Emin_2Ebool,type,
% 0.26/2.93 tyop_2Emin_2Ebool: d ).
% 0.26/2.93
% 0.26/2.93 thf(tyop_2Emin_2Efun,type,
% 0.26/2.93 tyop_2Emin_2Efun: d > d > d ).
% 0.26/2.93
% 0.26/2.93 thf(s,type,
% 0.26/2.93 s: d > u > du ).
% 0.26/2.93
% 0.26/2.93 thf(app_2E2,type,
% 0.26/2.93 app_2E2: du > du > u ).
% 0.26/2.93
% 0.26/2.93 thf(combin_i_2E0,type,
% 0.26/2.93 combin_i_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(combin_k_2E0,type,
% 0.26/2.93 combin_k_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(combin_s_2E0,type,
% 0.26/2.93 combin_s_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2E_21_2E0,type,
% 0.26/2.93 c_2Ebool_2E_21_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2E_21_2E1,type,
% 0.26/2.93 c_2Ebool_2E_21_2E1: du > u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.26/2.93 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.26/2.93 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Emin_2E_3D_2E0,type,
% 0.26/2.93 c_2Emin_2E_3D_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Emin_2E_3D_2E2,type,
% 0.26/2.93 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.26/2.93 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.26/2.93 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2E_3F_2E0,type,
% 0.26/2.93 c_2Ebool_2E_3F_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2E_3F_2E1,type,
% 0.26/2.93 c_2Ebool_2E_3F_2E1: du > u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2EF_2E0,type,
% 0.26/2.93 c_2Ebool_2EF_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2ET_2E0,type,
% 0.26/2.93 c_2Ebool_2ET_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.26/2.93 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.26/2.93 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2E_7E_2E0,type,
% 0.26/2.93 c_2Ebool_2E_7E_2E0: u ).
% 0.26/2.93
% 0.26/2.93 thf(c_2Ebool_2E_7E_2E1,type,
% 0.26/2.93 c_2Ebool_2E_7E_2E1: du > u ).
% 0.26/2.93
% 0.26/2.93 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.26/2.93 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.26/2.93
% 0.26/2.93 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.26/2.93 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.26/2.93
% 0.26/2.93 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.26/2.93 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.26/2.93
% 0.26/2.93 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.26/2.93 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.26/2.93
% 0.26/2.93 thf(mono_2Ec_2Ebool_2EF,type,
% 0.26/2.93 mono_2Ec_2Ebool_2EF: $o ).
% 0.26/2.93
% 0.26/2.93 thf(mono_2Ec_2Ebool_2ET,type,
% 0.26/2.93 mono_2Ec_2Ebool_2ET: $o ).
% 0.26/2.93
% 0.26/2.93 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.26/2.93 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.26/2.93
% 0.26/2.93 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.26/2.93 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.26/2.93
% 0.26/2.93 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.26/2.93 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.26/2.93
% 0.26/2.93 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.26/2.93 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.26/2.93
% 0.26/2.93 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.26/2.93 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.26/2.93
% 0.26/2.93 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.26/2.93 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.26/2.93
% 0.26/2.93 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.26/2.93 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.26/2.93
% 0.26/2.93 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.26/2.93 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.26/2.93
% 0.26/2.93 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.26/2.93 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.26/2.93 ( ! [V2x_2E0: u] :
% 0.26/2.93 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.26/2.93 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.26/2.93 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.26/2.93 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.26/2.93 ! [A_27a: d,V0x_2E0: u] :
% 0.26/2.93 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.26/2.93 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.26/2.93 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.26/2.93 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 0.26/2.93 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(reserved_2Eho_2Es__thm,axiom,
% 0.26/2.93 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.26/2.93 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.26/2.93 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.26/2.93 ! [V0: $o,V1: $o] :
% 0.26/2.93 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.26/2.93 <=> ( V0
% 0.26/2.93 & V1 ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.26/2.93 ! [V0: $o,V1: $o] :
% 0.26/2.93 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.26/2.93 <=> ( V0
% 0.26/2.93 | V1 ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(reserved_2Elogic_2E_7E,axiom,
% 0.26/2.93 ! [V0: $o] :
% 0.26/2.93 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.26/2.93 <=> ( (~) @ V0 ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.26/2.93 ! [V0: $o,V1: $o] :
% 0.26/2.93 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.26/2.93 <=> ( V0
% 0.26/2.93 => V1 ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(reserved_2Elogic_2E_3D,axiom,
% 0.26/2.93 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.26/2.93 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.26/2.93 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.26/2.93 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(reserved_2Equant_2E_21,axiom,
% 0.26/2.93 ! [A_27a: d,V0f_2E0: u] :
% 0.26/2.93 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.26/2.93 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(reserved_2Equant_2E_3F,axiom,
% 0.26/2.93 ! [A_27a: d,V0f_2E0: u] :
% 0.26/2.93 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.26/2.93 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.26/2.93 ! [V0_2E0: u] :
% 0.26/2.93 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.26/2.93 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.26/2.93 ! [V0_2E0: u] :
% 0.26/2.93 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.26/2.93 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.26/2.93 ! [V0_2E0: u] :
% 0.26/2.93 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.26/2.93 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.26/2.93 ! [V0: $o] :
% 0.26/2.93 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.26/2.93 = V0 ) ).
% 0.26/2.93
% 0.26/2.93 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.26/2.93 ! [V0: $o > $o] :
% 0.26/2.93 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.26/2.93 = V0 ) ).
% 0.26/2.93
% 0.26/2.93 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.26/2.93 ! [V0: $o > $o > $o] :
% 0.26/2.93 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 0.26/2.93 = V0 ) ).
% 0.26/2.93
% 0.26/2.93 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.26/2.93 ! [A_27a: d,X0_2E0: u] :
% 0.26/2.93 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.26/2.93 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.26/2.93 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.26/2.93 ( ( ( s @ A_27a @ X0_2E0 )
% 0.26/2.93 = ( s @ A_27a @ X1_2E0 ) )
% 0.26/2.93 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.26/2.93 ! [A_27a: d,X0_2E0: u] :
% 0.26/2.93 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.26/2.93 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.26/2.93 ! [V0: $o > $o,V1: $o] :
% 0.26/2.93 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.26/2.93 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.26/2.93 ! [V0: $o > $o > $o,V1: $o] :
% 0.26/2.93 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.26/2.93 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.26/2.93 ! [V0: $o > $o,V1: $o] :
% 0.26/2.93 ( ( V0 @ V1 )
% 0.26/2.93 = ( V0 @ V1 ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.26/2.93 ! [V0: $o > $o > $o,V1: $o] :
% 0.26/2.93 ( ( V0 @ V1 )
% 0.26/2.93 = ( V0 @ V1 ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(thm_2Ebool_2ET__DEF,axiom,
% 0.26/2.93 ( mono_2Ec_2Ebool_2ET
% 0.26/2.93 <=> ! [V0x: $o] : ( V0x = V0x ) ) ).
% 0.26/2.93
% 0.26/2.93 thf(thm_2Ebool_2ETRUTH,conjecture,
% 0.26/2.93 mono_2Ec_2Ebool_2ET ).
% 0.26/2.93 ------------------------
% 0.26/2.96 % (2976)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_2875 for (2999ds/27Mi)
% 0.26/2.96 % (2975)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_2875 for (2999ds/4Mi)
% 0.26/2.96 % (2974)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2875 for (2999ds/183Mi)
% 0.26/2.96 % (2980)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2875 for (2999ds/18Mi)
% 0.26/2.96 % (2977)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2875 for (2999ds/2Mi)
% 0.26/2.96 % (2979)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_2875 for (2999ds/275Mi)
% 0.26/2.96 % (2978)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_2875 for (2999ds/2Mi)
% 0.26/2.96 % (2977)Instruction limit reached!
% 0.26/2.96 % (2977)------------------------------
% 0.26/2.96 % (2977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.26/2.96 % (2977)Termination reason: Unknown
% 0.26/2.96 % (2977)Termination phase: shuffling
% 0.26/2.96
% 0.26/2.96 % (2977)Memory used [KB]: 1023
% 0.26/2.96 % (2977)Time elapsed: 0.003 s
% 0.26/2.96 % (2977)Instructions burned: 2 (million)
% 0.26/2.96 % (2977)------------------------------
% 0.26/2.96 % (2977)------------------------------
% 0.26/2.96 % (2978)Instruction limit reached!
% 0.26/2.96 % (2978)------------------------------
% 0.26/2.96 % (2978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.26/2.96 % (2978)Termination reason: Unknown
% 0.26/2.96 % (2978)Termination phase: shuffling
% 0.26/2.96
% 0.26/2.96 % (2978)Memory used [KB]: 1023
% 0.26/2.96 % (2978)Time elapsed: 0.003 s
% 0.26/2.96 % (2978)Instructions burned: 2 (million)
% 0.26/2.96 % (2978)------------------------------
% 0.26/2.96 % (2978)------------------------------
% 0.26/2.96 % (2975)Instruction limit reached!
% 0.26/2.96 % (2975)------------------------------
% 0.26/2.96 % (2975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.26/2.96 % (2975)Termination reason: Unknown
% 0.26/2.96 % (2975)Termination phase: shuffling
% 0.26/2.96
% 0.26/2.96 % (2975)Memory used [KB]: 1023
% 0.26/2.96 % (2975)Time elapsed: 0.004 s
% 0.26/2.96 % (2975)Instructions burned: 4 (million)
% 0.26/2.96 % (2975)------------------------------
% 0.26/2.96 % (2975)------------------------------
% 0.26/2.96 % (2979)First to succeed.
% 0.26/2.96 % (2979)Refutation found. Thanks to Tanya!
% 0.26/2.96 % SZS status Theorem for DTF2THF_2875
% 0.26/2.96 % SZS output start Proof for DTF2THF_2875
% 0.26/2.96 tff(type_def_5, type, d: $tType).
% 0.26/2.96 tff(type_def_7, type, u: $tType).
% 0.26/2.96 tff(type_def_8, type, du: $tType).
% 0.26/2.96 tff(func_def_0, type, u: $tType).
% 0.26/2.96 tff(func_def_1, type, d: $tType).
% 0.26/2.96 tff(func_def_2, type, du: $tType).
% 0.26/2.96 tff(func_def_3, type, tyop_2Emin_2Ebool: d).
% 0.26/2.96 tff(func_def_4, type, tyop_2Emin_2Efun: sTfun(d,sTfun(d,d))).
% 0.26/2.96 tff(func_def_5, type, s: sTfun(d,sTfun(u,du))).
% 0.26/2.96 tff(func_def_6, type, app_2E2: sTfun(du,sTfun(du,u))).
% 0.26/2.96 tff(func_def_7, type, combin_i_2E0: u).
% 0.26/2.96 tff(func_def_8, type, combin_k_2E0: u).
% 0.26/2.96 tff(func_def_9, type, combin_s_2E0: u).
% 0.26/2.96 tff(func_def_10, type, c_2Ebool_2E_21_2E0: u).
% 0.26/2.96 tff(func_def_11, type, c_2Ebool_2E_21_2E1: sTfun(du,u)).
% 0.26/2.96 tff(func_def_12, type, c_2Ebool_2E_2F_5C_2E0: u).
% 0.26/2.96 tff(func_def_13, type, c_2Ebool_2E_2F_5C_2E2: sTfun(du,sTfun(du,u))).
% 0.26/2.96 tff(func_def_14, type, c_2Emin_2E_3D_2E0: u).
% 0.26/2.96 tff(func_def_15, type, c_2Emin_2E_3D_2E2: sTfun(du,sTfun(du,u))).
% 0.26/2.96 tff(func_def_16, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 0.26/2.96 tff(func_def_17, type, c_2Emin_2E_3D_3D_3E_2E2: sTfun(du,sTfun(du,u))).
% 0.26/2.96 tff(func_def_18, type, c_2Ebool_2E_3F_2E0: u).
% 0.26/2.96 tff(func_def_19, type, c_2Ebool_2E_3F_2E1: sTfun(du,u)).
% 0.26/2.96 tff(func_def_20, type, c_2Ebool_2EF_2E0: u).
% 0.26/2.96 tff(func_def_21, type, c_2Ebool_2ET_2E0: u).
% 0.26/2.96 tff(func_def_22, type, c_2Ebool_2E_5C_2F_2E0: u).
% 0.26/2.96 tff(func_def_23, type, c_2Ebool_2E_5C_2F_2E2: sTfun(du,sTfun(du,u))).
% 0.26/2.96 tff(func_def_24, type, c_2Ebool_2E_7E_2E0: u).
% 0.26/2.96 tff(func_def_25, type, c_2Ebool_2E_7E_2E1: sTfun(du,u)).
% 0.26/2.96 tff(func_def_26, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: sTfun(sTfun($o,$o),sTfun($o,$o))).
% 0.26/2.96 tff(func_def_27, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: sTfun(sTfun($o,sTfun($o,$o)),sTfun($o,sTfun($o,$o)))).
% 0.26/2.96 tff(func_def_28, type, mono_2Ec_2Ebool_2E_2F_5C: sTfun($o,sTfun($o,$o))).
% 0.26/2.96 tff(func_def_29, type, mono_2Ec_2Emin_2E_3D_3D_3E: sTfun($o,sTfun($o,$o))).
% 0.26/2.96 tff(func_def_32, type, mono_2Ec_2Ebool_2E_5C_2F: sTfun($o,sTfun($o,$o))).
% 0.26/2.96 tff(func_def_33, type, mono_2Ec_2Ebool_2E_7E: sTfun($o,$o)).
% 0.26/2.96 tff(func_def_34, type, i_mono_2Etyop_2Emin_2Ebool: sTfun($o,u)).
% 0.26/2.96 tff(func_def_35, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: sTfun(sTfun($o,$o),u)).
% 0.26/2.96 tff(func_def_36, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: sTfun(sTfun($o,sTfun($o,$o)),u)).
% 0.26/2.96 tff(func_def_37, type, j_mono_2Etyop_2Emin_2Ebool: sTfun(du,$o)).
% 0.26/2.96 tff(func_def_38, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: sTfun(du,sTfun($o,$o))).
% 0.26/2.96 tff(func_def_39, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: sTfun(du,sTfun($o,sTfun($o,$o)))).
% 0.26/2.96 tff(f58,plain,(
% 0.26/2.96 $false),
% 0.26/2.96 inference(subsumption_resolution,[status(thm)],[f54,f57])).
% 0.26/2.96 tff(f57,plain,(
% 0.26/2.96 (mono_2Ec_2Ebool_2ET = $true)),
% 0.26/2.96 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 0.26/2.96 tff(f55,plain,(
% 0.26/2.96 (mono_2Ec_2Ebool_2ET = $true) | (sK0 != sK0)),
% 0.26/2.96 inference(cnf_transformation,[status(thm)],[f53])).
% 0.26/2.96 tff(f53,plain,(
% 0.26/2.96 (! [X0 : $o] : (X0 = X0) | (mono_2Ec_2Ebool_2ET != $true)) & ((mono_2Ec_2Ebool_2ET = $true) | (sK0 != sK0))),
% 0.26/2.96 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f51,f52])).
% 0.26/2.96 tff(f52,plain,(
% 0.26/2.96 ? [X1 : $o] : (X1 != X1) => (sK0 != sK0)),
% 0.26/2.96 introduced(definition,[],[choice_axiom])).
% 0.26/2.96 tff(f51,plain,(
% 0.26/2.96 (! [X0 : $o] : (X0 = X0) | (mono_2Ec_2Ebool_2ET != $true)) & ((mono_2Ec_2Ebool_2ET = $true) | ? [X1 : $o] : (X1 != X1))),
% 0.26/2.96 inference(rectify,[status(thm)],[f50])).
% 0.26/2.96 tff(f50,plain,(
% 0.26/2.96 (! [X0 : $o] : (X0 = X0) | (mono_2Ec_2Ebool_2ET != $true)) & ((mono_2Ec_2Ebool_2ET = $true) | ? [X0 : $o] : (X0 != X0))),
% 0.26/2.96 inference(nnf_transformation,[status(thm)],[f32])).
% 0.26/2.96 tff(f32,plain,(
% 0.26/2.96 ! [X0 : $o] : (X0 = X0) <=> (mono_2Ec_2Ebool_2ET = $true)),
% 0.26/2.96 inference(fool_elimination,[status(thm)],[f31])).
% 0.26/2.96 tff(f31,plain,(
% 0.26/2.96 mono_2Ec_2Ebool_2ET <=> ! [X0 : $o] : (X0 = X0)),
% 0.26/2.96 inference(rectify,[status(thm)],[f25])).
% 0.26/2.96 tff(f25,axiom,(
% 0.26/2.96 mono_2Ec_2Ebool_2ET <=> ! [X15 : $o] : (X15 = X15)),
% 0.26/2.96 file('/export/starexec/sandbox/tmp/tmp.7HGaHfDLGw/DTF2THF_2875.p',thm_2Ebool_2ET__DEF)).
% 0.26/2.96 tff(f54,plain,(
% 0.26/2.96 (mono_2Ec_2Ebool_2ET != $true)),
% 0.26/2.96 inference(cnf_transformation,[status(thm)],[f49])).
% 0.26/2.96 tff(f49,plain,(
% 0.26/2.96 (mono_2Ec_2Ebool_2ET != $true)),
% 0.26/2.96 inference(flattening,[status(thm)],[f40])).
% 0.26/2.96 tff(f40,plain,(
% 0.26/2.96 ~(mono_2Ec_2Ebool_2ET = $true)),
% 0.26/2.96 inference(fool_elimination,[status(thm)],[f39])).
% 0.26/2.96 tff(f39,plain,(
% 0.26/2.96 ~mono_2Ec_2Ebool_2ET),
% 0.26/2.96 inference(rectify,[status(thm)],[f27])).
% 0.26/2.96 tff(f27,negated_conjecture,(
% 0.26/2.96 ~mono_2Ec_2Ebool_2ET),
% 0.26/2.96 inference(negated_conjecture,[status(cth)],[f26])).
% 0.26/2.96 tff(f26,conjecture,(
% 0.26/2.96 mono_2Ec_2Ebool_2ET),
% 0.26/2.96 file('/export/starexec/sandbox/tmp/tmp.7HGaHfDLGw/DTF2THF_2875.p',thm_2Ebool_2ETRUTH)).
% 0.26/2.96 % SZS output end Proof for DTF2THF_2875
% 0.26/2.96 % (2979)------------------------------
% 0.26/2.96 % (2979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.26/2.96 % (2979)Termination reason: Refutation
% 0.26/2.96
% 0.26/2.96 % (2979)Memory used [KB]: 5500
% 0.26/2.96 % (2979)Time elapsed: 0.005 s
% 0.26/2.96 % (2979)Instructions burned: 4 (million)
% 0.26/2.96 % (2979)------------------------------
% 0.26/2.96 % (2979)------------------------------
% 0.26/2.96 % (2973)Success in time 0.025 s
%------------------------------------------------------------------------------