%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV646+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 : Sun Sep 27 08:48:18 AM UTC 2026
% Result : Theorem 8.63s 3.48s
% Output : Refutation 8.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 27
% Syntax : Number of formulae : 56 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 205 ( 20 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 780 ( 2 ~; 0 |; 1 &; 629 @)
% ( 1 <=>; 147 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 145 ( 0 ^; 145 !; 0 ?; 145 :)
% Comments :
%------------------------------------------------------------------------------
thf(cIntMap_2eFset_2eFSet___24t_decl,type,
cIntMap_2eFset_2eFSet___24t: $i > $o ).
thf(cMapaxioms_2eeqmap___24a3_decl,type,
cMapaxioms_2eeqmap___24a3: $i > $i > $i > $o ).
thf(cCoq_2eInit_2eDatatypes_2eunit_decl,type,
cCoq_2eInit_2eDatatypes_2eunit: $i ).
thf(cIntMap_2eFset_2eFSetUnion___24a2_decl,type,
cIntMap_2eFset_2eFSetUnion___24a2: $i > $i > $i ).
thf(cType___24t_decl,type,
cType___24t: $i > $o ).
thf(cIntMap_2eMap_2eMap___24t_decl,type,
cIntMap_2eMap_2eMap___24t: $i > $i > $o ).
thf(cIntMap_2eMap_2eMapMerge___24a3_decl,type,
cIntMap_2eMap_2eMapMerge___24a3: $i > $i > $i > $i ).
thf(happ_decl,type,
happ: $i > $i > $i ).
thf(cIntMap_2eFset_2ein__FSet_decl,type,
cIntMap_2eFset_2ein__FSet: $i ).
thf(cIntMap_2eFset_2ein__FSet___24a2_decl,type,
cIntMap_2eFset_2ein__FSet___24a2: $i > $i > $i ).
thf(cIntMap_2eMap_2eMapDelta___24a3_decl,type,
cIntMap_2eMap_2eMapDelta___24a3: $i > $i > $i > $i ).
thf(cIntMap_2eFset_2eMapDom_decl,type,
cIntMap_2eFset_2eMapDom: $i ).
thf(cIntMap_2eFset_2eMapDom___24a2_decl,type,
cIntMap_2eFset_2eMapDom___24a2: $i > $i > $i ).
thf(cIntMap_2eFset_2ein__dom_decl,type,
cIntMap_2eFset_2ein__dom: $i ).
thf(cIntMap_2eFset_2ein__dom___24a1_decl,type,
cIntMap_2eFset_2ein__dom___24a1: $i > $i ).
thf(cCoq_2eInit_2eDatatypes_2eorb_decl,type,
cCoq_2eInit_2eDatatypes_2eorb: $i ).
thf(cCoq_2eInit_2eDatatypes_2eorb___24a2_decl,type,
cCoq_2eInit_2eDatatypes_2eorb___24a2: $i > $i > $i ).
thf(cIntMap_2eFset_2eFSetUnion_decl,type,
cIntMap_2eFset_2eFSetUnion: $i ).
thf(cIntMap_2eMap_2ead___24t_decl,type,
cIntMap_2eMap_2ead___24t: $i > $o ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cCoq_2eInit_2eDatatypes_2eorb @ happ ) @ happ ) )
= ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eorb___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_Coq.Init.Datatypes.orb_$a2') ).
thf(69,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cCoq_2eInit_2eDatatypes_2eorb @ happ ) @ happ ) )
= ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eorb___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( C @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( ( D @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( D @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.eqmap_trans') ).
thf(37,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( C @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( ( D @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( D @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cIntMap_2eFset_2ein__FSet @ happ ) @ happ ) )
= ( B @ ( A @ cIntMap_2eFset_2ein__FSet___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_IntMap.Fset.in_FSet_$a2') ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cIntMap_2eFset_2ein__FSet @ happ ) @ happ ) )
= ( B @ ( A @ cIntMap_2eFset_2ein__FSet___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ! [B: $i] :
( ( B @ cIntMap_2eFset_2eFSet___24t )
=> ! [C: $i] :
( ( C @ cIntMap_2eMap_2ead___24t )
=> ( ( B @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( C @ cIntMap_2eFset_2ein__FSet___24a2 ) )
= ( B @ ( C @ cIntMap_2eFset_2ein__FSet___24a2 ) @ ( A @ ( C @ cIntMap_2eFset_2ein__FSet___24a2 ) @ cCoq_2eInit_2eDatatypes_2eorb___24a2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','IntMap.Fset.in_FSet_union') ).
thf(84,plain,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ! [B: $i] :
( ( B @ cIntMap_2eFset_2eFSet___24t )
=> ! [C: $i] :
( ( C @ cIntMap_2eMap_2ead___24t )
=> ( ( B @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( C @ cIntMap_2eFset_2ein__FSet___24a2 ) )
= ( B @ ( C @ cIntMap_2eFset_2ein__FSet___24a2 ) @ ( A @ ( C @ cIntMap_2eFset_2ein__FSet___24a2 ) @ cCoq_2eInit_2eDatatypes_2eorb___24a2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( C @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( D @ ( C @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( D @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.MapMerge_ext_l') ).
thf(41,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( C @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( D @ ( C @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( D @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( D @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( D @ ( B @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.MapDelta_ext_r') ).
thf(59,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( D @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( D @ ( B @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( D @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( D @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.MapMerge_ext_r') ).
thf(39,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( D @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( D @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ( cIntMap_2eFset_2ein__dom @ happ ) )
= ( A @ cIntMap_2eFset_2ein__dom___24a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_IntMap.Fset.in_dom_$a1') ).
thf(66,plain,
! [A: $i] :
( ( A @ ( cIntMap_2eFset_2ein__dom @ happ ) )
= ( A @ cIntMap_2eFset_2ein__dom___24a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( C @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( B @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.eqmap_sym') ).
thf(35,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( C @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( B @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( B @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.eqmap_refl') ).
thf(48,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( B @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( D @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( ( E @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( E @ ( D @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.MapMerge_ext') ).
thf(50,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( D @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( ( E @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( E @ ( D @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( C @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( D @ ( C @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( D @ ( B @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.MapDelta_ext_l') ).
thf(55,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( C @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( D @ ( C @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( D @ ( B @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
( cIntMap_2eFset_2ein__FSet
= ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eFset_2ein__dom___24a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_IntMap.Fset.in_FSet') ).
thf(82,plain,
( cIntMap_2eFset_2ein__FSet
= ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eFset_2ein__dom___24a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( D @ ( C @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( D @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.MapMerge_assoc') ).
thf(46,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( D @ ( C @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( D @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) )
= ( B @ ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMapMerge___24a3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_IntMap.Fset.FSetUnion') ).
thf(93,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) )
= ( B @ ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMapMerge___24a3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( D @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( ( E @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( E @ ( D @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.MapDelta_ext') ).
thf(57,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( ( D @ ( B @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( ( E @ ( C @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) )
=> ( E @ ( D @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ! [B: $i] :
( ( B @ cIntMap_2eFset_2eFSet___24t )
=> ! [C: $i] :
( ( C @ cIntMap_2eFset_2eFSet___24t )
=> ( C @ ( B @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( C @ ( B @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( cCoq_2eInit_2eDatatypes_2eunit @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ! [B: $i] :
( ( B @ cIntMap_2eFset_2eFSet___24t )
=> ! [C: $i] :
( ( C @ cIntMap_2eFset_2eFSet___24t )
=> ( C @ ( B @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( C @ ( B @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( cCoq_2eInit_2eDatatypes_2eunit @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ! [B: $i] :
( ( B @ cIntMap_2eFset_2eFSet___24t )
=> ! [C: $i] :
( ( C @ cIntMap_2eFset_2eFSet___24t )
=> ( C @ ( B @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( C @ ( B @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( cCoq_2eInit_2eDatatypes_2eunit @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cIntMap_2eFset_2eMapDom @ happ ) @ happ ) )
= ( B @ ( A @ cIntMap_2eFset_2eMapDom___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_IntMap.Fset.MapDom_$a2') ).
thf(61,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cIntMap_2eFset_2eMapDom @ happ ) @ happ ) )
= ( B @ ( A @ cIntMap_2eFset_2eMapDom___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cIntMap_2eFset_2eFSetUnion @ happ ) @ happ ) )
= ( B @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_IntMap.Fset.FSetUnion_$a2') ).
thf(74,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cIntMap_2eFset_2eFSetUnion @ happ ) @ happ ) )
= ( B @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ! [B: $i] :
( ( B @ cIntMap_2eFset_2eFSet___24t )
=> ( ! [C: $i] :
( ( C @ cIntMap_2eMap_2ead___24t )
=> ( ( A @ ( C @ cIntMap_2eFset_2ein__FSet___24a2 ) )
= ( B @ ( C @ cIntMap_2eFset_2ein__FSet___24a2 ) ) ) )
=> ( B @ ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.FSet_ext') ).
thf(77,plain,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ! [B: $i] :
( ( B @ cIntMap_2eFset_2eFSet___24t )
=> ( ! [C: $i] :
( ( C @ cIntMap_2eMap_2ead___24t )
=> ( ( A @ ( C @ cIntMap_2eFset_2ein__FSet___24a2 ) )
= ( B @ ( C @ cIntMap_2eFset_2ein__FSet___24a2 ) ) ) )
=> ( B @ ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ( ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eFset_2eMapDom___24a2 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','IntMap.Fset.FSet_Dom') ).
thf(96,plain,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ( ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eFset_2eMapDom___24a2 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
cCoq_2eInit_2eDatatypes_2eunit @ cType___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.unit') ).
thf(45,plain,
cCoq_2eInit_2eDatatypes_2eunit @ cType___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( B @ ( C @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.MapDelta_sym') ).
thf(64,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( B @ ( C @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( C @ ( B @ ( A @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ! [B: $i] :
( ( B @ cIntMap_2eFset_2eFSet___24t )
=> ( A @ ( B @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( B @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( cCoq_2eInit_2eDatatypes_2eunit @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.FSetUnion_comm') ).
thf(72,plain,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ! [B: $i] :
( ( B @ cIntMap_2eFset_2eFSet___24t )
=> ( A @ ( B @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( B @ ( A @ cIntMap_2eFset_2eFSetUnion___24a2 ) @ ( cCoq_2eInit_2eDatatypes_2eunit @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( B @ ( B @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.MapMerge_idempotent') ).
thf(43,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cIntMap_2eMap_2eMap___24t ) )
=> ( B @ ( B @ ( B @ ( A @ cIntMap_2eMap_2eMapMerge___24a3 ) ) @ ( A @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ! [B: $i] :
( ( B @ cIntMap_2eFset_2eFSet___24t )
=> ! [C: $i] :
( ( C @ cIntMap_2eFset_2eFSet___24t )
=> ( C @ ( B @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( C @ ( B @ ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( cCoq_2eInit_2eDatatypes_2eunit @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Mapaxioms.FSetDelta_assoc') ).
thf(99,plain,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ! [B: $i] :
( ( B @ cIntMap_2eFset_2eFSet___24t )
=> ! [C: $i] :
( ( C @ cIntMap_2eFset_2eFSet___24t )
=> ( C @ ( B @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( C @ ( B @ ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMapDelta___24a3 ) ) @ ( cCoq_2eInit_2eDatatypes_2eunit @ cMapaxioms_2eeqmap___24a3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ cIntMap_2eFset_2eFSet___24t )
<=> ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMap___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_IntMap.Fset.FSet') ).
thf(87,plain,
! [A: $i] :
( ( ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMap___24t ) )
=> ( A @ cIntMap_2eFset_2eFSet___24t ) )
& ( ( A @ cIntMap_2eFset_2eFSet___24t )
=> ( A @ ( cCoq_2eInit_2eDatatypes_2eunit @ cIntMap_2eMap_2eMap___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(101,plain,
$false,
inference(e,[status(thm)],[69,37,52,84,41,59,39,66,35,48,50,55,82,46,93,57,29,61,74,77,96,45,64,72,43,99,87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV646+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 11:30:36 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.27/1.68 % [INFO] Parsing done (700ms).
% 3.27/1.69 % [INFO] Running in sequential loop mode.
% 4.21/2.08 % [INFO] eprover registered as external prover.
% 4.21/2.08 % [INFO] Scanning for conjecture ...
% 5.01/2.39 % [INFO] Found a conjecture (or negated_conjecture) and 3067 axioms. Running axiom selection ...
% 6.39/2.62 % [INFO] Axiom selection finished. Selected 26 axioms (removed 3041 axioms).
% 6.39/2.70 % [INFO] Problem is first-order (TPTP FOF).
% 6.83/2.71 % [INFO] Type checking passed.
% 6.83/2.71 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 8.63/3.48 % External prover 'e' found a proof!
% 8.63/3.48 % [INFO] Killing All external provers ...
% 8.63/3.48 % Time passed: 2948ms (effective reasoning time: 1780ms)
% 8.63/3.48 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.63/3.48 % Axioms used in derivation (26): Mapaxioms.MapDelta_ext_l, Mapaxioms.MapDelta_sym, Mapaxioms.eqmap_refl, Mapaxioms.FSetDelta_assoc, $_typeof_Coq.Init.Datatypes.unit, Mapaxioms.FSetUnion_comm, $adef_IntMap.Fset.FSetUnion_$a2, $adef_IntMap.Fset.MapDom_$a2, $adef_IntMap.Fset.in_dom_$a1, Mapaxioms.eqmap_trans, Mapaxioms.MapMerge_idempotent, Mapaxioms.MapMerge_ext_l, Mapaxioms.eqmap_sym, Mapaxioms.MapMerge_ext, $adef_IntMap.Fset.in_FSet_$a2, $_def_IntMap.Fset.FSet, Mapaxioms.MapMerge_ext_r, Mapaxioms.MapMerge_assoc, IntMap.Fset.FSet_Dom, Mapaxioms.FSet_ext, IntMap.Fset.in_FSet_union, $adef_Coq.Init.Datatypes.orb_$a2, Mapaxioms.MapDelta_ext, Mapaxioms.MapDelta_ext_r, $_def_IntMap.Fset.in_FSet, $_def_IntMap.Fset.FSetUnion
% 8.63/3.48 % No. of inferences in proof: 56
% 8.63/3.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2948 ms resp. 1780 ms w/o parsing
% 8.95/3.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.95/3.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------