%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU224+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n028.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 Apr 9 08:53:16 PM UTC 2025
% Result : Theorem 62.44s 44.24s
% Output : CNFRefutation 62.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 45 ( 22 ~; 16 |; 3 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 139 ( 139 usr; 12 con; 0-5 aty)
% Number of variables : 15 ( 15 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > element > disjoint > are_equipotent > relation_empty_yielding > relation > one_to_one > function > empty > subset_difference > unordered_pair > union_of_subsets > subset_complement > set_union2 > set_intersection2 > set_difference > relation_rng_restriction > relation_inverse_image > relation_image > relation_dom_restriction > relation_composition > ordered_pair > meet_of_subsets > complements_of_subsets > cartesian_product2 > apply > #nlpp > union > singleton > set_meet > relation_rng > relation_inverse > relation_field > relation_dom > powerset > identity_relation > function_inverse > cast_to_subset > empty_set > #skF_13 > #skF_108 > #skF_104 > #skF_47 > #skF_24 > #skF_62 > #skF_35 > #skF_38 > #skF_22 > #skF_21 > #skF_80 > #skF_17 > #skF_109 > #skF_57 > #skF_56 > #skF_44 > #skF_97 > #skF_106 > #skF_26 > #skF_6 > #skF_53 > #skF_18 > #skF_48 > #skF_79 > #skF_87 > #skF_63 > #skF_32 > #skF_64 > #skF_12 > #skF_31 > #skF_72 > #skF_78 > #skF_3 > #skF_45 > #skF_39 > #skF_69 > #skF_34 > #skF_85 > #skF_20 > #skF_77 > #skF_92 > #skF_74 > #skF_81 > #skF_101 > #skF_71 > #skF_33 > #skF_5 > #skF_49 > #skF_19 > #skF_16 > #skF_65 > #skF_82 > #skF_84 > #skF_66 > #skF_54 > #skF_67 > #skF_99 > #skF_110 > #skF_37 > #skF_107 > #skF_89 > #skF_11 > #skF_36 > #skF_90 > #skF_43 > #skF_7 > #skF_60 > #skF_100 > #skF_9 > #skF_51 > #skF_28 > #skF_15 > #skF_40 > #skF_23 > #skF_46 > #skF_103 > #skF_14 > #skF_102 > #skF_95 > #skF_58 > #skF_52 > #skF_50 > #skF_55 > #skF_61 > #skF_94 > #skF_93 > #skF_25 > #skF_59 > #skF_2 > #skF_76 > #skF_105 > #skF_88 > #skF_68 > #skF_8 > #skF_83 > #skF_75 > #skF_41 > #skF_29 > #skF_27 > #skF_86 > #skF_1 > #skF_98 > #skF_91 > #skF_96 > #skF_30 > #skF_73 > #skF_70 > #skF_4 > #skF_42 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff(are_equipotent,type,
are_equipotent: ( $i * $i ) > $o ).
tff('#skF_108',type,
'#skF_108': ( $i * $i * $i ) > $i ).
tff(subset_difference,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff('#skF_104',type,
'#skF_104': ( $i * $i ) > $i ).
tff('#skF_47',type,
'#skF_47': ( $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff(complements_of_subsets,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff('#skF_62',type,
'#skF_62': ( $i * $i ) > $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i ) > $i ).
tff(relation_field,type,
relation_field: $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_38',type,
'#skF_38': ( $i * $i * $i ) > $i ).
tff(cast_to_subset,type,
cast_to_subset: $i > $i ).
tff(union,type,
union: $i > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': $i > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_80',type,
'#skF_80': ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_109',type,
'#skF_109': $i > $i ).
tff('#skF_57',type,
'#skF_57': ( $i * $i ) > $i ).
tff('#skF_56',type,
'#skF_56': ( $i * $i ) > $i ).
tff('#skF_44',type,
'#skF_44': ( $i * $i * $i ) > $i ).
tff(relation_inverse,type,
relation_inverse: $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_97',type,
'#skF_97': ( $i * $i ) > $i ).
tff('#skF_106',type,
'#skF_106': $i > $i ).
tff('#skF_26',type,
'#skF_26': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_53',type,
'#skF_53': ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff(meet_of_subsets,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff('#skF_48',type,
'#skF_48': ( $i * $i ) > $i ).
tff('#skF_79',type,
'#skF_79': $i > $i ).
tff('#skF_87',type,
'#skF_87': $i ).
tff('#skF_63',type,
'#skF_63': ( $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_32',type,
'#skF_32': ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff('#skF_64',type,
'#skF_64': ( $i * $i ) > $i ).
tff(relation_rng_restriction,type,
relation_rng_restriction: ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff(relation_inverse_image,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_31',type,
'#skF_31': ( $i * $i ) > $i ).
tff('#skF_72',type,
'#skF_72': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_78',type,
'#skF_78': ( $i * $i * $i ) > $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_45',type,
'#skF_45': ( $i * $i * $i * $i ) > $i ).
tff('#skF_39',type,
'#skF_39': ( $i * $i * $i ) > $i ).
tff('#skF_69',type,
'#skF_69': ( $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i ) > $i ).
tff('#skF_85',type,
'#skF_85': $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i * $i ) > $i ).
tff('#skF_77',type,
'#skF_77': ( $i * $i * $i ) > $i ).
tff('#skF_92',type,
'#skF_92': $i ).
tff('#skF_74',type,
'#skF_74': ( $i * $i * $i ) > $i ).
tff('#skF_81',type,
'#skF_81': $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff('#skF_101',type,
'#skF_101': ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_71',type,
'#skF_71': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(identity_relation,type,
identity_relation: $i > $i ).
tff(function_inverse,type,
function_inverse: $i > $i ).
tff('#skF_33',type,
'#skF_33': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_49',type,
'#skF_49': ( $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i * $i ) > $i ).
tff('#skF_65',type,
'#skF_65': ( $i * $i * $i ) > $i ).
tff('#skF_82',type,
'#skF_82': $i ).
tff('#skF_84',type,
'#skF_84': $i ).
tff('#skF_66',type,
'#skF_66': ( $i * $i ) > $i ).
tff('#skF_54',type,
'#skF_54': ( $i * $i ) > $i ).
tff('#skF_67',type,
'#skF_67': ( $i * $i ) > $i ).
tff('#skF_99',type,
'#skF_99': ( $i * $i ) > $i ).
tff(relation_image,type,
relation_image: ( $i * $i ) > $i ).
tff(relation_composition,type,
relation_composition: ( $i * $i ) > $i ).
tff('#skF_110',type,
'#skF_110': ( $i * $i ) > $i ).
tff('#skF_37',type,
'#skF_37': ( $i * $i * $i ) > $i ).
tff('#skF_107',type,
'#skF_107': $i > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_89',type,
'#skF_89': $i ).
tff(relation_dom_restriction,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_36',type,
'#skF_36': ( $i * $i ) > $i ).
tff('#skF_90',type,
'#skF_90': $i > $i ).
tff('#skF_43',type,
'#skF_43': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_60',type,
'#skF_60': ( $i * $i * $i ) > $i ).
tff('#skF_100',type,
'#skF_100': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_51',type,
'#skF_51': ( $i * $i * $i ) > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i ) > $i ).
tff(set_meet,type,
set_meet: $i > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_40',type,
'#skF_40': ( $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i ) > $i ).
tff('#skF_46',type,
'#skF_46': ( $i * $i * $i * $i ) > $i ).
tff('#skF_103',type,
'#skF_103': ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff('#skF_102',type,
'#skF_102': ( $i * $i ) > $i ).
tff('#skF_95',type,
'#skF_95': ( $i * $i * $i ) > $i ).
tff('#skF_58',type,
'#skF_58': ( $i * $i ) > $i ).
tff('#skF_52',type,
'#skF_52': ( $i * $i ) > $i ).
tff('#skF_50',type,
'#skF_50': ( $i * $i * $i ) > $i ).
tff('#skF_55',type,
'#skF_55': ( $i * $i * $i ) > $i ).
tff('#skF_61',type,
'#skF_61': ( $i * $i * $i ) > $i ).
tff('#skF_94',type,
'#skF_94': $i > $i ).
tff('#skF_93',type,
'#skF_93': $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i ) > $i ).
tff('#skF_59',type,
'#skF_59': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_76',type,
'#skF_76': ( $i * $i * $i ) > $i ).
tff(union_of_subsets,type,
union_of_subsets: ( $i * $i ) > $i ).
tff('#skF_105',type,
'#skF_105': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff('#skF_88',type,
'#skF_88': $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_68',type,
'#skF_68': ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff('#skF_83',type,
'#skF_83': $i ).
tff('#skF_75',type,
'#skF_75': ( $i * $i * $i ) > $i ).
tff('#skF_41',type,
'#skF_41': ( $i * $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i ) > $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i ) > $i ).
tff('#skF_86',type,
'#skF_86': $i > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_98',type,
'#skF_98': ( $i * $i ) > $i ).
tff('#skF_91',type,
'#skF_91': $i ).
tff('#skF_96',type,
'#skF_96': ( $i * $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': $i > $i ).
tff('#skF_73',type,
'#skF_73': ( $i * $i * $i ) > $i ).
tff('#skF_70',type,
'#skF_70': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_42',type,
'#skF_42': ( $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_708,negated_conjecture,
~ ! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,relation_dom(C))
& in(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
tff(f_1419,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,B)
& in(A,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
tff(c_628,plain,
( in('#skF_82',relation_dom(relation_dom_restriction('#skF_83','#skF_81')))
| in('#skF_82',relation_dom('#skF_83')) ),
inference(cnfTransformation,[status(thm)],[f_708]) ).
tff(c_1081,plain,
in('#skF_82',relation_dom('#skF_83')),
inference(splitLeft,[status(thm)],[c_628]) ).
tff(c_616,plain,
relation('#skF_83'),
inference(cnfTransformation,[status(thm)],[f_708]) ).
tff(c_624,plain,
( in('#skF_82',relation_dom(relation_dom_restriction('#skF_83','#skF_81')))
| in('#skF_82','#skF_81') ),
inference(cnfTransformation,[status(thm)],[f_708]) ).
tff(c_1059,plain,
in('#skF_82','#skF_81'),
inference(splitLeft,[status(thm)],[c_624]) ).
tff(c_82743,plain,
! [A_349986,C_349987,B_349988] :
( in(A_349986,relation_dom(relation_dom_restriction(C_349987,B_349988)))
| ~ in(A_349986,relation_dom(C_349987))
| ~ in(A_349986,B_349988)
| ~ relation(C_349987) ),
inference(cnfTransformation,[status(thm)],[f_1419]) ).
tff(c_618,plain,
( ~ in('#skF_82','#skF_81')
| ~ in('#skF_82',relation_dom('#skF_83'))
| ~ in('#skF_82',relation_dom(relation_dom_restriction('#skF_83','#skF_81'))) ),
inference(cnfTransformation,[status(thm)],[f_708]) ).
tff(c_1102,plain,
( ~ in('#skF_82',relation_dom('#skF_83'))
| ~ in('#skF_82',relation_dom(relation_dom_restriction('#skF_83','#skF_81'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_1059,c_618]) ).
tff(c_1103,plain,
~ in('#skF_82',relation_dom(relation_dom_restriction('#skF_83','#skF_81'))),
inference(splitLeft,[status(thm)],[c_1102]) ).
tff(c_83007,plain,
( ~ in('#skF_82',relation_dom('#skF_83'))
| ~ in('#skF_82','#skF_81')
| ~ relation('#skF_83') ),
inference(resolution,[status(thm)],[c_82743,c_1103]) ).
tff(c_83101,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_616,c_1059,c_1081,c_83007]) ).
tff(c_83102,plain,
~ in('#skF_82',relation_dom('#skF_83')),
inference(splitRight,[status(thm)],[c_1102]) ).
tff(c_83179,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1081,c_83102]) ).
tff(c_83181,plain,
~ in('#skF_82',relation_dom('#skF_83')),
inference(splitRight,[status(thm)],[c_628]) ).
tff(c_83180,plain,
in('#skF_82',relation_dom(relation_dom_restriction('#skF_83','#skF_81'))),
inference(splitRight,[status(thm)],[c_628]) ).
tff(c_137574,plain,
! [A_625557,C_625558,B_625559] :
( in(A_625557,relation_dom(C_625558))
| ~ in(A_625557,relation_dom(relation_dom_restriction(C_625558,B_625559)))
| ~ relation(C_625558) ),
inference(cnfTransformation,[status(thm)],[f_1419]) ).
tff(c_137659,plain,
( in('#skF_82',relation_dom('#skF_83'))
| ~ relation('#skF_83') ),
inference(resolution,[status(thm)],[c_83180,c_137574]) ).
tff(c_137682,plain,
in('#skF_82',relation_dom('#skF_83')),
inference(demodulation,[status(thm),theory(equality)],[c_616,c_137659]) ).
tff(c_137684,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_83181,c_137682]) ).
tff(c_137686,plain,
~ in('#skF_82','#skF_81'),
inference(splitRight,[status(thm)],[c_624]) ).
tff(c_137685,plain,
in('#skF_82',relation_dom(relation_dom_restriction('#skF_83','#skF_81'))),
inference(splitRight,[status(thm)],[c_624]) ).
tff(c_162844,plain,
! [A_626711,B_626712,C_626713] :
( in(A_626711,B_626712)
| ~ in(A_626711,relation_dom(relation_dom_restriction(C_626713,B_626712)))
| ~ relation(C_626713) ),
inference(cnfTransformation,[status(thm)],[f_1419]) ).
tff(c_162887,plain,
( in('#skF_82','#skF_81')
| ~ relation('#skF_83') ),
inference(resolution,[status(thm)],[c_137685,c_162844]) ).
tff(c_162899,plain,
in('#skF_82','#skF_81'),
inference(demodulation,[status(thm),theory(equality)],[c_616,c_162887]) ).
tff(c_162901,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_137686,c_162899]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU224+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 22:23:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 62.44/44.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.44/44.24
% 62.44/44.24 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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