%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU188+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 : n021.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 08:53:08 PM UTC 2025
% Result : Theorem 11.71s 3.92s
% Output : CNFRefutation 11.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 28 ~; 19 |; 4 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 90 ( 90 usr; 6 con; 0-5 aty)
% Number of variables : 18 ( 16 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > element > disjoint > are_equipotent > relation > empty > subset_difference > unordered_pair > union_of_subsets > subset_complement > set_union2 > set_intersection2 > set_difference > relation_composition > ordered_pair > meet_of_subsets > complements_of_subsets > cartesian_product2 > #nlpp > union > singleton > set_meet > relation_rng > relation_inverse > relation_field > relation_dom > powerset > cast_to_subset > empty_set > #skF_13 > #skF_49 > #skF_24 > #skF_37 > #skF_62 > #skF_11 > #skF_41 > #skF_44 > #skF_6 > #skF_17 > #skF_33 > #skF_26 > #skF_30 > #skF_1 > #skF_18 > #skF_47 > #skF_55 > #skF_63 > #skF_32 > #skF_56 > #skF_60 > #skF_31 > #skF_38 > #skF_4 > #skF_3 > #skF_39 > #skF_29 > #skF_64 > #skF_12 > #skF_53 > #skF_48 > #skF_45 > #skF_10 > #skF_35 > #skF_19 > #skF_42 > #skF_8 > #skF_36 > #skF_57 > #skF_59 > #skF_20 > #skF_28 > #skF_34 > #skF_15 > #skF_23 > #skF_14 > #skF_67 > #skF_54 > #skF_52 > #skF_50 > #skF_46 > #skF_2 > #skF_21 > #skF_66 > #skF_40 > #skF_68 > #skF_25 > #skF_43 > #skF_7 > #skF_27 > #skF_61 > #skF_9 > #skF_5 > #skF_22 > #skF_58 > #skF_65 > #skF_16 > #skF_51
%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(subset_difference,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff('#skF_49',type,
'#skF_49': ( $i * $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_37',type,
'#skF_37': ( $i * $i ) > $i ).
tff('#skF_62',type,
'#skF_62': ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(relation_field,type,
relation_field: $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(cast_to_subset,type,
cast_to_subset: $i > $i ).
tff(union,type,
union: $i > $i ).
tff('#skF_41',type,
'#skF_41': ( $i * $i ) > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_44',type,
'#skF_44': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': ( $i * $i * $i ) > $i ).
tff(relation_inverse,type,
relation_inverse: $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_26',type,
'#skF_26': ( $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff('#skF_47',type,
'#skF_47': ( $i * $i * $i ) > $i ).
tff(meet_of_subsets,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff('#skF_55',type,
'#skF_55': $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('#skF_56',type,
'#skF_56': $i ).
tff('#skF_60',type,
'#skF_60': ( $i * $i ) > $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i ) > $i ).
tff('#skF_38',type,
'#skF_38': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_39',type,
'#skF_39': ( $i * $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i * $i ) > $i ).
tff('#skF_64',type,
'#skF_64': $i > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff('#skF_53',type,
'#skF_53': $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_48',type,
'#skF_48': ( $i * $i * $i ) > $i ).
tff('#skF_45',type,
'#skF_45': ( $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_35',type,
'#skF_35': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff(relation_composition,type,
relation_composition: ( $i * $i ) > $i ).
tff('#skF_42',type,
'#skF_42': ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_36',type,
'#skF_36': ( $i * $i ) > $i ).
tff('#skF_57',type,
'#skF_57': $i > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_59',type,
'#skF_59': $i > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i ) > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i ) > $i ).
tff(set_meet,type,
set_meet: $i > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff('#skF_67',type,
'#skF_67': $i > $i ).
tff('#skF_54',type,
'#skF_54': $i > $i ).
tff('#skF_52',type,
'#skF_52': ( $i * $i ) > $i ).
tff('#skF_50',type,
'#skF_50': ( $i * $i * $i ) > $i ).
tff('#skF_46',type,
'#skF_46': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i * $i ) > $i ).
tff('#skF_66',type,
'#skF_66': $i ).
tff(union_of_subsets,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_40',type,
'#skF_40': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_68',type,
'#skF_68': ( $i * $i ) > $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i ) > $i ).
tff('#skF_43',type,
'#skF_43': ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_61',type,
'#skF_61': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i * $i ) > $i ).
tff('#skF_58',type,
'#skF_58': $i ).
tff('#skF_65',type,
'#skF_65': $i > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff('#skF_51',type,
'#skF_51': $i > $i ).
tff(f_462,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
tff(f_874,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_473,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_863,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ( ( relation_dom(A) = empty_set )
| ( relation_rng(A) = empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
tff(f_358,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
tff(f_366,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
tff(f_372,axiom,
! [A] :
( empty(A)
=> ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
tff(c_424,plain,
empty('#skF_53'),
inference(cnfTransformation,[status(thm)],[f_462]) ).
tff(c_4325,plain,
! [A_940] :
( ( empty_set = A_940 )
| ~ empty(A_940) ),
inference(cnfTransformation,[status(thm)],[f_874]) ).
tff(c_4340,plain,
empty_set = '#skF_53',
inference(resolution,[status(thm)],[c_424,c_4325]) ).
tff(c_430,plain,
empty('#skF_55'),
inference(cnfTransformation,[status(thm)],[f_473]) ).
tff(c_4339,plain,
empty_set = '#skF_55',
inference(resolution,[status(thm)],[c_430,c_4325]) ).
tff(c_4362,plain,
'#skF_55' = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_4340,c_4339]) ).
tff(c_724,plain,
! [A_691] :
( ( empty_set = A_691 )
| ~ empty(A_691) ),
inference(cnfTransformation,[status(thm)],[f_874]) ).
tff(c_739,plain,
empty_set = '#skF_53',
inference(resolution,[status(thm)],[c_424,c_724]) ).
tff(c_738,plain,
empty_set = '#skF_55',
inference(resolution,[status(thm)],[c_430,c_724]) ).
tff(c_761,plain,
'#skF_55' = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_739,c_738]) ).
tff(c_618,plain,
empty_set != '#skF_66',
inference(cnfTransformation,[status(thm)],[f_863]) ).
tff(c_755,plain,
'#skF_55' != '#skF_66',
inference(demodulation,[status(thm),theory(equality)],[c_738,c_618]) ).
tff(c_767,plain,
'#skF_53' != '#skF_66',
inference(demodulation,[status(thm),theory(equality)],[c_761,c_755]) ).
tff(c_622,plain,
relation('#skF_66'),
inference(cnfTransformation,[status(thm)],[f_863]) ).
tff(c_620,plain,
( ( relation_rng('#skF_66') = empty_set )
| ( relation_dom('#skF_66') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_863]) ).
tff(c_675,plain,
relation_dom('#skF_66') = empty_set,
inference(splitLeft,[status(thm)],[c_620]) ).
tff(c_748,plain,
relation_dom('#skF_66') = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_738,c_675]) ).
tff(c_797,plain,
relation_dom('#skF_66') = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_761,c_748]) ).
tff(c_4232,plain,
! [A_929] :
( ~ empty(relation_dom(A_929))
| ~ relation(A_929)
| empty(A_929) ),
inference(cnfTransformation,[status(thm)],[f_358]) ).
tff(c_4247,plain,
( ~ empty('#skF_53')
| ~ relation('#skF_66')
| empty('#skF_66') ),
inference(superposition,[status(thm),theory(equality)],[c_797,c_4232]) ).
tff(c_4257,plain,
empty('#skF_66'),
inference(demodulation,[status(thm),theory(equality)],[c_622,c_424,c_4247]) ).
tff(c_630,plain,
! [A_617] :
( ( empty_set = A_617 )
| ~ empty(A_617) ),
inference(cnfTransformation,[status(thm)],[f_874]) ).
tff(c_742,plain,
! [A_617] :
( ( A_617 = '#skF_55' )
| ~ empty(A_617) ),
inference(demodulation,[status(thm),theory(equality)],[c_738,c_630]) ).
tff(c_895,plain,
! [A_617] :
( ( A_617 = '#skF_53' )
| ~ empty(A_617) ),
inference(demodulation,[status(thm),theory(equality)],[c_761,c_742]) ).
tff(c_4273,plain,
'#skF_53' = '#skF_66',
inference(resolution,[status(thm)],[c_4257,c_895]) ).
tff(c_4282,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_767,c_4273]) ).
tff(c_4284,plain,
relation_dom('#skF_66') != empty_set,
inference(splitRight,[status(thm)],[c_620]) ).
tff(c_4350,plain,
relation_dom('#skF_66') != '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_4339,c_4284]) ).
tff(c_4418,plain,
relation_dom('#skF_66') != '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_4362,c_4350]) ).
tff(c_4283,plain,
relation_rng('#skF_66') = empty_set,
inference(splitRight,[status(thm)],[c_620]) ).
tff(c_4351,plain,
relation_rng('#skF_66') = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_4339,c_4283]) ).
tff(c_4371,plain,
relation_rng('#skF_66') = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_4362,c_4351]) ).
tff(c_6043,plain,
! [A_1107] :
( ~ empty(relation_rng(A_1107))
| ~ relation(A_1107)
| empty(A_1107) ),
inference(cnfTransformation,[status(thm)],[f_366]) ).
tff(c_6049,plain,
( ~ empty('#skF_53')
| ~ relation('#skF_66')
| empty('#skF_66') ),
inference(superposition,[status(thm),theory(equality)],[c_4371,c_6043]) ).
tff(c_6055,plain,
empty('#skF_66'),
inference(demodulation,[status(thm),theory(equality)],[c_622,c_424,c_6049]) ).
tff(c_4585,plain,
! [A_974] :
( empty(relation_dom(A_974))
| ~ empty(A_974) ),
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_4343,plain,
! [A_617] :
( ( A_617 = '#skF_55' )
| ~ empty(A_617) ),
inference(demodulation,[status(thm),theory(equality)],[c_4339,c_630]) ).
tff(c_4529,plain,
! [A_617] :
( ( A_617 = '#skF_53' )
| ~ empty(A_617) ),
inference(demodulation,[status(thm),theory(equality)],[c_4362,c_4343]) ).
tff(c_4592,plain,
! [A_974] :
( ( relation_dom(A_974) = '#skF_53' )
| ~ empty(A_974) ),
inference(resolution,[status(thm)],[c_4585,c_4529]) ).
tff(c_6068,plain,
relation_dom('#skF_66') = '#skF_53',
inference(resolution,[status(thm)],[c_6055,c_4592]) ).
tff(c_6079,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4418,c_6068]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEU188+2 : TPTP v9.0.0. Released v3.3.0.
% 0.09/0.11 % 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
% 0.11/0.31 % Computer : n021.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Apr 8 22:15:44 EDT 2025
% 0.11/0.31 % CPUTime :
% 11.71/3.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.71/3.93
% 11.71/3.93 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------