%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU186+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n016.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 08:53:07 PM UTC 2025
% Result : Theorem 28.90s 9.03s
% Output : CNFRefutation 28.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 11 |; 2 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 88 ( 88 usr; 6 con; 0-5 aty)
% Number of variables : 22 ( 21 !; 1 ?; 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_12 > #skF_53 > #skF_48 > #skF_45 > #skF_10 > #skF_35 > #skF_19 > #skF_66 > #skF_42 > #skF_8 > #skF_36 > #skF_57 > #skF_59 > #skF_20 > #skF_64 > #skF_28 > #skF_34 > #skF_15 > #skF_23 > #skF_14 > #skF_54 > #skF_52 > #skF_50 > #skF_46 > #skF_2 > #skF_21 > #skF_40 > #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_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('#skF_66',type,
'#skF_66': ( $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_64',type,
'#skF_64': $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_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(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_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_434,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
tff(f_835,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_806,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
tff(f_94,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_62,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( in(B,A)
& ! [C,D] : ( B != ordered_pair(C,D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
tff(c_412,plain,
empty('#skF_53'),
inference(cnfTransformation,[status(thm)],[f_434]) ).
tff(c_696,plain,
! [A_692] :
( ( empty_set = A_692 )
| ~ empty(A_692) ),
inference(cnfTransformation,[status(thm)],[f_835]) ).
tff(c_711,plain,
empty_set = '#skF_53',
inference(resolution,[status(thm)],[c_412,c_696]) ).
tff(c_594,plain,
empty_set != '#skF_64',
inference(cnfTransformation,[status(thm)],[f_806]) ).
tff(c_729,plain,
'#skF_53' != '#skF_64',
inference(demodulation,[status(thm),theory(equality)],[c_711,c_594]) ).
tff(c_598,plain,
relation('#skF_64'),
inference(cnfTransformation,[status(thm)],[f_806]) ).
tff(c_62,plain,
! [A_56] :
( ( empty_set = A_56 )
| in('#skF_10'(A_56),A_56) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_1003,plain,
! [A_56] :
( ( A_56 = '#skF_53' )
| in('#skF_10'(A_56),A_56) ),
inference(demodulation,[status(thm),theory(equality)],[c_711,c_62]) ).
tff(c_23671,plain,
! [A_84124,B_84125] :
( ( ordered_pair('#skF_2'(A_84124,B_84125),'#skF_3'(A_84124,B_84125)) = B_84125 )
| ~ in(B_84125,A_84124)
| ~ relation(A_84124) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_596,plain,
! [B_601,C_602] : ~ in(ordered_pair(B_601,C_602),'#skF_64'),
inference(cnfTransformation,[status(thm)],[f_806]) ).
tff(c_24402,plain,
! [B_85568,A_85569] :
( ~ in(B_85568,'#skF_64')
| ~ in(B_85568,A_85569)
| ~ relation(A_85569) ),
inference(superposition,[status(thm),theory(equality)],[c_23671,c_596]) ).
tff(c_24436,plain,
! [A_85569] :
( ~ in('#skF_10'('#skF_64'),A_85569)
| ~ relation(A_85569)
| ( '#skF_53' = '#skF_64' ) ),
inference(resolution,[status(thm)],[c_1003,c_24402]) ).
tff(c_24451,plain,
! [A_85748] :
( ~ in('#skF_10'('#skF_64'),A_85748)
| ~ relation(A_85748) ),
inference(negUnitSimplification,[status(thm)],[c_729,c_24436]) ).
tff(c_24511,plain,
( ~ relation('#skF_64')
| ( '#skF_53' = '#skF_64' ) ),
inference(resolution,[status(thm)],[c_1003,c_24451]) ).
tff(c_24548,plain,
'#skF_53' = '#skF_64',
inference(demodulation,[status(thm),theory(equality)],[c_598,c_24511]) ).
tff(c_24550,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_729,c_24548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEU186+2 : TPTP v9.0.0. Released v3.3.0.
% 0.02/0.10 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.30 % Computer : n016.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Apr 8 22:14:53 EDT 2025
% 0.09/0.30 % CPUTime :
% 28.90/9.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.94/9.04
% 28.94/9.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------