%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU169+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 : n008.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 08:53:03 PM UTC 2025
% Result : Theorem 13.85s 4.39s
% Output : CNFRefutation 13.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 32 ( 12 ~; 9 |; 1 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 48 ( 48 usr; 6 con; 0-4 aty)
% Number of variables : 25 ( 25 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > element > disjoint > are_equipotent > empty > unordered_pair > set_union2 > set_intersection2 > set_difference > ordered_pair > cartesian_product2 > #nlpp > union > singleton > powerset > empty_set > #skF_13 > #skF_25 > #skF_24 > #skF_35 > #skF_17 > #skF_6 > #skF_31 > #skF_18 > #skF_20 > #skF_37 > #skF_22 > #skF_12 > #skF_38 > #skF_34 > #skF_15 > #skF_29 > #skF_26 > #skF_32 > #skF_23 > #skF_19 > #skF_33 > #skF_11 > #skF_36 > #skF_7 > #skF_9 > #skF_30 > #skF_3 > #skF_28 > #skF_2 > #skF_27 > #skF_8 > #skF_14 > #skF_1 > #skF_16 > #skF_21 > #skF_5 > #skF_4 > #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_25',type,
'#skF_25': $i > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i ) > $i ).
tff(union,type,
union: $i > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_31',type,
'#skF_31': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_37',type,
'#skF_37': $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_38',type,
'#skF_38': ( $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': $i > $i ).
tff('#skF_26',type,
'#skF_26': $i ).
tff('#skF_32',type,
'#skF_32': $i > $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_33',type,
'#skF_33': ( $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_36',type,
'#skF_36': ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_223,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
tff(f_167,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
tff(f_81,axiom,
! [A,B] :
( ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) )
& ( empty(A)
=> ( element(B,A)
<=> empty(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
tff(f_68,axiom,
! [A,B] :
( ( B = powerset(A) )
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
tff(f_118,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
tff(c_242,plain,
~ in('#skF_28','#skF_26'),
inference(cnfTransformation,[status(thm)],[f_223]) ).
tff(c_246,plain,
element('#skF_27',powerset('#skF_26')),
inference(cnfTransformation,[status(thm)],[f_223]) ).
tff(c_210,plain,
! [A_119] : ~ empty(powerset(A_119)),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_6069,plain,
! [B_685,A_686] :
( in(B_685,A_686)
| ~ element(B_685,A_686)
| empty(A_686) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_34,plain,
! [C_26,A_22] :
( subset(C_26,A_22)
| ~ in(C_26,powerset(A_22)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_6163,plain,
! [B_685,A_22] :
( subset(B_685,A_22)
| ~ element(B_685,powerset(A_22))
| empty(powerset(A_22)) ),
inference(resolution,[status(thm)],[c_6069,c_34]) ).
tff(c_16159,plain,
! [B_988,A_989] :
( subset(B_988,A_989)
| ~ element(B_988,powerset(A_989)) ),
inference(negUnitSimplification,[status(thm)],[c_210,c_6163]) ).
tff(c_16201,plain,
subset('#skF_27','#skF_26'),
inference(resolution,[status(thm)],[c_246,c_16159]) ).
tff(c_244,plain,
in('#skF_28','#skF_27'),
inference(cnfTransformation,[status(thm)],[f_223]) ).
tff(c_6619,plain,
! [C_704,B_705,A_706] :
( in(C_704,B_705)
| ~ in(C_704,A_706)
| ~ subset(A_706,B_705) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_6676,plain,
! [B_705] :
( in('#skF_28',B_705)
| ~ subset('#skF_27',B_705) ),
inference(resolution,[status(thm)],[c_244,c_6619]) ).
tff(c_16216,plain,
in('#skF_28','#skF_26'),
inference(resolution,[status(thm)],[c_16201,c_6676]) ).
tff(c_16242,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_242,c_16216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SEU169+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.15 % 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
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 8 22:12:02 EDT 2025
% 0.14/0.37 % CPUTime :
% 13.85/4.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.85/4.39
% 13.85/4.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------