%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU114+1 : TPTP v9.0.0. Released v3.2.0.
% 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 : n020.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 08:52:47 PM UTC 2025
% Result : Theorem 13.23s 4.21s
% Output : CNFRefutation 13.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 61 ( 22 ~; 23 |; 5 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 47 ( 47 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation > preboolean > ordinal > one_to_one > natural > function > finite > epsilon_transitive > epsilon_connected > empty > diff_closed > cup_closed > cap_closed > #nlpp > powerset > finite_subsets > empty_set > #skF_9 > #skF_7 > #skF_4 > #skF_11 > #skF_3 > #skF_14 > #skF_5 > #skF_10 > #skF_6 > #skF_8 > #skF_13 > #skF_2 > #skF_12 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(cup_closed,type,
cup_closed: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(finite_subsets,type,
finite_subsets: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(finite,type,
finite: $i > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(preboolean,type,
preboolean: $i > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(diff_closed,type,
diff_closed: $i > $o ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(cap_closed,type,
cap_closed: $i > $o ).
tff(natural,type,
natural: $i > $o ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_206,negated_conjecture,
~ ! [A] :
( finite(A)
=> ( finite_subsets(A) = powerset(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).
tff(f_71,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
tff(f_199,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
tff(f_48,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
tff(f_216,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
tff(f_109,axiom,
! [A] :
( ~ empty(finite_subsets(A))
& cup_closed(finite_subsets(A))
& diff_closed(finite_subsets(A))
& preboolean(finite_subsets(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finsub_1) ).
tff(f_82,axiom,
! [A,B] :
( preboolean(B)
=> ( ( B = finite_subsets(A) )
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
tff(f_201,axiom,
! [A] : subset(finite_subsets(A),powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
tff(f_64,axiom,
! [A,B] :
( ( A = B )
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
tff(c_136,plain,
powerset('#skF_14') != finite_subsets('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_138,plain,
finite('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_383,plain,
! [A_130,B_131] :
( in('#skF_1'(A_130,B_131),A_130)
| subset(A_130,B_131) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_132,plain,
! [A_43,B_44] :
( element(A_43,B_44)
| ~ in(A_43,B_44) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_875,plain,
! [A_165,B_166] :
( element('#skF_1'(A_165,B_166),A_165)
| subset(A_165,B_166) ),
inference(resolution,[status(thm)],[c_383,c_132]) ).
tff(c_10,plain,
! [B_7,A_5] :
( finite(B_7)
| ~ element(B_7,powerset(A_5))
| ~ finite(A_5) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_901,plain,
! [A_5,B_166] :
( finite('#skF_1'(powerset(A_5),B_166))
| ~ finite(A_5)
| subset(powerset(A_5),B_166) ),
inference(resolution,[status(thm)],[c_875,c_10]) ).
tff(c_142,plain,
! [A_48,B_49] :
( subset(A_48,B_49)
| ~ element(A_48,powerset(B_49)) ),
inference(cnfTransformation,[status(thm)],[f_216]) ).
tff(c_902,plain,
! [B_49,B_166] :
( subset('#skF_1'(powerset(B_49),B_166),B_49)
| subset(powerset(B_49),B_166) ),
inference(resolution,[status(thm)],[c_875,c_142]) ).
tff(c_68,plain,
! [A_28] : preboolean(finite_subsets(A_28)),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_40,plain,
! [C_22,A_18] :
( in(C_22,finite_subsets(A_18))
| ~ finite(C_22)
| ~ subset(C_22,A_18)
| ~ preboolean(finite_subsets(A_18)) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_904,plain,
! [C_167,A_168] :
( in(C_167,finite_subsets(A_168))
| ~ finite(C_167)
| ~ subset(C_167,A_168) ),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_40]) ).
tff(c_24,plain,
! [A_13,B_14] :
( ~ in('#skF_1'(A_13,B_14),B_14)
| subset(A_13,B_14) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_6204,plain,
! [A_414,A_415] :
( subset(A_414,finite_subsets(A_415))
| ~ finite('#skF_1'(A_414,finite_subsets(A_415)))
| ~ subset('#skF_1'(A_414,finite_subsets(A_415)),A_415) ),
inference(resolution,[status(thm)],[c_904,c_24]) ).
tff(c_19502,plain,
! [B_701] :
( ~ finite('#skF_1'(powerset(B_701),finite_subsets(B_701)))
| subset(powerset(B_701),finite_subsets(B_701)) ),
inference(resolution,[status(thm)],[c_902,c_6204]) ).
tff(c_19516,plain,
! [A_702] :
( ~ finite(A_702)
| subset(powerset(A_702),finite_subsets(A_702)) ),
inference(resolution,[status(thm)],[c_901,c_19502]) ).
tff(c_134,plain,
! [A_45] : subset(finite_subsets(A_45),powerset(A_45)),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_479,plain,
! [B_140,A_141] :
( ( B_140 = A_141 )
| ~ subset(B_140,A_141)
| ~ subset(A_141,B_140) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_502,plain,
! [A_45] :
( ( powerset(A_45) = finite_subsets(A_45) )
| ~ subset(powerset(A_45),finite_subsets(A_45)) ),
inference(resolution,[status(thm)],[c_134,c_479]) ).
tff(c_19585,plain,
! [A_703] :
( ( powerset(A_703) = finite_subsets(A_703) )
| ~ finite(A_703) ),
inference(resolution,[status(thm)],[c_19516,c_502]) ).
tff(c_19642,plain,
powerset('#skF_14') = finite_subsets('#skF_14'),
inference(resolution,[status(thm)],[c_138,c_19585]) ).
tff(c_19665,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_136,c_19642]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU114+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % 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
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Apr 8 22:04:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 13.23/4.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.23/4.21
% 13.23/4.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------