%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU169+1 : 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 : n018.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 3.49s 1.97s
% Output : CNFRefutation 3.75s
% 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > empty > #nlpp > powerset > empty_set > #skF_4 > #skF_8 > #skF_7 > #skF_3 > #skF_10 > #skF_5 > #skF_6 > #skF_9 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_74,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
tff(f_65,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
tff(f_51,axiom,
! [A,B] :
( ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) )
& ( empty(A)
=> ( element(B,A)
<=> empty(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
tff(f_38,axiom,
! [A,B] :
( ( B = powerset(A) )
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
tff(f_58,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
tff(c_42,plain,
~ in('#skF_7','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_46,plain,
element('#skF_6',powerset('#skF_5')),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_38,plain,
! [A_17] : ~ empty(powerset(A_17)),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_280,plain,
! [B_67,A_68] :
( in(B_67,A_68)
| ~ element(B_67,A_68)
| empty(A_68) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_4,plain,
! [C_7,A_3] :
( subset(C_7,A_3)
| ~ in(C_7,powerset(A_3)) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_295,plain,
! [B_67,A_3] :
( subset(B_67,A_3)
| ~ element(B_67,powerset(A_3))
| empty(powerset(A_3)) ),
inference(resolution,[status(thm)],[c_280,c_4]) ).
tff(c_328,plain,
! [B_69,A_70] :
( subset(B_69,A_70)
| ~ element(B_69,powerset(A_70)) ),
inference(negUnitSimplification,[status(thm)],[c_38,c_295]) ).
tff(c_349,plain,
subset('#skF_6','#skF_5'),
inference(resolution,[status(thm)],[c_46,c_328]) ).
tff(c_44,plain,
in('#skF_7','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_351,plain,
! [C_71,B_72,A_73] :
( in(C_71,B_72)
| ~ in(C_71,A_73)
| ~ subset(A_73,B_72) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_365,plain,
! [B_75] :
( in('#skF_7',B_75)
| ~ subset('#skF_6',B_75) ),
inference(resolution,[status(thm)],[c_44,c_351]) ).
tff(c_368,plain,
in('#skF_7','#skF_5'),
inference(resolution,[status(thm)],[c_349,c_365]) ).
tff(c_380,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU169+1 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.11 % 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
% 0.12/0.31 % Computer : n018.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Apr 8 22:11:32 EDT 2025
% 0.12/0.31 % CPUTime :
% 3.49/1.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.49/1.97
% 3.49/1.97 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------