%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU171+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 : n013.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 08:53:04 PM UTC 2025
% Result : Theorem 4.25s 2.20s
% Output : CNFRefutation 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 13 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 50 ( 23 ~; 13 |; 2 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 25 ( 24 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > element > empty > subset_complement > set_difference > #nlpp > powerset > empty_set > #skF_1 > #skF_4 > #skF_7 > #skF_10 > #skF_5 > #skF_2 > #skF_9 > #skF_8 > #skF_3 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_85,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_116,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_112,negated_conjecture,
~ ! [A] :
( ( A != empty_set )
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
tff(f_44,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_54,axiom,
! [A,B,C] :
( ( C = set_difference(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
tff(f_58,axiom,
! [A,B] :
( element(B,powerset(A))
=> ( subset_complement(A,B) = set_difference(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
tff(c_54,plain,
empty('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_91,plain,
! [A_39] :
( ( empty_set = A_39 )
| ~ empty(A_39) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_102,plain,
empty_set = '#skF_5',
inference(resolution,[status(thm)],[c_54,c_91]) ).
tff(c_74,plain,
empty_set != '#skF_8',
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_108,plain,
'#skF_5' != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_102,c_74]) ).
tff(c_70,plain,
element('#skF_10','#skF_8'),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_167,plain,
! [B_54,A_55] :
( empty(B_54)
| ~ element(B_54,A_55)
| ~ empty(A_55) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_188,plain,
( empty('#skF_10')
| ~ empty('#skF_8') ),
inference(resolution,[status(thm)],[c_70,c_167]) ).
tff(c_189,plain,
~ empty('#skF_8'),
inference(splitLeft,[status(thm)],[c_188]) ).
tff(c_6,plain,
! [B_4,A_3] :
( in(B_4,A_3)
| ~ element(B_4,A_3)
| empty(A_3) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_68,plain,
~ in('#skF_10','#skF_9'),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_649,plain,
! [D_102,A_103,B_104] :
( in(D_102,set_difference(A_103,B_104))
| in(D_102,B_104)
| ~ in(D_102,A_103) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_72,plain,
element('#skF_9',powerset('#skF_8')),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_375,plain,
! [A_85,B_86] :
( ( subset_complement(A_85,B_86) = set_difference(A_85,B_86) )
| ~ element(B_86,powerset(A_85)) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_398,plain,
subset_complement('#skF_8','#skF_9') = set_difference('#skF_8','#skF_9'),
inference(resolution,[status(thm)],[c_72,c_375]) ).
tff(c_66,plain,
~ in('#skF_10',subset_complement('#skF_8','#skF_9')),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_433,plain,
~ in('#skF_10',set_difference('#skF_8','#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_398,c_66]) ).
tff(c_652,plain,
( in('#skF_10','#skF_9')
| ~ in('#skF_10','#skF_8') ),
inference(resolution,[status(thm)],[c_649,c_433]) ).
tff(c_681,plain,
~ in('#skF_10','#skF_8'),
inference(negUnitSimplification,[status(thm)],[c_68,c_652]) ).
tff(c_690,plain,
( ~ element('#skF_10','#skF_8')
| empty('#skF_8') ),
inference(resolution,[status(thm)],[c_6,c_681]) ).
tff(c_693,plain,
empty('#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_70,c_690]) ).
tff(c_695,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_189,c_693]) ).
tff(c_697,plain,
empty('#skF_8'),
inference(splitRight,[status(thm)],[c_188]) ).
tff(c_76,plain,
! [A_30] :
( ( empty_set = A_30 )
| ~ empty(A_30) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_105,plain,
! [A_30] :
( ( A_30 = '#skF_5' )
| ~ empty(A_30) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_76]) ).
tff(c_709,plain,
'#skF_5' = '#skF_8',
inference(resolution,[status(thm)],[c_697,c_105]) ).
tff(c_714,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_108,c_709]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU171+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % 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
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 22:11:47 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.25/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.25/2.20
% 4.25/2.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------