%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU174+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/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 08:53:05 PM UTC 2025
% Result : Theorem 4.75s 2.14s
% Output : CNFRefutation 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 19 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 76 ( 36 ~; 25 |; 5 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 55 ( 52 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > empty > subset_complement > complements_of_subsets > #nlpp > powerset > empty_set > #skF_4 > #skF_7 > #skF_5 > #skF_2 > #skF_9 > #skF_8 > #skF_3 > #skF_1 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(complements_of_subsets,type,
complements_of_subsets: ( $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(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
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_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_87,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_137,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_120,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( ( B != empty_set )
& ( complements_of_subsets(A,B) = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
tff(f_64,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
tff(f_107,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
tff(f_126,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
tff(f_92,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
tff(f_133,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
tff(f_76,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( complements_of_subsets(A,complements_of_subsets(A,B)) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
tff(f_52,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( ( C = complements_of_subsets(A,B) )
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
tff(c_48,plain,
empty('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_85,plain,
! [A_57] :
( ( empty_set = A_57 )
| ~ empty(A_57) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_98,plain,
empty_set = '#skF_5',
inference(resolution,[status(thm)],[c_48,c_85]) ).
tff(c_68,plain,
empty_set != '#skF_9',
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_106,plain,
'#skF_5' != '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_98,c_68]) ).
tff(c_34,plain,
! [A_23] : element('#skF_3'(A_23),A_23),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_60,plain,
! [A_38,B_39] :
( in(A_38,B_39)
| empty(B_39)
| ~ element(A_38,B_39) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_70,plain,
element('#skF_9',powerset(powerset('#skF_8'))),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_319,plain,
! [A_111,C_112,B_113] :
( element(A_111,C_112)
| ~ element(B_113,powerset(C_112))
| ~ in(A_111,B_113) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_340,plain,
! [A_111] :
( element(A_111,powerset('#skF_8'))
| ~ in(A_111,'#skF_9') ),
inference(resolution,[status(thm)],[c_70,c_319]) ).
tff(c_50,plain,
! [A_32] : empty('#skF_6'(A_32)),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_95,plain,
! [A_32] : ( '#skF_6'(A_32) = empty_set ),
inference(resolution,[status(thm)],[c_50,c_85]) ).
tff(c_112,plain,
! [A_32] : ( '#skF_6'(A_32) = '#skF_5' ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_95]) ).
tff(c_52,plain,
! [A_32] : element('#skF_6'(A_32),powerset(A_32)),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_133,plain,
! [A_32] : element('#skF_5',powerset(A_32)),
inference(demodulation,[status(thm),theory(equality)],[c_112,c_52]) ).
tff(c_234,plain,
! [C_95,B_96,A_97] :
( ~ empty(C_95)
| ~ element(B_96,powerset(C_95))
| ~ in(A_97,B_96) ),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_253,plain,
! [A_32,A_97] :
( ~ empty(A_32)
| ~ in(A_97,'#skF_5') ),
inference(resolution,[status(thm)],[c_133,c_234]) ).
tff(c_255,plain,
! [A_97] : ~ in(A_97,'#skF_5'),
inference(splitLeft,[status(thm)],[c_253]) ).
tff(c_66,plain,
complements_of_subsets('#skF_8','#skF_9') = empty_set,
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_103,plain,
complements_of_subsets('#skF_8','#skF_9') = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_98,c_66]) ).
tff(c_692,plain,
! [A_138,B_139] :
( ( complements_of_subsets(A_138,complements_of_subsets(A_138,B_139)) = B_139 )
| ~ element(B_139,powerset(powerset(A_138))) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_706,plain,
complements_of_subsets('#skF_8',complements_of_subsets('#skF_8','#skF_9')) = '#skF_9',
inference(resolution,[status(thm)],[c_70,c_692]) ).
tff(c_720,plain,
complements_of_subsets('#skF_8','#skF_5') = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_103,c_706]) ).
tff(c_1338,plain,
! [A_187,D_188,B_189] :
( in(subset_complement(A_187,D_188),B_189)
| ~ in(D_188,complements_of_subsets(A_187,B_189))
| ~ element(D_188,powerset(A_187))
| ~ element(complements_of_subsets(A_187,B_189),powerset(powerset(A_187)))
| ~ element(B_189,powerset(powerset(A_187))) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_1350,plain,
! [D_188] :
( in(subset_complement('#skF_8',D_188),'#skF_5')
| ~ in(D_188,complements_of_subsets('#skF_8','#skF_5'))
| ~ element(D_188,powerset('#skF_8'))
| ~ element('#skF_9',powerset(powerset('#skF_8')))
| ~ element('#skF_5',powerset(powerset('#skF_8'))) ),
inference(superposition,[status(thm),theory(equality)],[c_720,c_1338]) ).
tff(c_1362,plain,
! [D_188] :
( in(subset_complement('#skF_8',D_188),'#skF_5')
| ~ in(D_188,'#skF_9')
| ~ element(D_188,powerset('#skF_8')) ),
inference(demodulation,[status(thm),theory(equality)],[c_133,c_70,c_720,c_1350]) ).
tff(c_1367,plain,
! [D_190] :
( ~ in(D_190,'#skF_9')
| ~ element(D_190,powerset('#skF_8')) ),
inference(negUnitSimplification,[status(thm)],[c_255,c_1362]) ).
tff(c_1409,plain,
! [A_191] : ~ in(A_191,'#skF_9'),
inference(resolution,[status(thm)],[c_340,c_1367]) ).
tff(c_1423,plain,
! [A_38] :
( empty('#skF_9')
| ~ element(A_38,'#skF_9') ),
inference(resolution,[status(thm)],[c_60,c_1409]) ).
tff(c_1444,plain,
! [A_193] : ~ element(A_193,'#skF_9'),
inference(splitLeft,[status(thm)],[c_1423]) ).
tff(c_1455,plain,
$false,
inference(resolution,[status(thm)],[c_34,c_1444]) ).
tff(c_1456,plain,
empty('#skF_9'),
inference(splitRight,[status(thm)],[c_1423]) ).
tff(c_76,plain,
! [A_48] :
( ( empty_set = A_48 )
| ~ empty(A_48) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_104,plain,
! [A_48] :
( ( A_48 = '#skF_5' )
| ~ empty(A_48) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_76]) ).
tff(c_1461,plain,
'#skF_5' = '#skF_9',
inference(resolution,[status(thm)],[c_1456,c_104]) ).
tff(c_1466,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_106,c_1461]) ).
tff(c_1467,plain,
! [A_32] : ~ empty(A_32),
inference(splitRight,[status(thm)],[c_253]) ).
tff(c_1482,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1467,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU174+1 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.13 % 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
% 0.13/0.34 % Computer : n020.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 22:12:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.75/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.75/2.15
% 4.75/2.15 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------