%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU354+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 : n005.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 08:53:44 PM UTC 2025
% Result : Theorem 6.29s 2.50s
% Output : CNFRefutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 10 |; 1 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 21 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_element > in > element > v5_membered > v4_membered > v3_membered > v2_membered > v1_xreal_0 > v1_xcmplx_0 > v1_rat_1 > v1_membered > v1_int_1 > natural > empty > union_of_subsets > #nlpp > union > powerset > k1_pcomps_1 > empty_set > #skF_5 > #skF_4 > #skF_1 > #skF_7 > #skF_6 > #skF_2 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(k1_pcomps_1,type,
k1_pcomps_1: $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(union,type,
union: $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(v1_int_1,type,
v1_int_1: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(proper_element,type,
proper_element: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(v3_membered,type,
v3_membered: $i > $o ).
tff(empty,type,
empty: $i > $o ).
tff(v1_xreal_0,type,
v1_xreal_0: $i > $o ).
tff(v5_membered,type,
v5_membered: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(v2_membered,type,
v2_membered: $i > $o ).
tff(v1_membered,type,
v1_membered: $i > $o ).
tff(v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(union_of_subsets,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(v1_rat_1,type,
v1_rat_1: $i > $o ).
tff(powerset,type,
powerset: $i > $i ).
tff(natural,type,
natural: $i > $o ).
tff(v4_membered,type,
v4_membered: $i > $o ).
tff(f_235,axiom,
! [A] : ( k1_pcomps_1(A) = powerset(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
tff(f_233,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& ~ proper_element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_2) ).
tff(f_295,axiom,
! [A] : ( union(powerset(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
tff(f_176,axiom,
! [A,B] :
( element(B,A)
=> ( proper_element(B,A)
<=> ( B != union(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_2) ).
tff(f_276,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
tff(c_138,plain,
! [A_52] : ( powerset(A_52) = k1_pcomps_1(A_52) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_136,plain,
! [A_50] : element('#skF_5'(A_50),powerset(A_50)),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_182,plain,
! [A_50] : element('#skF_5'(A_50),k1_pcomps_1(A_50)),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_136]) ).
tff(c_172,plain,
! [A_74] : ( union(powerset(A_74)) = A_74 ),
inference(cnfTransformation,[status(thm)],[f_295]) ).
tff(c_173,plain,
! [A_74] : ( union(k1_pcomps_1(A_74)) = A_74 ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_172]) ).
tff(c_1793,plain,
! [B_277,A_278] :
( proper_element(B_277,A_278)
| ( union(A_278) = B_277 )
| ~ element(B_277,A_278) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_134,plain,
! [A_50] : ~ proper_element('#skF_5'(A_50),powerset(A_50)),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_183,plain,
! [A_50] : ~ proper_element('#skF_5'(A_50),k1_pcomps_1(A_50)),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_134]) ).
tff(c_1800,plain,
! [A_50] :
( ( union(k1_pcomps_1(A_50)) = '#skF_5'(A_50) )
| ~ element('#skF_5'(A_50),k1_pcomps_1(A_50)) ),
inference(resolution,[status(thm)],[c_1793,c_183]) ).
tff(c_1805,plain,
! [A_50] : ( '#skF_5'(A_50) = A_50 ),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_173,c_1800]) ).
tff(c_1811,plain,
! [A_50] : ~ proper_element(A_50,k1_pcomps_1(A_50)),
inference(demodulation,[status(thm),theory(equality)],[c_1805,c_183]) ).
tff(c_164,plain,
( proper_element('#skF_7',powerset('#skF_6'))
| ( '#skF_7' != '#skF_6' ) ),
inference(cnfTransformation,[status(thm)],[f_276]) ).
tff(c_174,plain,
( proper_element('#skF_7',k1_pcomps_1('#skF_6'))
| ( '#skF_7' != '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_164]) ).
tff(c_287,plain,
'#skF_7' != '#skF_6',
inference(splitLeft,[status(thm)],[c_174]) ).
tff(c_156,plain,
element('#skF_7',powerset('#skF_6')),
inference(cnfTransformation,[status(thm)],[f_276]) ).
tff(c_176,plain,
element('#skF_7',k1_pcomps_1('#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_156]) ).
tff(c_980,plain,
! [B_177,A_178] :
( proper_element(B_177,A_178)
| ( union(A_178) = B_177 )
| ~ element(B_177,A_178) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_158,plain,
( ( '#skF_7' = '#skF_6' )
| ~ proper_element('#skF_7',powerset('#skF_6')) ),
inference(cnfTransformation,[status(thm)],[f_276]) ).
tff(c_175,plain,
( ( '#skF_7' = '#skF_6' )
| ~ proper_element('#skF_7',k1_pcomps_1('#skF_6')) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_158]) ).
tff(c_218,plain,
~ proper_element('#skF_7',k1_pcomps_1('#skF_6')),
inference(splitLeft,[status(thm)],[c_175]) ).
tff(c_990,plain,
( ( union(k1_pcomps_1('#skF_6')) = '#skF_7' )
| ~ element('#skF_7',k1_pcomps_1('#skF_6')) ),
inference(resolution,[status(thm)],[c_980,c_218]) ).
tff(c_998,plain,
'#skF_7' = '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_176,c_173,c_990]) ).
tff(c_1000,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_287,c_998]) ).
tff(c_1002,plain,
'#skF_7' = '#skF_6',
inference(splitRight,[status(thm)],[c_174]) ).
tff(c_1032,plain,
~ proper_element('#skF_6',k1_pcomps_1('#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_1002,c_218]) ).
tff(c_1001,plain,
proper_element('#skF_7',k1_pcomps_1('#skF_6')),
inference(splitRight,[status(thm)],[c_174]) ).
tff(c_1033,plain,
proper_element('#skF_6',k1_pcomps_1('#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_1002,c_1001]) ).
tff(c_1034,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1032,c_1033]) ).
tff(c_1035,plain,
'#skF_7' = '#skF_6',
inference(splitRight,[status(thm)],[c_175]) ).
tff(c_1036,plain,
proper_element('#skF_7',k1_pcomps_1('#skF_6')),
inference(splitRight,[status(thm)],[c_175]) ).
tff(c_1042,plain,
proper_element('#skF_6',k1_pcomps_1('#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_1035,c_1036]) ).
tff(c_1914,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1811,c_1042]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU354+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.14 % 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
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 8 22:55:42 EDT 2025
% 0.14/0.35 % CPUTime :
% 6.29/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.29/2.51
% 6.29/2.51 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------