%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET641+3 : TPTP v9.0.0. Released v2.2.0.
% 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 : n007.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 08:38:58 PM UTC 2025
% Result : Theorem 8.40s 2.99s
% Output : CNFRefutation 8.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 104 ( 38 ~; 38 |; 3 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 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 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 4 con; 0-3 aty)
% Number of variables : 64 ( 64 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > ilf_type > relation_like > empty > relation_type > ordered_pair > cross_product > #nlpp > subset_type > power_set > member_type > set_type > #skF_7 > #skF_5 > #skF_6 > #skF_8 > #skF_14 > #skF_13 > #skF_10 > #skF_2 > #skF_11 > #skF_3 > #skF_1 > #skF_9 > #skF_12 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation_type,type,
relation_type: ( $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(set_type,type,
set_type: $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(ilf_type,type,
ilf_type: ( $i * $i ) > $o ).
tff(member_type,type,
member_type: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(subset_type,type,
subset_type: $i > $i ).
tff(relation_like,type,
relation_like: $i > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_234,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( subset(B,cross_product(C,D))
=> ilf_type(B,relation_type(C,D)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_3) ).
tff(f_220,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
tff(f_140,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
tff(f_96,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
tff(f_148,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
tff(f_161,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
tff(f_114,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
tff(f_41,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
tff(c_82,plain,
~ ilf_type('#skF_12',relation_type('#skF_13','#skF_14')),
inference(cnfTransformation,[status(thm)],[f_234]) ).
tff(c_84,plain,
subset('#skF_12',cross_product('#skF_13','#skF_14')),
inference(cnfTransformation,[status(thm)],[f_234]) ).
tff(c_80,plain,
! [B_147] : ilf_type(B_147,set_type),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_44,plain,
! [B_93,C_99] :
( member('#skF_6'(B_93,C_99),B_93)
| member(B_93,power_set(C_99))
| ~ ilf_type(C_99,set_type)
| ~ ilf_type(B_93,set_type) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_129,plain,
! [B_93,C_99] :
( member('#skF_6'(B_93,C_99),B_93)
| member(B_93,power_set(C_99)) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_44]) ).
tff(c_22,plain,
! [D_83,C_80,B_74] :
( member(D_83,C_80)
| ~ member(D_83,B_74)
| ~ ilf_type(D_83,set_type)
| ~ subset(B_74,C_80)
| ~ ilf_type(C_80,set_type)
| ~ ilf_type(B_74,set_type) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_337,plain,
! [D_205,C_206,B_207] :
( member(D_205,C_206)
| ~ member(D_205,B_207)
| ~ subset(B_207,C_206) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_80,c_22]) ).
tff(c_2348,plain,
! [B_437,C_438,C_439] :
( member('#skF_6'(B_437,C_438),C_439)
| ~ subset(B_437,C_439)
| member(B_437,power_set(C_438)) ),
inference(resolution,[status(thm)],[c_129,c_337]) ).
tff(c_42,plain,
! [B_93,C_99] :
( ~ member('#skF_6'(B_93,C_99),C_99)
| member(B_93,power_set(C_99))
| ~ ilf_type(C_99,set_type)
| ~ ilf_type(B_93,set_type) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_131,plain,
! [B_93,C_99] :
( ~ member('#skF_6'(B_93,C_99),C_99)
| member(B_93,power_set(C_99)) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_42]) ).
tff(c_2419,plain,
! [B_440,C_441] :
( ~ subset(B_440,C_441)
| member(B_440,power_set(C_441)) ),
inference(resolution,[status(thm)],[c_2348,c_131]) ).
tff(c_50,plain,
! [B_103] :
( ~ empty(power_set(B_103))
| ~ ilf_type(B_103,set_type) ),
inference(cnfTransformation,[status(thm)],[f_148]) ).
tff(c_123,plain,
! [B_103] : ~ empty(power_set(B_103)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_50]) ).
tff(c_52,plain,
! [B_104,C_106] :
( ilf_type(B_104,member_type(C_106))
| ~ member(B_104,C_106)
| ~ ilf_type(C_106,set_type)
| empty(C_106)
| ~ ilf_type(B_104,set_type) ),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_241,plain,
! [B_187,C_188] :
( ilf_type(B_187,member_type(C_188))
| ~ member(B_187,C_188)
| empty(C_188) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_52]) ).
tff(c_32,plain,
! [C_89,B_87] :
( ilf_type(C_89,subset_type(B_87))
| ~ ilf_type(C_89,member_type(power_set(B_87)))
| ~ ilf_type(C_89,set_type)
| ~ ilf_type(B_87,set_type) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_141,plain,
! [C_89,B_87] :
( ilf_type(C_89,subset_type(B_87))
| ~ ilf_type(C_89,member_type(power_set(B_87))) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_32]) ).
tff(c_245,plain,
! [B_187,B_87] :
( ilf_type(B_187,subset_type(B_87))
| ~ member(B_187,power_set(B_87))
| empty(power_set(B_87)) ),
inference(resolution,[status(thm)],[c_241,c_141]) ).
tff(c_248,plain,
! [B_187,B_87] :
( ilf_type(B_187,subset_type(B_87))
| ~ member(B_187,power_set(B_87)) ),
inference(negUnitSimplification,[status(thm)],[c_123,c_245]) ).
tff(c_2665,plain,
! [B_451,C_452] :
( ilf_type(B_451,subset_type(C_452))
| ~ subset(B_451,C_452) ),
inference(resolution,[status(thm)],[c_2419,c_248]) ).
tff(c_4,plain,
! [D_10,B_1,C_7] :
( ilf_type(D_10,relation_type(B_1,C_7))
| ~ ilf_type(D_10,subset_type(cross_product(B_1,C_7)))
| ~ ilf_type(C_7,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_169,plain,
! [D_10,B_1,C_7] :
( ilf_type(D_10,relation_type(B_1,C_7))
| ~ ilf_type(D_10,subset_type(cross_product(B_1,C_7))) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_4]) ).
tff(c_9481,plain,
! [B_805,B_806,C_807] :
( ilf_type(B_805,relation_type(B_806,C_807))
| ~ subset(B_805,cross_product(B_806,C_807)) ),
inference(resolution,[status(thm)],[c_2665,c_169]) ).
tff(c_9643,plain,
ilf_type('#skF_12',relation_type('#skF_13','#skF_14')),
inference(resolution,[status(thm)],[c_84,c_9481]) ).
tff(c_9695,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_82,c_9643]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET641+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % 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
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 8 21:21:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 8.40/2.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.40/3.00
% 8.40/3.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------