%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET662+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/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 08:39:01 PM UTC 2025
% Result : Theorem 4.35s 2.14s
% Output : CNFRefutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 27 ~; 23 |; 3 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 47 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ type > subset > member > ilf_type > relation_like > empty > relation_type > ordered_pair > cross_product > #nlpp > subset_type > power_set > member_type > set_type > empty_set > #skF_9 > #skF_2 > #skF_4 > #skF_11 > #skF_3 > #skF_10 > #skF_8 > #skF_7 > #skF_1 > #skF_5 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff(relation_type,type,
relation_type: ( $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(set_type,type,
set_type: $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': ( $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(empty_set,type,
empty_set: $i ).
tff(type,type,
type: ( $i * $i ) > $o ).
tff(subset_type,type,
subset_type: $i > $i ).
tff(relation_like,type,
relation_like: $i > $o ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_215,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
tff(f_138,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/sandbox/benchmark/theBenchmark.p',p12) ).
tff(f_64,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
tff(f_146,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
tff(f_159,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/sandbox/benchmark/theBenchmark.p',p14) ).
tff(f_86,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/sandbox/benchmark/theBenchmark.p',p7) ).
tff(f_49,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/sandbox/benchmark/theBenchmark.p',p2) ).
tff(f_224,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_25) ).
tff(c_76,plain,
! [B_98] : ilf_type(B_98,set_type),
inference(cnfTransformation,[status(thm)],[f_215]) ).
tff(c_44,plain,
! [B_45,C_51] :
( member('#skF_5'(B_45,C_51),B_45)
| member(B_45,power_set(C_51))
| ~ ilf_type(C_51,set_type)
| ~ ilf_type(B_45,set_type) ),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_227,plain,
! [B_139,C_140] :
( member('#skF_5'(B_139,C_140),B_139)
| member(B_139,power_set(C_140)) ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_76,c_44]) ).
tff(c_10,plain,
! [B_21] :
( ~ member(B_21,empty_set)
| ~ ilf_type(B_21,set_type) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_146,plain,
! [B_21] : ~ member(B_21,empty_set),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_10]) ).
tff(c_244,plain,
! [C_140] : member(empty_set,power_set(C_140)),
inference(resolution,[status(thm)],[c_227,c_146]) ).
tff(c_50,plain,
! [B_55] :
( ~ empty(power_set(B_55))
| ~ ilf_type(B_55,set_type) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_110,plain,
! [B_55] : ~ empty(power_set(B_55)),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_50]) ).
tff(c_52,plain,
! [B_56,C_58] :
( ilf_type(B_56,member_type(C_58))
| ~ member(B_56,C_58)
| ~ ilf_type(C_58,set_type)
| empty(C_58)
| ~ ilf_type(B_56,set_type) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_108,plain,
! [B_56,C_58] :
( ilf_type(B_56,member_type(C_58))
| ~ member(B_56,C_58)
| empty(C_58) ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_76,c_52]) ).
tff(c_18,plain,
! [C_27,B_25] :
( ilf_type(C_27,subset_type(B_25))
| ~ ilf_type(C_27,member_type(power_set(B_25)))
| ~ ilf_type(C_27,set_type)
| ~ ilf_type(B_25,set_type) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_332,plain,
! [C_152,B_153] :
( ilf_type(C_152,subset_type(B_153))
| ~ ilf_type(C_152,member_type(power_set(B_153))) ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_76,c_18]) ).
tff(c_336,plain,
! [B_56,B_153] :
( ilf_type(B_56,subset_type(B_153))
| ~ member(B_56,power_set(B_153))
| empty(power_set(B_153)) ),
inference(resolution,[status(thm)],[c_108,c_332]) ).
tff(c_404,plain,
! [B_162,B_163] :
( ilf_type(B_162,subset_type(B_163))
| ~ member(B_162,power_set(B_163)) ),
inference(negUnitSimplification,[status(thm)],[c_110,c_336]) ).
tff(c_442,plain,
! [C_140] : ilf_type(empty_set,subset_type(C_140)),
inference(resolution,[status(thm)],[c_244,c_404]) ).
tff(c_6,plain,
! [D_13,B_4,C_10] :
( ilf_type(D_13,relation_type(B_4,C_10))
| ~ ilf_type(D_13,subset_type(cross_product(B_4,C_10)))
| ~ ilf_type(C_10,set_type)
| ~ ilf_type(B_4,set_type) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_487,plain,
! [D_179,B_180,C_181] :
( ilf_type(D_179,relation_type(B_180,C_181))
| ~ ilf_type(D_179,subset_type(cross_product(B_180,C_181))) ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_76,c_6]) ).
tff(c_519,plain,
! [B_180,C_181] : ilf_type(empty_set,relation_type(B_180,C_181)),
inference(resolution,[status(thm)],[c_442,c_487]) ).
tff(c_78,plain,
~ ilf_type(empty_set,relation_type('#skF_10','#skF_11')),
inference(cnfTransformation,[status(thm)],[f_224]) ).
tff(c_525,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_519,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET662+3 : TPTP v9.0.0. Released v2.2.0.
% 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 21:22:57 EDT 2025
% 0.14/0.35 % CPUTime :
% 4.35/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.35/2.14
% 4.35/2.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------