TSTP Solution File: SET666+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET666+3 : TPTP v8.1.2. 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 : n029.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 : Tue Aug 22 10:56:50 EDT 2023
% Result : Theorem 6.16s 2.52s
% Output : CNFRefutation 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 37
% Syntax : Number of formulae : 66 ( 8 unt; 27 typ; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 43 ~; 43 |; 3 &)
% ( 5 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 23 >; 11 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 4 con; 0-2 aty)
% Number of variables : 73 (; 73 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > ilf_type > relation_like > empty > relation_type > ordered_pair > cross_product > #nlpp > subset_type > power_set > member_type > identity_relation_of_type > identity_relation_of > set_type > binary_relation_type > #skF_7 > #skF_6 > #skF_2 > #skF_4 > #skF_10 > #skF_3 > #skF_8 > #skF_11 > #skF_1 > #skF_9 > #skF_5 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(identity_relation_of_type,type,
identity_relation_of_type: $i > $i ).
tff('#skF_7',type,
'#skF_7': $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('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(identity_relation_of,type,
identity_relation_of: $i > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(set_type,type,
set_type: $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
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('#skF_11',type,
'#skF_11': $i > $i ).
tff(subset_type,type,
subset_type: $i > $i ).
tff(binary_relation_type,type,
binary_relation_type: $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_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_250,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
tff(f_55,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(identity_relation_of(B),cross_product(B,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
tff(f_170,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',p16) ).
tff(f_150,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',p14) ).
tff(f_178,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',p17) ).
tff(f_191,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',p18) ).
tff(f_129,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',p12) ).
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(f_85,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
tff(f_256,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_29) ).
tff(c_92,plain,
! [B_109] : ilf_type(B_109,set_type),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_8,plain,
! [B_18] :
( subset(identity_relation_of(B_18),cross_product(B_18,B_18))
| ~ ilf_type(B_18,set_type) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_177,plain,
! [B_18] : subset(identity_relation_of(B_18),cross_product(B_18,B_18)),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_8]) ).
tff(c_56,plain,
! [B_55,C_61] :
( member('#skF_6'(B_55,C_61),B_55)
| member(B_55,power_set(C_61))
| ~ ilf_type(C_61,set_type)
| ~ ilf_type(B_55,set_type) ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_133,plain,
! [B_55,C_61] :
( member('#skF_6'(B_55,C_61),B_55)
| member(B_55,power_set(C_61)) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_92,c_56]) ).
tff(c_42,plain,
! [D_53,C_50,B_44] :
( member(D_53,C_50)
| ~ member(D_53,B_44)
| ~ ilf_type(D_53,set_type)
| ~ subset(B_44,C_50)
| ~ ilf_type(C_50,set_type)
| ~ ilf_type(B_44,set_type) ),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_254,plain,
! [D_150,C_151,B_152] :
( member(D_150,C_151)
| ~ member(D_150,B_152)
| ~ subset(B_152,C_151) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_92,c_92,c_42]) ).
tff(c_1733,plain,
! [B_339,C_340,C_341] :
( member('#skF_6'(B_339,C_340),C_341)
| ~ subset(B_339,C_341)
| member(B_339,power_set(C_340)) ),
inference(resolution,[status(thm)],[c_133,c_254]) ).
tff(c_54,plain,
! [B_55,C_61] :
( ~ member('#skF_6'(B_55,C_61),C_61)
| member(B_55,power_set(C_61))
| ~ ilf_type(C_61,set_type)
| ~ ilf_type(B_55,set_type) ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_135,plain,
! [B_55,C_61] :
( ~ member('#skF_6'(B_55,C_61),C_61)
| member(B_55,power_set(C_61)) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_92,c_54]) ).
tff(c_1778,plain,
! [B_342,C_343] :
( ~ subset(B_342,C_343)
| member(B_342,power_set(C_343)) ),
inference(resolution,[status(thm)],[c_1733,c_135]) ).
tff(c_62,plain,
! [B_65] :
( ~ empty(power_set(B_65))
| ~ ilf_type(B_65,set_type) ),
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_127,plain,
! [B_65] : ~ empty(power_set(B_65)),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_62]) ).
tff(c_64,plain,
! [B_66,C_68] :
( ilf_type(B_66,member_type(C_68))
| ~ member(B_66,C_68)
| ~ ilf_type(C_68,set_type)
| empty(C_68)
| ~ ilf_type(B_66,set_type) ),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_363,plain,
! [B_177,C_178] :
( ilf_type(B_177,member_type(C_178))
| ~ member(B_177,C_178)
| empty(C_178) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_92,c_64]) ).
tff(c_36,plain,
! [C_41,B_39] :
( ilf_type(C_41,subset_type(B_39))
| ~ ilf_type(C_41,member_type(power_set(B_39)))
| ~ ilf_type(C_41,set_type)
| ~ ilf_type(B_39,set_type) ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_153,plain,
! [C_41,B_39] :
( ilf_type(C_41,subset_type(B_39))
| ~ ilf_type(C_41,member_type(power_set(B_39))) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_92,c_36]) ).
tff(c_370,plain,
! [B_177,B_39] :
( ilf_type(B_177,subset_type(B_39))
| ~ member(B_177,power_set(B_39))
| empty(power_set(B_39)) ),
inference(resolution,[status(thm)],[c_363,c_153]) ).
tff(c_374,plain,
! [B_177,B_39] :
( ilf_type(B_177,subset_type(B_39))
| ~ member(B_177,power_set(B_39)) ),
inference(negUnitSimplification,[status(thm)],[c_127,c_370]) ).
tff(c_1852,plain,
! [B_346,C_347] :
( ilf_type(B_346,subset_type(C_347))
| ~ subset(B_346,C_347) ),
inference(resolution,[status(thm)],[c_1778,c_374]) ).
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_181,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_92,c_92,c_4]) ).
tff(c_2824,plain,
! [B_433,B_434,C_435] :
( ilf_type(B_433,relation_type(B_434,C_435))
| ~ subset(B_433,cross_product(B_434,C_435)) ),
inference(resolution,[status(thm)],[c_1852,c_181]) ).
tff(c_2908,plain,
! [B_436] : ilf_type(identity_relation_of(B_436),relation_type(B_436,B_436)),
inference(resolution,[status(thm)],[c_177,c_2824]) ).
tff(c_18,plain,
! [C_29,B_27] :
( ilf_type(C_29,identity_relation_of_type(B_27))
| ~ ilf_type(C_29,relation_type(B_27,B_27))
| ~ ilf_type(C_29,set_type)
| ~ ilf_type(B_27,set_type) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_167,plain,
! [C_29,B_27] :
( ilf_type(C_29,identity_relation_of_type(B_27))
| ~ ilf_type(C_29,relation_type(B_27,B_27)) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_92,c_18]) ).
tff(c_2917,plain,
! [B_436] : ilf_type(identity_relation_of(B_436),identity_relation_of_type(B_436)),
inference(resolution,[status(thm)],[c_2908,c_167]) ).
tff(c_94,plain,
~ ilf_type(identity_relation_of('#skF_12'),identity_relation_of_type('#skF_12')),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_2920,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2917,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % 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
% 0.17/0.35 % Computer : n029.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 3 16:56:22 EDT 2023
% 0.17/0.35 % CPUTime :
% 6.16/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.16/2.52
% 6.16/2.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.16/2.56
% 6.16/2.56 Inference rules
% 6.16/2.56 ----------------------
% 6.16/2.56 #Ref : 1
% 6.16/2.56 #Sup : 608
% 6.16/2.56 #Fact : 0
% 6.16/2.56 #Define : 0
% 6.16/2.56 #Split : 1
% 6.16/2.56 #Chain : 0
% 6.16/2.56 #Close : 0
% 6.16/2.56
% 6.16/2.56 Ordering : KBO
% 6.16/2.56
% 6.16/2.56 Simplification rules
% 6.16/2.56 ----------------------
% 6.16/2.56 #Subsume : 219
% 6.16/2.56 #Demod : 127
% 6.16/2.56 #Tautology : 75
% 6.16/2.56 #SimpNegUnit : 25
% 6.16/2.56 #BackRed : 1
% 6.16/2.56
% 6.16/2.56 #Partial instantiations: 0
% 6.16/2.56 #Strategies tried : 1
% 6.16/2.56
% 6.16/2.56 Timing (in seconds)
% 6.16/2.56 ----------------------
% 6.16/2.56 Preprocessing : 0.63
% 6.16/2.56 Parsing : 0.34
% 6.16/2.56 CNF conversion : 0.05
% 6.16/2.56 Main loop : 0.85
% 6.16/2.56 Inferencing : 0.33
% 6.16/2.56 Reduction : 0.23
% 6.16/2.56 Demodulation : 0.16
% 6.16/2.56 BG Simplification : 0.04
% 6.16/2.56 Subsumption : 0.19
% 6.16/2.56 Abstraction : 0.03
% 6.16/2.56 MUC search : 0.00
% 6.16/2.56 Cooper : 0.00
% 6.16/2.56 Total : 1.53
% 6.16/2.56 Index Insertion : 0.00
% 6.16/2.56 Index Deletion : 0.00
% 6.16/2.56 Index Matching : 0.00
% 6.16/2.56 BG Taut test : 0.00
%------------------------------------------------------------------------------