TSTP Solution File: SET637+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET637+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 : n022.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 10:56:46 EDT 2023
% Result : Theorem 6.40s 2.56s
% Output : CNFRefutation 6.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of formulae : 100 ( 28 unt; 14 typ; 0 def)
% Number of atoms : 159 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 132 ( 59 ~; 63 |; 2 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 114 (; 113 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ not_equal > member > intersect > empty > intersection > #nlpp > empty_set > #skF_4 > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_8 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(intersect,type,
intersect: ( $i * $i ) > $o ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(not_equal,type,
not_equal: ( $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_59,axiom,
! [B,C] :
( not_equal(B,C)
<=> ( B != C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
tff(f_74,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
tff(f_33,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
tff(f_41,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
tff(f_67,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
tff(f_53,axiom,
! [B,C] :
( ( B = C )
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
tff(f_45,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_80,negated_conjecture,
~ ! [B,C] :
( intersect(B,C)
<=> not_equal(intersection(B,C),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th119) ).
tff(f_62,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(c_28,plain,
! [C_16] : ~ not_equal(C_16,C_16),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_38,plain,
! [B_21] :
( empty(B_21)
| member('#skF_4'(B_21),B_21) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_3203,plain,
! [D_186,C_187,B_188] :
( member(D_186,C_187)
| ~ member(D_186,intersection(B_188,C_187)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_4422,plain,
! [B_269,C_270] :
( member('#skF_4'(intersection(B_269,C_270)),C_270)
| empty(intersection(B_269,C_270)) ),
inference(resolution,[status(thm)],[c_38,c_3203]) ).
tff(c_3272,plain,
! [B_202,C_203,D_204] :
( intersect(B_202,C_203)
| ~ member(D_204,C_203)
| ~ member(D_204,B_202) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_3281,plain,
! [B_202,B_21] :
( intersect(B_202,B_21)
| ~ member('#skF_4'(B_21),B_202)
| empty(B_21) ),
inference(resolution,[status(thm)],[c_38,c_3272]) ).
tff(c_4682,plain,
! [C_280,B_281] :
( intersect(C_280,intersection(B_281,C_280))
| empty(intersection(B_281,C_280)) ),
inference(resolution,[status(thm)],[c_4422,c_3281]) ).
tff(c_34,plain,
! [C_20,B_19] :
( intersect(C_20,B_19)
| ~ intersect(B_19,C_20) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_4723,plain,
! [B_281,C_280] :
( intersect(intersection(B_281,C_280),C_280)
| empty(intersection(B_281,C_280)) ),
inference(resolution,[status(thm)],[c_4682,c_34]) ).
tff(c_3248,plain,
! [B_195,C_196] :
( member('#skF_1'(B_195,C_196),B_195)
| ~ intersect(B_195,C_196) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_6,plain,
! [D_3,B_1,C_2] :
( member(D_3,B_1)
| ~ member(D_3,intersection(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_5916,plain,
! [B_317,C_318,C_319] :
( member('#skF_1'(intersection(B_317,C_318),C_319),B_317)
| ~ intersect(intersection(B_317,C_318),C_319) ),
inference(resolution,[status(thm)],[c_3248,c_6]) ).
tff(c_10,plain,
! [B_4,C_5] :
( member('#skF_1'(B_4,C_5),C_5)
| ~ intersect(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_3280,plain,
! [B_202,C_5,B_4] :
( intersect(B_202,C_5)
| ~ member('#skF_1'(B_4,C_5),B_202)
| ~ intersect(B_4,C_5) ),
inference(resolution,[status(thm)],[c_10,c_3272]) ).
tff(c_6251,plain,
! [B_328,C_329,C_330] :
( intersect(B_328,C_329)
| ~ intersect(intersection(B_328,C_330),C_329) ),
inference(resolution,[status(thm)],[c_5916,c_3280]) ).
tff(c_6348,plain,
! [B_331,C_332] :
( intersect(B_331,C_332)
| empty(intersection(B_331,C_332)) ),
inference(resolution,[status(thm)],[c_4723,c_6251]) ).
tff(c_3391,plain,
! [B_215,C_216] :
( member('#skF_2'(B_215,C_216),C_216)
| member('#skF_3'(B_215,C_216),B_215)
| ( C_216 = B_215 ) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_14,plain,
! [B_9] : ~ member(B_9,empty_set),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_3448,plain,
! [C_221] :
( member('#skF_2'(empty_set,C_221),C_221)
| ( empty_set = C_221 ) ),
inference(resolution,[status(thm)],[c_3391,c_14]) ).
tff(c_36,plain,
! [C_24,B_21] :
( ~ member(C_24,B_21)
| ~ empty(B_21) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_3469,plain,
! [C_221] :
( ~ empty(C_221)
| ( empty_set = C_221 ) ),
inference(resolution,[status(thm)],[c_3448,c_36]) ).
tff(c_6494,plain,
! [B_335,C_336] :
( ( intersection(B_335,C_336) = empty_set )
| intersect(B_335,C_336) ),
inference(resolution,[status(thm)],[c_6348,c_3469]) ).
tff(c_44,plain,
( ~ intersect('#skF_5','#skF_6')
| intersect('#skF_7','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_71,plain,
~ intersect('#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_6545,plain,
intersection('#skF_5','#skF_6') = empty_set,
inference(resolution,[status(thm)],[c_6494,c_71]) ).
tff(c_32,plain,
! [C_18,B_17] : ( intersection(C_18,B_17) = intersection(B_17,C_18) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_6879,plain,
intersection('#skF_6','#skF_5') = empty_set,
inference(superposition,[status(thm),theory(equality)],[c_6545,c_32]) ).
tff(c_175,plain,
! [D_49,C_50,B_51] :
( member(D_49,C_50)
| ~ member(D_49,intersection(B_51,C_50)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_424,plain,
! [B_74,C_75] :
( member('#skF_4'(intersection(B_74,C_75)),C_75)
| empty(intersection(B_74,C_75)) ),
inference(resolution,[status(thm)],[c_38,c_175]) ).
tff(c_197,plain,
! [B_52,C_53,D_54] :
( intersect(B_52,C_53)
| ~ member(D_54,C_53)
| ~ member(D_54,B_52) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_206,plain,
! [B_52,B_21] :
( intersect(B_52,B_21)
| ~ member('#skF_4'(B_21),B_52)
| empty(B_21) ),
inference(resolution,[status(thm)],[c_38,c_197]) ).
tff(c_497,plain,
! [C_84,B_85] :
( intersect(C_84,intersection(B_85,C_84))
| empty(intersection(B_85,C_84)) ),
inference(resolution,[status(thm)],[c_424,c_206]) ).
tff(c_515,plain,
! [B_17,C_18] :
( intersect(B_17,intersection(B_17,C_18))
| empty(intersection(C_18,B_17)) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_497]) ).
tff(c_2548,plain,
! [B_165,B_166,C_167] :
( member('#skF_1'(B_165,intersection(B_166,C_167)),C_167)
| ~ intersect(B_165,intersection(B_166,C_167)) ),
inference(resolution,[status(thm)],[c_10,c_175]) ).
tff(c_12,plain,
! [B_4,C_5] :
( member('#skF_1'(B_4,C_5),B_4)
| ~ intersect(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_205,plain,
! [B_52,B_4,C_5] :
( intersect(B_52,B_4)
| ~ member('#skF_1'(B_4,C_5),B_52)
| ~ intersect(B_4,C_5) ),
inference(resolution,[status(thm)],[c_12,c_197]) ).
tff(c_2755,plain,
! [C_174,B_175,B_176] :
( intersect(C_174,B_175)
| ~ intersect(B_175,intersection(B_176,C_174)) ),
inference(resolution,[status(thm)],[c_2548,c_205]) ).
tff(c_2825,plain,
! [C_177,B_178] :
( intersect(C_177,B_178)
| empty(intersection(C_177,B_178)) ),
inference(resolution,[status(thm)],[c_515,c_2755]) ).
tff(c_594,plain,
! [B_94,C_95] :
( member('#skF_2'(B_94,C_95),C_95)
| member('#skF_3'(B_94,C_95),B_94)
| ( C_95 = B_94 ) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_643,plain,
! [C_96] :
( member('#skF_2'(empty_set,C_96),C_96)
| ( empty_set = C_96 ) ),
inference(resolution,[status(thm)],[c_594,c_14]) ).
tff(c_668,plain,
! [C_96] :
( ~ empty(C_96)
| ( empty_set = C_96 ) ),
inference(resolution,[status(thm)],[c_643,c_36]) ).
tff(c_2891,plain,
! [C_179,B_180] :
( ( intersection(C_179,B_180) = empty_set )
| intersect(C_179,B_180) ),
inference(resolution,[status(thm)],[c_2825,c_668]) ).
tff(c_2938,plain,
intersection('#skF_5','#skF_6') = empty_set,
inference(resolution,[status(thm)],[c_2891,c_71]) ).
tff(c_3036,plain,
intersection('#skF_6','#skF_5') = empty_set,
inference(superposition,[status(thm),theory(equality)],[c_32,c_2938]) ).
tff(c_46,plain,
( not_equal(intersection('#skF_5','#skF_6'),empty_set)
| intersect('#skF_7','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_48,plain,
( not_equal(intersection('#skF_6','#skF_5'),empty_set)
| intersect('#skF_7','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_46]) ).
tff(c_72,plain,
intersect('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_30,plain,
! [B_15,C_16] :
( not_equal(B_15,C_16)
| ( C_16 = B_15 ) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_42,plain,
( not_equal(intersection('#skF_5','#skF_6'),empty_set)
| ~ not_equal(intersection('#skF_7','#skF_8'),empty_set) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_49,plain,
( not_equal(intersection('#skF_6','#skF_5'),empty_set)
| ~ not_equal(intersection('#skF_8','#skF_7'),empty_set) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_32,c_42]) ).
tff(c_236,plain,
~ not_equal(intersection('#skF_8','#skF_7'),empty_set),
inference(splitLeft,[status(thm)],[c_49]) ).
tff(c_240,plain,
intersection('#skF_8','#skF_7') = empty_set,
inference(resolution,[status(thm)],[c_30,c_236]) ).
tff(c_309,plain,
! [D_62,B_63,C_64] :
( member(D_62,intersection(B_63,C_64))
| ~ member(D_62,C_64)
| ~ member(D_62,B_63) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_327,plain,
! [D_62] :
( member(D_62,empty_set)
| ~ member(D_62,'#skF_7')
| ~ member(D_62,'#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_309]) ).
tff(c_352,plain,
! [D_67] :
( ~ member(D_67,'#skF_7')
| ~ member(D_67,'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_14,c_327]) ).
tff(c_386,plain,
! [C_70] :
( ~ member('#skF_1'('#skF_7',C_70),'#skF_8')
| ~ intersect('#skF_7',C_70) ),
inference(resolution,[status(thm)],[c_12,c_352]) ).
tff(c_390,plain,
~ intersect('#skF_7','#skF_8'),
inference(resolution,[status(thm)],[c_10,c_386]) ).
tff(c_394,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_72,c_390]) ).
tff(c_395,plain,
not_equal(intersection('#skF_6','#skF_5'),empty_set),
inference(splitRight,[status(thm)],[c_49]) ).
tff(c_3164,plain,
not_equal(empty_set,empty_set),
inference(demodulation,[status(thm),theory(equality)],[c_3036,c_395]) ).
tff(c_3167,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_3164]) ).
tff(c_3168,plain,
not_equal(intersection('#skF_6','#skF_5'),empty_set),
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_7078,plain,
not_equal(empty_set,empty_set),
inference(demodulation,[status(thm),theory(equality)],[c_6879,c_3168]) ).
tff(c_7080,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_7078]) ).
tff(c_7081,plain,
intersect('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_7085,plain,
intersect('#skF_8','#skF_7'),
inference(resolution,[status(thm)],[c_7081,c_34]) ).
tff(c_7082,plain,
intersect('#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_40,plain,
( ~ intersect('#skF_5','#skF_6')
| ~ not_equal(intersection('#skF_7','#skF_8'),empty_set) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_47,plain,
( ~ intersect('#skF_5','#skF_6')
| ~ not_equal(intersection('#skF_8','#skF_7'),empty_set) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_40]) ).
tff(c_7160,plain,
~ not_equal(intersection('#skF_8','#skF_7'),empty_set),
inference(demodulation,[status(thm),theory(equality)],[c_7082,c_47]) ).
tff(c_7164,plain,
intersection('#skF_8','#skF_7') = empty_set,
inference(resolution,[status(thm)],[c_30,c_7160]) ).
tff(c_7264,plain,
! [D_363,B_364,C_365] :
( member(D_363,intersection(B_364,C_365))
| ~ member(D_363,C_365)
| ~ member(D_363,B_364) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_7282,plain,
! [D_363] :
( member(D_363,empty_set)
| ~ member(D_363,'#skF_7')
| ~ member(D_363,'#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_7164,c_7264]) ).
tff(c_7319,plain,
! [D_367] :
( ~ member(D_367,'#skF_7')
| ~ member(D_367,'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_14,c_7282]) ).
tff(c_7337,plain,
! [B_368] :
( ~ member('#skF_1'(B_368,'#skF_7'),'#skF_8')
| ~ intersect(B_368,'#skF_7') ),
inference(resolution,[status(thm)],[c_10,c_7319]) ).
tff(c_7341,plain,
~ intersect('#skF_8','#skF_7'),
inference(resolution,[status(thm)],[c_12,c_7337]) ).
tff(c_7345,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7085,c_7341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET637+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
% 0.18/0.35 % Computer : n022.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 3 16:46:48 EDT 2023
% 0.18/0.35 % CPUTime :
% 6.40/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.46/2.57
% 6.46/2.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.46/2.61
% 6.46/2.61 Inference rules
% 6.46/2.61 ----------------------
% 6.46/2.61 #Ref : 0
% 6.46/2.61 #Sup : 1829
% 6.46/2.61 #Fact : 0
% 6.46/2.61 #Define : 0
% 6.46/2.61 #Split : 3
% 6.46/2.61 #Chain : 0
% 6.46/2.61 #Close : 0
% 6.46/2.61
% 6.46/2.61 Ordering : KBO
% 6.46/2.61
% 6.46/2.61 Simplification rules
% 6.46/2.61 ----------------------
% 6.46/2.61 #Subsume : 562
% 6.46/2.61 #Demod : 752
% 6.46/2.61 #Tautology : 703
% 6.46/2.61 #SimpNegUnit : 175
% 6.46/2.61 #BackRed : 9
% 6.46/2.61
% 6.46/2.61 #Partial instantiations: 0
% 6.46/2.61 #Strategies tried : 1
% 6.46/2.61
% 6.46/2.61 Timing (in seconds)
% 6.46/2.61 ----------------------
% 6.68/2.61 Preprocessing : 0.47
% 6.68/2.61 Parsing : 0.24
% 6.68/2.61 CNF conversion : 0.04
% 6.68/2.61 Main loop : 1.06
% 6.68/2.61 Inferencing : 0.37
% 6.68/2.61 Reduction : 0.35
% 6.68/2.61 Demodulation : 0.25
% 6.68/2.61 BG Simplification : 0.04
% 6.68/2.61 Subsumption : 0.23
% 6.68/2.61 Abstraction : 0.04
% 6.68/2.61 MUC search : 0.00
% 6.68/2.61 Cooper : 0.00
% 6.68/2.61 Total : 1.60
% 6.68/2.61 Index Insertion : 0.00
% 6.68/2.61 Index Deletion : 0.00
% 6.68/2.61 Index Matching : 0.00
% 6.68/2.61 BG Taut test : 0.00
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