TSTP Solution File: SET008+3 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET008+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/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 : n004.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 10:55:29 EDT 2023
% Result : Theorem 21.07s 10.22s
% Output : CNFRefutation 21.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 20
% Syntax : Number of formulae : 41 ( 11 unt; 12 typ; 0 def)
% Number of atoms : 52 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 19 ~; 14 |; 3 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 53 (; 53 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > intersection > difference > #nlpp > empty_set > #skF_2 > #skF_3 > #skF_5 > #skF_6 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
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(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_74,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
tff(f_34,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
tff(f_42,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
tff(f_64,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(f_46,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_53,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
tff(f_56,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_86,negated_conjecture,
~ ! [B,C] : ( intersection(difference(B,C),C) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_difference_empty_set) ).
tff(c_34,plain,
! [B_18] :
( empty(B_18)
| member('#skF_2'(B_18),B_18) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_183,plain,
! [D_52,B_53,C_54] :
( member(D_52,B_53)
| ~ member(D_52,intersection(B_53,C_54)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_199,plain,
! [B_53,C_54] :
( member('#skF_2'(intersection(B_53,C_54)),B_53)
| empty(intersection(B_53,C_54)) ),
inference(resolution,[status(thm)],[c_34,c_183]) ).
tff(c_211,plain,
! [D_58,C_59,B_60] :
( member(D_58,C_59)
| ~ member(D_58,intersection(B_60,C_59)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_1286,plain,
! [B_123,C_124] :
( member('#skF_2'(intersection(B_123,C_124)),C_124)
| empty(intersection(B_123,C_124)) ),
inference(resolution,[status(thm)],[c_34,c_211]) ).
tff(c_10,plain,
! [D_6,C_5,B_4] :
( ~ member(D_6,C_5)
| ~ member(D_6,difference(B_4,C_5)) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_98878,plain,
! [B_1139,B_1140,C_1141] :
( ~ member('#skF_2'(intersection(B_1139,difference(B_1140,C_1141))),C_1141)
| empty(intersection(B_1139,difference(B_1140,C_1141))) ),
inference(resolution,[status(thm)],[c_1286,c_10]) ).
tff(c_99218,plain,
! [B_1142,B_1143] : empty(intersection(B_1142,difference(B_1143,B_1142))),
inference(resolution,[status(thm)],[c_199,c_98878]) ).
tff(c_106,plain,
! [B_38,C_39] :
( member('#skF_1'(B_38,C_39),B_38)
| subset(B_38,C_39) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_32,plain,
! [C_21,B_18] :
( ~ member(C_21,B_18)
| ~ empty(B_18) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_120,plain,
! [B_38,C_39] :
( ~ empty(B_38)
| subset(B_38,C_39) ),
inference(resolution,[status(thm)],[c_106,c_32]) ).
tff(c_14,plain,
! [B_7] : ~ member(B_7,empty_set),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_122,plain,
! [C_40] : subset(empty_set,C_40),
inference(resolution,[status(thm)],[c_106,c_14]) ).
tff(c_16,plain,
! [C_9,B_8] :
( ( C_9 = B_8 )
| ~ subset(C_9,B_8)
| ~ subset(B_8,C_9) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_130,plain,
! [C_43] :
( ( empty_set = C_43 )
| ~ subset(C_43,empty_set) ),
inference(resolution,[status(thm)],[c_122,c_16]) ).
tff(c_143,plain,
! [B_38] :
( ( empty_set = B_38 )
| ~ empty(B_38) ),
inference(resolution,[status(thm)],[c_120,c_130]) ).
tff(c_99564,plain,
! [B_1142,B_1143] : ( intersection(B_1142,difference(B_1143,B_1142)) = empty_set ),
inference(resolution,[status(thm)],[c_99218,c_143]) ).
tff(c_22,plain,
! [C_11,B_10] : ( intersection(C_11,B_10) = intersection(B_10,C_11) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_48,plain,
intersection(difference('#skF_5','#skF_6'),'#skF_6') != empty_set,
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_49,plain,
intersection('#skF_6',difference('#skF_5','#skF_6')) != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_48]) ).
tff(c_99620,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_99564,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SET008+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14 % 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 : n004.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 : Thu Aug 3 16:47:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 21.07/10.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.07/10.23
% 21.07/10.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.28/10.26
% 21.28/10.26 Inference rules
% 21.28/10.26 ----------------------
% 21.28/10.26 #Ref : 0
% 21.28/10.26 #Sup : 27372
% 21.28/10.26 #Fact : 0
% 21.28/10.26 #Define : 0
% 21.28/10.26 #Split : 0
% 21.28/10.26 #Chain : 0
% 21.28/10.26 #Close : 0
% 21.28/10.26
% 21.28/10.26 Ordering : KBO
% 21.28/10.26
% 21.28/10.26 Simplification rules
% 21.28/10.26 ----------------------
% 21.28/10.26 #Subsume : 12669
% 21.28/10.26 #Demod : 13496
% 21.28/10.26 #Tautology : 7828
% 21.28/10.26 #SimpNegUnit : 226
% 21.28/10.26 #BackRed : 9
% 21.28/10.26
% 21.28/10.26 #Partial instantiations: 0
% 21.28/10.26 #Strategies tried : 1
% 21.28/10.26
% 21.28/10.26 Timing (in seconds)
% 21.28/10.26 ----------------------
% 21.28/10.27 Preprocessing : 0.48
% 21.28/10.27 Parsing : 0.24
% 21.28/10.27 CNF conversion : 0.04
% 21.28/10.27 Main loop : 8.71
% 21.28/10.27 Inferencing : 1.62
% 21.28/10.27 Reduction : 2.57
% 21.28/10.27 Demodulation : 2.02
% 21.28/10.27 BG Simplification : 0.13
% 21.28/10.27 Subsumption : 3.89
% 21.28/10.27 Abstraction : 0.20
% 21.28/10.27 MUC search : 0.00
% 21.28/10.27 Cooper : 0.00
% 21.28/10.27 Total : 9.25
% 21.28/10.27 Index Insertion : 0.00
% 21.28/10.27 Index Deletion : 0.00
% 21.28/10.27 Index Matching : 0.00
% 21.28/10.27 BG Taut test : 0.00
%------------------------------------------------------------------------------