TSTP Solution File: SET015+4 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET015+4 : 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 : n027.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 10:55:32 EDT 2023
% Result : Theorem 106.01s 90.72s
% Output : CNFRefutation 106.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 37 ( 6 unt; 17 typ; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 31 ( 11 ~; 15 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 14 >; 10 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 45 (; 45 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > equal_set > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_3 > #skF_5 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(equal_set,type,
equal_set: ( $i * $i ) > $o ).
tff(power_set,type,
power_set: $i > $i ).
tff(product,type,
product: $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(sum,type,
sum: $i > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $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(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_56,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
tff(f_78,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,A)
| member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).
tff(f_62,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
tff(f_117,negated_conjecture,
~ ! [A,B] : equal_set(union(A,B),union(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI07) ).
tff(c_6,plain,
! [A_1,B_2] :
( member('#skF_1'(A_1,B_2),A_1)
| subset(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_685,plain,
! [X_131,B_132,A_133] :
( member(X_131,B_132)
| member(X_131,A_133)
| ~ member(X_131,union(A_133,B_132)) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_19613,plain,
! [A_832,B_833,B_834] :
( member('#skF_1'(union(A_832,B_833),B_834),B_833)
| member('#skF_1'(union(A_832,B_833),B_834),A_832)
| subset(union(A_832,B_833),B_834) ),
inference(resolution,[status(thm)],[c_6,c_685]) ).
tff(c_26,plain,
! [X_13,B_15,A_14] :
( ~ member(X_13,B_15)
| member(X_13,union(A_14,B_15)) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_83,plain,
! [A_63,B_64] :
( ~ member('#skF_1'(A_63,B_64),B_64)
| subset(A_63,B_64) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_96,plain,
! [A_63,A_14,B_15] :
( subset(A_63,union(A_14,B_15))
| ~ member('#skF_1'(A_63,union(A_14,B_15)),B_15) ),
inference(resolution,[status(thm)],[c_26,c_83]) ).
tff(c_202781,plain,
! [A_3220,B_3221,A_3222] :
( member('#skF_1'(union(A_3220,B_3221),union(A_3222,A_3220)),B_3221)
| subset(union(A_3220,B_3221),union(A_3222,A_3220)) ),
inference(resolution,[status(thm)],[c_19613,c_96]) ).
tff(c_28,plain,
! [X_13,A_14,B_15] :
( ~ member(X_13,A_14)
| member(X_13,union(A_14,B_15)) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_97,plain,
! [A_63,A_14,B_15] :
( subset(A_63,union(A_14,B_15))
| ~ member('#skF_1'(A_63,union(A_14,B_15)),A_14) ),
inference(resolution,[status(thm)],[c_28,c_83]) ).
tff(c_203382,plain,
! [A_3220,B_3221] : subset(union(A_3220,B_3221),union(B_3221,A_3220)),
inference(resolution,[status(thm)],[c_202781,c_97]) ).
tff(c_203409,plain,
! [A_3223,B_3224] : subset(union(A_3223,B_3224),union(B_3224,A_3223)),
inference(resolution,[status(thm)],[c_202781,c_97]) ).
tff(c_8,plain,
! [A_6,B_7] :
( equal_set(A_6,B_7)
| ~ subset(B_7,A_6)
| ~ subset(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_203433,plain,
! [B_3224,A_3223] :
( equal_set(union(B_3224,A_3223),union(A_3223,B_3224))
| ~ subset(union(B_3224,A_3223),union(A_3223,B_3224)) ),
inference(resolution,[status(thm)],[c_203409,c_8]) ).
tff(c_203447,plain,
! [B_3224,A_3223] : equal_set(union(B_3224,A_3223),union(A_3223,B_3224)),
inference(demodulation,[status(thm),theory(equality)],[c_203382,c_203433]) ).
tff(c_60,plain,
~ equal_set(union('#skF_4','#skF_5'),union('#skF_5','#skF_4')),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_203450,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_203447,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET015+4 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.14 % 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
% 0.12/0.35 % Computer : n027.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Aug 3 16:49:53 EDT 2023
% 0.12/0.35 % CPUTime :
% 106.01/90.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.01/90.73
% 106.01/90.73 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 106.01/90.75
% 106.01/90.75 Inference rules
% 106.01/90.75 ----------------------
% 106.01/90.75 #Ref : 0
% 106.01/90.75 #Sup : 48634
% 106.01/90.75 #Fact : 14
% 106.01/90.75 #Define : 0
% 106.01/90.75 #Split : 2
% 106.01/90.75 #Chain : 0
% 106.01/90.75 #Close : 0
% 106.01/90.75
% 106.01/90.75 Ordering : KBO
% 106.01/90.75
% 106.01/90.75 Simplification rules
% 106.01/90.76 ----------------------
% 106.01/90.76 #Subsume : 2746
% 106.01/90.76 #Demod : 7310
% 106.01/90.76 #Tautology : 7362
% 106.01/90.76 #SimpNegUnit : 116
% 106.01/90.76 #BackRed : 5
% 106.01/90.76
% 106.01/90.76 #Partial instantiations: 0
% 106.01/90.76 #Strategies tried : 1
% 106.01/90.76
% 106.01/90.76 Timing (in seconds)
% 106.01/90.76 ----------------------
% 106.01/90.76 Preprocessing : 0.50
% 106.01/90.76 Parsing : 0.26
% 106.01/90.76 CNF conversion : 0.04
% 106.01/90.76 Main loop : 89.16
% 106.01/90.76 Inferencing : 6.29
% 106.01/90.76 Reduction : 50.22
% 106.01/90.76 Demodulation : 41.41
% 106.01/90.76 BG Simplification : 0.26
% 106.01/90.76 Subsumption : 27.36
% 106.01/90.76 Abstraction : 0.42
% 106.01/90.76 MUC search : 0.00
% 106.01/90.76 Cooper : 0.00
% 106.01/90.76 Total : 89.71
% 106.01/90.76 Index Insertion : 0.00
% 106.01/90.76 Index Deletion : 0.00
% 106.01/90.76 Index Matching : 0.00
% 106.01/90.76 BG Taut test : 0.00
%------------------------------------------------------------------------------