TSTP Solution File: SET002+4 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET002+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/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 : n009.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 10:55:28 EDT 2023
% Result : Theorem 22.11s 10.99s
% Output : CNFRefutation 22.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 20
% Syntax : Number of formulae : 40 ( 7 unt; 16 typ; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 41 ( 16 ~; 20 |; 1 &)
% ( 3 <=>; 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 : 24 ( 14 >; 10 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 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_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(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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
tff(f_117,negated_conjecture,
~ ! [A] : equal_set(union(A,A),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI14) ).
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_85,plain,
! [X_53,A_54,B_55] :
( ~ member(X_53,A_54)
| member(X_53,union(A_54,B_55)) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_4,plain,
! [A_1,B_2] :
( ~ member('#skF_1'(A_1,B_2),B_2)
| subset(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_7589,plain,
! [A_427,A_428,B_429] :
( subset(A_427,union(A_428,B_429))
| ~ member('#skF_1'(A_427,union(A_428,B_429)),A_428) ),
inference(resolution,[status(thm)],[c_85,c_4]) ).
tff(c_7800,plain,
! [A_1,B_429] : subset(A_1,union(A_1,B_429)),
inference(resolution,[status(thm)],[c_6,c_7589]) ).
tff(c_848,plain,
! [X_140,B_141,A_142] :
( member(X_140,B_141)
| member(X_140,A_142)
| ~ member(X_140,union(A_142,B_141)) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_18992,plain,
! [A_827,B_828,B_829] :
( member('#skF_1'(union(A_827,B_828),B_829),B_828)
| member('#skF_1'(union(A_827,B_828),B_829),A_827)
| subset(union(A_827,B_828),B_829) ),
inference(resolution,[status(thm)],[c_6,c_848]) ).
tff(c_41077,plain,
! [A_1279,B_1280] :
( member('#skF_1'(union(A_1279,B_1280),A_1279),B_1280)
| subset(union(A_1279,B_1280),A_1279) ),
inference(resolution,[status(thm)],[c_18992,c_4]) ).
tff(c_41383,plain,
! [B_1281] : subset(union(B_1281,B_1281),B_1281),
inference(resolution,[status(thm)],[c_41077,c_4]) ).
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_41419,plain,
! [B_1281] :
( equal_set(B_1281,union(B_1281,B_1281))
| ~ subset(B_1281,union(B_1281,B_1281)) ),
inference(resolution,[status(thm)],[c_41383,c_8]) ).
tff(c_41729,plain,
! [B_1286] : equal_set(B_1286,union(B_1286,B_1286)),
inference(demodulation,[status(thm),theory(equality)],[c_7800,c_41419]) ).
tff(c_10,plain,
! [B_7,A_6] :
( subset(B_7,A_6)
| ~ equal_set(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_12,plain,
! [A_6,B_7] :
( subset(A_6,B_7)
| ~ equal_set(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_268,plain,
! [A_92,B_93] :
( equal_set(A_92,B_93)
| ~ subset(B_93,A_92)
| ~ subset(A_92,B_93) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_2671,plain,
! [B_238,A_239] :
( equal_set(B_238,A_239)
| ~ subset(B_238,A_239)
| ~ equal_set(A_239,B_238) ),
inference(resolution,[status(thm)],[c_12,c_268]) ).
tff(c_2761,plain,
! [B_7,A_6] :
( equal_set(B_7,A_6)
| ~ equal_set(A_6,B_7) ),
inference(resolution,[status(thm)],[c_10,c_2671]) ).
tff(c_41773,plain,
! [B_1286] : equal_set(union(B_1286,B_1286),B_1286),
inference(resolution,[status(thm)],[c_41729,c_2761]) ).
tff(c_60,plain,
~ equal_set(union('#skF_4','#skF_4'),'#skF_4'),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_42614,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_41773,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET002+4 : 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
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 16:49:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 22.11/10.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.11/10.99
% 22.11/10.99 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.11/11.02
% 22.11/11.02 Inference rules
% 22.11/11.02 ----------------------
% 22.11/11.02 #Ref : 0
% 22.11/11.02 #Sup : 9766
% 22.11/11.02 #Fact : 6
% 22.11/11.02 #Define : 0
% 22.11/11.02 #Split : 1
% 22.11/11.02 #Chain : 0
% 22.11/11.02 #Close : 0
% 22.11/11.02
% 22.11/11.02 Ordering : KBO
% 22.11/11.02
% 22.11/11.02 Simplification rules
% 22.11/11.02 ----------------------
% 22.11/11.02 #Subsume : 713
% 22.11/11.02 #Demod : 1674
% 22.11/11.02 #Tautology : 1692
% 22.11/11.02 #SimpNegUnit : 54
% 22.11/11.02 #BackRed : 4
% 22.11/11.02
% 22.11/11.02 #Partial instantiations: 0
% 22.11/11.02 #Strategies tried : 1
% 22.11/11.02
% 22.11/11.02 Timing (in seconds)
% 22.11/11.02 ----------------------
% 22.11/11.02 Preprocessing : 0.50
% 22.11/11.02 Parsing : 0.26
% 22.11/11.02 CNF conversion : 0.04
% 22.11/11.02 Main loop : 9.38
% 22.11/11.02 Inferencing : 1.61
% 22.11/11.02 Reduction : 4.45
% 22.11/11.02 Demodulation : 3.46
% 22.11/11.02 BG Simplification : 0.08
% 22.11/11.02 Subsumption : 2.63
% 22.11/11.02 Abstraction : 0.11
% 22.11/11.02 MUC search : 0.00
% 22.11/11.02 Cooper : 0.00
% 22.11/11.02 Total : 9.92
% 22.11/11.02 Index Insertion : 0.00
% 22.11/11.02 Index Deletion : 0.00
% 22.11/11.02 Index Matching : 0.00
% 22.11/11.02 BG Taut test : 0.00
%------------------------------------------------------------------------------