TSTP Solution File: SET603+4 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET603+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 : n001.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 10:56:40 EDT 2023
% Result : Theorem 22.75s 11.53s
% Output : CNFRefutation 22.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 37 ( 8 unt; 16 typ; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 12 ~; 13 |; 2 &)
% ( 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 : 38 (; 38 !; 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/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
tff(f_88,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( member(B,E)
& ~ member(B,A) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
tff(f_81,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
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,
~ ! [E] : equal_set(difference(E,empty_set),E),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI30) ).
tff(c_100,plain,
! [A_68,B_69] :
( member('#skF_1'(A_68,B_69),A_68)
| subset(A_68,B_69) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_36,plain,
! [B_17,E_19,A_18] :
( member(B_17,E_19)
| ~ member(B_17,difference(E_19,A_18)) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_7096,plain,
! [E_399,A_400,B_401] :
( member('#skF_1'(difference(E_399,A_400),B_401),E_399)
| subset(difference(E_399,A_400),B_401) ),
inference(resolution,[status(thm)],[c_100,c_36]) ).
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_7222,plain,
! [E_399,A_400] : subset(difference(E_399,A_400),E_399),
inference(resolution,[status(thm)],[c_7096,c_4]) ).
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,
! [B_131,E_132,A_133] :
( member(B_131,difference(E_132,A_133))
| member(B_131,A_133)
| ~ member(B_131,E_132) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_19667,plain,
! [A_839,E_840,A_841] :
( subset(A_839,difference(E_840,A_841))
| member('#skF_1'(A_839,difference(E_840,A_841)),A_841)
| ~ member('#skF_1'(A_839,difference(E_840,A_841)),E_840) ),
inference(resolution,[status(thm)],[c_685,c_4]) ).
tff(c_44119,plain,
! [A_1315,A_1316] :
( member('#skF_1'(A_1315,difference(A_1315,A_1316)),A_1316)
| subset(A_1315,difference(A_1315,A_1316)) ),
inference(resolution,[status(thm)],[c_6,c_19667]) ).
tff(c_30,plain,
! [X_16] : ~ member(X_16,empty_set),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_44420,plain,
! [A_1317] : subset(A_1317,difference(A_1317,empty_set)),
inference(resolution,[status(thm)],[c_44119,c_30]) ).
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_44476,plain,
! [A_1317] :
( equal_set(difference(A_1317,empty_set),A_1317)
| ~ subset(difference(A_1317,empty_set),A_1317) ),
inference(resolution,[status(thm)],[c_44420,c_8]) ).
tff(c_44503,plain,
! [A_1317] : equal_set(difference(A_1317,empty_set),A_1317),
inference(demodulation,[status(thm),theory(equality)],[c_7222,c_44476]) ).
tff(c_60,plain,
~ equal_set(difference('#skF_4',empty_set),'#skF_4'),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_44508,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_44503,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET603+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % 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 : n001.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 17:16:10 EDT 2023
% 0.14/0.36 % CPUTime :
% 22.75/11.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.75/11.54
% 22.75/11.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.75/11.56
% 22.75/11.56 Inference rules
% 22.75/11.56 ----------------------
% 22.75/11.56 #Ref : 0
% 22.75/11.56 #Sup : 10181
% 22.75/11.56 #Fact : 6
% 22.75/11.56 #Define : 0
% 22.75/11.56 #Split : 1
% 22.75/11.56 #Chain : 0
% 22.75/11.56 #Close : 0
% 22.75/11.56
% 22.75/11.56 Ordering : KBO
% 22.75/11.56
% 22.75/11.56 Simplification rules
% 22.75/11.56 ----------------------
% 22.75/11.56 #Subsume : 723
% 22.75/11.56 #Demod : 1776
% 22.75/11.56 #Tautology : 1793
% 22.75/11.56 #SimpNegUnit : 56
% 22.75/11.56 #BackRed : 4
% 22.75/11.56
% 22.75/11.56 #Partial instantiations: 0
% 22.75/11.56 #Strategies tried : 1
% 22.75/11.56
% 22.75/11.56 Timing (in seconds)
% 22.75/11.56 ----------------------
% 22.75/11.57 Preprocessing : 0.50
% 22.75/11.57 Parsing : 0.26
% 22.75/11.57 CNF conversion : 0.04
% 22.75/11.57 Main loop : 9.92
% 22.75/11.57 Inferencing : 1.65
% 22.75/11.57 Reduction : 4.75
% 22.75/11.57 Demodulation : 3.70
% 22.75/11.57 BG Simplification : 0.08
% 22.75/11.57 Subsumption : 2.79
% 22.75/11.57 Abstraction : 0.11
% 22.75/11.57 MUC search : 0.00
% 22.75/11.57 Cooper : 0.00
% 22.75/11.57 Total : 10.46
% 22.75/11.57 Index Insertion : 0.00
% 22.75/11.57 Index Deletion : 0.00
% 22.75/11.57 Index Matching : 0.00
% 22.75/11.57 BG Taut test : 0.00
%------------------------------------------------------------------------------