TSTP Solution File: SET961+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 : n005.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 10:57:25 EDT 2023
% Result : Theorem 3.58s 1.99s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 51 ( 14 unt; 14 typ; 0 def)
% Number of atoms : 74 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 65 ( 28 ~; 31 |; 1 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 9 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 49 (; 49 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > empty_set > #skF_6 > #skF_1 > #skF_5 > #skF_2 > #skF_3 > #skF_4 > #skF_7
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(f_66,negated_conjecture,
~ ! [A,B] :
( ( cartesian_product2(A,B) = cartesian_product2(B,A) )
=> ( ( A = empty_set )
| ( B = empty_set )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).
tff(f_73,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
tff(f_40,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_52,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
tff(c_26,plain,
'#skF_5' != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_28,plain,
empty_set != '#skF_5',
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_294,plain,
! [A_53,B_54] :
( in('#skF_6'(A_53,B_54),B_54)
| in('#skF_7'(A_53,B_54),A_53)
| ( B_54 = A_53 ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_6,plain,
! [B_8] : ~ in(B_8,empty_set),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_311,plain,
! [A_53] :
( in('#skF_7'(A_53,empty_set),A_53)
| ( empty_set = A_53 ) ),
inference(resolution,[status(thm)],[c_294,c_6]) ).
tff(c_348,plain,
! [A_65,B_66,C_67,D_68] :
( in(ordered_pair(A_65,B_66),cartesian_product2(C_67,D_68))
| ~ in(B_66,D_68)
| ~ in(A_65,C_67) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_32,plain,
cartesian_product2('#skF_5','#skF_4') = cartesian_product2('#skF_4','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_152,plain,
! [A_33,C_34,B_35,D_36] :
( in(A_33,C_34)
| ~ in(ordered_pair(A_33,B_35),cartesian_product2(C_34,D_36)) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_155,plain,
! [A_33,B_35] :
( in(A_33,'#skF_5')
| ~ in(ordered_pair(A_33,B_35),cartesian_product2('#skF_4','#skF_5')) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_152]) ).
tff(c_370,plain,
! [A_65,B_66] :
( in(A_65,'#skF_5')
| ~ in(B_66,'#skF_5')
| ~ in(A_65,'#skF_4') ),
inference(resolution,[status(thm)],[c_348,c_155]) ).
tff(c_458,plain,
! [B_77] : ~ in(B_77,'#skF_5'),
inference(splitLeft,[status(thm)],[c_370]) ).
tff(c_462,plain,
empty_set = '#skF_5',
inference(resolution,[status(thm)],[c_311,c_458]) ).
tff(c_480,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_462]) ).
tff(c_481,plain,
! [A_65] :
( in(A_65,'#skF_5')
| ~ in(A_65,'#skF_4') ),
inference(splitRight,[status(thm)],[c_370]) ).
tff(c_36,plain,
! [A_17,B_18] :
( in('#skF_6'(A_17,B_18),B_18)
| ~ in('#skF_7'(A_17,B_18),B_18)
| ( B_18 = A_17 ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_30,plain,
empty_set != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_271,plain,
! [B_43,D_44,A_45,C_46] :
( in(B_43,D_44)
| ~ in(ordered_pair(A_45,B_43),cartesian_product2(C_46,D_44)) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_274,plain,
! [B_43,A_45] :
( in(B_43,'#skF_4')
| ~ in(ordered_pair(A_45,B_43),cartesian_product2('#skF_4','#skF_5')) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_271]) ).
tff(c_368,plain,
! [B_66,A_65] :
( in(B_66,'#skF_4')
| ~ in(B_66,'#skF_5')
| ~ in(A_65,'#skF_4') ),
inference(resolution,[status(thm)],[c_348,c_274]) ).
tff(c_375,plain,
! [A_69] : ~ in(A_69,'#skF_4'),
inference(splitLeft,[status(thm)],[c_368]) ).
tff(c_379,plain,
empty_set = '#skF_4',
inference(resolution,[status(thm)],[c_311,c_375]) ).
tff(c_397,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_379]) ).
tff(c_399,plain,
! [B_70] :
( in(B_70,'#skF_4')
| ~ in(B_70,'#skF_5') ),
inference(splitRight,[status(thm)],[c_368]) ).
tff(c_509,plain,
! [A_80] :
( in('#skF_6'(A_80,'#skF_5'),'#skF_4')
| ~ in('#skF_7'(A_80,'#skF_5'),'#skF_5')
| ( A_80 = '#skF_5' ) ),
inference(resolution,[status(thm)],[c_36,c_399]) ).
tff(c_34,plain,
! [A_17,B_18] :
( ~ in('#skF_6'(A_17,B_18),A_17)
| ~ in('#skF_7'(A_17,B_18),B_18)
| ( B_18 = A_17 ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_516,plain,
( ~ in('#skF_7'('#skF_4','#skF_5'),'#skF_5')
| ( '#skF_5' = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_509,c_34]) ).
tff(c_523,plain,
~ in('#skF_7'('#skF_4','#skF_5'),'#skF_5'),
inference(negUnitSimplification,[status(thm)],[c_26,c_26,c_516]) ).
tff(c_548,plain,
~ in('#skF_7'('#skF_4','#skF_5'),'#skF_4'),
inference(resolution,[status(thm)],[c_481,c_523]) ).
tff(c_40,plain,
! [A_17,B_18] :
( in('#skF_6'(A_17,B_18),B_18)
| in('#skF_7'(A_17,B_18),A_17)
| ( B_18 = A_17 ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_640,plain,
! [A_87] :
( in('#skF_6'(A_87,'#skF_5'),'#skF_4')
| in('#skF_7'(A_87,'#skF_5'),A_87)
| ( A_87 = '#skF_5' ) ),
inference(resolution,[status(thm)],[c_40,c_399]) ).
tff(c_38,plain,
! [A_17,B_18] :
( ~ in('#skF_6'(A_17,B_18),A_17)
| in('#skF_7'(A_17,B_18),A_17)
| ( B_18 = A_17 ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_648,plain,
( in('#skF_7'('#skF_4','#skF_5'),'#skF_4')
| ( '#skF_5' = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_640,c_38]) ).
tff(c_670,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_548,c_26,c_548,c_648]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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
% 0.18/0.36 % Computer : n005.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Thu Aug 3 16:44:41 EDT 2023
% 0.18/0.36 % CPUTime :
% 3.58/1.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.94/1.99
% 3.94/1.99 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.94/2.02
% 3.94/2.02 Inference rules
% 3.94/2.02 ----------------------
% 3.94/2.02 #Ref : 0
% 3.94/2.02 #Sup : 141
% 3.94/2.02 #Fact : 0
% 3.94/2.02 #Define : 0
% 3.94/2.02 #Split : 2
% 3.94/2.02 #Chain : 0
% 3.94/2.02 #Close : 0
% 3.94/2.02
% 3.94/2.02 Ordering : KBO
% 3.94/2.02
% 3.94/2.02 Simplification rules
% 3.94/2.02 ----------------------
% 3.94/2.02 #Subsume : 8
% 3.94/2.02 #Demod : 19
% 3.94/2.02 #Tautology : 53
% 3.94/2.02 #SimpNegUnit : 12
% 3.94/2.02 #BackRed : 2
% 3.94/2.02
% 3.94/2.02 #Partial instantiations: 0
% 3.94/2.02 #Strategies tried : 1
% 3.94/2.02
% 3.94/2.02 Timing (in seconds)
% 3.94/2.02 ----------------------
% 3.94/2.03 Preprocessing : 0.49
% 3.94/2.03 Parsing : 0.25
% 3.94/2.03 CNF conversion : 0.04
% 3.94/2.03 Main loop : 0.46
% 3.94/2.03 Inferencing : 0.18
% 3.94/2.03 Reduction : 0.13
% 3.94/2.03 Demodulation : 0.09
% 3.94/2.03 BG Simplification : 0.02
% 3.94/2.03 Subsumption : 0.10
% 3.94/2.03 Abstraction : 0.02
% 3.94/2.03 MUC search : 0.00
% 3.94/2.03 Cooper : 0.00
% 3.94/2.03 Total : 1.00
% 3.94/2.03 Index Insertion : 0.00
% 3.94/2.03 Index Deletion : 0.00
% 3.94/2.03 Index Matching : 0.00
% 3.94/2.03 BG Taut test : 0.00
%------------------------------------------------------------------------------