TSTP Solution File: SET893+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET893+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : 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 10:57:17 EDT 2023
% Result : Theorem 3.78s 2.04s
% Output : CNFRefutation 4.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 73 ( 32 unt; 18 typ; 0 def)
% Number of atoms : 87 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 67 ( 35 ~; 26 |; 2 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 34 (; 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_11 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_2 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_40,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_51,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
tff(f_63,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).
tff(c_8,plain,
! [C_9] : in(C_9,singleton(C_9)),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_22,plain,
! [A_14,B_15,C_16,D_17] :
( in(ordered_pair(A_14,B_15),cartesian_product2(C_16,D_17))
| ~ in(B_15,D_17)
| ~ in(A_14,C_16) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_486,plain,
! [A_69,B_70,C_71,D_72] :
( in(ordered_pair(A_69,B_70),cartesian_product2(C_71,D_72))
| ~ in(B_70,D_72)
| ~ in(A_69,C_71) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_34,plain,
( ( '#skF_6' = '#skF_8' )
| ( '#skF_10' != '#skF_12' )
| ( '#skF_11' != '#skF_9' ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_45,plain,
'#skF_11' != '#skF_9',
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_42,plain,
( ( '#skF_7' = '#skF_5' )
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_56,plain,
in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))),
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_154,plain,
! [A_32,C_33,B_34,D_35] :
( in(A_32,C_33)
| ~ in(ordered_pair(A_32,B_34),cartesian_product2(C_33,D_35)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_158,plain,
in('#skF_9',singleton('#skF_11')),
inference(resolution,[status(thm)],[c_56,c_154]) ).
tff(c_6,plain,
! [C_9,A_5] :
( ( C_9 = A_5 )
| ~ in(C_9,singleton(A_5)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_163,plain,
'#skF_11' = '#skF_9',
inference(resolution,[status(thm)],[c_158,c_6]) ).
tff(c_168,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_45,c_163]) ).
tff(c_170,plain,
~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))),
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_40,plain,
( ( '#skF_6' = '#skF_8' )
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_176,plain,
in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))),
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_243,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_170,c_176]) ).
tff(c_245,plain,
~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_244,plain,
'#skF_6' = '#skF_8',
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_169,plain,
'#skF_7' = '#skF_5',
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_38,plain,
( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_7'),singleton('#skF_8')))
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_458,plain,
( ~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2(singleton('#skF_5'),singleton('#skF_8')))
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_244,c_169,c_38]) ).
tff(c_459,plain,
~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2(singleton('#skF_5'),singleton('#skF_8'))),
inference(negUnitSimplification,[status(thm)],[c_245,c_458]) ).
tff(c_492,plain,
( ~ in('#skF_8',singleton('#skF_8'))
| ~ in('#skF_5',singleton('#skF_5')) ),
inference(resolution,[status(thm)],[c_486,c_459]) ).
tff(c_505,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_8,c_492]) ).
tff(c_507,plain,
'#skF_11' = '#skF_9',
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_980,plain,
! [A_122,B_123,C_124,D_125] :
( in(ordered_pair(A_122,B_123),cartesian_product2(C_124,D_125))
| ~ in(B_123,D_125)
| ~ in(A_122,C_124) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_506,plain,
( ( '#skF_10' != '#skF_12' )
| ( '#skF_6' = '#skF_8' ) ),
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_512,plain,
'#skF_10' != '#skF_12',
inference(splitLeft,[status(thm)],[c_506]) ).
tff(c_559,plain,
( ( '#skF_7' = '#skF_5' )
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_507,c_42]) ).
tff(c_560,plain,
in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))),
inference(splitLeft,[status(thm)],[c_559]) ).
tff(c_746,plain,
! [B_92,D_93,A_94,C_95] :
( in(B_92,D_93)
| ~ in(ordered_pair(A_94,B_92),cartesian_product2(C_95,D_93)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_750,plain,
in('#skF_10',singleton('#skF_12')),
inference(resolution,[status(thm)],[c_560,c_746]) ).
tff(c_755,plain,
'#skF_10' = '#skF_12',
inference(resolution,[status(thm)],[c_750,c_6]) ).
tff(c_760,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_512,c_755]) ).
tff(c_762,plain,
~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))),
inference(splitRight,[status(thm)],[c_559]) ).
tff(c_800,plain,
( ( '#skF_6' = '#skF_8' )
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_507,c_40]) ).
tff(c_801,plain,
in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))),
inference(splitLeft,[status(thm)],[c_800]) ).
tff(c_802,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_762,c_801]) ).
tff(c_803,plain,
'#skF_6' = '#skF_8',
inference(splitRight,[status(thm)],[c_800]) ).
tff(c_761,plain,
'#skF_7' = '#skF_5',
inference(splitRight,[status(thm)],[c_559]) ).
tff(c_956,plain,
( ~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2(singleton('#skF_5'),singleton('#skF_8')))
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_507,c_803,c_761,c_38]) ).
tff(c_957,plain,
~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2(singleton('#skF_5'),singleton('#skF_8'))),
inference(negUnitSimplification,[status(thm)],[c_762,c_956]) ).
tff(c_983,plain,
( ~ in('#skF_8',singleton('#skF_8'))
| ~ in('#skF_5',singleton('#skF_5')) ),
inference(resolution,[status(thm)],[c_980,c_957]) ).
tff(c_998,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_8,c_983]) ).
tff(c_1000,plain,
'#skF_10' = '#skF_12',
inference(splitRight,[status(thm)],[c_506]) ).
tff(c_36,plain,
( ( '#skF_7' = '#skF_5' )
| ( '#skF_10' != '#skF_12' )
| ( '#skF_11' != '#skF_9' ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_1010,plain,
'#skF_7' = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_507,c_1000,c_36]) ).
tff(c_999,plain,
'#skF_6' = '#skF_8',
inference(splitRight,[status(thm)],[c_506]) ).
tff(c_32,plain,
( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_7'),singleton('#skF_8')))
| ( '#skF_10' != '#skF_12' )
| ( '#skF_11' != '#skF_9' ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_1265,plain,
~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2(singleton('#skF_5'),singleton('#skF_8'))),
inference(demodulation,[status(thm),theory(equality)],[c_507,c_1000,c_1010,c_999,c_32]) ).
tff(c_1268,plain,
( ~ in('#skF_8',singleton('#skF_8'))
| ~ in('#skF_5',singleton('#skF_5')) ),
inference(resolution,[status(thm)],[c_22,c_1265]) ).
tff(c_1272,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_8,c_1268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET893+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % 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
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 17:26:25 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.78/2.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.78/2.04
% 3.78/2.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.20/2.07
% 4.20/2.07 Inference rules
% 4.20/2.07 ----------------------
% 4.20/2.07 #Ref : 0
% 4.20/2.07 #Sup : 315
% 4.20/2.07 #Fact : 0
% 4.20/2.07 #Define : 0
% 4.20/2.07 #Split : 6
% 4.20/2.07 #Chain : 0
% 4.20/2.07 #Close : 0
% 4.20/2.07
% 4.20/2.07 Ordering : KBO
% 4.20/2.07
% 4.20/2.07 Simplification rules
% 4.20/2.07 ----------------------
% 4.20/2.07 #Subsume : 6
% 4.20/2.07 #Demod : 84
% 4.20/2.07 #Tautology : 170
% 4.20/2.07 #SimpNegUnit : 6
% 4.20/2.07 #BackRed : 0
% 4.20/2.07
% 4.20/2.07 #Partial instantiations: 0
% 4.20/2.07 #Strategies tried : 1
% 4.20/2.07
% 4.20/2.07 Timing (in seconds)
% 4.20/2.07 ----------------------
% 4.20/2.07 Preprocessing : 0.49
% 4.20/2.08 Parsing : 0.26
% 4.20/2.08 CNF conversion : 0.03
% 4.20/2.08 Main loop : 0.50
% 4.20/2.08 Inferencing : 0.19
% 4.20/2.08 Reduction : 0.15
% 4.20/2.08 Demodulation : 0.12
% 4.20/2.08 BG Simplification : 0.03
% 4.20/2.08 Subsumption : 0.09
% 4.20/2.08 Abstraction : 0.02
% 4.20/2.08 MUC search : 0.00
% 4.20/2.08 Cooper : 0.00
% 4.20/2.08 Total : 1.05
% 4.20/2.08 Index Insertion : 0.00
% 4.20/2.08 Index Deletion : 0.00
% 4.20/2.08 Index Matching : 0.00
% 4.20/2.08 BG Taut test : 0.00
%------------------------------------------------------------------------------