TSTP Solution File: SET935+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET935+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 : n010.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 10:57:23 EDT 2023
% Result : Theorem 13.95s 4.40s
% Output : CNFRefutation 13.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 70 ( 28 unt; 14 typ; 0 def)
% Number of atoms : 93 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 26 ~; 28 |; 1 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 10 >; 10 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 65 (; 65 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > inclusion_comparable > in > empty > set_union2 > #nlpp > powerset > #skF_4 > #skF_7 > #skF_5 > #skF_6 > #skF_8 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(inclusion_comparable,type,
inclusion_comparable: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_95,negated_conjecture,
~ ! [A,B] :
( ( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B)) )
=> inclusion_comparable(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_zfmisc_1) ).
tff(f_82,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_46,axiom,
! [A,B] :
( ( B = powerset(A) )
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
tff(f_33,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_55,axiom,
! [A,B,C] :
( ( C = set_union2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
tff(f_90,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
tff(f_39,axiom,
! [A,B] :
( ( A = B )
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
tff(f_61,axiom,
! [A,B] :
( inclusion_comparable(A,B)
<=> ( subset(A,B)
| subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_xboole_0) ).
tff(f_88,axiom,
! [A,B] :
( inclusion_comparable(A,B)
=> inclusion_comparable(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r3_xboole_0) ).
tff(c_66,plain,
~ inclusion_comparable('#skF_7','#skF_8'),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_58,plain,
! [A_26] : subset(A_26,A_26),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_14,plain,
! [C_11,A_7] :
( in(C_11,powerset(A_7))
| ~ subset(C_11,A_7) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_4,plain,
! [B_4,A_3] : ( set_union2(B_4,A_3) = set_union2(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_68,plain,
set_union2(powerset('#skF_7'),powerset('#skF_8')) = powerset(set_union2('#skF_7','#skF_8')),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_71,plain,
set_union2(powerset('#skF_7'),powerset('#skF_8')) = powerset(set_union2('#skF_8','#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_68]) ).
tff(c_559,plain,
! [D_85,B_86,A_87] :
( in(D_85,B_86)
| in(D_85,A_87)
| ~ in(D_85,set_union2(A_87,B_86)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_3244,plain,
! [D_265] :
( in(D_265,powerset('#skF_8'))
| in(D_265,powerset('#skF_7'))
| ~ in(D_265,powerset(set_union2('#skF_8','#skF_7'))) ),
inference(superposition,[status(thm),theory(equality)],[c_71,c_559]) ).
tff(c_11351,plain,
! [C_750] :
( in(C_750,powerset('#skF_8'))
| in(C_750,powerset('#skF_7'))
| ~ subset(C_750,set_union2('#skF_8','#skF_7')) ),
inference(resolution,[status(thm)],[c_14,c_3244]) ).
tff(c_11429,plain,
( in(set_union2('#skF_8','#skF_7'),powerset('#skF_8'))
| in(set_union2('#skF_8','#skF_7'),powerset('#skF_7')) ),
inference(resolution,[status(thm)],[c_58,c_11351]) ).
tff(c_11518,plain,
in(set_union2('#skF_8','#skF_7'),powerset('#skF_7')),
inference(splitLeft,[status(thm)],[c_11429]) ).
tff(c_12,plain,
! [C_11,A_7] :
( subset(C_11,A_7)
| ~ in(C_11,powerset(A_7)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_11544,plain,
subset(set_union2('#skF_8','#skF_7'),'#skF_7'),
inference(resolution,[status(thm)],[c_11518,c_12]) ).
tff(c_88,plain,
! [B_39,A_40] : ( set_union2(B_39,A_40) = set_union2(A_40,B_39) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_64,plain,
! [A_32,B_33] : subset(A_32,set_union2(A_32,B_33)),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_103,plain,
! [A_40,B_39] : subset(A_40,set_union2(B_39,A_40)),
inference(superposition,[status(thm),theory(equality)],[c_88,c_64]) ).
tff(c_342,plain,
! [B_69,A_70] :
( ( B_69 = A_70 )
| ~ subset(B_69,A_70)
| ~ subset(A_70,B_69) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_355,plain,
! [B_39,A_40] :
( ( set_union2(B_39,A_40) = A_40 )
| ~ subset(set_union2(B_39,A_40),A_40) ),
inference(resolution,[status(thm)],[c_103,c_342]) ).
tff(c_11607,plain,
set_union2('#skF_8','#skF_7') = '#skF_7',
inference(resolution,[status(thm)],[c_11544,c_355]) ).
tff(c_159,plain,
set_union2(powerset('#skF_8'),powerset('#skF_7')) = powerset(set_union2('#skF_8','#skF_7')),
inference(superposition,[status(thm),theory(equality)],[c_4,c_71]) ).
tff(c_712,plain,
! [A_97,B_98] :
( ( set_union2(A_97,B_98) = A_97 )
| ~ subset(set_union2(A_97,B_98),A_97) ),
inference(resolution,[status(thm)],[c_64,c_342]) ).
tff(c_726,plain,
( ( set_union2(powerset('#skF_7'),powerset('#skF_8')) = powerset('#skF_7') )
| ~ subset(powerset(set_union2('#skF_8','#skF_7')),powerset('#skF_7')) ),
inference(superposition,[status(thm),theory(equality)],[c_71,c_712]) ).
tff(c_743,plain,
( ( powerset(set_union2('#skF_8','#skF_7')) = powerset('#skF_7') )
| ~ subset(powerset(set_union2('#skF_8','#skF_7')),powerset('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_4,c_726]) ).
tff(c_10884,plain,
~ subset(powerset(set_union2('#skF_8','#skF_7')),powerset('#skF_7')),
inference(splitLeft,[status(thm)],[c_743]) ).
tff(c_11633,plain,
~ subset(powerset('#skF_7'),powerset('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_11607,c_10884]) ).
tff(c_11740,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_58,c_11633]) ).
tff(c_11741,plain,
in(set_union2('#skF_8','#skF_7'),powerset('#skF_8')),
inference(splitRight,[status(thm)],[c_11429]) ).
tff(c_11768,plain,
subset(set_union2('#skF_8','#skF_7'),'#skF_8'),
inference(resolution,[status(thm)],[c_11741,c_12]) ).
tff(c_1231,plain,
! [B_131,A_132] :
( ( set_union2(B_131,A_132) = A_132 )
| ~ subset(set_union2(B_131,A_132),A_132) ),
inference(resolution,[status(thm)],[c_103,c_342]) ).
tff(c_1251,plain,
! [B_4,A_3] :
( ( set_union2(B_4,A_3) = A_3 )
| ~ subset(set_union2(A_3,B_4),A_3) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1231]) ).
tff(c_11790,plain,
set_union2('#skF_7','#skF_8') = '#skF_8',
inference(resolution,[status(thm)],[c_11768,c_1251]) ).
tff(c_240,plain,
! [A_55,B_56] :
( ~ subset(A_55,B_56)
| inclusion_comparable(A_55,B_56) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_255,plain,
! [A_32,B_33] : inclusion_comparable(A_32,set_union2(A_32,B_33)),
inference(resolution,[status(thm)],[c_64,c_240]) ).
tff(c_12048,plain,
inclusion_comparable('#skF_7','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_11790,c_255]) ).
tff(c_12118,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66,c_12048]) ).
tff(c_12119,plain,
powerset(set_union2('#skF_8','#skF_7')) = powerset('#skF_7'),
inference(splitRight,[status(thm)],[c_743]) ).
tff(c_373,plain,
! [D_71,B_72,A_73] :
( ~ in(D_71,B_72)
| in(D_71,set_union2(A_73,B_72)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_382,plain,
! [D_71] :
( ~ in(D_71,powerset('#skF_8'))
| in(D_71,powerset(set_union2('#skF_8','#skF_7'))) ),
inference(superposition,[status(thm),theory(equality)],[c_71,c_373]) ).
tff(c_13549,plain,
! [D_766] :
( ~ in(D_766,powerset('#skF_8'))
| in(D_766,powerset('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_12119,c_382]) ).
tff(c_13858,plain,
! [D_767] :
( subset(D_767,'#skF_7')
| ~ in(D_767,powerset('#skF_8')) ),
inference(resolution,[status(thm)],[c_13549,c_12]) ).
tff(c_14063,plain,
! [C_768] :
( subset(C_768,'#skF_7')
| ~ subset(C_768,'#skF_8') ),
inference(resolution,[status(thm)],[c_14,c_13858]) ).
tff(c_46,plain,
! [A_18,B_19] :
( ~ subset(A_18,B_19)
| inclusion_comparable(A_18,B_19) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_14307,plain,
! [C_769] :
( inclusion_comparable(C_769,'#skF_7')
| ~ subset(C_769,'#skF_8') ),
inference(resolution,[status(thm)],[c_14063,c_46]) ).
tff(c_14364,plain,
inclusion_comparable('#skF_8','#skF_7'),
inference(resolution,[status(thm)],[c_58,c_14307]) ).
tff(c_62,plain,
! [B_31,A_30] :
( inclusion_comparable(B_31,A_30)
| ~ inclusion_comparable(A_30,B_31) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_14410,plain,
inclusion_comparable('#skF_7','#skF_8'),
inference(resolution,[status(thm)],[c_14364,c_62]) ).
tff(c_14414,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66,c_14410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET935+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % 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
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 16:05:13 EDT 2023
% 0.15/0.35 % CPUTime :
% 13.95/4.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.95/4.40
% 13.95/4.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.95/4.43
% 13.95/4.43 Inference rules
% 13.95/4.43 ----------------------
% 13.95/4.43 #Ref : 0
% 13.95/4.43 #Sup : 3403
% 13.95/4.43 #Fact : 40
% 13.95/4.43 #Define : 0
% 13.95/4.43 #Split : 10
% 13.95/4.43 #Chain : 0
% 13.95/4.43 #Close : 0
% 13.95/4.43
% 13.95/4.43 Ordering : KBO
% 13.95/4.43
% 13.95/4.43 Simplification rules
% 13.95/4.43 ----------------------
% 13.95/4.43 #Subsume : 1428
% 13.95/4.43 #Demod : 1337
% 13.95/4.43 #Tautology : 180
% 13.95/4.43 #SimpNegUnit : 5
% 13.95/4.43 #BackRed : 210
% 13.95/4.43
% 13.95/4.43 #Partial instantiations: 0
% 13.95/4.43 #Strategies tried : 1
% 13.95/4.43
% 13.95/4.43 Timing (in seconds)
% 13.95/4.43 ----------------------
% 13.95/4.44 Preprocessing : 0.51
% 13.95/4.44 Parsing : 0.26
% 13.95/4.44 CNF conversion : 0.04
% 13.95/4.44 Main loop : 2.82
% 13.95/4.44 Inferencing : 0.78
% 14.24/4.44 Reduction : 1.01
% 14.24/4.44 Demodulation : 0.71
% 14.24/4.44 BG Simplification : 0.07
% 14.24/4.44 Subsumption : 0.76
% 14.24/4.44 Abstraction : 0.07
% 14.24/4.44 MUC search : 0.00
% 14.24/4.44 Cooper : 0.00
% 14.24/4.44 Total : 3.38
% 14.24/4.44 Index Insertion : 0.00
% 14.24/4.44 Index Deletion : 0.00
% 14.24/4.44 Index Matching : 0.00
% 14.24/4.44 BG Taut test : 0.00
%------------------------------------------------------------------------------