TSTP Solution File: SEU061+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU061+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 : n027.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 10:57:33 EDT 2023
% Result : Theorem 23.66s 12.21s
% Output : CNFRefutation 23.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 47
% Syntax : Number of formulae : 100 ( 33 unt; 39 typ; 0 def)
% Number of atoms : 114 ( 38 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 93 ( 40 ~; 39 |; 2 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 28 >; 22 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 11 con; 0-4 aty)
% Number of variables : 59 (; 55 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > one_to_one > function > empty > unordered_pair > relation_inverse_image > ordered_pair > #nlpp > singleton > relation_rng > powerset > empty_set > #skF_7 > #skF_6 > #skF_1 > #skF_20 > #skF_18 > #skF_17 > #skF_19 > #skF_16 > #skF_15 > #skF_14 > #skF_13 > #skF_10 > #skF_2 > #skF_8 > #skF_21 > #skF_11 > #skF_4 > #skF_22 > #skF_3 > #skF_24 > #skF_23 > #skF_12 > #skF_9 > #skF_5
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(relation_inverse_image,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(function,type,
function: $i > $o ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_16',type,
'#skF_16': $i ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff(f_188,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( in(A,relation_rng(B))
<=> ( relation_inverse_image(B,singleton(A)) != empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).
tff(f_138,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
tff(f_219,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_149,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_79,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_66,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( ( C = relation_inverse_image(A,B) )
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(ordered_pair(D,E),A)
& in(E,B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
tff(f_73,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_90,axiom,
! [A] :
( relation(A)
=> ! [B] :
( ( B = relation_rng(A) )
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
tff(c_134,plain,
relation('#skF_24'),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_98,plain,
empty('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_84370,plain,
! [A_1368] :
( ( empty_set = A_1368 )
| ~ empty(A_1368) ),
inference(cnfTransformation,[status(thm)],[f_219]) ).
tff(c_84388,plain,
empty_set = '#skF_14',
inference(resolution,[status(thm)],[c_98,c_84370]) ).
tff(c_136,plain,
( ( relation_inverse_image('#skF_24',singleton('#skF_23')) = empty_set )
| ~ in('#skF_23',relation_rng('#skF_24')) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_164,plain,
~ in('#skF_23',relation_rng('#skF_24')),
inference(splitLeft,[status(thm)],[c_136]) ).
tff(c_172,plain,
! [A_140] :
( ( empty_set = A_140 )
| ~ empty(A_140) ),
inference(cnfTransformation,[status(thm)],[f_219]) ).
tff(c_190,plain,
empty_set = '#skF_14',
inference(resolution,[status(thm)],[c_98,c_172]) ).
tff(c_142,plain,
( in('#skF_23',relation_rng('#skF_24'))
| ( relation_inverse_image('#skF_24',singleton('#skF_23')) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_165,plain,
relation_inverse_image('#skF_24',singleton('#skF_23')) != empty_set,
inference(splitLeft,[status(thm)],[c_142]) ).
tff(c_231,plain,
relation_inverse_image('#skF_24',singleton('#skF_23')) != '#skF_14',
inference(demodulation,[status(thm),theory(equality)],[c_190,c_165]) ).
tff(c_104,plain,
empty('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_189,plain,
empty_set = '#skF_16',
inference(resolution,[status(thm)],[c_104,c_172]) ).
tff(c_213,plain,
'#skF_16' = '#skF_14',
inference(demodulation,[status(thm),theory(equality)],[c_190,c_189]) ).
tff(c_46,plain,
! [B_58] : ~ in(B_58,empty_set),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_195,plain,
! [B_58] : ~ in(B_58,'#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_189,c_46]) ).
tff(c_236,plain,
! [B_58] : ~ in(B_58,'#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_213,c_195]) ).
tff(c_1821,plain,
! [A_289,B_290,C_291] :
( in('#skF_2'(A_289,B_290,C_291),B_290)
| in('#skF_3'(A_289,B_290,C_291),C_291)
| ( relation_inverse_image(A_289,B_290) = C_291 )
| ~ relation(A_289) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_34,plain,
! [C_54,A_50] :
( ( C_54 = A_50 )
| ~ in(C_54,singleton(A_50)) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_38602,plain,
! [A_1035,A_1036,C_1037] :
( ( '#skF_2'(A_1035,singleton(A_1036),C_1037) = A_1036 )
| in('#skF_3'(A_1035,singleton(A_1036),C_1037),C_1037)
| ( relation_inverse_image(A_1035,singleton(A_1036)) = C_1037 )
| ~ relation(A_1035) ),
inference(resolution,[status(thm)],[c_1821,c_34]) ).
tff(c_83748,plain,
! [A_1352,A_1353] :
( ( '#skF_2'(A_1352,singleton(A_1353),'#skF_14') = A_1353 )
| ( relation_inverse_image(A_1352,singleton(A_1353)) = '#skF_14' )
| ~ relation(A_1352) ),
inference(resolution,[status(thm)],[c_38602,c_236]) ).
tff(c_84077,plain,
( ( '#skF_2'('#skF_24',singleton('#skF_23'),'#skF_14') = '#skF_23' )
| ~ relation('#skF_24') ),
inference(superposition,[status(thm),theory(equality)],[c_83748,c_231]) ).
tff(c_84246,plain,
'#skF_2'('#skF_24',singleton('#skF_23'),'#skF_14') = '#skF_23',
inference(demodulation,[status(thm),theory(equality)],[c_134,c_84077]) ).
tff(c_2815,plain,
! [A_338,B_339,C_340] :
( in(ordered_pair('#skF_1'(A_338,B_339,C_340),'#skF_2'(A_338,B_339,C_340)),A_338)
| in('#skF_3'(A_338,B_339,C_340),C_340)
| ( relation_inverse_image(A_338,B_339) = C_340 )
| ~ relation(A_338) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_52,plain,
! [C_95,A_59,D_98] :
( in(C_95,relation_rng(A_59))
| ~ in(ordered_pair(D_98,C_95),A_59)
| ~ relation(A_59) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_2884,plain,
! [A_338,B_339,C_340] :
( in('#skF_2'(A_338,B_339,C_340),relation_rng(A_338))
| in('#skF_3'(A_338,B_339,C_340),C_340)
| ( relation_inverse_image(A_338,B_339) = C_340 )
| ~ relation(A_338) ),
inference(resolution,[status(thm)],[c_2815,c_52]) ).
tff(c_84280,plain,
( in('#skF_23',relation_rng('#skF_24'))
| in('#skF_3'('#skF_24',singleton('#skF_23'),'#skF_14'),'#skF_14')
| ( relation_inverse_image('#skF_24',singleton('#skF_23')) = '#skF_14' )
| ~ relation('#skF_24') ),
inference(superposition,[status(thm),theory(equality)],[c_84246,c_2884]) ).
tff(c_84316,plain,
( in('#skF_23',relation_rng('#skF_24'))
| in('#skF_3'('#skF_24',singleton('#skF_23'),'#skF_14'),'#skF_14')
| ( relation_inverse_image('#skF_24',singleton('#skF_23')) = '#skF_14' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_84280]) ).
tff(c_84318,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_231,c_236,c_164,c_84316]) ).
tff(c_84319,plain,
in('#skF_23',relation_rng('#skF_24')),
inference(splitRight,[status(thm)],[c_142]) ).
tff(c_84360,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_164,c_84319]) ).
tff(c_84361,plain,
relation_inverse_image('#skF_24',singleton('#skF_23')) = empty_set,
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_84429,plain,
relation_inverse_image('#skF_24',singleton('#skF_23')) = '#skF_14',
inference(demodulation,[status(thm),theory(equality)],[c_84388,c_84361]) ).
tff(c_84363,plain,
relation_inverse_image('#skF_24',singleton('#skF_23')) != empty_set,
inference(splitLeft,[status(thm)],[c_142]) ).
tff(c_84455,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_84429,c_84388,c_84363]) ).
tff(c_84456,plain,
in('#skF_23',relation_rng('#skF_24')),
inference(splitRight,[status(thm)],[c_142]) ).
tff(c_50,plain,
! [A_59,C_95] :
( in(ordered_pair('#skF_11'(A_59,relation_rng(A_59),C_95),C_95),A_59)
| ~ in(C_95,relation_rng(A_59))
| ~ relation(A_59) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_84467,plain,
! [A_1386] :
( ( empty_set = A_1386 )
| ~ empty(A_1386) ),
inference(cnfTransformation,[status(thm)],[f_219]) ).
tff(c_84485,plain,
empty_set = '#skF_14',
inference(resolution,[status(thm)],[c_98,c_84467]) ).
tff(c_84484,plain,
empty_set = '#skF_16',
inference(resolution,[status(thm)],[c_104,c_84467]) ).
tff(c_84499,plain,
'#skF_16' = '#skF_14',
inference(demodulation,[status(thm),theory(equality)],[c_84485,c_84484]) ).
tff(c_84490,plain,
! [B_58] : ~ in(B_58,'#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_84484,c_46]) ).
tff(c_84538,plain,
! [B_58] : ~ in(B_58,'#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_84499,c_84490]) ).
tff(c_84457,plain,
relation_inverse_image('#skF_24',singleton('#skF_23')) = empty_set,
inference(splitRight,[status(thm)],[c_142]) ).
tff(c_84522,plain,
relation_inverse_image('#skF_24',singleton('#skF_23')) = '#skF_14',
inference(demodulation,[status(thm),theory(equality)],[c_84485,c_84457]) ).
tff(c_36,plain,
! [C_54] : in(C_54,singleton(C_54)),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_85526,plain,
! [D_1497,A_1498,B_1499,E_1500] :
( in(D_1497,relation_inverse_image(A_1498,B_1499))
| ~ in(E_1500,B_1499)
| ~ in(ordered_pair(D_1497,E_1500),A_1498)
| ~ relation(A_1498) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_94128,plain,
! [D_1817,A_1818,C_1819] :
( in(D_1817,relation_inverse_image(A_1818,singleton(C_1819)))
| ~ in(ordered_pair(D_1817,C_1819),A_1818)
| ~ relation(A_1818) ),
inference(resolution,[status(thm)],[c_36,c_85526]) ).
tff(c_94260,plain,
! [D_1817] :
( in(D_1817,'#skF_14')
| ~ in(ordered_pair(D_1817,'#skF_23'),'#skF_24')
| ~ relation('#skF_24') ),
inference(superposition,[status(thm),theory(equality)],[c_84522,c_94128]) ).
tff(c_94302,plain,
! [D_1817] :
( in(D_1817,'#skF_14')
| ~ in(ordered_pair(D_1817,'#skF_23'),'#skF_24') ),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_94260]) ).
tff(c_94304,plain,
! [D_1820] : ~ in(ordered_pair(D_1820,'#skF_23'),'#skF_24'),
inference(negUnitSimplification,[status(thm)],[c_84538,c_94302]) ).
tff(c_94308,plain,
( ~ in('#skF_23',relation_rng('#skF_24'))
| ~ relation('#skF_24') ),
inference(resolution,[status(thm)],[c_50,c_94304]) ).
tff(c_94315,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_134,c_84456,c_94308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU061+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.13/0.35 % Computer : n027.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 12:16:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 23.66/12.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.66/12.21
% 23.66/12.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.81/12.25
% 23.81/12.25 Inference rules
% 23.81/12.25 ----------------------
% 23.81/12.25 #Ref : 0
% 23.81/12.25 #Sup : 25527
% 23.81/12.25 #Fact : 0
% 23.81/12.25 #Define : 0
% 23.81/12.25 #Split : 58
% 23.81/12.25 #Chain : 0
% 23.81/12.25 #Close : 0
% 23.81/12.25
% 23.81/12.25 Ordering : KBO
% 23.81/12.25
% 23.81/12.25 Simplification rules
% 23.81/12.25 ----------------------
% 23.81/12.25 #Subsume : 10005
% 23.81/12.25 #Demod : 9325
% 23.81/12.25 #Tautology : 4320
% 23.81/12.25 #SimpNegUnit : 317
% 23.81/12.25 #BackRed : 48
% 23.81/12.25
% 23.81/12.25 #Partial instantiations: 0
% 23.81/12.25 #Strategies tried : 1
% 23.81/12.25
% 23.81/12.25 Timing (in seconds)
% 23.81/12.25 ----------------------
% 23.81/12.25 Preprocessing : 0.61
% 23.81/12.25 Parsing : 0.31
% 23.81/12.25 CNF conversion : 0.06
% 23.81/12.25 Main loop : 10.49
% 23.81/12.25 Inferencing : 1.79
% 23.81/12.25 Reduction : 2.95
% 23.81/12.25 Demodulation : 2.13
% 23.81/12.25 BG Simplification : 0.15
% 23.81/12.25 Subsumption : 5.07
% 23.81/12.25 Abstraction : 0.20
% 23.81/12.25 MUC search : 0.00
% 23.81/12.25 Cooper : 0.00
% 23.81/12.25 Total : 11.16
% 23.81/12.25 Index Insertion : 0.00
% 23.81/12.25 Index Deletion : 0.00
% 23.81/12.25 Index Matching : 0.00
% 23.81/12.25 BG Taut test : 0.00
%------------------------------------------------------------------------------