TSTP Solution File: SEU292+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n016.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 10:58:17 EDT 2023
% Result : Theorem 8.37s 2.94s
% Output : CNFRefutation 8.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 51
% Syntax : Number of formulae : 89 ( 25 unt; 40 typ; 0 def)
% Number of atoms : 108 ( 36 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 91 ( 32 ~; 32 |; 10 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 24 >; 18 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 16 con; 0-3 aty)
% Number of variables : 56 (; 53 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > quasi_total > subset > in > element > relation_empty_yielding > relation > one_to_one > function > empty > relation_dom_as_subset > relation_composition > cartesian_product2 > apply > #nlpp > relation_dom > powerset > empty_set > #skF_11 > #skF_20 > #skF_2 > #skF_18 > #skF_17 > #skF_15 > #skF_8 > #skF_19 > #skF_7 > #skF_3 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_21 > #skF_9 > #skF_13 > #skF_4 > #skF_22 > #skF_1 > #skF_5 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(quasi_total,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(relation_dom_as_subset,type,
relation_dom_as_subset: ( $i * $i * $i ) > $i ).
tff(relation_composition,type,
relation_composition: ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff(relation_of2,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(relation_of2_as_subset,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_270,negated_conjecture,
~ ! [A,B,C,D] :
( ( function(D)
& quasi_total(D,A,B)
& relation_of2_as_subset(D,A,B) )
=> ! [E] :
( ( relation(E)
& function(E) )
=> ( in(C,A)
=> ( ( B = empty_set )
| ( apply(relation_composition(D,E),C) = apply(E,apply(D,C)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_2) ).
tff(f_88,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
tff(f_43,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
tff(f_196,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_310,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_181,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
tff(f_185,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
tff(f_246,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
tff(f_242,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> ( relation_dom_as_subset(A,B,C) = relation_dom(C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
tff(f_73,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( quasi_total(C,A,B)
<=> ( A = relation_dom_as_subset(A,B,C) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( quasi_total(C,A,B)
<=> ( C = empty_set ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
tff(f_283,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(B))
=> ( apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
tff(c_174,plain,
relation('#skF_22'),
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_172,plain,
function('#skF_22'),
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_170,plain,
in('#skF_20','#skF_18'),
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_176,plain,
relation_of2_as_subset('#skF_21','#skF_18','#skF_19'),
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_650,plain,
! [C_167,A_168,B_169] :
( element(C_167,powerset(cartesian_product2(A_168,B_169)))
| ~ relation_of2_as_subset(C_167,A_168,B_169) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_8,plain,
! [C_7,A_5,B_6] :
( relation(C_7)
| ~ element(C_7,powerset(cartesian_product2(A_5,B_6))) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_670,plain,
! [C_172,A_173,B_174] :
( relation(C_172)
| ~ relation_of2_as_subset(C_172,A_173,B_174) ),
inference(resolution,[status(thm)],[c_650,c_8]) ).
tff(c_682,plain,
relation('#skF_21'),
inference(resolution,[status(thm)],[c_176,c_670]) ).
tff(c_180,plain,
function('#skF_21'),
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_116,plain,
empty('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_210,plain,
! [A_90] :
( ( empty_set = A_90 )
| ~ empty(A_90) ),
inference(cnfTransformation,[status(thm)],[f_310]) ).
tff(c_234,plain,
empty_set = '#skF_9',
inference(resolution,[status(thm)],[c_116,c_210]) ).
tff(c_100,plain,
empty('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_233,plain,
empty_set = '#skF_6',
inference(resolution,[status(thm)],[c_100,c_210]) ).
tff(c_252,plain,
'#skF_6' = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_234,c_233]) ).
tff(c_110,plain,
empty('#skF_7'),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_232,plain,
empty_set = '#skF_7',
inference(resolution,[status(thm)],[c_110,c_210]) ).
tff(c_247,plain,
'#skF_7' = '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_233,c_232]) ).
tff(c_279,plain,
'#skF_7' = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_252,c_247]) ).
tff(c_168,plain,
empty_set != '#skF_19',
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_240,plain,
'#skF_19' != '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_232,c_168]) ).
tff(c_281,plain,
'#skF_19' != '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_279,c_240]) ).
tff(c_178,plain,
quasi_total('#skF_21','#skF_18','#skF_19'),
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_503,plain,
! [C_145,A_146,B_147] :
( relation_of2(C_145,A_146,B_147)
| ~ relation_of2_as_subset(C_145,A_146,B_147) ),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_511,plain,
relation_of2('#skF_21','#skF_18','#skF_19'),
inference(resolution,[status(thm)],[c_176,c_503]) ).
tff(c_716,plain,
! [A_184,B_185,C_186] :
( ( relation_dom_as_subset(A_184,B_185,C_186) = relation_dom(C_186) )
| ~ relation_of2(C_186,A_184,B_185) ),
inference(cnfTransformation,[status(thm)],[f_242]) ).
tff(c_733,plain,
relation_dom_as_subset('#skF_18','#skF_19','#skF_21') = relation_dom('#skF_21'),
inference(resolution,[status(thm)],[c_511,c_716]) ).
tff(c_26,plain,
! [B_10,A_9,C_11] :
( ( empty_set = B_10 )
| ( relation_dom_as_subset(A_9,B_10,C_11) = A_9 )
| ~ quasi_total(C_11,A_9,B_10)
| ~ relation_of2_as_subset(C_11,A_9,B_10) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_3642,plain,
! [B_285,A_286,C_287] :
( ( B_285 = '#skF_9' )
| ( relation_dom_as_subset(A_286,B_285,C_287) = A_286 )
| ~ quasi_total(C_287,A_286,B_285)
| ~ relation_of2_as_subset(C_287,A_286,B_285) ),
inference(demodulation,[status(thm),theory(equality)],[c_234,c_26]) ).
tff(c_3651,plain,
( ( '#skF_19' = '#skF_9' )
| ( relation_dom_as_subset('#skF_18','#skF_19','#skF_21') = '#skF_18' )
| ~ quasi_total('#skF_21','#skF_18','#skF_19') ),
inference(resolution,[status(thm)],[c_176,c_3642]) ).
tff(c_3656,plain,
( ( '#skF_19' = '#skF_9' )
| ( relation_dom('#skF_21') = '#skF_18' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_178,c_733,c_3651]) ).
tff(c_3657,plain,
relation_dom('#skF_21') = '#skF_18',
inference(negUnitSimplification,[status(thm)],[c_281,c_3656]) ).
tff(c_4011,plain,
! [B_290,C_291,A_292] :
( ( apply(relation_composition(B_290,C_291),A_292) = apply(C_291,apply(B_290,A_292)) )
| ~ in(A_292,relation_dom(B_290))
| ~ function(C_291)
| ~ relation(C_291)
| ~ function(B_290)
| ~ relation(B_290) ),
inference(cnfTransformation,[status(thm)],[f_283]) ).
tff(c_4013,plain,
! [C_291,A_292] :
( ( apply(relation_composition('#skF_21',C_291),A_292) = apply(C_291,apply('#skF_21',A_292)) )
| ~ in(A_292,'#skF_18')
| ~ function(C_291)
| ~ relation(C_291)
| ~ function('#skF_21')
| ~ relation('#skF_21') ),
inference(superposition,[status(thm),theory(equality)],[c_3657,c_4011]) ).
tff(c_6883,plain,
! [C_395,A_396] :
( ( apply(relation_composition('#skF_21',C_395),A_396) = apply(C_395,apply('#skF_21',A_396)) )
| ~ in(A_396,'#skF_18')
| ~ function(C_395)
| ~ relation(C_395) ),
inference(demodulation,[status(thm),theory(equality)],[c_682,c_180,c_4013]) ).
tff(c_166,plain,
apply(relation_composition('#skF_21','#skF_22'),'#skF_20') != apply('#skF_22',apply('#skF_21','#skF_20')),
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_6889,plain,
( ~ in('#skF_20','#skF_18')
| ~ function('#skF_22')
| ~ relation('#skF_22') ),
inference(superposition,[status(thm),theory(equality)],[c_6883,c_166]) ).
tff(c_6933,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_174,c_172,c_170,c_6889]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% 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
% 0.13/0.35 % Computer : n016.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 12:30:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 8.37/2.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.37/2.95
% 8.37/2.95 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.37/2.98
% 8.37/2.98 Inference rules
% 8.37/2.98 ----------------------
% 8.37/2.98 #Ref : 0
% 8.37/2.98 #Sup : 1499
% 8.37/2.98 #Fact : 0
% 8.37/2.98 #Define : 0
% 8.37/2.98 #Split : 5
% 8.37/2.98 #Chain : 0
% 8.37/2.98 #Close : 0
% 8.37/2.98
% 8.37/2.98 Ordering : KBO
% 8.37/2.98
% 8.37/2.98 Simplification rules
% 8.37/2.98 ----------------------
% 8.37/2.98 #Subsume : 264
% 8.37/2.98 #Demod : 1803
% 8.37/2.98 #Tautology : 1002
% 8.37/2.98 #SimpNegUnit : 3
% 8.37/2.98 #BackRed : 23
% 8.37/2.98
% 8.37/2.98 #Partial instantiations: 0
% 8.37/2.98 #Strategies tried : 1
% 8.37/2.98
% 8.37/2.98 Timing (in seconds)
% 8.37/2.98 ----------------------
% 8.37/2.98 Preprocessing : 0.64
% 8.37/2.98 Parsing : 0.33
% 8.37/2.98 CNF conversion : 0.05
% 8.37/2.98 Main loop : 1.28
% 8.37/2.98 Inferencing : 0.41
% 8.37/2.98 Reduction : 0.47
% 8.37/2.98 Demodulation : 0.36
% 8.37/2.98 BG Simplification : 0.05
% 8.37/2.98 Subsumption : 0.27
% 8.37/2.98 Abstraction : 0.04
% 8.37/2.98 MUC search : 0.00
% 8.37/2.98 Cooper : 0.00
% 8.37/2.98 Total : 1.97
% 8.37/2.98 Index Insertion : 0.00
% 8.37/2.98 Index Deletion : 0.00
% 8.37/2.98 Index Matching : 0.00
% 8.37/2.98 BG Taut test : 0.00
%------------------------------------------------------------------------------