TSTP Solution File: SEU098+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU098+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 : n012.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 10:57:36 EDT 2023
% Result : Theorem 12.89s 4.51s
% Output : CNFRefutation 13.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 74
% Syntax : Number of formulae : 115 ( 22 unt; 62 typ; 0 def)
% Number of atoms : 121 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 117 ( 49 ~; 45 |; 11 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 56 ( 38 >; 18 *; 0 +; 0 <<)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 24 con; 0-4 aty)
% Number of variables : 70 (; 70 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > quasi_total > subset > in > element > with_non_empty_elements > transfinite_sequence > relation_non_empty > relation_empty_yielding > relation > ordinal_yielding > ordinal > one_to_one > natural > function_yielding > function > finite > epsilon_transitive > epsilon_connected > empty > being_limit_ordinal > function_image > relation_image > first_projection_as_func_of > first_projection > cartesian_product2 > #nlpp > relation_rng > relation_dom > powerset > positive_rationals > empty_set > #skF_20 > #skF_2 > #skF_18 > #skF_17 > #skF_15 > #skF_19 > #skF_25 > #skF_22 > #skF_7 > #skF_3 > #skF_10 > #skF_16 > #skF_5 > #skF_6 > #skF_13 > #skF_21 > #skF_9 > #skF_26 > #skF_8 > #skF_30 > #skF_4 > #skF_11 > #skF_14 > #skF_29 > #skF_28 > #skF_24 > #skF_27 > #skF_23 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(with_non_empty_elements,type,
with_non_empty_elements: $i > $o ).
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(positive_rationals,type,
positive_rationals: $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff(relation_non_empty,type,
relation_non_empty: $i > $o ).
tff(quasi_total,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_19',type,
'#skF_19': $i > $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff('#skF_22',type,
'#skF_22': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(finite,type,
finite: $i > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(ordinal_yielding,type,
ordinal_yielding: $i > $o ).
tff(function,type,
function: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff(first_projection,type,
first_projection: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(first_projection_as_func_of,type,
first_projection_as_func_of: ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(relation_image,type,
relation_image: ( $i * $i ) > $i ).
tff(function_image,type,
function_image: ( $i * $i * $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(function_yielding,type,
function_yielding: $i > $o ).
tff('#skF_26',type,
'#skF_26': $i > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff(being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff(natural,type,
natural: $i > $o ).
tff(transfinite_sequence,type,
transfinite_sequence: $i > $o ).
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_12',type,
'#skF_12': $i ).
tff(f_518,negated_conjecture,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( finite(relation_dom(A))
<=> finite(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finset_1) ).
tff(f_133,axiom,
! [A,B] :
( relation(first_projection(A,B))
& function(first_projection(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_3) ).
tff(f_461,axiom,
! [A,B] : ( first_projection_as_func_of(A,B) = first_projection(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_funct_3) ).
tff(f_139,axiom,
! [A,B] :
( function(first_projection_as_func_of(A,B))
& quasi_total(first_projection_as_func_of(A,B),cartesian_product2(A,B),A)
& relation_of2_as_subset(first_projection_as_func_of(A,B),cartesian_product2(A,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_funct_3) ).
tff(f_465,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_459,axiom,
! [A,B,C,D] :
( ( function(C)
& quasi_total(C,A,B)
& relation_of2(C,A,B) )
=> ( function_image(A,B,C,D) = relation_image(C,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
tff(f_473,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( function_image(cartesian_product2(relation_dom(A),relation_rng(A)),relation_dom(A),first_projection_as_func_of(relation_dom(A),relation_rng(A)),A) = relation_dom(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_funct_3) ).
tff(f_487,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( finite(A)
=> finite(relation_image(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
tff(f_509,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( finite(relation_dom(A))
=> finite(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
tff(f_493,axiom,
! [A,B] :
( ( finite(A)
& finite(B) )
=> finite(cartesian_product2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_finset_1) ).
tff(f_501,axiom,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
tff(f_479,axiom,
! [A,B] :
( ( subset(A,B)
& finite(B) )
=> finite(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
tff(c_334,plain,
relation('#skF_30'),
inference(cnfTransformation,[status(thm)],[f_518]) ).
tff(c_332,plain,
function('#skF_30'),
inference(cnfTransformation,[status(thm)],[f_518]) ).
tff(c_342,plain,
( finite(relation_dom('#skF_30'))
| finite('#skF_30') ),
inference(cnfTransformation,[status(thm)],[f_518]) ).
tff(c_371,plain,
finite('#skF_30'),
inference(splitLeft,[status(thm)],[c_342]) ).
tff(c_56,plain,
! [A_25,B_26] : relation(first_projection(A_25,B_26)),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_310,plain,
! [A_67,B_68] : ( first_projection_as_func_of(A_67,B_68) = first_projection(A_67,B_68) ),
inference(cnfTransformation,[status(thm)],[f_461]) ).
tff(c_60,plain,
! [A_27,B_28] : function(first_projection_as_func_of(A_27,B_28)),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_368,plain,
! [A_27,B_28] : function(first_projection(A_27,B_28)),
inference(demodulation,[status(thm),theory(equality)],[c_310,c_60]) ).
tff(c_62,plain,
! [A_27,B_28] : quasi_total(first_projection_as_func_of(A_27,B_28),cartesian_product2(A_27,B_28),A_27),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_367,plain,
! [A_27,B_28] : quasi_total(first_projection(A_27,B_28),cartesian_product2(A_27,B_28),A_27),
inference(demodulation,[status(thm),theory(equality)],[c_310,c_62]) ).
tff(c_64,plain,
! [A_27,B_28] : relation_of2_as_subset(first_projection_as_func_of(A_27,B_28),cartesian_product2(A_27,B_28),A_27),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_1260,plain,
! [A_211,B_212] : relation_of2_as_subset(first_projection(A_211,B_212),cartesian_product2(A_211,B_212),A_211),
inference(demodulation,[status(thm),theory(equality)],[c_310,c_64]) ).
tff(c_312,plain,
! [C_71,A_69,B_70] :
( relation_of2(C_71,A_69,B_70)
| ~ relation_of2_as_subset(C_71,A_69,B_70) ),
inference(cnfTransformation,[status(thm)],[f_465]) ).
tff(c_1264,plain,
! [A_211,B_212] : relation_of2(first_projection(A_211,B_212),cartesian_product2(A_211,B_212),A_211),
inference(resolution,[status(thm)],[c_1260,c_312]) ).
tff(c_1814,plain,
! [A_291,B_292,C_293,D_294] :
( ( function_image(A_291,B_292,C_293,D_294) = relation_image(C_293,D_294) )
| ~ relation_of2(C_293,A_291,B_292)
| ~ quasi_total(C_293,A_291,B_292)
| ~ function(C_293) ),
inference(cnfTransformation,[status(thm)],[f_459]) ).
tff(c_1816,plain,
! [A_211,B_212,D_294] :
( ( function_image(cartesian_product2(A_211,B_212),A_211,first_projection(A_211,B_212),D_294) = relation_image(first_projection(A_211,B_212),D_294) )
| ~ quasi_total(first_projection(A_211,B_212),cartesian_product2(A_211,B_212),A_211)
| ~ function(first_projection(A_211,B_212)) ),
inference(resolution,[status(thm)],[c_1264,c_1814]) ).
tff(c_1823,plain,
! [A_211,B_212,D_294] : ( function_image(cartesian_product2(A_211,B_212),A_211,first_projection(A_211,B_212),D_294) = relation_image(first_projection(A_211,B_212),D_294) ),
inference(demodulation,[status(thm),theory(equality)],[c_368,c_367,c_1816]) ).
tff(c_318,plain,
! [A_74] :
( ( function_image(cartesian_product2(relation_dom(A_74),relation_rng(A_74)),relation_dom(A_74),first_projection_as_func_of(relation_dom(A_74),relation_rng(A_74)),A_74) = relation_dom(A_74) )
| ~ function(A_74)
| ~ relation(A_74) ),
inference(cnfTransformation,[status(thm)],[f_473]) ).
tff(c_359,plain,
! [A_74] :
( ( function_image(cartesian_product2(relation_dom(A_74),relation_rng(A_74)),relation_dom(A_74),first_projection(relation_dom(A_74),relation_rng(A_74)),A_74) = relation_dom(A_74) )
| ~ function(A_74)
| ~ relation(A_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_310,c_318]) ).
tff(c_13048,plain,
! [A_622] :
( ( relation_image(first_projection(relation_dom(A_622),relation_rng(A_622)),A_622) = relation_dom(A_622) )
| ~ function(A_622)
| ~ relation(A_622) ),
inference(demodulation,[status(thm),theory(equality)],[c_1823,c_359]) ).
tff(c_322,plain,
! [B_78,A_77] :
( finite(relation_image(B_78,A_77))
| ~ finite(A_77)
| ~ function(B_78)
| ~ relation(B_78) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_13063,plain,
! [A_622] :
( finite(relation_dom(A_622))
| ~ finite(A_622)
| ~ function(first_projection(relation_dom(A_622),relation_rng(A_622)))
| ~ relation(first_projection(relation_dom(A_622),relation_rng(A_622)))
| ~ function(A_622)
| ~ relation(A_622) ),
inference(superposition,[status(thm),theory(equality)],[c_13048,c_322]) ).
tff(c_13226,plain,
! [A_630] :
( finite(relation_dom(A_630))
| ~ finite(A_630)
| ~ function(A_630)
| ~ relation(A_630) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_368,c_13063]) ).
tff(c_336,plain,
( ~ finite('#skF_30')
| ~ finite(relation_dom('#skF_30')) ),
inference(cnfTransformation,[status(thm)],[f_518]) ).
tff(c_370,plain,
~ finite(relation_dom('#skF_30')),
inference(splitLeft,[status(thm)],[c_336]) ).
tff(c_13235,plain,
( ~ finite('#skF_30')
| ~ function('#skF_30')
| ~ relation('#skF_30') ),
inference(resolution,[status(thm)],[c_13226,c_370]) ).
tff(c_13301,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_334,c_332,c_371,c_13235]) ).
tff(c_13302,plain,
finite(relation_dom('#skF_30')),
inference(splitRight,[status(thm)],[c_342]) ).
tff(c_13305,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_13302,c_370]) ).
tff(c_13306,plain,
~ finite('#skF_30'),
inference(splitRight,[status(thm)],[c_336]) ).
tff(c_13308,plain,
finite(relation_dom('#skF_30')),
inference(negUnitSimplification,[status(thm)],[c_13306,c_342]) ).
tff(c_330,plain,
! [A_84] :
( finite(relation_rng(A_84))
| ~ finite(relation_dom(A_84))
| ~ function(A_84)
| ~ relation(A_84) ),
inference(cnfTransformation,[status(thm)],[f_509]) ).
tff(c_324,plain,
! [A_79,B_80] :
( finite(cartesian_product2(A_79,B_80))
| ~ finite(B_80)
| ~ finite(A_79) ),
inference(cnfTransformation,[status(thm)],[f_493]) ).
tff(c_14504,plain,
! [A_771] :
( subset(A_771,cartesian_product2(relation_dom(A_771),relation_rng(A_771)))
| ~ relation(A_771) ),
inference(cnfTransformation,[status(thm)],[f_501]) ).
tff(c_320,plain,
! [A_75,B_76] :
( finite(A_75)
| ~ finite(B_76)
| ~ subset(A_75,B_76) ),
inference(cnfTransformation,[status(thm)],[f_479]) ).
tff(c_14918,plain,
! [A_857] :
( finite(A_857)
| ~ finite(cartesian_product2(relation_dom(A_857),relation_rng(A_857)))
| ~ relation(A_857) ),
inference(resolution,[status(thm)],[c_14504,c_320]) ).
tff(c_15249,plain,
! [A_893] :
( finite(A_893)
| ~ relation(A_893)
| ~ finite(relation_rng(A_893))
| ~ finite(relation_dom(A_893)) ),
inference(resolution,[status(thm)],[c_324,c_14918]) ).
tff(c_15273,plain,
! [A_894] :
( finite(A_894)
| ~ finite(relation_dom(A_894))
| ~ function(A_894)
| ~ relation(A_894) ),
inference(resolution,[status(thm)],[c_330,c_15249]) ).
tff(c_15288,plain,
( finite('#skF_30')
| ~ function('#skF_30')
| ~ relation('#skF_30') ),
inference(resolution,[status(thm)],[c_13308,c_15273]) ).
tff(c_15298,plain,
finite('#skF_30'),
inference(demodulation,[status(thm),theory(equality)],[c_334,c_332,c_15288]) ).
tff(c_15300,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13306,c_15298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU098+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 : n012.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 11:28:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 12.89/4.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.41/4.52
% 13.41/4.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.55/4.56
% 13.55/4.56 Inference rules
% 13.55/4.56 ----------------------
% 13.55/4.56 #Ref : 0
% 13.55/4.56 #Sup : 4041
% 13.55/4.56 #Fact : 0
% 13.55/4.56 #Define : 0
% 13.55/4.56 #Split : 38
% 13.55/4.56 #Chain : 0
% 13.55/4.56 #Close : 0
% 13.55/4.56
% 13.55/4.56 Ordering : KBO
% 13.55/4.56
% 13.55/4.56 Simplification rules
% 13.55/4.56 ----------------------
% 13.55/4.56 #Subsume : 1106
% 13.55/4.56 #Demod : 1598
% 13.55/4.56 #Tautology : 799
% 13.55/4.56 #SimpNegUnit : 60
% 13.55/4.56 #BackRed : 86
% 13.55/4.56
% 13.55/4.56 #Partial instantiations: 0
% 13.55/4.56 #Strategies tried : 1
% 13.55/4.56
% 13.55/4.56 Timing (in seconds)
% 13.55/4.56 ----------------------
% 13.55/4.56 Preprocessing : 0.69
% 13.55/4.56 Parsing : 0.35
% 13.55/4.56 CNF conversion : 0.06
% 13.55/4.56 Main loop : 2.79
% 13.55/4.56 Inferencing : 0.80
% 13.55/4.56 Reduction : 1.04
% 13.55/4.56 Demodulation : 0.78
% 13.55/4.56 BG Simplification : 0.08
% 13.55/4.56 Subsumption : 0.67
% 13.55/4.56 Abstraction : 0.06
% 13.55/4.56 MUC search : 0.00
% 13.55/4.56 Cooper : 0.00
% 13.55/4.56 Total : 3.55
% 13.55/4.56 Index Insertion : 0.00
% 13.55/4.56 Index Deletion : 0.00
% 13.55/4.56 Index Matching : 0.00
% 13.55/4.56 BG Taut test : 0.00
%------------------------------------------------------------------------------