TSTP Solution File: SEU353+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU353+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 : n017.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 10:58:29 EDT 2023
% Result : Theorem 6.79s 2.50s
% Output : CNFRefutation 6.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 56
% Syntax : Number of formulae : 92 ( 22 unt; 45 typ; 0 def)
% Number of atoms : 102 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 92 ( 37 ~; 31 |; 14 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 37 >; 24 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 8 con; 0-4 aty)
% Number of variables : 51 (; 51 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ v1_partfun1 > relation_of2_as_subset > relation_of2 > quasi_total > onto > bijective > subset > in > element > transitive > symmetric > relation > reflexive > one_to_one > one_sorted_str > function > empty_carrier > empty > antisymmetric > apply_as_element > cartesian_product2 > apply > #nlpp > the_carrier > powerset > identity_relation > identity_on_carrier > identity_as_relation_of > empty_set > #skF_9 > #skF_7 > #skF_17 > #skF_16 > #skF_15 > #skF_14 > #skF_6 > #skF_10 > #skF_1 > #skF_8 > #skF_13 > #skF_3 > #skF_11 > #skF_2 > #skF_5 > #skF_12 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff(antisymmetric,type,
antisymmetric: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(empty_carrier,type,
empty_carrier: $i > $o ).
tff(identity_on_carrier,type,
identity_on_carrier: $i > $i ).
tff(relation,type,
relation: $i > $o ).
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(v1_partfun1,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(symmetric,type,
symmetric: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
tff(onto,type,
onto: ( $i * $i * $i ) > $o ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(identity_as_relation_of,type,
identity_as_relation_of: $i > $i ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(identity_relation,type,
identity_relation: $i > $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_of2,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(bijective,type,
bijective: ( $i * $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff(apply_as_element,type,
apply_as_element: ( $i * $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(transitive,type,
transitive: $i > $o ).
tff(powerset,type,
powerset: $i > $i ).
tff(reflexive,type,
reflexive: $i > $o ).
tff(cartesian_product2,type,
cartesian_product2: ( $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('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_394,negated_conjecture,
~ ! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ( apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B) = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tmap_1) ).
tff(f_329,axiom,
! [A,B,C,D] :
( ( ~ empty(A)
& function(C)
& quasi_total(C,A,B)
& relation_of2(C,A,B)
& element(D,A) )
=> ( apply_as_element(A,B,C,D) = apply(C,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
tff(f_200,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ~ empty(the_carrier(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
tff(f_345,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
tff(f_316,axiom,
! [A] : ( identity_as_relation_of(A) = identity_relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
tff(f_349,axiom,
! [A,B] :
( in(B,A)
=> ( apply(identity_relation(A),B) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
tff(f_149,axiom,
! [A] :
( one_sorted_str(A)
=> ( identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_grcat_1) ).
tff(f_216,axiom,
! [A] :
( relation(identity_relation(A))
& function(identity_relation(A))
& reflexive(identity_relation(A))
& symmetric(identity_relation(A))
& antisymmetric(identity_relation(A))
& transitive(identity_relation(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_partfun1) ).
tff(f_154,axiom,
! [A] :
( v1_partfun1(identity_as_relation_of(A),A,A)
& relation_of2_as_subset(identity_as_relation_of(A),A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
tff(f_333,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_41,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> ( ( function(C)
& v1_partfun1(C,A,B) )
=> ( function(C)
& quasi_total(C,A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
tff(c_220,plain,
~ empty_carrier('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_394]) ).
tff(c_218,plain,
one_sorted_str('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_394]) ).
tff(c_216,plain,
element('#skF_17',the_carrier('#skF_16')),
inference(cnfTransformation,[status(thm)],[f_394]) ).
tff(c_1292,plain,
! [A_328,B_329,C_330,D_331] :
( ( apply_as_element(A_328,B_329,C_330,D_331) = apply(C_330,D_331) )
| ~ element(D_331,A_328)
| ~ relation_of2(C_330,A_328,B_329)
| ~ quasi_total(C_330,A_328,B_329)
| ~ function(C_330)
| empty(A_328) ),
inference(cnfTransformation,[status(thm)],[f_329]) ).
tff(c_1326,plain,
! [B_329,C_330] :
( ( apply_as_element(the_carrier('#skF_16'),B_329,C_330,'#skF_17') = apply(C_330,'#skF_17') )
| ~ relation_of2(C_330,the_carrier('#skF_16'),B_329)
| ~ quasi_total(C_330,the_carrier('#skF_16'),B_329)
| ~ function(C_330)
| empty(the_carrier('#skF_16')) ),
inference(resolution,[status(thm)],[c_216,c_1292]) ).
tff(c_1372,plain,
empty(the_carrier('#skF_16')),
inference(splitLeft,[status(thm)],[c_1326]) ).
tff(c_94,plain,
! [A_45] :
( ~ empty(the_carrier(A_45))
| ~ one_sorted_str(A_45)
| empty_carrier(A_45) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_1379,plain,
( ~ one_sorted_str('#skF_16')
| empty_carrier('#skF_16') ),
inference(resolution,[status(thm)],[c_1372,c_94]) ).
tff(c_1389,plain,
empty_carrier('#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_1379]) ).
tff(c_1391,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_220,c_1389]) ).
tff(c_1393,plain,
~ empty(the_carrier('#skF_16')),
inference(splitRight,[status(thm)],[c_1326]) ).
tff(c_196,plain,
! [A_78,B_79] :
( in(A_78,B_79)
| empty(B_79)
| ~ element(A_78,B_79) ),
inference(cnfTransformation,[status(thm)],[f_345]) ).
tff(c_184,plain,
! [A_66] : ( identity_relation(A_66) = identity_as_relation_of(A_66) ),
inference(cnfTransformation,[status(thm)],[f_316]) ).
tff(c_198,plain,
! [A_80,B_81] :
( ( apply(identity_relation(A_80),B_81) = B_81 )
| ~ in(B_81,A_80) ),
inference(cnfTransformation,[status(thm)],[f_349]) ).
tff(c_221,plain,
! [A_80,B_81] :
( ( apply(identity_as_relation_of(A_80),B_81) = B_81 )
| ~ in(B_81,A_80) ),
inference(demodulation,[status(thm),theory(equality)],[c_184,c_198]) ).
tff(c_52,plain,
! [A_26] :
( ( identity_as_relation_of(the_carrier(A_26)) = identity_on_carrier(A_26) )
| ~ one_sorted_str(A_26) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_102,plain,
! [A_47] : function(identity_relation(A_47)),
inference(cnfTransformation,[status(thm)],[f_216]) ).
tff(c_226,plain,
! [A_47] : function(identity_as_relation_of(A_47)),
inference(demodulation,[status(thm),theory(equality)],[c_184,c_102]) ).
tff(c_64,plain,
! [A_27] : relation_of2_as_subset(identity_as_relation_of(A_27),A_27,A_27),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_487,plain,
! [C_191,A_192,B_193] :
( relation_of2(C_191,A_192,B_193)
| ~ relation_of2_as_subset(C_191,A_192,B_193) ),
inference(cnfTransformation,[status(thm)],[f_333]) ).
tff(c_499,plain,
! [A_27] : relation_of2(identity_as_relation_of(A_27),A_27,A_27),
inference(resolution,[status(thm)],[c_64,c_487]) ).
tff(c_62,plain,
! [A_27] : v1_partfun1(identity_as_relation_of(A_27),A_27,A_27),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_671,plain,
! [C_241,A_242,B_243] :
( quasi_total(C_241,A_242,B_243)
| ~ v1_partfun1(C_241,A_242,B_243)
| ~ function(C_241)
| ~ relation_of2(C_241,A_242,B_243) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_677,plain,
! [A_27] :
( quasi_total(identity_as_relation_of(A_27),A_27,A_27)
| ~ function(identity_as_relation_of(A_27))
| ~ relation_of2(identity_as_relation_of(A_27),A_27,A_27) ),
inference(resolution,[status(thm)],[c_62,c_671]) ).
tff(c_684,plain,
! [A_27] : quasi_total(identity_as_relation_of(A_27),A_27,A_27),
inference(demodulation,[status(thm),theory(equality)],[c_499,c_226,c_677]) ).
tff(c_1436,plain,
! [B_351,C_352] :
( ( apply_as_element(the_carrier('#skF_16'),B_351,C_352,'#skF_17') = apply(C_352,'#skF_17') )
| ~ relation_of2(C_352,the_carrier('#skF_16'),B_351)
| ~ quasi_total(C_352,the_carrier('#skF_16'),B_351)
| ~ function(C_352) ),
inference(splitRight,[status(thm)],[c_1326]) ).
tff(c_1448,plain,
( ( apply_as_element(the_carrier('#skF_16'),the_carrier('#skF_16'),identity_as_relation_of(the_carrier('#skF_16')),'#skF_17') = apply(identity_as_relation_of(the_carrier('#skF_16')),'#skF_17') )
| ~ quasi_total(identity_as_relation_of(the_carrier('#skF_16')),the_carrier('#skF_16'),the_carrier('#skF_16'))
| ~ function(identity_as_relation_of(the_carrier('#skF_16'))) ),
inference(resolution,[status(thm)],[c_499,c_1436]) ).
tff(c_1475,plain,
apply_as_element(the_carrier('#skF_16'),the_carrier('#skF_16'),identity_as_relation_of(the_carrier('#skF_16')),'#skF_17') = apply(identity_as_relation_of(the_carrier('#skF_16')),'#skF_17'),
inference(demodulation,[status(thm),theory(equality)],[c_226,c_684,c_1448]) ).
tff(c_1676,plain,
( ( apply_as_element(the_carrier('#skF_16'),the_carrier('#skF_16'),identity_on_carrier('#skF_16'),'#skF_17') = apply(identity_as_relation_of(the_carrier('#skF_16')),'#skF_17') )
| ~ one_sorted_str('#skF_16') ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_1475]) ).
tff(c_1683,plain,
apply_as_element(the_carrier('#skF_16'),the_carrier('#skF_16'),identity_on_carrier('#skF_16'),'#skF_17') = apply(identity_as_relation_of(the_carrier('#skF_16')),'#skF_17'),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_1676]) ).
tff(c_214,plain,
apply_as_element(the_carrier('#skF_16'),the_carrier('#skF_16'),identity_on_carrier('#skF_16'),'#skF_17') != '#skF_17',
inference(cnfTransformation,[status(thm)],[f_394]) ).
tff(c_1722,plain,
apply(identity_as_relation_of(the_carrier('#skF_16')),'#skF_17') != '#skF_17',
inference(demodulation,[status(thm),theory(equality)],[c_1683,c_214]) ).
tff(c_1740,plain,
~ in('#skF_17',the_carrier('#skF_16')),
inference(superposition,[status(thm),theory(equality)],[c_221,c_1722]) ).
tff(c_1745,plain,
( empty(the_carrier('#skF_16'))
| ~ element('#skF_17',the_carrier('#skF_16')) ),
inference(resolution,[status(thm)],[c_196,c_1740]) ).
tff(c_1748,plain,
empty(the_carrier('#skF_16')),
inference(demodulation,[status(thm),theory(equality)],[c_216,c_1745]) ).
tff(c_1750,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1393,c_1748]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU353+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
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 11:39:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 6.79/2.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.79/2.50
% 6.79/2.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.79/2.54
% 6.79/2.54 Inference rules
% 6.79/2.54 ----------------------
% 6.79/2.54 #Ref : 0
% 6.79/2.54 #Sup : 322
% 6.79/2.54 #Fact : 0
% 6.79/2.54 #Define : 0
% 6.79/2.54 #Split : 6
% 6.79/2.54 #Chain : 0
% 6.79/2.54 #Close : 0
% 6.79/2.54
% 6.79/2.54 Ordering : KBO
% 6.79/2.54
% 6.79/2.54 Simplification rules
% 6.79/2.54 ----------------------
% 6.79/2.54 #Subsume : 83
% 6.79/2.54 #Demod : 134
% 6.79/2.54 #Tautology : 86
% 6.79/2.54 #SimpNegUnit : 32
% 6.79/2.54 #BackRed : 10
% 6.79/2.54
% 6.79/2.54 #Partial instantiations: 0
% 6.79/2.54 #Strategies tried : 1
% 6.79/2.54
% 6.79/2.54 Timing (in seconds)
% 6.79/2.54 ----------------------
% 6.79/2.54 Preprocessing : 0.66
% 6.79/2.54 Parsing : 0.34
% 6.79/2.54 CNF conversion : 0.06
% 6.79/2.54 Main loop : 0.82
% 6.79/2.54 Inferencing : 0.31
% 6.79/2.54 Reduction : 0.26
% 6.79/2.54 Demodulation : 0.17
% 6.79/2.54 BG Simplification : 0.04
% 6.79/2.54 Subsumption : 0.16
% 6.79/2.54 Abstraction : 0.03
% 6.79/2.54 MUC search : 0.00
% 6.79/2.54 Cooper : 0.00
% 6.79/2.54 Total : 1.53
% 6.79/2.54 Index Insertion : 0.00
% 6.79/2.54 Index Deletion : 0.00
% 6.79/2.54 Index Matching : 0.00
% 6.79/2.54 BG Taut test : 0.00
%------------------------------------------------------------------------------