TSTP Solution File: NUM404+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM404+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 : n025.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 10:51:35 EDT 2023
% Result : Theorem 11.86s 3.93s
% Output : CNFRefutation 11.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 41
% Syntax : Number of formulae : 82 ( 13 unt; 33 typ; 0 def)
% Number of atoms : 108 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 102 ( 43 ~; 40 |; 7 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 18 >; 4 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 15 con; 0-2 aty)
% Number of variables : 44 (; 44 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_5 > #skF_2 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_1 > #skF_19 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_8 > #skF_3 > #skF_12 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(relation_non_empty,type,
relation_non_empty: $i > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $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('#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_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_14',type,
'#skF_14': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_95,axiom,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
~ ( in(B,A)
& in(C,A)
& ~ in(B,C)
& ( B != C )
& ~ in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
tff(f_78,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
tff(f_250,negated_conjecture,
~ ! [A] :
~ ! [B] :
( in(B,A)
<=> ordinal(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).
tff(f_108,axiom,
! [A] :
( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
tff(f_31,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
tff(f_102,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
tff(f_222,axiom,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
tff(f_237,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(A,B)
& ( A != B )
& ~ in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
tff(c_1613,plain,
! [A_195] :
( ( '#skF_2'(A_195) != '#skF_3'(A_195) )
| epsilon_connected(A_195) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_365,plain,
! [A_74] :
( in('#skF_1'(A_74),A_74)
| epsilon_transitive(A_74) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_168,plain,
! [B_40] :
( ordinal(B_40)
| ~ in(B_40,'#skF_19') ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_374,plain,
( ordinal('#skF_1'('#skF_19'))
| epsilon_transitive('#skF_19') ),
inference(resolution,[status(thm)],[c_365,c_168]) ).
tff(c_376,plain,
epsilon_transitive('#skF_19'),
inference(splitLeft,[status(thm)],[c_374]) ).
tff(c_334,plain,
! [A_71] :
( in('#skF_2'(A_71),A_71)
| epsilon_connected(A_71) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_343,plain,
( ordinal('#skF_2'('#skF_19'))
| epsilon_connected('#skF_19') ),
inference(resolution,[status(thm)],[c_334,c_168]) ).
tff(c_344,plain,
epsilon_connected('#skF_19'),
inference(splitLeft,[status(thm)],[c_343]) ).
tff(c_50,plain,
! [A_25] :
( ordinal(A_25)
| ~ epsilon_connected(A_25)
| ~ epsilon_transitive(A_25) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_170,plain,
! [B_40] :
( in(B_40,'#skF_19')
| ~ ordinal(B_40) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_378,plain,
! [B_77,A_78] :
( ~ in(B_77,A_78)
| ~ in(A_78,B_77) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_391,plain,
! [B_79] :
( ~ in('#skF_19',B_79)
| ~ ordinal(B_79) ),
inference(resolution,[status(thm)],[c_170,c_378]) ).
tff(c_396,plain,
~ ordinal('#skF_19'),
inference(resolution,[status(thm)],[c_170,c_391]) ).
tff(c_399,plain,
( ~ epsilon_connected('#skF_19')
| ~ epsilon_transitive('#skF_19') ),
inference(resolution,[status(thm)],[c_50,c_396]) ).
tff(c_406,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_376,c_344,c_399]) ).
tff(c_408,plain,
~ epsilon_transitive('#skF_19'),
inference(splitRight,[status(thm)],[c_374]) ).
tff(c_407,plain,
ordinal('#skF_1'('#skF_19')),
inference(splitRight,[status(thm)],[c_374]) ).
tff(c_695,plain,
! [A_114,B_115] :
( in('#skF_4'(A_114,B_115),A_114)
| subset(A_114,B_115) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_162,plain,
! [A_32,B_33] :
( ordinal(A_32)
| ~ in(A_32,B_33)
| ~ ordinal(B_33) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_1520,plain,
! [A_190,B_191] :
( ordinal('#skF_4'(A_190,B_191))
| ~ ordinal(A_190)
| subset(A_190,B_191) ),
inference(resolution,[status(thm)],[c_695,c_162]) ).
tff(c_521,plain,
! [A_102,B_103] :
( ~ in('#skF_4'(A_102,B_103),B_103)
| subset(A_102,B_103) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_526,plain,
! [A_102] :
( subset(A_102,'#skF_19')
| ~ ordinal('#skF_4'(A_102,'#skF_19')) ),
inference(resolution,[status(thm)],[c_170,c_521]) ).
tff(c_1534,plain,
! [A_192] :
( ~ ordinal(A_192)
| subset(A_192,'#skF_19') ),
inference(resolution,[status(thm)],[c_1520,c_526]) ).
tff(c_28,plain,
! [A_9] :
( ~ subset('#skF_1'(A_9),A_9)
| epsilon_transitive(A_9) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_1556,plain,
( epsilon_transitive('#skF_19')
| ~ ordinal('#skF_1'('#skF_19')) ),
inference(resolution,[status(thm)],[c_1534,c_28]) ).
tff(c_1565,plain,
epsilon_transitive('#skF_19'),
inference(demodulation,[status(thm),theory(equality)],[c_407,c_1556]) ).
tff(c_1567,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_408,c_1565]) ).
tff(c_1569,plain,
~ epsilon_connected('#skF_19'),
inference(splitRight,[status(thm)],[c_343]) ).
tff(c_1617,plain,
'#skF_2'('#skF_19') != '#skF_3'('#skF_19'),
inference(resolution,[status(thm)],[c_1613,c_1569]) ).
tff(c_1574,plain,
! [A_193] :
( in('#skF_3'(A_193),A_193)
| epsilon_connected(A_193) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_1581,plain,
( ordinal('#skF_3'('#skF_19'))
| epsilon_connected('#skF_19') ),
inference(resolution,[status(thm)],[c_1574,c_168]) ).
tff(c_1585,plain,
ordinal('#skF_3'('#skF_19')),
inference(negUnitSimplification,[status(thm)],[c_1569,c_1581]) ).
tff(c_1568,plain,
ordinal('#skF_2'('#skF_19')),
inference(splitRight,[status(thm)],[c_343]) ).
tff(c_2251,plain,
! [B_275,A_276] :
( in(B_275,A_276)
| ( B_275 = A_276 )
| in(A_276,B_275)
| ~ ordinal(B_275)
| ~ ordinal(A_276) ),
inference(cnfTransformation,[status(thm)],[f_237]) ).
tff(c_38,plain,
! [A_13] :
( ~ in('#skF_2'(A_13),'#skF_3'(A_13))
| epsilon_connected(A_13) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_5931,plain,
! [A_463] :
( epsilon_connected(A_463)
| in('#skF_3'(A_463),'#skF_2'(A_463))
| ( '#skF_2'(A_463) = '#skF_3'(A_463) )
| ~ ordinal('#skF_3'(A_463))
| ~ ordinal('#skF_2'(A_463)) ),
inference(resolution,[status(thm)],[c_2251,c_38]) ).
tff(c_34,plain,
! [A_13] :
( ~ in('#skF_3'(A_13),'#skF_2'(A_13))
| epsilon_connected(A_13) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_13140,plain,
! [A_587] :
( epsilon_connected(A_587)
| ( '#skF_2'(A_587) = '#skF_3'(A_587) )
| ~ ordinal('#skF_3'(A_587))
| ~ ordinal('#skF_2'(A_587)) ),
inference(resolution,[status(thm)],[c_5931,c_34]) ).
tff(c_13149,plain,
( epsilon_connected('#skF_19')
| ( '#skF_2'('#skF_19') = '#skF_3'('#skF_19') )
| ~ ordinal('#skF_3'('#skF_19')) ),
inference(resolution,[status(thm)],[c_1568,c_13140]) ).
tff(c_13157,plain,
( epsilon_connected('#skF_19')
| ( '#skF_2'('#skF_19') = '#skF_3'('#skF_19') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1585,c_13149]) ).
tff(c_13159,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1617,c_1569,c_13157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM404+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % 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
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 15:01:49 EDT 2023
% 0.15/0.36 % CPUTime :
% 11.86/3.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.86/3.93
% 11.86/3.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.86/3.97
% 11.86/3.97 Inference rules
% 11.86/3.97 ----------------------
% 11.86/3.97 #Ref : 0
% 11.86/3.97 #Sup : 2779
% 12.15/3.97 #Fact : 8
% 12.15/3.97 #Define : 0
% 12.15/3.97 #Split : 29
% 12.15/3.97 #Chain : 0
% 12.15/3.97 #Close : 0
% 12.15/3.97
% 12.15/3.97 Ordering : KBO
% 12.15/3.97
% 12.15/3.97 Simplification rules
% 12.15/3.97 ----------------------
% 12.15/3.97 #Subsume : 1304
% 12.15/3.97 #Demod : 741
% 12.15/3.97 #Tautology : 465
% 12.15/3.97 #SimpNegUnit : 213
% 12.15/3.97 #BackRed : 204
% 12.15/3.97
% 12.15/3.97 #Partial instantiations: 0
% 12.15/3.97 #Strategies tried : 1
% 12.15/3.97
% 12.15/3.97 Timing (in seconds)
% 12.15/3.97 ----------------------
% 12.15/3.97 Preprocessing : 0.59
% 12.15/3.97 Parsing : 0.30
% 12.15/3.97 CNF conversion : 0.05
% 12.15/3.97 Main loop : 2.29
% 12.15/3.97 Inferencing : 0.73
% 12.15/3.97 Reduction : 0.74
% 12.15/3.97 Demodulation : 0.52
% 12.15/3.97 BG Simplification : 0.06
% 12.15/3.97 Subsumption : 0.58
% 12.15/3.97 Abstraction : 0.06
% 12.15/3.97 MUC search : 0.00
% 12.15/3.97 Cooper : 0.00
% 12.15/3.97 Total : 2.93
% 12.15/3.97 Index Insertion : 0.00
% 12.15/3.97 Index Deletion : 0.00
% 12.15/3.97 Index Matching : 0.00
% 12.15/3.97 BG Taut test : 0.00
%------------------------------------------------------------------------------