TSTP Solution File: NUM412+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM412+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 : n014.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 10:51:36 EDT 2023
% Result : Theorem 7.50s 2.73s
% Output : CNFRefutation 7.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 45
% Syntax : Number of formulae : 68 ( 10 unt; 39 typ; 0 def)
% Number of atoms : 84 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 41 ~; 36 |; 10 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 21 >; 6 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 18 con; 0-2 aty)
% Number of variables : 35 (; 35 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ transfinite_sequence_of > subset > in > element > with_non_empty_elements > transfinite_sequence > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > tseq_dom_restriction > relation_dom_restriction > #nlpp > relation_rng > powerset > empty_set > #skF_2 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_1 > #skF_19 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #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_2',type,
'#skF_2': $i > $i ).
tff(transfinite_sequence_of,type,
transfinite_sequence_of: ( $i * $i ) > $o ).
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('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff(relation_dom_restriction,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(tseq_dom_restriction,type,
tseq_dom_restriction: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff(transfinite_sequence,type,
transfinite_sequence: $i > $o ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_293,negated_conjecture,
~ ! [A,B] :
( transfinite_sequence_of(B,A)
=> ! [C] :
( ordinal(C)
=> transfinite_sequence_of(tseq_dom_restriction(B,C),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_ordinal1) ).
tff(f_103,axiom,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ( relation(B)
& function(B)
& transfinite_sequence(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
tff(f_81,axiom,
! [A,B] :
( ( relation(B)
& function(B)
& transfinite_sequence(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
tff(f_262,axiom,
! [A,B] :
( ( relation(A)
& function(A)
& transfinite_sequence(A)
& ordinal(B) )
=> ( tseq_dom_restriction(A,B) = relation_dom_restriction(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_ordinal1) ).
tff(f_91,axiom,
! [A,B] :
( ( relation(A)
& function(A)
& transfinite_sequence(A)
& ordinal(B) )
=> transfinite_sequence_of(tseq_dom_restriction(A,B),relation_rng(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_ordinal1) ).
tff(f_285,axiom,
! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_ordinal1) ).
tff(c_184,plain,
transfinite_sequence_of('#skF_18','#skF_17'),
inference(cnfTransformation,[status(thm)],[f_293]) ).
tff(c_373,plain,
! [B_72,A_73] :
( relation(B_72)
| ~ transfinite_sequence_of(B_72,A_73) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_381,plain,
relation('#skF_18'),
inference(resolution,[status(thm)],[c_184,c_373]) ).
tff(c_356,plain,
! [B_68,A_69] :
( function(B_68)
| ~ transfinite_sequence_of(B_68,A_69) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_364,plain,
function('#skF_18'),
inference(resolution,[status(thm)],[c_184,c_356]) ).
tff(c_382,plain,
! [B_74,A_75] :
( transfinite_sequence(B_74)
| ~ transfinite_sequence_of(B_74,A_75) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_390,plain,
transfinite_sequence('#skF_18'),
inference(resolution,[status(thm)],[c_184,c_382]) ).
tff(c_28,plain,
! [B_10,A_9] :
( subset(relation_rng(B_10),A_9)
| ~ transfinite_sequence_of(B_10,A_9)
| ~ transfinite_sequence(B_10)
| ~ function(B_10)
| ~ relation(B_10) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_182,plain,
ordinal('#skF_19'),
inference(cnfTransformation,[status(thm)],[f_293]) ).
tff(c_1162,plain,
! [A_172,B_173] :
( ( tseq_dom_restriction(A_172,B_173) = relation_dom_restriction(A_172,B_173) )
| ~ ordinal(B_173)
| ~ transfinite_sequence(A_172)
| ~ function(A_172)
| ~ relation(A_172) ),
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_1255,plain,
! [A_176] :
( ( tseq_dom_restriction(A_176,'#skF_19') = relation_dom_restriction(A_176,'#skF_19') )
| ~ transfinite_sequence(A_176)
| ~ function(A_176)
| ~ relation(A_176) ),
inference(resolution,[status(thm)],[c_182,c_1162]) ).
tff(c_1261,plain,
( ( tseq_dom_restriction('#skF_18','#skF_19') = relation_dom_restriction('#skF_18','#skF_19') )
| ~ function('#skF_18')
| ~ relation('#skF_18') ),
inference(resolution,[status(thm)],[c_390,c_1255]) ).
tff(c_1270,plain,
tseq_dom_restriction('#skF_18','#skF_19') = relation_dom_restriction('#skF_18','#skF_19'),
inference(demodulation,[status(thm),theory(equality)],[c_381,c_364,c_1261]) ).
tff(c_1014,plain,
! [A_165,B_166] :
( transfinite_sequence_of(tseq_dom_restriction(A_165,B_166),relation_rng(A_165))
| ~ ordinal(B_166)
| ~ transfinite_sequence(A_165)
| ~ function(A_165)
| ~ relation(A_165) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_178,plain,
! [C_41,B_39,A_38] :
( transfinite_sequence_of(C_41,B_39)
| ~ transfinite_sequence_of(C_41,A_38)
| ~ subset(A_38,B_39) ),
inference(cnfTransformation,[status(thm)],[f_285]) ).
tff(c_2723,plain,
! [A_219,B_220,B_221] :
( transfinite_sequence_of(tseq_dom_restriction(A_219,B_220),B_221)
| ~ subset(relation_rng(A_219),B_221)
| ~ ordinal(B_220)
| ~ transfinite_sequence(A_219)
| ~ function(A_219)
| ~ relation(A_219) ),
inference(resolution,[status(thm)],[c_1014,c_178]) ).
tff(c_2788,plain,
! [B_221] :
( transfinite_sequence_of(relation_dom_restriction('#skF_18','#skF_19'),B_221)
| ~ subset(relation_rng('#skF_18'),B_221)
| ~ ordinal('#skF_19')
| ~ transfinite_sequence('#skF_18')
| ~ function('#skF_18')
| ~ relation('#skF_18') ),
inference(superposition,[status(thm),theory(equality)],[c_1270,c_2723]) ).
tff(c_3067,plain,
! [B_236] :
( transfinite_sequence_of(relation_dom_restriction('#skF_18','#skF_19'),B_236)
| ~ subset(relation_rng('#skF_18'),B_236) ),
inference(demodulation,[status(thm),theory(equality)],[c_381,c_364,c_390,c_182,c_2788]) ).
tff(c_180,plain,
~ transfinite_sequence_of(tseq_dom_restriction('#skF_18','#skF_19'),'#skF_17'),
inference(cnfTransformation,[status(thm)],[f_293]) ).
tff(c_1274,plain,
~ transfinite_sequence_of(relation_dom_restriction('#skF_18','#skF_19'),'#skF_17'),
inference(demodulation,[status(thm),theory(equality)],[c_1270,c_180]) ).
tff(c_3082,plain,
~ subset(relation_rng('#skF_18'),'#skF_17'),
inference(resolution,[status(thm)],[c_3067,c_1274]) ).
tff(c_3092,plain,
( ~ transfinite_sequence_of('#skF_18','#skF_17')
| ~ transfinite_sequence('#skF_18')
| ~ function('#skF_18')
| ~ relation('#skF_18') ),
inference(resolution,[status(thm)],[c_28,c_3082]) ).
tff(c_3096,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_381,c_364,c_390,c_184,c_3092]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % 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 : n014.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 14:53:18 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.50/2.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.50/2.73
% 7.50/2.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.50/2.76
% 7.50/2.76 Inference rules
% 7.50/2.76 ----------------------
% 7.50/2.76 #Ref : 0
% 7.50/2.76 #Sup : 628
% 7.50/2.76 #Fact : 0
% 7.50/2.76 #Define : 0
% 7.50/2.76 #Split : 10
% 7.50/2.76 #Chain : 0
% 7.50/2.76 #Close : 0
% 7.50/2.76
% 7.50/2.76 Ordering : KBO
% 7.50/2.76
% 7.50/2.76 Simplification rules
% 7.50/2.76 ----------------------
% 7.50/2.76 #Subsume : 94
% 7.50/2.76 #Demod : 959
% 7.50/2.76 #Tautology : 191
% 7.50/2.76 #SimpNegUnit : 9
% 7.50/2.76 #BackRed : 27
% 7.50/2.76
% 7.50/2.76 #Partial instantiations: 0
% 7.50/2.76 #Strategies tried : 1
% 7.50/2.76
% 7.50/2.76 Timing (in seconds)
% 7.50/2.76 ----------------------
% 7.50/2.76 Preprocessing : 0.59
% 7.50/2.76 Parsing : 0.31
% 7.50/2.76 CNF conversion : 0.05
% 7.50/2.76 Main loop : 1.12
% 7.50/2.77 Inferencing : 0.37
% 7.50/2.77 Reduction : 0.41
% 7.50/2.77 Demodulation : 0.29
% 7.50/2.77 BG Simplification : 0.05
% 7.50/2.77 Subsumption : 0.20
% 7.50/2.77 Abstraction : 0.04
% 7.50/2.77 MUC search : 0.00
% 7.50/2.77 Cooper : 0.00
% 7.50/2.77 Total : 1.76
% 7.50/2.77 Index Insertion : 0.00
% 7.50/2.77 Index Deletion : 0.00
% 7.50/2.77 Index Matching : 0.00
% 7.50/2.77 BG Taut test : 0.00
%------------------------------------------------------------------------------