TSTP Solution File: NUM410+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM410+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 : n027.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 4.91s 2.28s
% Output : CNFRefutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 40
% Syntax : Number of formulae : 52 ( 8 unt; 36 typ; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 41 ( 17 ~; 14 |; 4 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 20 >; 4 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 16 con; 0-1 aty)
% Number of variables : 11 (; 11 !; 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 > #nlpp > relation_rng > relation_dom > powerset > empty_set > #skF_2 > #skF_17 > #skF_11 > #skF_15 > #skF_1 > #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_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_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('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_8',type,
'#skF_8': $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_269,negated_conjecture,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( ordinal(relation_dom(A))
=> transfinite_sequence_of(A,relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_ordinal1) ).
tff(f_79,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).
tff(f_246,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_89,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(c_180,plain,
relation('#skF_17'),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_178,plain,
function('#skF_17'),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_176,plain,
ordinal(relation_dom('#skF_17')),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_737,plain,
! [A_96] :
( transfinite_sequence(A_96)
| ~ ordinal(relation_dom(A_96))
| ~ function(A_96)
| ~ relation(A_96) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_755,plain,
( transfinite_sequence('#skF_17')
| ~ function('#skF_17')
| ~ relation('#skF_17') ),
inference(resolution,[status(thm)],[c_176,c_737]) ).
tff(c_766,plain,
transfinite_sequence('#skF_17'),
inference(demodulation,[status(thm),theory(equality)],[c_180,c_178,c_755]) ).
tff(c_164,plain,
! [A_23] : subset(A_23,A_23),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_883,plain,
! [B_122,A_123] :
( transfinite_sequence_of(B_122,A_123)
| ~ subset(relation_rng(B_122),A_123)
| ~ transfinite_sequence(B_122)
| ~ function(B_122)
| ~ relation(B_122) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_1001,plain,
! [B_137] :
( transfinite_sequence_of(B_137,relation_rng(B_137))
| ~ transfinite_sequence(B_137)
| ~ function(B_137)
| ~ relation(B_137) ),
inference(resolution,[status(thm)],[c_164,c_883]) ).
tff(c_174,plain,
~ transfinite_sequence_of('#skF_17',relation_rng('#skF_17')),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_1017,plain,
( ~ transfinite_sequence('#skF_17')
| ~ function('#skF_17')
| ~ relation('#skF_17') ),
inference(resolution,[status(thm)],[c_1001,c_174]) ).
tff(c_1036,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_180,c_178,c_766,c_1017]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM410+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 : n027.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 14:57:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.91/2.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.91/2.29
% 4.91/2.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.91/2.31
% 4.91/2.31 Inference rules
% 4.91/2.31 ----------------------
% 4.91/2.31 #Ref : 0
% 4.91/2.31 #Sup : 181
% 4.91/2.31 #Fact : 0
% 4.91/2.31 #Define : 0
% 4.91/2.31 #Split : 7
% 4.91/2.31 #Chain : 0
% 4.91/2.31 #Close : 0
% 4.91/2.31
% 4.91/2.31 Ordering : KBO
% 4.91/2.31
% 4.91/2.31 Simplification rules
% 4.91/2.31 ----------------------
% 4.91/2.31 #Subsume : 16
% 4.91/2.31 #Demod : 164
% 4.91/2.31 #Tautology : 111
% 4.91/2.31 #SimpNegUnit : 0
% 4.91/2.31 #BackRed : 23
% 4.91/2.31
% 4.91/2.31 #Partial instantiations: 0
% 4.91/2.31 #Strategies tried : 1
% 4.91/2.31
% 4.91/2.31 Timing (in seconds)
% 4.91/2.31 ----------------------
% 4.91/2.32 Preprocessing : 0.59
% 4.91/2.32 Parsing : 0.32
% 4.91/2.32 CNF conversion : 0.05
% 4.91/2.32 Main loop : 0.61
% 4.91/2.32 Inferencing : 0.22
% 4.91/2.32 Reduction : 0.19
% 4.91/2.32 Demodulation : 0.14
% 4.91/2.32 BG Simplification : 0.04
% 4.91/2.32 Subsumption : 0.12
% 4.91/2.32 Abstraction : 0.02
% 4.91/2.32 MUC search : 0.00
% 4.91/2.32 Cooper : 0.00
% 4.91/2.32 Total : 1.25
% 4.91/2.32 Index Insertion : 0.00
% 4.91/2.32 Index Deletion : 0.00
% 4.91/2.32 Index Matching : 0.00
% 4.91/2.32 BG Taut test : 0.00
%------------------------------------------------------------------------------