%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM411+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n024.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 : Wed Apr 9 07:55:50 PM UTC 2025
% Result : Theorem 6.29s 2.47s
% Output : CNFRefutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 64 ( 28 ~; 25 |; 5 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 18 con; 0-1 aty)
% Number of variables : 26 ( 26 !; 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 > 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('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $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_252,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_ordinal1) ).
tff(f_89,axiom,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ( relation(B)
& function(B)
& transfinite_sequence(B) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
tff(f_234,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
tff(c_168,plain,
transfinite_sequence_of('#skF_19','#skF_17'),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_383,plain,
! [B_62,A_63] :
( relation(B_62)
| ~ transfinite_sequence_of(B_62,A_63) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_391,plain,
relation('#skF_19'),
inference(resolution,[status(thm)],[c_168,c_383]) ).
tff(c_326,plain,
! [B_54,A_55] :
( function(B_54)
| ~ transfinite_sequence_of(B_54,A_55) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_334,plain,
function('#skF_19'),
inference(resolution,[status(thm)],[c_168,c_326]) ).
tff(c_392,plain,
! [B_64,A_65] :
( transfinite_sequence(B_64)
| ~ transfinite_sequence_of(B_64,A_65) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_400,plain,
transfinite_sequence('#skF_19'),
inference(resolution,[status(thm)],[c_168,c_392]) ).
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_170,plain,
subset('#skF_17','#skF_18'),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_600,plain,
! [A_89,C_90,B_91] :
( subset(A_89,C_90)
| ~ subset(B_91,C_90)
| ~ subset(A_89,B_91) ),
inference(cnfTransformation,[status(thm)],[f_234]) ).
tff(c_609,plain,
! [A_89] :
( subset(A_89,'#skF_18')
| ~ subset(A_89,'#skF_17') ),
inference(resolution,[status(thm)],[c_170,c_600]) ).
tff(c_795,plain,
! [B_133,A_134] :
( transfinite_sequence_of(B_133,A_134)
| ~ subset(relation_rng(B_133),A_134)
| ~ transfinite_sequence(B_133)
| ~ function(B_133)
| ~ relation(B_133) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_994,plain,
! [B_140] :
( transfinite_sequence_of(B_140,'#skF_18')
| ~ transfinite_sequence(B_140)
| ~ function(B_140)
| ~ relation(B_140)
| ~ subset(relation_rng(B_140),'#skF_17') ),
inference(resolution,[status(thm)],[c_609,c_795]) ).
tff(c_1573,plain,
! [B_174] :
( transfinite_sequence_of(B_174,'#skF_18')
| ~ transfinite_sequence_of(B_174,'#skF_17')
| ~ transfinite_sequence(B_174)
| ~ function(B_174)
| ~ relation(B_174) ),
inference(resolution,[status(thm)],[c_28,c_994]) ).
tff(c_166,plain,
~ transfinite_sequence_of('#skF_19','#skF_18'),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_1585,plain,
( ~ transfinite_sequence_of('#skF_19','#skF_17')
| ~ transfinite_sequence('#skF_19')
| ~ function('#skF_19')
| ~ relation('#skF_19') ),
inference(resolution,[status(thm)],[c_1573,c_166]) ).
tff(c_1592,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_391,c_334,c_400,c_168,c_1585]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM411+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n024.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 : Tue Apr 8 12:09:51 EDT 2025
% 0.14/0.35 % CPUTime :
% 6.29/2.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.29/2.48
% 6.29/2.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------