%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM414+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 : n021.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 07:55:51 PM UTC 2025
% Result : Theorem 6.41s 2.64s
% Output : CNFRefutation 6.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 64 ( 30 ~; 23 |; 5 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 17 con; 0-1 aty)
% Number of variables : 16 ( 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > ordinal_subset > in > element > transfinite_sequence > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_17 > #skF_11 > #skF_15 > #skF_1 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(relation,type,
relation: $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(proper_subset,type,
proper_subset: ( $i * $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_2',type,
'#skF_2': $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(ordinal_subset,type,
ordinal_subset: ( $i * $i ) > $o ).
tff(transfinite_sequence,type,
transfinite_sequence: $i > $o ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_254,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ proper_subset(A,B)
& ( A != B )
& ~ proper_subset(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_ordinal1) ).
tff(f_210,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
tff(f_91,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( subset(A,B)
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
tff(f_84,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
| ordinal_subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
tff(c_166,plain,
'#skF_17' != '#skF_16',
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_172,plain,
ordinal('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_170,plain,
ordinal('#skF_17'),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_563,plain,
! [A_104,B_105] :
( subset(A_104,B_105)
| ~ ordinal_subset(A_104,B_105)
| ~ ordinal(B_105)
| ~ ordinal(A_104) ),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_30,plain,
! [A_13,B_14] :
( proper_subset(A_13,B_14)
| ( B_14 = A_13 )
| ~ subset(A_13,B_14) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_605,plain,
! [A_117,B_118] :
( proper_subset(A_117,B_118)
| ( B_118 = A_117 )
| ~ ordinal_subset(A_117,B_118)
| ~ ordinal(B_118)
| ~ ordinal(A_117) ),
inference(resolution,[status(thm)],[c_563,c_30]) ).
tff(c_168,plain,
~ proper_subset('#skF_16','#skF_17'),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_621,plain,
( ( '#skF_17' = '#skF_16' )
| ~ ordinal_subset('#skF_16','#skF_17')
| ~ ordinal('#skF_17')
| ~ ordinal('#skF_16') ),
inference(resolution,[status(thm)],[c_605,c_168]) ).
tff(c_632,plain,
( ( '#skF_17' = '#skF_16' )
| ~ ordinal_subset('#skF_16','#skF_17') ),
inference(demodulation,[status(thm),theory(equality)],[c_172,c_170,c_621]) ).
tff(c_633,plain,
~ ordinal_subset('#skF_16','#skF_17'),
inference(negUnitSimplification,[status(thm)],[c_166,c_632]) ).
tff(c_28,plain,
! [B_12,A_11] :
( ordinal_subset(B_12,A_11)
| ordinal_subset(A_11,B_12)
| ~ ordinal(B_12)
| ~ ordinal(A_11) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_164,plain,
~ proper_subset('#skF_17','#skF_16'),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_624,plain,
( ( '#skF_17' = '#skF_16' )
| ~ ordinal_subset('#skF_17','#skF_16')
| ~ ordinal('#skF_16')
| ~ ordinal('#skF_17') ),
inference(resolution,[status(thm)],[c_605,c_164]) ).
tff(c_636,plain,
( ( '#skF_17' = '#skF_16' )
| ~ ordinal_subset('#skF_17','#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_170,c_172,c_624]) ).
tff(c_637,plain,
~ ordinal_subset('#skF_17','#skF_16'),
inference(negUnitSimplification,[status(thm)],[c_166,c_636]) ).
tff(c_642,plain,
( ordinal_subset('#skF_16','#skF_17')
| ~ ordinal('#skF_17')
| ~ ordinal('#skF_16') ),
inference(resolution,[status(thm)],[c_28,c_637]) ).
tff(c_648,plain,
ordinal_subset('#skF_16','#skF_17'),
inference(demodulation,[status(thm),theory(equality)],[c_172,c_170,c_642]) ).
tff(c_650,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_633,c_648]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM414+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.09 % 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
% 0.09/0.28 % Computer : n021.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Tue Apr 8 12:10:28 EDT 2025
% 0.09/0.28 % CPUTime :
% 6.41/2.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.41/2.64
% 6.41/2.64 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------