%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM393+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 : n019.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 07:55:49 PM UTC 2025
% Result : Theorem 4.45s 2.11s
% Output : CNFRefutation 4.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 51 ( 21 ~; 22 |; 2 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 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 : 15 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 14 con; 0-1 aty)
% Number of variables : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > ordinal_subset > inclusion_comparable > in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_11 > #skF_1 > #skF_7 > #skF_10 > #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_11',type,
'#skF_11': $i ).
tff(relation_non_empty,type,
relation_non_empty: $i > $o ).
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(inclusion_comparable,type,
inclusion_comparable: ( $i * $i ) > $o ).
tff('#skF_10',type,
'#skF_10': $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_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('#skF_12',type,
'#skF_12': $i ).
tff(f_175,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> inclusion_comparable(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_ordinal1) ).
tff(f_71,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(f_149,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_77,axiom,
! [A,B] :
( inclusion_comparable(A,B)
<=> ( subset(A,B)
| subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_xboole_0) ).
tff(c_108,plain,
ordinal('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_110,plain,
ordinal('#skF_13'),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_20,plain,
! [B_9,A_8] :
( ordinal_subset(B_9,A_8)
| ordinal_subset(A_8,B_9)
| ~ ordinal(B_9)
| ~ ordinal(A_8) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_442,plain,
! [A_97,B_98] :
( subset(A_97,B_98)
| ~ ordinal_subset(A_97,B_98)
| ~ ordinal(B_98)
| ~ ordinal(A_97) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_26,plain,
! [A_10,B_11] :
( ~ subset(A_10,B_11)
| inclusion_comparable(A_10,B_11) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_465,plain,
! [A_104,B_105] :
( inclusion_comparable(A_104,B_105)
| ~ ordinal_subset(A_104,B_105)
| ~ ordinal(B_105)
| ~ ordinal(A_104) ),
inference(resolution,[status(thm)],[c_442,c_26]) ).
tff(c_493,plain,
! [B_108,A_109] :
( inclusion_comparable(B_108,A_109)
| ordinal_subset(A_109,B_108)
| ~ ordinal(B_108)
| ~ ordinal(A_109) ),
inference(resolution,[status(thm)],[c_20,c_465]) ).
tff(c_24,plain,
! [B_11,A_10] :
( ~ subset(B_11,A_10)
| inclusion_comparable(A_10,B_11) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_454,plain,
! [B_98,A_97] :
( inclusion_comparable(B_98,A_97)
| ~ ordinal_subset(A_97,B_98)
| ~ ordinal(B_98)
| ~ ordinal(A_97) ),
inference(resolution,[status(thm)],[c_442,c_24]) ).
tff(c_502,plain,
! [B_110,A_111] :
( inclusion_comparable(B_110,A_111)
| ~ ordinal(B_110)
| ~ ordinal(A_111) ),
inference(resolution,[status(thm)],[c_493,c_454]) ).
tff(c_106,plain,
~ inclusion_comparable('#skF_13','#skF_14'),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_507,plain,
( ~ ordinal('#skF_13')
| ~ ordinal('#skF_14') ),
inference(resolution,[status(thm)],[c_502,c_106]) ).
tff(c_512,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_108,c_110,c_507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM393+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.13 % 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
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 12:07:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.45/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.45/2.12
% 4.45/2.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------