%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU268+1 : TPTP v9.0.0. Released v3.3.0.
% 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 : n020.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 08:53:27 PM UTC 2025
% Result : Theorem 5.53s 2.26s
% Output : CNFRefutation 5.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 4 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 22 |; 2 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 11 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > is_reflexive_in > in > element > relation_empty_yielding > relation > reflexive > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > unordered_pair > set_union2 > ordered_pair > #nlpp > singleton > relation_rng > relation_field > relation_dom > powerset > inclusion_relation > empty_set > #skF_4 > #skF_11 > #skF_7 > #skF_3 > #skF_10 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_9 > #skF_8 > #skF_2 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(relation_field,type,
relation_field: $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(is_reflexive_in,type,
is_reflexive_in: ( $i * $i ) > $o ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(inclusion_relation,type,
inclusion_relation: $i > $i ).
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_3',type,
'#skF_3': ( $i * $i ) > $i ).
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(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_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(reflexive,type,
reflexive: $i > $o ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_111,axiom,
! [A] : relation(inclusion_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
tff(f_81,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
tff(f_205,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_96,axiom,
! [A,B] :
( relation(B)
=> ( ( B = inclusion_relation(A) )
<=> ( ( relation_field(B) = A )
& ! [C,D] :
( ( in(C,A)
& in(D,A) )
=> ( in(ordered_pair(C,D),B)
<=> subset(C,D) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord2) ).
tff(f_108,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
tff(f_220,negated_conjecture,
~ ! [A] : reflexive(inclusion_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
tff(c_64,plain,
! [A_34] : relation(inclusion_relation(A_34)),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_32,plain,
! [A_12,B_18] :
( in('#skF_1'(A_12,B_18),B_18)
| is_reflexive_in(A_12,B_18)
| ~ relation(A_12) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_164,plain,
! [A_45] : subset(A_45,A_45),
inference(cnfTransformation,[status(thm)],[f_205]) ).
tff(c_48,plain,
! [C_28,D_29,A_22] :
( in(ordered_pair(C_28,D_29),inclusion_relation(A_22))
| ~ subset(C_28,D_29)
| ~ in(D_29,A_22)
| ~ in(C_28,A_22)
| ~ relation(inclusion_relation(A_22)) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_1361,plain,
! [C_176,D_177,A_178] :
( in(ordered_pair(C_176,D_177),inclusion_relation(A_178))
| ~ subset(C_176,D_177)
| ~ in(D_177,A_178)
| ~ in(C_176,A_178) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_48]) ).
tff(c_30,plain,
! [A_12,B_18] :
( ~ in(ordered_pair('#skF_1'(A_12,B_18),'#skF_1'(A_12,B_18)),A_12)
| is_reflexive_in(A_12,B_18)
| ~ relation(A_12) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_1369,plain,
! [A_178,B_18] :
( is_reflexive_in(inclusion_relation(A_178),B_18)
| ~ relation(inclusion_relation(A_178))
| ~ subset('#skF_1'(inclusion_relation(A_178),B_18),'#skF_1'(inclusion_relation(A_178),B_18))
| ~ in('#skF_1'(inclusion_relation(A_178),B_18),A_178) ),
inference(resolution,[status(thm)],[c_1361,c_30]) ).
tff(c_1402,plain,
! [A_179,B_180] :
( is_reflexive_in(inclusion_relation(A_179),B_180)
| ~ in('#skF_1'(inclusion_relation(A_179),B_180),A_179) ),
inference(demodulation,[status(thm),theory(equality)],[c_164,c_64,c_1369]) ).
tff(c_1406,plain,
! [B_18] :
( is_reflexive_in(inclusion_relation(B_18),B_18)
| ~ relation(inclusion_relation(B_18)) ),
inference(resolution,[status(thm)],[c_32,c_1402]) ).
tff(c_1413,plain,
! [B_18] : is_reflexive_in(inclusion_relation(B_18),B_18),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_1406]) ).
tff(c_46,plain,
! [A_22] :
( ( relation_field(inclusion_relation(A_22)) = A_22 )
| ~ relation(inclusion_relation(A_22)) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_193,plain,
! [A_22] : ( relation_field(inclusion_relation(A_22)) = A_22 ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_46]) ).
tff(c_607,plain,
! [A_107] :
( reflexive(A_107)
| ~ is_reflexive_in(A_107,relation_field(A_107))
| ~ relation(A_107) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_610,plain,
! [A_22] :
( reflexive(inclusion_relation(A_22))
| ~ is_reflexive_in(inclusion_relation(A_22),A_22)
| ~ relation(inclusion_relation(A_22)) ),
inference(superposition,[status(thm),theory(equality)],[c_193,c_607]) ).
tff(c_612,plain,
! [A_22] :
( reflexive(inclusion_relation(A_22))
| ~ is_reflexive_in(inclusion_relation(A_22),A_22) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_610]) ).
tff(c_1417,plain,
! [A_22] : reflexive(inclusion_relation(A_22)),
inference(demodulation,[status(thm),theory(equality)],[c_1413,c_612]) ).
tff(c_172,plain,
~ reflexive(inclusion_relation('#skF_14')),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_1423,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1417,c_172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU268+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n020.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 22:35:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 5.53/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.53/2.27
% 5.53/2.27 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------