%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU244+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 : 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 08:53:22 PM UTC 2025
% Result : Theorem 3.71s 1.91s
% Output : CNFRefutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 89 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 231 ( 113 ~; 94 |; 8 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 14 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ well_orders > is_well_founded_in > is_transitive_in > is_reflexive_in > is_connected_in > is_antisymmetric_in > well_ordering > well_founded_relation > transitive > relation > reflexive > connected > antisymmetric > set_union2 > #nlpp > relation_rng > relation_field > relation_dom > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(well_ordering,type,
well_ordering: $i > $o ).
tff(antisymmetric,type,
antisymmetric: $i > $o ).
tff(relation_field,type,
relation_field: $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(connected,type,
connected: $i > $o ).
tff(is_reflexive_in,type,
is_reflexive_in: ( $i * $i ) > $o ).
tff(well_founded_relation,type,
well_founded_relation: $i > $o ).
tff(is_well_founded_in,type,
is_well_founded_in: ( $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(well_orders,type,
well_orders: ( $i * $i ) > $o ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff(transitive,type,
transitive: $i > $o ).
tff(is_connected_in,type,
is_connected_in: ( $i * $i ) > $o ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(reflexive,type,
reflexive: $i > $o ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff(is_transitive_in,type,
is_transitive_in: ( $i * $i ) > $o ).
tff(is_antisymmetric_in,type,
is_antisymmetric_in: ( $i * $i ) > $o ).
tff(f_101,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
tff(f_60,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( reflexive(A)
& transitive(A)
& antisymmetric(A)
& connected(A)
& well_founded_relation(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
tff(f_34,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
tff(f_40,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
tff(f_46,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
tff(f_94,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
tff(f_85,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_75,axiom,
! [A] :
( relation(A)
=> ! [B] :
( well_orders(A,B)
<=> ( is_reflexive_in(A,B)
& is_transitive_in(A,B)
& is_antisymmetric_in(A,B)
& is_connected_in(A,B)
& is_well_founded_in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).
tff(c_60,plain,
relation('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_62,plain,
( ~ well_ordering('#skF_1')
| ~ well_orders('#skF_1',relation_field('#skF_1')) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_78,plain,
~ well_orders('#skF_1',relation_field('#skF_1')),
inference(splitLeft,[status(thm)],[c_62]) ).
tff(c_68,plain,
( well_orders('#skF_1',relation_field('#skF_1'))
| well_ordering('#skF_1') ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_115,plain,
well_ordering('#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_78,c_68]) ).
tff(c_22,plain,
! [A_6] :
( antisymmetric(A_6)
| ~ well_ordering(A_6)
| ~ relation(A_6) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_121,plain,
( antisymmetric('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_115,c_22]) ).
tff(c_130,plain,
antisymmetric('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_121]) ).
tff(c_6,plain,
! [A_3] :
( is_antisymmetric_in(A_3,relation_field(A_3))
| ~ antisymmetric(A_3)
| ~ relation(A_3) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_20,plain,
! [A_6] :
( connected(A_6)
| ~ well_ordering(A_6)
| ~ relation(A_6) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_118,plain,
( connected('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_115,c_20]) ).
tff(c_127,plain,
connected('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_118]) ).
tff(c_10,plain,
! [A_4] :
( is_connected_in(A_4,relation_field(A_4))
| ~ connected(A_4)
| ~ relation(A_4) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_24,plain,
! [A_6] :
( transitive(A_6)
| ~ well_ordering(A_6)
| ~ relation(A_6) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_124,plain,
( transitive('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_115,c_24]) ).
tff(c_133,plain,
transitive('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_124]) ).
tff(c_14,plain,
! [A_5] :
( is_transitive_in(A_5,relation_field(A_5))
| ~ transitive(A_5)
| ~ relation(A_5) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_141,plain,
! [A_22] :
( well_founded_relation(A_22)
| ~ well_ordering(A_22)
| ~ relation(A_22) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_144,plain,
( well_founded_relation('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_115,c_141]) ).
tff(c_147,plain,
well_founded_relation('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_144]) ).
tff(c_58,plain,
! [A_14] :
( is_well_founded_in(A_14,relation_field(A_14))
| ~ well_founded_relation(A_14)
| ~ relation(A_14) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_134,plain,
! [A_21] :
( reflexive(A_21)
| ~ well_ordering(A_21)
| ~ relation(A_21) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_137,plain,
( reflexive('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_115,c_134]) ).
tff(c_140,plain,
reflexive('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_137]) ).
tff(c_44,plain,
! [A_11] :
( is_reflexive_in(A_11,relation_field(A_11))
| ~ reflexive(A_11)
| ~ relation(A_11) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_213,plain,
! [A_45,B_46] :
( well_orders(A_45,B_46)
| ~ is_well_founded_in(A_45,B_46)
| ~ is_connected_in(A_45,B_46)
| ~ is_antisymmetric_in(A_45,B_46)
| ~ is_transitive_in(A_45,B_46)
| ~ is_reflexive_in(A_45,B_46)
| ~ relation(A_45) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_231,plain,
( ~ is_well_founded_in('#skF_1',relation_field('#skF_1'))
| ~ is_connected_in('#skF_1',relation_field('#skF_1'))
| ~ is_antisymmetric_in('#skF_1',relation_field('#skF_1'))
| ~ is_transitive_in('#skF_1',relation_field('#skF_1'))
| ~ is_reflexive_in('#skF_1',relation_field('#skF_1'))
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_213,c_78]) ).
tff(c_239,plain,
( ~ is_well_founded_in('#skF_1',relation_field('#skF_1'))
| ~ is_connected_in('#skF_1',relation_field('#skF_1'))
| ~ is_antisymmetric_in('#skF_1',relation_field('#skF_1'))
| ~ is_transitive_in('#skF_1',relation_field('#skF_1'))
| ~ is_reflexive_in('#skF_1',relation_field('#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_231]) ).
tff(c_240,plain,
~ is_reflexive_in('#skF_1',relation_field('#skF_1')),
inference(splitLeft,[status(thm)],[c_239]) ).
tff(c_243,plain,
( ~ reflexive('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_44,c_240]) ).
tff(c_247,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_140,c_243]) ).
tff(c_248,plain,
( ~ is_transitive_in('#skF_1',relation_field('#skF_1'))
| ~ is_antisymmetric_in('#skF_1',relation_field('#skF_1'))
| ~ is_connected_in('#skF_1',relation_field('#skF_1'))
| ~ is_well_founded_in('#skF_1',relation_field('#skF_1')) ),
inference(splitRight,[status(thm)],[c_239]) ).
tff(c_256,plain,
~ is_well_founded_in('#skF_1',relation_field('#skF_1')),
inference(splitLeft,[status(thm)],[c_248]) ).
tff(c_259,plain,
( ~ well_founded_relation('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_58,c_256]) ).
tff(c_263,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_147,c_259]) ).
tff(c_264,plain,
( ~ is_connected_in('#skF_1',relation_field('#skF_1'))
| ~ is_antisymmetric_in('#skF_1',relation_field('#skF_1'))
| ~ is_transitive_in('#skF_1',relation_field('#skF_1')) ),
inference(splitRight,[status(thm)],[c_248]) ).
tff(c_272,plain,
~ is_transitive_in('#skF_1',relation_field('#skF_1')),
inference(splitLeft,[status(thm)],[c_264]) ).
tff(c_275,plain,
( ~ transitive('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_14,c_272]) ).
tff(c_279,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_133,c_275]) ).
tff(c_280,plain,
( ~ is_antisymmetric_in('#skF_1',relation_field('#skF_1'))
| ~ is_connected_in('#skF_1',relation_field('#skF_1')) ),
inference(splitRight,[status(thm)],[c_264]) ).
tff(c_288,plain,
~ is_connected_in('#skF_1',relation_field('#skF_1')),
inference(splitLeft,[status(thm)],[c_280]) ).
tff(c_291,plain,
( ~ connected('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_10,c_288]) ).
tff(c_295,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_127,c_291]) ).
tff(c_296,plain,
~ is_antisymmetric_in('#skF_1',relation_field('#skF_1')),
inference(splitRight,[status(thm)],[c_280]) ).
tff(c_300,plain,
( ~ antisymmetric('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_6,c_296]) ).
tff(c_304,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_130,c_300]) ).
tff(c_306,plain,
well_orders('#skF_1',relation_field('#skF_1')),
inference(splitRight,[status(thm)],[c_62]) ).
tff(c_349,plain,
! [A_56,B_57] :
( is_reflexive_in(A_56,B_57)
| ~ well_orders(A_56,B_57)
| ~ relation(A_56) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_352,plain,
( is_reflexive_in('#skF_1',relation_field('#skF_1'))
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_306,c_349]) ).
tff(c_355,plain,
is_reflexive_in('#skF_1',relation_field('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_352]) ).
tff(c_431,plain,
! [A_73] :
( reflexive(A_73)
| ~ is_reflexive_in(A_73,relation_field(A_73))
| ~ relation(A_73) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_434,plain,
( reflexive('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_355,c_431]) ).
tff(c_440,plain,
reflexive('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_434]) ).
tff(c_418,plain,
! [A_71,B_72] :
( is_transitive_in(A_71,B_72)
| ~ well_orders(A_71,B_72)
| ~ relation(A_71) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_421,plain,
( is_transitive_in('#skF_1',relation_field('#skF_1'))
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_306,c_418]) ).
tff(c_424,plain,
is_transitive_in('#skF_1',relation_field('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_421]) ).
tff(c_12,plain,
! [A_5] :
( transitive(A_5)
| ~ is_transitive_in(A_5,relation_field(A_5))
| ~ relation(A_5) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_427,plain,
( transitive('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_424,c_12]) ).
tff(c_430,plain,
transitive('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_427]) ).
tff(c_388,plain,
! [A_64,B_65] :
( is_antisymmetric_in(A_64,B_65)
| ~ well_orders(A_64,B_65)
| ~ relation(A_64) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_391,plain,
( is_antisymmetric_in('#skF_1',relation_field('#skF_1'))
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_306,c_388]) ).
tff(c_394,plain,
is_antisymmetric_in('#skF_1',relation_field('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_391]) ).
tff(c_395,plain,
! [A_66] :
( antisymmetric(A_66)
| ~ is_antisymmetric_in(A_66,relation_field(A_66))
| ~ relation(A_66) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_398,plain,
( antisymmetric('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_394,c_395]) ).
tff(c_401,plain,
antisymmetric('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_398]) ).
tff(c_356,plain,
! [A_58,B_59] :
( is_connected_in(A_58,B_59)
| ~ well_orders(A_58,B_59)
| ~ relation(A_58) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_359,plain,
( is_connected_in('#skF_1',relation_field('#skF_1'))
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_306,c_356]) ).
tff(c_362,plain,
is_connected_in('#skF_1',relation_field('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_359]) ).
tff(c_377,plain,
! [A_63] :
( connected(A_63)
| ~ is_connected_in(A_63,relation_field(A_63))
| ~ relation(A_63) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_383,plain,
( connected('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_362,c_377]) ).
tff(c_387,plain,
connected('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_383]) ).
tff(c_363,plain,
! [A_60,B_61] :
( is_well_founded_in(A_60,B_61)
| ~ well_orders(A_60,B_61)
| ~ relation(A_60) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_366,plain,
( is_well_founded_in('#skF_1',relation_field('#skF_1'))
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_306,c_363]) ).
tff(c_369,plain,
is_well_founded_in('#skF_1',relation_field('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_366]) ).
tff(c_56,plain,
! [A_14] :
( well_founded_relation(A_14)
| ~ is_well_founded_in(A_14,relation_field(A_14))
| ~ relation(A_14) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_372,plain,
( well_founded_relation('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_369,c_56]) ).
tff(c_375,plain,
well_founded_relation('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_372]) ).
tff(c_451,plain,
! [A_75] :
( well_ordering(A_75)
| ~ well_founded_relation(A_75)
| ~ connected(A_75)
| ~ antisymmetric(A_75)
| ~ transitive(A_75)
| ~ reflexive(A_75)
| ~ relation(A_75) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_305,plain,
~ well_ordering('#skF_1'),
inference(splitRight,[status(thm)],[c_62]) ).
tff(c_469,plain,
( ~ well_founded_relation('#skF_1')
| ~ connected('#skF_1')
| ~ antisymmetric('#skF_1')
| ~ transitive('#skF_1')
| ~ reflexive('#skF_1')
| ~ relation('#skF_1') ),
inference(resolution,[status(thm)],[c_451,c_305]) ).
tff(c_478,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_440,c_430,c_401,c_387,c_375,c_469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU244+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.13 % 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
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 22:29:32 EDT 2025
% 0.14/0.34 % CPUTime :
% 3.71/1.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.98/1.92
% 3.98/1.92 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------