%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU275+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/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 : n014.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 08:53:28 PM UTC 2025
% Result : Theorem 2.92s 1.74s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 45 ( 22 ~; 14 |; 4 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 11 ( 10 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 15 ( 15 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ well_ordering > well_founded_relation > transitive > relation > reflexive > ordinal > epsilon_transitive > epsilon_connected > connected > antisymmetric > #nlpp > inclusion_relation > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(well_ordering,type,
well_ordering: $i > $o ).
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(antisymmetric,type,
antisymmetric: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff(connected,type,
connected: $i > $o ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(inclusion_relation,type,
inclusion_relation: $i > $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff(well_founded_relation,type,
well_founded_relation: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(transitive,type,
transitive: $i > $o ).
tff(reflexive,type,
reflexive: $i > $o ).
tff(f_79,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_wellord2) ).
tff(f_74,axiom,
! [A] :
( ordinal(A)
=> well_founded_relation(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_wellord2) ).
tff(f_68,axiom,
! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_wellord2) ).
tff(f_54,axiom,
! [A] : relation(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
tff(f_62,axiom,
! [A] : reflexive(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
tff(f_64,axiom,
! [A] : transitive(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_wellord2) ).
tff(f_70,axiom,
! [A] : antisymmetric(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord2) ).
tff(f_52,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( reflexive(A)
& transitive(A)
& antisymmetric(A)
& connected(A)
& well_founded_relation(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
tff(c_40,plain,
ordinal('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_36,plain,
! [A_9] :
( well_founded_relation(inclusion_relation(A_9))
| ~ ordinal(A_9) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_32,plain,
! [A_7] :
( connected(inclusion_relation(A_7))
| ~ ordinal(A_7) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_20,plain,
! [A_4] : relation(inclusion_relation(A_4)),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_28,plain,
! [A_5] : reflexive(inclusion_relation(A_5)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_30,plain,
! [A_6] : transitive(inclusion_relation(A_6)),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_34,plain,
! [A_8] : antisymmetric(inclusion_relation(A_8)),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_81,plain,
! [A_24] :
( well_ordering(A_24)
| ~ well_founded_relation(A_24)
| ~ connected(A_24)
| ~ antisymmetric(A_24)
| ~ transitive(A_24)
| ~ reflexive(A_24)
| ~ relation(A_24) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_38,plain,
~ well_ordering(inclusion_relation('#skF_2')),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_99,plain,
( ~ well_founded_relation(inclusion_relation('#skF_2'))
| ~ connected(inclusion_relation('#skF_2'))
| ~ antisymmetric(inclusion_relation('#skF_2'))
| ~ transitive(inclusion_relation('#skF_2'))
| ~ reflexive(inclusion_relation('#skF_2'))
| ~ relation(inclusion_relation('#skF_2')) ),
inference(resolution,[status(thm)],[c_81,c_38]) ).
tff(c_107,plain,
( ~ well_founded_relation(inclusion_relation('#skF_2'))
| ~ connected(inclusion_relation('#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_28,c_30,c_34,c_99]) ).
tff(c_108,plain,
~ connected(inclusion_relation('#skF_2')),
inference(splitLeft,[status(thm)],[c_107]) ).
tff(c_111,plain,
~ ordinal('#skF_2'),
inference(resolution,[status(thm)],[c_32,c_108]) ).
tff(c_115,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_111]) ).
tff(c_116,plain,
~ well_founded_relation(inclusion_relation('#skF_2')),
inference(splitRight,[status(thm)],[c_107]) ).
tff(c_120,plain,
~ ordinal('#skF_2'),
inference(resolution,[status(thm)],[c_36,c_116]) ).
tff(c_124,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU275+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % 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 : n014.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 22:37:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.92/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.92/1.75
% 2.92/1.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------