%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU257+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 : n015.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 08:53:24 PM UTC 2025
% Result : Theorem 3.63s 1.95s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 142 ( 71 ~; 52 |; 4 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 33 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ well_ordering > well_founded_relation > transitive > relation > reflexive > connected > antisymmetric > set_intersection2 > relation_restriction > cartesian_product2 > #nlpp > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(well_ordering,type,
well_ordering: $i > $o ).
tff(antisymmetric,type,
antisymmetric: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff(connected,type,
connected: $i > $o ).
tff(well_founded_relation,type,
well_founded_relation: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(relation_restriction,type,
relation_restriction: ( $i * $i ) > $i ).
tff(transitive,type,
transitive: $i > $o ).
tff(reflexive,type,
reflexive: $i > $o ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(f_91,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_wellord1) ).
tff(f_42,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_78,axiom,
! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord1) ).
tff(f_72,axiom,
! [A,B] :
( relation(B)
=> ( transitive(B)
=> transitive(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
tff(f_66,axiom,
! [A,B] :
( relation(B)
=> ( connected(B)
=> connected(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_wellord1) ).
tff(f_60,axiom,
! [A,B] :
( relation(B)
=> ( reflexive(B)
=> reflexive(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_wellord1) ).
tff(f_84,axiom,
! [A,B] :
( relation(B)
=> ( well_founded_relation(B)
=> well_founded_relation(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_wellord1) ).
tff(f_51,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
tff(c_40,plain,
relation('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_38,plain,
well_ordering('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_57,plain,
! [A_23] :
( antisymmetric(A_23)
| ~ well_ordering(A_23)
| ~ relation(A_23) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_60,plain,
( antisymmetric('#skF_2')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_38,c_57]) ).
tff(c_63,plain,
antisymmetric('#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_60]) ).
tff(c_32,plain,
! [B_18,A_17] :
( antisymmetric(relation_restriction(B_18,A_17))
| ~ antisymmetric(B_18)
| ~ relation(B_18) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_111,plain,
! [A_28] :
( transitive(A_28)
| ~ well_ordering(A_28)
| ~ relation(A_28) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_114,plain,
( transitive('#skF_2')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_38,c_111]) ).
tff(c_117,plain,
transitive('#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_114]) ).
tff(c_30,plain,
! [B_16,A_15] :
( transitive(relation_restriction(B_16,A_15))
| ~ transitive(B_16)
| ~ relation(B_16) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_50,plain,
! [A_22] :
( connected(A_22)
| ~ well_ordering(A_22)
| ~ relation(A_22) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_53,plain,
( connected('#skF_2')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_38,c_50]) ).
tff(c_56,plain,
connected('#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_53]) ).
tff(c_28,plain,
! [B_14,A_13] :
( connected(relation_restriction(B_14,A_13))
| ~ connected(B_14)
| ~ relation(B_14) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_64,plain,
! [A_24] :
( reflexive(A_24)
| ~ well_ordering(A_24)
| ~ relation(A_24) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_67,plain,
( reflexive('#skF_2')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_38,c_64]) ).
tff(c_70,plain,
reflexive('#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_67]) ).
tff(c_26,plain,
! [B_12,A_11] :
( reflexive(relation_restriction(B_12,A_11))
| ~ reflexive(B_12)
| ~ relation(B_12) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_104,plain,
! [A_27] :
( well_founded_relation(A_27)
| ~ well_ordering(A_27)
| ~ relation(A_27) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_107,plain,
( well_founded_relation('#skF_2')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_38,c_104]) ).
tff(c_110,plain,
well_founded_relation('#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_107]) ).
tff(c_34,plain,
! [B_20,A_19] :
( well_founded_relation(relation_restriction(B_20,A_19))
| ~ well_founded_relation(B_20)
| ~ relation(B_20) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_18,plain,
! [A_7,B_8] :
( relation(relation_restriction(A_7,B_8))
| ~ relation(A_7) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_194,plain,
! [A_45] :
( well_ordering(A_45)
| ~ well_founded_relation(A_45)
| ~ connected(A_45)
| ~ antisymmetric(A_45)
| ~ transitive(A_45)
| ~ reflexive(A_45)
| ~ relation(A_45) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_36,plain,
~ well_ordering(relation_restriction('#skF_2','#skF_1')),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_218,plain,
( ~ well_founded_relation(relation_restriction('#skF_2','#skF_1'))
| ~ connected(relation_restriction('#skF_2','#skF_1'))
| ~ antisymmetric(relation_restriction('#skF_2','#skF_1'))
| ~ transitive(relation_restriction('#skF_2','#skF_1'))
| ~ reflexive(relation_restriction('#skF_2','#skF_1'))
| ~ relation(relation_restriction('#skF_2','#skF_1')) ),
inference(resolution,[status(thm)],[c_194,c_36]) ).
tff(c_220,plain,
~ relation(relation_restriction('#skF_2','#skF_1')),
inference(splitLeft,[status(thm)],[c_218]) ).
tff(c_223,plain,
~ relation('#skF_2'),
inference(resolution,[status(thm)],[c_18,c_220]) ).
tff(c_227,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_223]) ).
tff(c_228,plain,
( ~ reflexive(relation_restriction('#skF_2','#skF_1'))
| ~ transitive(relation_restriction('#skF_2','#skF_1'))
| ~ antisymmetric(relation_restriction('#skF_2','#skF_1'))
| ~ connected(relation_restriction('#skF_2','#skF_1'))
| ~ well_founded_relation(relation_restriction('#skF_2','#skF_1')) ),
inference(splitRight,[status(thm)],[c_218]) ).
tff(c_231,plain,
~ well_founded_relation(relation_restriction('#skF_2','#skF_1')),
inference(splitLeft,[status(thm)],[c_228]) ).
tff(c_234,plain,
( ~ well_founded_relation('#skF_2')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_34,c_231]) ).
tff(c_238,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_110,c_234]) ).
tff(c_239,plain,
( ~ connected(relation_restriction('#skF_2','#skF_1'))
| ~ antisymmetric(relation_restriction('#skF_2','#skF_1'))
| ~ transitive(relation_restriction('#skF_2','#skF_1'))
| ~ reflexive(relation_restriction('#skF_2','#skF_1')) ),
inference(splitRight,[status(thm)],[c_228]) ).
tff(c_241,plain,
~ reflexive(relation_restriction('#skF_2','#skF_1')),
inference(splitLeft,[status(thm)],[c_239]) ).
tff(c_244,plain,
( ~ reflexive('#skF_2')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_26,c_241]) ).
tff(c_248,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_70,c_244]) ).
tff(c_249,plain,
( ~ transitive(relation_restriction('#skF_2','#skF_1'))
| ~ antisymmetric(relation_restriction('#skF_2','#skF_1'))
| ~ connected(relation_restriction('#skF_2','#skF_1')) ),
inference(splitRight,[status(thm)],[c_239]) ).
tff(c_251,plain,
~ connected(relation_restriction('#skF_2','#skF_1')),
inference(splitLeft,[status(thm)],[c_249]) ).
tff(c_254,plain,
( ~ connected('#skF_2')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_28,c_251]) ).
tff(c_258,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_56,c_254]) ).
tff(c_259,plain,
( ~ antisymmetric(relation_restriction('#skF_2','#skF_1'))
| ~ transitive(relation_restriction('#skF_2','#skF_1')) ),
inference(splitRight,[status(thm)],[c_249]) ).
tff(c_261,plain,
~ transitive(relation_restriction('#skF_2','#skF_1')),
inference(splitLeft,[status(thm)],[c_259]) ).
tff(c_264,plain,
( ~ transitive('#skF_2')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_30,c_261]) ).
tff(c_268,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_117,c_264]) ).
tff(c_269,plain,
~ antisymmetric(relation_restriction('#skF_2','#skF_1')),
inference(splitRight,[status(thm)],[c_259]) ).
tff(c_273,plain,
( ~ antisymmetric('#skF_2')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_32,c_269]) ).
tff(c_277,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_63,c_273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU257+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % 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 : n015.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 22:32:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.63/1.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/1.96
% 3.63/1.96 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------