%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU271+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 : n003.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 71.28s 55.03s
% Output : CNFRefutation 71.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 116 ( 18 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 127 ( 49 ~; 62 |; 6 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 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 : 25 ( 25 usr; 11 con; 0-2 aty)
% Number of variables : 59 ( 59 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > is_antisymmetric_in > in > element > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > antisymmetric > unordered_pair > set_union2 > ordered_pair > #nlpp > singleton > relation_rng > relation_field > relation_dom > powerset > inclusion_relation > empty_set > #skF_5 > #skF_11 > #skF_15 > #skF_7 > #skF_3 > #skF_10 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_8 > #skF_2 > #skF_1 > #skF_12 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(antisymmetric,type,
antisymmetric: $i > $o ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation_field,type,
relation_field: $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_15',type,
'#skF_15': $i ).
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(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(relation_rng,type,
relation_rng: $i > $i ).
tff(is_antisymmetric_in,type,
is_antisymmetric_in: ( $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_123,axiom,
! [A] : relation(inclusion_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
tff(f_114,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_antisymmetric_in(A,B)
<=> ! [C,D] :
( ( in(C,B)
& in(D,B)
& in(ordered_pair(C,D),A)
& in(ordered_pair(D,C),A) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
tff(f_98,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_77,axiom,
! [A,B] :
( ( A = B )
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
tff(f_83,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_249,negated_conjecture,
~ ! [A] : antisymmetric(inclusion_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord2) ).
tff(c_76,plain,
! [A_43] : relation(inclusion_relation(A_43)),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_64,plain,
! [A_23,B_33] :
( in('#skF_4'(A_23,B_33),B_33)
| is_antisymmetric_in(A_23,B_33)
| ~ relation(A_23) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_66,plain,
! [A_23,B_33] :
( in('#skF_3'(A_23,B_33),B_33)
| is_antisymmetric_in(A_23,B_33)
| ~ relation(A_23) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_62,plain,
! [A_23,B_33] :
( in(ordered_pair('#skF_3'(A_23,B_33),'#skF_4'(A_23,B_33)),A_23)
| is_antisymmetric_in(A_23,B_33)
| ~ relation(A_23) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_54,plain,
! [C_21,D_22,A_15] :
( subset(C_21,D_22)
| ~ in(ordered_pair(C_21,D_22),inclusion_relation(A_15))
| ~ in(D_22,A_15)
| ~ in(C_21,A_15)
| ~ relation(inclusion_relation(A_15)) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_1560,plain,
! [C_198,D_199,A_200] :
( subset(C_198,D_199)
| ~ in(ordered_pair(C_198,D_199),inclusion_relation(A_200))
| ~ in(D_199,A_200)
| ~ in(C_198,A_200) ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_54]) ).
tff(c_1571,plain,
! [A_200,B_33] :
( subset('#skF_3'(inclusion_relation(A_200),B_33),'#skF_4'(inclusion_relation(A_200),B_33))
| ~ in('#skF_4'(inclusion_relation(A_200),B_33),A_200)
| ~ in('#skF_3'(inclusion_relation(A_200),B_33),A_200)
| is_antisymmetric_in(inclusion_relation(A_200),B_33)
| ~ relation(inclusion_relation(A_200)) ),
inference(resolution,[status(thm)],[c_62,c_1560]) ).
tff(c_1585,plain,
! [A_200,B_33] :
( subset('#skF_3'(inclusion_relation(A_200),B_33),'#skF_4'(inclusion_relation(A_200),B_33))
| ~ in('#skF_4'(inclusion_relation(A_200),B_33),A_200)
| ~ in('#skF_3'(inclusion_relation(A_200),B_33),A_200)
| is_antisymmetric_in(inclusion_relation(A_200),B_33) ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_1571]) ).
tff(c_60,plain,
! [A_23,B_33] :
( in(ordered_pair('#skF_4'(A_23,B_33),'#skF_3'(A_23,B_33)),A_23)
| is_antisymmetric_in(A_23,B_33)
| ~ relation(A_23) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_1575,plain,
! [A_200,B_33] :
( subset('#skF_4'(inclusion_relation(A_200),B_33),'#skF_3'(inclusion_relation(A_200),B_33))
| ~ in('#skF_3'(inclusion_relation(A_200),B_33),A_200)
| ~ in('#skF_4'(inclusion_relation(A_200),B_33),A_200)
| is_antisymmetric_in(inclusion_relation(A_200),B_33)
| ~ relation(inclusion_relation(A_200)) ),
inference(resolution,[status(thm)],[c_60,c_1560]) ).
tff(c_4883,plain,
! [A_367,B_368] :
( subset('#skF_4'(inclusion_relation(A_367),B_368),'#skF_3'(inclusion_relation(A_367),B_368))
| ~ in('#skF_3'(inclusion_relation(A_367),B_368),A_367)
| ~ in('#skF_4'(inclusion_relation(A_367),B_368),A_367)
| is_antisymmetric_in(inclusion_relation(A_367),B_368) ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_1575]) ).
tff(c_28,plain,
! [B_13,A_12] :
( ( B_13 = A_12 )
| ~ subset(B_13,A_12)
| ~ subset(A_12,B_13) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_26540,plain,
! [A_859,B_860] :
( ( '#skF_3'(inclusion_relation(A_859),B_860) = '#skF_4'(inclusion_relation(A_859),B_860) )
| ~ subset('#skF_3'(inclusion_relation(A_859),B_860),'#skF_4'(inclusion_relation(A_859),B_860))
| ~ in('#skF_3'(inclusion_relation(A_859),B_860),A_859)
| ~ in('#skF_4'(inclusion_relation(A_859),B_860),A_859)
| is_antisymmetric_in(inclusion_relation(A_859),B_860) ),
inference(resolution,[status(thm)],[c_4883,c_28]) ).
tff(c_259352,plain,
! [A_2164,B_2165] :
( ( '#skF_3'(inclusion_relation(A_2164),B_2165) = '#skF_4'(inclusion_relation(A_2164),B_2165) )
| ~ in('#skF_4'(inclusion_relation(A_2164),B_2165),A_2164)
| ~ in('#skF_3'(inclusion_relation(A_2164),B_2165),A_2164)
| is_antisymmetric_in(inclusion_relation(A_2164),B_2165) ),
inference(resolution,[status(thm)],[c_1585,c_26540]) ).
tff(c_259371,plain,
! [B_33] :
( ( '#skF_3'(inclusion_relation(B_33),B_33) = '#skF_4'(inclusion_relation(B_33),B_33) )
| ~ in('#skF_4'(inclusion_relation(B_33),B_33),B_33)
| is_antisymmetric_in(inclusion_relation(B_33),B_33)
| ~ relation(inclusion_relation(B_33)) ),
inference(resolution,[status(thm)],[c_66,c_259352]) ).
tff(c_259402,plain,
! [B_2169] :
( ( '#skF_3'(inclusion_relation(B_2169),B_2169) = '#skF_4'(inclusion_relation(B_2169),B_2169) )
| ~ in('#skF_4'(inclusion_relation(B_2169),B_2169),B_2169)
| is_antisymmetric_in(inclusion_relation(B_2169),B_2169) ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_259371]) ).
tff(c_259421,plain,
! [B_33] :
( ( '#skF_3'(inclusion_relation(B_33),B_33) = '#skF_4'(inclusion_relation(B_33),B_33) )
| is_antisymmetric_in(inclusion_relation(B_33),B_33)
| ~ relation(inclusion_relation(B_33)) ),
inference(resolution,[status(thm)],[c_64,c_259402]) ).
tff(c_259437,plain,
! [B_2170] :
( ( '#skF_3'(inclusion_relation(B_2170),B_2170) = '#skF_4'(inclusion_relation(B_2170),B_2170) )
| is_antisymmetric_in(inclusion_relation(B_2170),B_2170) ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_259421]) ).
tff(c_50,plain,
! [A_15] :
( ( relation_field(inclusion_relation(A_15)) = A_15 )
| ~ relation(inclusion_relation(A_15)) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_205,plain,
! [A_15] : ( relation_field(inclusion_relation(A_15)) = A_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_50]) ).
tff(c_570,plain,
! [A_113] :
( antisymmetric(A_113)
| ~ is_antisymmetric_in(A_113,relation_field(A_113))
| ~ relation(A_113) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_573,plain,
! [A_15] :
( antisymmetric(inclusion_relation(A_15))
| ~ is_antisymmetric_in(inclusion_relation(A_15),A_15)
| ~ relation(inclusion_relation(A_15)) ),
inference(superposition,[status(thm),theory(equality)],[c_205,c_570]) ).
tff(c_575,plain,
! [A_15] :
( antisymmetric(inclusion_relation(A_15))
| ~ is_antisymmetric_in(inclusion_relation(A_15),A_15) ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_573]) ).
tff(c_259446,plain,
! [B_2171] :
( antisymmetric(inclusion_relation(B_2171))
| ( '#skF_3'(inclusion_relation(B_2171),B_2171) = '#skF_4'(inclusion_relation(B_2171),B_2171) ) ),
inference(resolution,[status(thm)],[c_259437,c_575]) ).
tff(c_921,plain,
! [A_156,B_157] :
( ( '#skF_3'(A_156,B_157) != '#skF_4'(A_156,B_157) )
| is_antisymmetric_in(A_156,B_157)
| ~ relation(A_156) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_34,plain,
! [A_14] :
( antisymmetric(A_14)
| ~ is_antisymmetric_in(A_14,relation_field(A_14))
| ~ relation(A_14) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_1672,plain,
! [A_213] :
( antisymmetric(A_213)
| ( '#skF_3'(A_213,relation_field(A_213)) != '#skF_4'(A_213,relation_field(A_213)) )
| ~ relation(A_213) ),
inference(resolution,[status(thm)],[c_921,c_34]) ).
tff(c_1675,plain,
! [A_15] :
( antisymmetric(inclusion_relation(A_15))
| ( '#skF_4'(inclusion_relation(A_15),relation_field(inclusion_relation(A_15))) != '#skF_3'(inclusion_relation(A_15),A_15) )
| ~ relation(inclusion_relation(A_15)) ),
inference(superposition,[status(thm),theory(equality)],[c_205,c_1672]) ).
tff(c_1677,plain,
! [A_15] :
( antisymmetric(inclusion_relation(A_15))
| ( '#skF_3'(inclusion_relation(A_15),A_15) != '#skF_4'(inclusion_relation(A_15),A_15) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_205,c_1675]) ).
tff(c_259801,plain,
! [B_2171] : antisymmetric(inclusion_relation(B_2171)),
inference(superposition,[status(thm),theory(equality)],[c_259446,c_1677]) ).
tff(c_192,plain,
~ antisymmetric(inclusion_relation('#skF_15')),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_259854,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_259801,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU271+1 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.13 % 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 : n003.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 22:35:48 EDT 2025
% 0.13/0.34 % CPUTime :
% 71.28/55.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 71.28/55.03
% 71.28/55.03 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------