%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU241+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 : n024.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 08:53:21 PM UTC 2025
% Result : Theorem 5.20s 2.29s
% Output : CNFRefutation 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 114 ( 18 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 123 ( 53 ~; 55 |; 5 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_antisymmetric_in > in > element > relation > one_to_one > function > empty > antisymmetric > unordered_pair > set_union2 > ordered_pair > #nlpp > singleton > relation_rng > relation_field > relation_dom > empty_set > #skF_11 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_9 > #skF_8 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(antisymmetric,type,
antisymmetric: $i > $o ).
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(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
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(function,type,
function: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $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_4',type,
'#skF_4': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $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(f_113,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(B,C),A)
& in(ordered_pair(C,B),A) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
tff(f_73,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_57,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_154,axiom,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(A,relation_field(C))
& in(B,relation_field(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
tff(c_66,plain,
relation('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_68,plain,
( ( '#skF_5' != '#skF_6' )
| ~ antisymmetric('#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_165,plain,
~ antisymmetric('#skF_4'),
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_872,plain,
! [A_159,B_160] :
( in(ordered_pair('#skF_1'(A_159,B_160),'#skF_2'(A_159,B_160)),A_159)
| is_antisymmetric_in(A_159,B_160)
| ~ relation(A_159) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_766,plain,
! [A_147,B_148] :
( in(ordered_pair('#skF_2'(A_147,B_148),'#skF_1'(A_147,B_148)),A_147)
| is_antisymmetric_in(A_147,B_148)
| ~ relation(A_147) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_82,plain,
! [C_45,B_44] :
( antisymmetric('#skF_4')
| ( C_45 = B_44 )
| ~ in(ordered_pair(C_45,B_44),'#skF_4')
| ~ in(ordered_pair(B_44,C_45),'#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_404,plain,
! [C_45,B_44] :
( ( C_45 = B_44 )
| ~ in(ordered_pair(C_45,B_44),'#skF_4')
| ~ in(ordered_pair(B_44,C_45),'#skF_4') ),
inference(negUnitSimplification,[status(thm)],[c_165,c_82]) ).
tff(c_782,plain,
! [B_148] :
( ( '#skF_2'('#skF_4',B_148) = '#skF_1'('#skF_4',B_148) )
| ~ in(ordered_pair('#skF_1'('#skF_4',B_148),'#skF_2'('#skF_4',B_148)),'#skF_4')
| is_antisymmetric_in('#skF_4',B_148)
| ~ relation('#skF_4') ),
inference(resolution,[status(thm)],[c_766,c_404]) ).
tff(c_801,plain,
! [B_148] :
( ( '#skF_2'('#skF_4',B_148) = '#skF_1'('#skF_4',B_148) )
| ~ in(ordered_pair('#skF_1'('#skF_4',B_148),'#skF_2'('#skF_4',B_148)),'#skF_4')
| is_antisymmetric_in('#skF_4',B_148) ),
inference(demodulation,[status(thm),theory(equality)],[c_66,c_782]) ).
tff(c_876,plain,
! [B_160] :
( ( '#skF_2'('#skF_4',B_160) = '#skF_1'('#skF_4',B_160) )
| is_antisymmetric_in('#skF_4',B_160)
| ~ relation('#skF_4') ),
inference(resolution,[status(thm)],[c_872,c_801]) ).
tff(c_918,plain,
! [B_161] :
( ( '#skF_2'('#skF_4',B_161) = '#skF_1'('#skF_4',B_161) )
| is_antisymmetric_in('#skF_4',B_161) ),
inference(demodulation,[status(thm),theory(equality)],[c_66,c_876]) ).
tff(c_16,plain,
! [A_9] :
( antisymmetric(A_9)
| ~ is_antisymmetric_in(A_9,relation_field(A_9))
| ~ relation(A_9) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_922,plain,
( antisymmetric('#skF_4')
| ~ relation('#skF_4')
| ( '#skF_2'('#skF_4',relation_field('#skF_4')) = '#skF_1'('#skF_4',relation_field('#skF_4')) ) ),
inference(resolution,[status(thm)],[c_918,c_16]) ).
tff(c_925,plain,
( antisymmetric('#skF_4')
| ( '#skF_2'('#skF_4',relation_field('#skF_4')) = '#skF_1'('#skF_4',relation_field('#skF_4')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_66,c_922]) ).
tff(c_926,plain,
'#skF_2'('#skF_4',relation_field('#skF_4')) = '#skF_1'('#skF_4',relation_field('#skF_4')),
inference(negUnitSimplification,[status(thm)],[c_165,c_925]) ).
tff(c_709,plain,
! [A_129,B_130] :
( ( '#skF_2'(A_129,B_130) != '#skF_1'(A_129,B_130) )
| is_antisymmetric_in(A_129,B_130)
| ~ relation(A_129) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_714,plain,
! [A_129] :
( antisymmetric(A_129)
| ( '#skF_2'(A_129,relation_field(A_129)) != '#skF_1'(A_129,relation_field(A_129)) )
| ~ relation(A_129) ),
inference(resolution,[status(thm)],[c_709,c_16]) ).
tff(c_939,plain,
( antisymmetric('#skF_4')
| ~ relation('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_926,c_714]) ).
tff(c_959,plain,
antisymmetric('#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_66,c_939]) ).
tff(c_961,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_165,c_959]) ).
tff(c_963,plain,
antisymmetric('#skF_4'),
inference(splitRight,[status(thm)],[c_68]) ).
tff(c_70,plain,
( in(ordered_pair('#skF_6','#skF_5'),'#skF_4')
| ~ antisymmetric('#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_1001,plain,
in(ordered_pair('#skF_6','#skF_5'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_963,c_70]) ).
tff(c_1520,plain,
! [A_212,C_213,B_214] :
( in(A_212,relation_field(C_213))
| ~ in(ordered_pair(A_212,B_214),C_213)
| ~ relation(C_213) ),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_1530,plain,
( in('#skF_6',relation_field('#skF_4'))
| ~ relation('#skF_4') ),
inference(resolution,[status(thm)],[c_1001,c_1520]) ).
tff(c_1537,plain,
in('#skF_6',relation_field('#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_66,c_1530]) ).
tff(c_72,plain,
( in(ordered_pair('#skF_5','#skF_6'),'#skF_4')
| ~ antisymmetric('#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_964,plain,
~ antisymmetric('#skF_4'),
inference(splitLeft,[status(thm)],[c_72]) ).
tff(c_966,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_963,c_964]) ).
tff(c_967,plain,
in(ordered_pair('#skF_5','#skF_6'),'#skF_4'),
inference(splitRight,[status(thm)],[c_72]) ).
tff(c_1527,plain,
( in('#skF_5',relation_field('#skF_4'))
| ~ relation('#skF_4') ),
inference(resolution,[status(thm)],[c_967,c_1520]) ).
tff(c_1534,plain,
in('#skF_5',relation_field('#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_66,c_1527]) ).
tff(c_18,plain,
! [A_9] :
( is_antisymmetric_in(A_9,relation_field(A_9))
| ~ antisymmetric(A_9)
| ~ relation(A_9) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_962,plain,
'#skF_5' != '#skF_6',
inference(splitRight,[status(thm)],[c_68]) ).
tff(c_1724,plain,
! [D_238,C_239,A_240,B_241] :
( ( D_238 = C_239 )
| ~ in(ordered_pair(D_238,C_239),A_240)
| ~ in(ordered_pair(C_239,D_238),A_240)
| ~ in(D_238,B_241)
| ~ in(C_239,B_241)
| ~ is_antisymmetric_in(A_240,B_241)
| ~ relation(A_240) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1733,plain,
! [B_241] :
( ( '#skF_5' = '#skF_6' )
| ~ in(ordered_pair('#skF_6','#skF_5'),'#skF_4')
| ~ in('#skF_5',B_241)
| ~ in('#skF_6',B_241)
| ~ is_antisymmetric_in('#skF_4',B_241)
| ~ relation('#skF_4') ),
inference(resolution,[status(thm)],[c_967,c_1724]) ).
tff(c_1741,plain,
! [B_241] :
( ( '#skF_5' = '#skF_6' )
| ~ in('#skF_5',B_241)
| ~ in('#skF_6',B_241)
| ~ is_antisymmetric_in('#skF_4',B_241) ),
inference(demodulation,[status(thm),theory(equality)],[c_66,c_1001,c_1733]) ).
tff(c_1747,plain,
! [B_242] :
( ~ in('#skF_5',B_242)
| ~ in('#skF_6',B_242)
| ~ is_antisymmetric_in('#skF_4',B_242) ),
inference(negUnitSimplification,[status(thm)],[c_962,c_1741]) ).
tff(c_1763,plain,
( ~ in('#skF_5',relation_field('#skF_4'))
| ~ in('#skF_6',relation_field('#skF_4'))
| ~ antisymmetric('#skF_4')
| ~ relation('#skF_4') ),
inference(resolution,[status(thm)],[c_18,c_1747]) ).
tff(c_1776,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_66,c_963,c_1537,c_1534,c_1763]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU241+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/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
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 22:29:21 EDT 2025
% 0.12/0.34 % CPUTime :
% 5.20/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.20/2.29
% 5.20/2.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------