%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU263+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 : n028.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 08:53:26 PM UTC 2025
% Result : Theorem 8.53s 3.18s
% Output : CNFRefutation 8.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 62 ( 26 ~; 23 |; 3 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > subset > element > relation > cartesian_product2 > #nlpp > relation_rng > relation_dom > powerset > #skF_2 > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(relation,type,
relation: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff(relation_of2,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(relation_of2_as_subset,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(f_52,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
tff(f_73,negated_conjecture,
~ ! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
tff(f_66,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_dom(C),A)
& subset(relation_rng(C),B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
tff(f_34,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
<=> subset(C,cartesian_product2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
tff(f_87,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
tff(f_30,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
tff(f_83,axiom,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
tff(f_60,axiom,
! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
tff(f_79,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
tff(c_119,plain,
! [C_65,A_66,B_67] :
( relation_of2_as_subset(C_65,A_66,B_67)
| ~ relation_of2(C_65,A_66,B_67) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_40,plain,
~ relation_of2_as_subset('#skF_7','#skF_6','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_129,plain,
~ relation_of2('#skF_7','#skF_6','#skF_5'),
inference(resolution,[status(thm)],[c_119,c_40]) ).
tff(c_44,plain,
relation_of2_as_subset('#skF_7','#skF_6','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_77,plain,
! [C_52,A_53,B_54] :
( subset(relation_dom(C_52),A_53)
| ~ relation_of2_as_subset(C_52,A_53,B_54) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_83,plain,
subset(relation_dom('#skF_7'),'#skF_6'),
inference(resolution,[status(thm)],[c_44,c_77]) ).
tff(c_133,plain,
! [C_76,A_77,B_78] :
( relation_of2(C_76,A_77,B_78)
| ~ relation_of2_as_subset(C_76,A_77,B_78) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_145,plain,
relation_of2('#skF_7','#skF_6','#skF_4'),
inference(resolution,[status(thm)],[c_44,c_133]) ).
tff(c_146,plain,
! [C_79,A_80,B_81] :
( subset(C_79,cartesian_product2(A_80,B_81))
| ~ relation_of2(C_79,A_80,B_81) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_52,plain,
! [A_34,B_35] :
( element(A_34,powerset(B_35))
| ~ subset(A_34,B_35) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_84,plain,
! [C_55,A_56,B_57] :
( relation(C_55)
| ~ element(C_55,powerset(cartesian_product2(A_56,B_57))) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_93,plain,
! [A_34,A_56,B_57] :
( relation(A_34)
| ~ subset(A_34,cartesian_product2(A_56,B_57)) ),
inference(resolution,[status(thm)],[c_52,c_84]) ).
tff(c_152,plain,
! [C_84,A_85,B_86] :
( relation(C_84)
| ~ relation_of2(C_84,A_85,B_86) ),
inference(resolution,[status(thm)],[c_146,c_93]) ).
tff(c_163,plain,
relation('#skF_7'),
inference(resolution,[status(thm)],[c_145,c_152]) ).
tff(c_42,plain,
subset(relation_rng('#skF_7'),'#skF_5'),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_48,plain,
! [A_33] :
( subset(A_33,cartesian_product2(relation_dom(A_33),relation_rng(A_33)))
| ~ relation(A_33) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_528,plain,
! [A_146,C_147,B_148,D_149] :
( subset(cartesian_product2(A_146,C_147),cartesian_product2(B_148,D_149))
| ~ subset(C_147,D_149)
| ~ subset(A_146,B_148) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_46,plain,
! [A_30,C_32,B_31] :
( subset(A_30,C_32)
| ~ subset(B_31,C_32)
| ~ subset(A_30,B_31) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_1361,plain,
! [B_212,A_214,D_216,C_213,A_215] :
( subset(A_215,cartesian_product2(B_212,D_216))
| ~ subset(A_215,cartesian_product2(A_214,C_213))
| ~ subset(C_213,D_216)
| ~ subset(A_214,B_212) ),
inference(resolution,[status(thm)],[c_528,c_46]) ).
tff(c_6259,plain,
! [A_442,B_443,D_444] :
( subset(A_442,cartesian_product2(B_443,D_444))
| ~ subset(relation_rng(A_442),D_444)
| ~ subset(relation_dom(A_442),B_443)
| ~ relation(A_442) ),
inference(resolution,[status(thm)],[c_48,c_1361]) ).
tff(c_6343,plain,
! [B_443] :
( subset('#skF_7',cartesian_product2(B_443,'#skF_5'))
| ~ subset(relation_dom('#skF_7'),B_443)
| ~ relation('#skF_7') ),
inference(resolution,[status(thm)],[c_42,c_6259]) ).
tff(c_6545,plain,
! [B_446] :
( subset('#skF_7',cartesian_product2(B_446,'#skF_5'))
| ~ subset(relation_dom('#skF_7'),B_446) ),
inference(demodulation,[status(thm),theory(equality)],[c_163,c_6343]) ).
tff(c_6573,plain,
subset('#skF_7',cartesian_product2('#skF_6','#skF_5')),
inference(resolution,[status(thm)],[c_83,c_6545]) ).
tff(c_6,plain,
! [C_6,A_4,B_5] :
( relation_of2(C_6,A_4,B_5)
| ~ subset(C_6,cartesian_product2(A_4,B_5)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_6588,plain,
relation_of2('#skF_7','#skF_6','#skF_5'),
inference(resolution,[status(thm)],[c_6573,c_6]) ).
tff(c_6602,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_129,c_6588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU263+1 : TPTP v9.0.0. Released v3.3.0.
% 0.13/0.14 % 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
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 8 22:34:19 EDT 2025
% 0.14/0.36 % CPUTime :
% 8.53/3.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.53/3.19
% 8.53/3.19 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------