%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU217+3 : TPTP v9.0.0. Released v3.2.0.
% 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 : n013.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 08:53:14 PM UTC 2025
% Result : Theorem 3.83s 1.98s
% Output : CNFRefutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 22 ( 9 ~; 6 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > function > empty > apply > #nlpp > relation_dom > powerset > identity_relation > empty_set > #skF_4 > #skF_11 > #skF_1 > #skF_7 > #skF_10 > #skF_12 > #skF_5 > #skF_6 > #skF_2 > #skF_9 > #skF_8 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(relation,type,
relation: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
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_10',type,
'#skF_10': $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(identity_relation,type,
identity_relation: $i > $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $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_3',type,
'#skF_3': $i > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(f_161,negated_conjecture,
~ ! [A,B] :
( in(B,A)
=> ( apply(identity_relation(A),B) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
tff(f_111,axiom,
! [A] :
( relation(identity_relation(A))
& function(identity_relation(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
tff(f_174,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( ( B = identity_relation(A) )
<=> ( ( relation_dom(B) = A )
& ! [C] :
( in(C,A)
=> ( apply(B,C) = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
tff(c_86,plain,
in('#skF_11','#skF_10'),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_48,plain,
! [A_26] : relation(identity_relation(A_26)),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_50,plain,
! [A_26] : function(identity_relation(A_26)),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_92,plain,
! [A_35,C_39] :
( ( apply(identity_relation(A_35),C_39) = C_39 )
| ~ in(C_39,A_35)
| ~ function(identity_relation(A_35))
| ~ relation(identity_relation(A_35)) ),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_98,plain,
! [A_35,C_39] :
( ( apply(identity_relation(A_35),C_39) = C_39 )
| ~ in(C_39,A_35)
| ~ relation(identity_relation(A_35)) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_92]) ).
tff(c_409,plain,
! [A_83,C_84] :
( ( apply(identity_relation(A_83),C_84) = C_84 )
| ~ in(C_84,A_83) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_98]) ).
tff(c_84,plain,
apply(identity_relation('#skF_10'),'#skF_11') != '#skF_11',
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_415,plain,
~ in('#skF_11','#skF_10'),
inference(superposition,[status(thm),theory(equality)],[c_409,c_84]) ).
tff(c_426,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_86,c_415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU217+3 : TPTP v9.0.0. Released v3.2.0.
% 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 : n013.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 22:22:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.83/1.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.83/1.98
% 3.83/1.98 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------