%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU219+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n011.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 08:53:15 PM UTC 2025
% Result : Theorem 5.86s 2.37s
% Output : CNFRefutation 5.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 21 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 43 ( 19 ~; 15 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 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 : 18 ( 18 usr; 10 con; 0-1 aty)
% Number of variables : 7 ( 7 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > one_to_one > function > empty > #nlpp > relation_rng > relation_inverse > relation_dom > powerset > function_inverse > empty_set > #skF_4 > #skF_11 > #skF_1 > #skF_8 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_9 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(relation,type,
relation: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(relation_inverse,type,
relation_inverse: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff('#skF_8',type,
'#skF_8': $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_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(function_inverse,type,
function_inverse: $i > $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $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(powerset,type,
powerset: $i > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_221,negated_conjecture,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> ( ( relation_rng(A) = relation_dom(function_inverse(A)) )
& ( relation_dom(A) = relation_rng(function_inverse(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
tff(f_59,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> ( function_inverse(A) = relation_inverse(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
tff(f_200,axiom,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = relation_dom(relation_inverse(A)) )
& ( relation_dom(A) = relation_rng(relation_inverse(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
tff(c_116,plain,
( ( relation_rng(function_inverse('#skF_12')) != relation_dom('#skF_12') )
| ( relation_dom(function_inverse('#skF_12')) != relation_rng('#skF_12') ) ),
inference(cnfTransformation,[status(thm)],[f_221]) ).
tff(c_181,plain,
relation_dom(function_inverse('#skF_12')) != relation_rng('#skF_12'),
inference(splitLeft,[status(thm)],[c_116]) ).
tff(c_122,plain,
relation('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_221]) ).
tff(c_120,plain,
function('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_221]) ).
tff(c_118,plain,
one_to_one('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_221]) ).
tff(c_1242,plain,
! [A_123] :
( ( relation_inverse(A_123) = function_inverse(A_123) )
| ~ one_to_one(A_123)
| ~ function(A_123)
| ~ relation(A_123) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_1284,plain,
( ( relation_inverse('#skF_12') = function_inverse('#skF_12') )
| ~ one_to_one('#skF_12')
| ~ function('#skF_12') ),
inference(resolution,[status(thm)],[c_122,c_1242]) ).
tff(c_1306,plain,
relation_inverse('#skF_12') = function_inverse('#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_120,c_118,c_1284]) ).
tff(c_108,plain,
! [A_29] :
( ( relation_dom(relation_inverse(A_29)) = relation_rng(A_29) )
| ~ relation(A_29) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_1387,plain,
( ( relation_dom(function_inverse('#skF_12')) = relation_rng('#skF_12') )
| ~ relation('#skF_12') ),
inference(superposition,[status(thm),theory(equality)],[c_1306,c_108]) ).
tff(c_1421,plain,
relation_dom(function_inverse('#skF_12')) = relation_rng('#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_1387]) ).
tff(c_1423,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_181,c_1421]) ).
tff(c_1424,plain,
relation_rng(function_inverse('#skF_12')) != relation_dom('#skF_12'),
inference(splitRight,[status(thm)],[c_116]) ).
tff(c_2526,plain,
! [A_196] :
( ( relation_inverse(A_196) = function_inverse(A_196) )
| ~ one_to_one(A_196)
| ~ function(A_196)
| ~ relation(A_196) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_2568,plain,
( ( relation_inverse('#skF_12') = function_inverse('#skF_12') )
| ~ one_to_one('#skF_12')
| ~ function('#skF_12') ),
inference(resolution,[status(thm)],[c_122,c_2526]) ).
tff(c_2590,plain,
relation_inverse('#skF_12') = function_inverse('#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_120,c_118,c_2568]) ).
tff(c_106,plain,
! [A_29] :
( ( relation_rng(relation_inverse(A_29)) = relation_dom(A_29) )
| ~ relation(A_29) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_2672,plain,
( ( relation_rng(function_inverse('#skF_12')) = relation_dom('#skF_12') )
| ~ relation('#skF_12') ),
inference(superposition,[status(thm),theory(equality)],[c_2590,c_106]) ).
tff(c_2707,plain,
relation_rng(function_inverse('#skF_12')) = relation_dom('#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_2672]) ).
tff(c_2709,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1424,c_2707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU219+3 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n011.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 22:22:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 5.86/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.86/2.38
% 5.86/2.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------