%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU189+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 : n032.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 08:53:08 PM UTC 2025
% Result : Theorem 3.38s 1.94s
% Output : CNFRefutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 51 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 29 ~; 20 |; 4 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 17 ( 15 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > element > relation > empty > #nlpp > relation_rng > relation_dom > empty_set > #skF_1 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(relation,type,
relation: $i > $o ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $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(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff(f_88,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_112,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_49,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
tff(f_122,axiom,
( ( relation_dom(empty_set) = empty_set )
& ( relation_rng(empty_set) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
tff(f_119,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ( relation_dom(A) = empty_set )
<=> ( relation_rng(A) = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
tff(f_130,axiom,
! [A] :
( relation(A)
=> ( ( ( relation_dom(A) = empty_set )
| ( relation_rng(A) = empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
tff(f_66,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
tff(f_86,axiom,
! [A] :
( empty(A)
=> ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
tff(c_34,plain,
empty('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_407,plain,
! [A_45] :
( ( empty_set = A_45 )
| ~ empty(A_45) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_418,plain,
empty_set = '#skF_4',
inference(resolution,[status(thm)],[c_34,c_407]) ).
tff(c_14,plain,
empty('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_417,plain,
empty_set = '#skF_2',
inference(resolution,[status(thm)],[c_14,c_407]) ).
tff(c_434,plain,
'#skF_2' = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_418,c_417]) ).
tff(c_83,plain,
! [A_20] :
( ( empty_set = A_20 )
| ~ empty(A_20) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_94,plain,
empty_set = '#skF_4',
inference(resolution,[status(thm)],[c_34,c_83]) ).
tff(c_93,plain,
empty_set = '#skF_2',
inference(resolution,[status(thm)],[c_14,c_83]) ).
tff(c_110,plain,
'#skF_2' = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_94,c_93]) ).
tff(c_68,plain,
relation_dom(empty_set) = empty_set,
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_99,plain,
relation_dom('#skF_2') = '#skF_2',
inference(demodulation,[status(thm),theory(equality)],[c_93,c_93,c_68]) ).
tff(c_129,plain,
relation_dom('#skF_4') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_110,c_110,c_99]) ).
tff(c_64,plain,
( ( relation_dom('#skF_6') = empty_set )
| ( relation_rng('#skF_6') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_122,plain,
( ( relation_dom('#skF_6') = '#skF_4' )
| ( relation_rng('#skF_6') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_94,c_64]) ).
tff(c_123,plain,
relation_rng('#skF_6') = '#skF_4',
inference(splitLeft,[status(thm)],[c_122]) ).
tff(c_56,plain,
relation('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_70,plain,
! [A_19] :
( ( relation_rng(A_19) != empty_set )
| ( empty_set = A_19 )
| ~ relation(A_19) ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_327,plain,
! [A_41] :
( ( relation_rng(A_41) != '#skF_4' )
| ( A_41 = '#skF_4' )
| ~ relation(A_41) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_94,c_70]) ).
tff(c_345,plain,
( ( relation_rng('#skF_6') != '#skF_4' )
| ( '#skF_6' = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_56,c_327]) ).
tff(c_356,plain,
'#skF_6' = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_123,c_345]) ).
tff(c_58,plain,
( ( relation_rng('#skF_6') != empty_set )
| ( relation_dom('#skF_6') != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_74,plain,
relation_dom('#skF_6') != empty_set,
inference(splitLeft,[status(thm)],[c_58]) ).
tff(c_98,plain,
relation_dom('#skF_6') != '#skF_2',
inference(demodulation,[status(thm),theory(equality)],[c_93,c_74]) ).
tff(c_138,plain,
relation_dom('#skF_6') != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_110,c_98]) ).
tff(c_357,plain,
relation_dom('#skF_4') != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_356,c_138]) ).
tff(c_362,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_129,c_357]) ).
tff(c_363,plain,
relation_dom('#skF_6') = '#skF_4',
inference(splitRight,[status(thm)],[c_122]) ).
tff(c_381,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_363,c_110,c_98]) ).
tff(c_382,plain,
relation_rng('#skF_6') != empty_set,
inference(splitRight,[status(thm)],[c_58]) ).
tff(c_392,plain,
relation_rng('#skF_6') = empty_set,
inference(splitLeft,[status(thm)],[c_64]) ).
tff(c_397,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_382,c_392]) ).
tff(c_399,plain,
relation_rng('#skF_6') != empty_set,
inference(splitRight,[status(thm)],[c_64]) ).
tff(c_422,plain,
relation_rng('#skF_6') != '#skF_2',
inference(demodulation,[status(thm),theory(equality)],[c_417,c_399]) ).
tff(c_462,plain,
relation_rng('#skF_6') != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_434,c_422]) ).
tff(c_383,plain,
relation_dom('#skF_6') = empty_set,
inference(splitRight,[status(thm)],[c_58]) ).
tff(c_423,plain,
relation_dom('#skF_6') = '#skF_2',
inference(demodulation,[status(thm),theory(equality)],[c_417,c_383]) ).
tff(c_446,plain,
relation_dom('#skF_6') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_434,c_423]) ).
tff(c_550,plain,
! [A_61] :
( ~ empty(relation_dom(A_61))
| ~ relation(A_61)
| empty(A_61) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_559,plain,
( ~ empty('#skF_4')
| ~ relation('#skF_6')
| empty('#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_446,c_550]) ).
tff(c_564,plain,
empty('#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_34,c_559]) ).
tff(c_500,plain,
! [A_52] :
( empty(relation_rng(A_52))
| ~ empty(A_52) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_54,plain,
! [A_18] :
( ( empty_set = A_18 )
| ~ empty(A_18) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_421,plain,
! [A_18] :
( ( A_18 = '#skF_2' )
| ~ empty(A_18) ),
inference(demodulation,[status(thm),theory(equality)],[c_417,c_54]) ).
tff(c_473,plain,
! [A_18] :
( ( A_18 = '#skF_4' )
| ~ empty(A_18) ),
inference(demodulation,[status(thm),theory(equality)],[c_434,c_421]) ).
tff(c_507,plain,
! [A_52] :
( ( relation_rng(A_52) = '#skF_4' )
| ~ empty(A_52) ),
inference(resolution,[status(thm)],[c_500,c_473]) ).
tff(c_569,plain,
relation_rng('#skF_6') = '#skF_4',
inference(resolution,[status(thm)],[c_564,c_507]) ).
tff(c_580,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_462,c_569]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : SEU189+1 : TPTP v9.0.0. Released v3.3.0.
% 0.02/0.09 % 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
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Tue Apr 8 22:15:15 EDT 2025
% 0.09/0.28 % CPUTime :
% 3.38/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.38/1.95
% 3.38/1.95 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------