%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU010+1 : 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 : n004.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 08:52:38 PM UTC 2025
% Result : Theorem 8.80s 3.61s
% Output : CNFRefutation 9.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 13 ~; 7 |; 2 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > function > empty > relation_composition > #nlpp > relation_rng > relation_dom > powerset > identity_relation > empty_set > #skF_4 > #skF_1 > #skF_7 > #skF_10 > #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_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(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(relation_composition,type,
relation_composition: ( $i * $i ) > $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(relation_rng,type,
relation_rng: $i > $i ).
tff(f_213,negated_conjecture,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( ( relation_composition(identity_relation(relation_dom(A)),A) = A )
& ( relation_composition(A,identity_relation(relation_rng(A))) = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funct_1) ).
tff(f_140,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_225,axiom,
! [A,B] :
( relation(B)
=> ( subset(relation_rng(B),A)
=> ( relation_composition(B,identity_relation(A)) = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_relat_1) ).
tff(f_219,axiom,
! [A,B] :
( relation(B)
=> ( subset(relation_dom(B),A)
=> ( relation_composition(identity_relation(A),B) = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_relat_1) ).
tff(c_108,plain,
relation('#skF_10'),
inference(cnfTransformation,[status(thm)],[f_213]) ).
tff(c_58,plain,
! [A_31] : subset(A_31,A_31),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_2397,plain,
! [B_233,A_234] :
( ( relation_composition(B_233,identity_relation(A_234)) = B_233 )
| ~ subset(relation_rng(B_233),A_234)
| ~ relation(B_233) ),
inference(cnfTransformation,[status(thm)],[f_225]) ).
tff(c_3087,plain,
! [B_252] :
( ( relation_composition(B_252,identity_relation(relation_rng(B_252))) = B_252 )
| ~ relation(B_252) ),
inference(resolution,[status(thm)],[c_58,c_2397]) ).
tff(c_1076,plain,
! [A_138,B_139] :
( ( relation_composition(identity_relation(A_138),B_139) = B_139 )
| ~ subset(relation_dom(B_139),A_138)
| ~ relation(B_139) ),
inference(cnfTransformation,[status(thm)],[f_219]) ).
tff(c_1597,plain,
! [B_151] :
( ( relation_composition(identity_relation(relation_dom(B_151)),B_151) = B_151 )
| ~ relation(B_151) ),
inference(resolution,[status(thm)],[c_58,c_1076]) ).
tff(c_104,plain,
( ( relation_composition('#skF_10',identity_relation(relation_rng('#skF_10'))) != '#skF_10' )
| ( relation_composition(identity_relation(relation_dom('#skF_10')),'#skF_10') != '#skF_10' ) ),
inference(cnfTransformation,[status(thm)],[f_213]) ).
tff(c_117,plain,
relation_composition(identity_relation(relation_dom('#skF_10')),'#skF_10') != '#skF_10',
inference(splitLeft,[status(thm)],[c_104]) ).
tff(c_1628,plain,
~ relation('#skF_10'),
inference(superposition,[status(thm),theory(equality)],[c_1597,c_117]) ).
tff(c_1664,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_108,c_1628]) ).
tff(c_1665,plain,
relation_composition('#skF_10',identity_relation(relation_rng('#skF_10'))) != '#skF_10',
inference(splitRight,[status(thm)],[c_104]) ).
tff(c_3116,plain,
~ relation('#skF_10'),
inference(superposition,[status(thm),theory(equality)],[c_3087,c_1665]) ).
tff(c_3152,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_108,c_3116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU010+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % 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 : n004.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 21:55:22 EDT 2025
% 0.13/0.34 % CPUTime :
% 8.80/3.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.04/3.61
% 9.04/3.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------