%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM395+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 : n025.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 07:55:49 PM UTC 2025
% Result : Theorem 3.52s 1.95s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 4 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-1 aty)
% Number of variables : 5 ( 4 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > empty_set > #skF_11 > #skF_1 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(relation_non_empty,type,
relation_non_empty: $i > $o ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $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(ordinal,type,
ordinal: $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('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_105,axiom,
? [A] :
( relation(A)
& empty(A)
& function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
tff(f_154,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_165,axiom,
( epsilon_transitive(empty_set)
& epsilon_connected(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l18_ordinal1) ).
tff(f_162,axiom,
! [A] :
( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
tff(f_156,negated_conjecture,
~ ordinal(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_ordinal1) ).
tff(c_42,plain,
empty('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_108,plain,
! [A_20] :
( ( empty_set = A_20 )
| ~ empty(A_20) ),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_123,plain,
empty_set = '#skF_4',
inference(resolution,[status(thm)],[c_42,c_108]) ).
tff(c_104,plain,
epsilon_transitive(empty_set),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_132,plain,
epsilon_transitive('#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_123,c_104]) ).
tff(c_102,plain,
epsilon_connected(empty_set),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_131,plain,
epsilon_connected('#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_123,c_102]) ).
tff(c_182,plain,
! [A_33] :
( ordinal(A_33)
| ~ epsilon_connected(A_33)
| ~ epsilon_transitive(A_33) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_94,plain,
~ ordinal(empty_set),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_129,plain,
~ ordinal('#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_123,c_94]) ).
tff(c_191,plain,
( ~ epsilon_connected('#skF_4')
| ~ epsilon_transitive('#skF_4') ),
inference(resolution,[status(thm)],[c_182,c_129]) ).
tff(c_197,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_132,c_131,c_191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM395+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.14 % 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 : n025.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 12:07:20 EDT 2025
% 0.13/0.35 % CPUTime :
% 3.52/1.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.52/1.95
% 3.52/1.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------