%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU090+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 : n028.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 08:52:44 PM UTC 2025
% Result : Theorem 9.82s 3.51s
% Output : CNFRefutation 9.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 34 ( 15 ~; 10 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 20 ( 18 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 27 con; 0-4 aty)
% Number of variables : 26 ( 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > transfinite_sequence > relation_non_empty > relation_empty_yielding > relation > ordinal_yielding > ordinal > one_to_one > natural > function_yielding > function > finite > epsilon_transitive > epsilon_connected > empty > being_limit_ordinal > cartesian_product4 > cartesian_product3 > cartesian_product2 > #nlpp > powerset > positive_rationals > empty_set > #skF_9 > #skF_18 > #skF_11 > #skF_15 > #skF_1 > #skF_25 > #skF_19 > #skF_7 > #skF_10 > #skF_16 > #skF_26 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_21 > #skF_8 > #skF_30 > #skF_4 > #skF_17 > #skF_22 > #skF_29 > #skF_28 > #skF_24 > #skF_27 > #skF_23 > #skF_12 > #skF_20
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(cartesian_product4,type,
cartesian_product4: ( $i * $i * $i * $i ) > $i ).
tff(positive_rationals,type,
positive_rationals: $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(relation_non_empty,type,
relation_non_empty: $i > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(cartesian_product3,type,
cartesian_product3: ( $i * $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(finite,type,
finite: $i > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(ordinal_yielding,type,
ordinal_yielding: $i > $o ).
tff(function,type,
function: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i ).
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_16',type,
'#skF_16': $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff('#skF_26',type,
'#skF_26': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_21',type,
'#skF_21': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(function_yielding,type,
function_yielding: $i > $o ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff(being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_17',type,
'#skF_17': $i > $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(natural,type,
natural: $i > $o ).
tff(transfinite_sequence,type,
transfinite_sequence: $i > $o ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff(f_424,negated_conjecture,
~ ! [A,B,C,D] :
( ( finite(A)
& finite(B)
& finite(C)
& finite(D) )
=> finite(cartesian_product4(A,B,C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finset_1) ).
tff(f_413,axiom,
! [A,B,C] :
( ( finite(A)
& finite(B)
& finite(C) )
=> finite(cartesian_product3(A,B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finset_1) ).
tff(f_123,axiom,
! [A,B,C,D] : ( cartesian_product4(A,B,C,D) = cartesian_product2(cartesian_product3(A,B,C),D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_zfmisc_1) ).
tff(f_401,axiom,
! [A,B] :
( ( finite(A)
& finite(B) )
=> finite(cartesian_product2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
tff(c_286,plain,
finite('#skF_27'),
inference(cnfTransformation,[status(thm)],[f_424]) ).
tff(c_284,plain,
finite('#skF_28'),
inference(cnfTransformation,[status(thm)],[f_424]) ).
tff(c_282,plain,
finite('#skF_29'),
inference(cnfTransformation,[status(thm)],[f_424]) ).
tff(c_276,plain,
! [A_56,B_57,C_58] :
( finite(cartesian_product3(A_56,B_57,C_58))
| ~ finite(C_58)
| ~ finite(B_57)
| ~ finite(A_56) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_280,plain,
finite('#skF_30'),
inference(cnfTransformation,[status(thm)],[f_424]) ).
tff(c_1100,plain,
! [A_183,B_184,C_185,D_186] : ( cartesian_product2(cartesian_product3(A_183,B_184,C_185),D_186) = cartesian_product4(A_183,B_184,C_185,D_186) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_272,plain,
! [A_52,B_53] :
( finite(cartesian_product2(A_52,B_53))
| ~ finite(B_53)
| ~ finite(A_52) ),
inference(cnfTransformation,[status(thm)],[f_401]) ).
tff(c_1367,plain,
! [A_256,B_257,C_258,D_259] :
( finite(cartesian_product4(A_256,B_257,C_258,D_259))
| ~ finite(D_259)
| ~ finite(cartesian_product3(A_256,B_257,C_258)) ),
inference(superposition,[status(thm),theory(equality)],[c_1100,c_272]) ).
tff(c_278,plain,
~ finite(cartesian_product4('#skF_27','#skF_28','#skF_29','#skF_30')),
inference(cnfTransformation,[status(thm)],[f_424]) ).
tff(c_1370,plain,
( ~ finite('#skF_30')
| ~ finite(cartesian_product3('#skF_27','#skF_28','#skF_29')) ),
inference(resolution,[status(thm)],[c_1367,c_278]) ).
tff(c_1373,plain,
~ finite(cartesian_product3('#skF_27','#skF_28','#skF_29')),
inference(demodulation,[status(thm),theory(equality)],[c_280,c_1370]) ).
tff(c_1376,plain,
( ~ finite('#skF_29')
| ~ finite('#skF_28')
| ~ finite('#skF_27') ),
inference(resolution,[status(thm)],[c_276,c_1373]) ).
tff(c_1383,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_286,c_284,c_282,c_1376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU090+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.11 % 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
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Apr 8 22:02:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 9.82/3.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.82/3.52
% 9.82/3.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------