%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM405+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/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 : n021.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 07:55:50 PM UTC 2025
% Result : Theorem 6.89s 2.64s
% Output : CNFRefutation 6.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 65 ( 31 ~; 26 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 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 : 12 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 15 con; 0-1 aty)
% Number of variables : 31 ( 30 !; 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_16 > #skF_18 > #skF_11 > #skF_1 > #skF_7 > #skF_10 > #skF_15 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_17 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_16',type,
'#skF_16': $i > $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_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('#skF_15',type,
'#skF_15': $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
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_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_17',type,
'#skF_17': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_197,axiom,
! [A] :
~ ! [B] :
( in(B,A)
<=> ordinal(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).
tff(f_181,axiom,
! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( in(C,A)
& ordinal(C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_43__ordinal1) ).
tff(f_41,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
tff(f_63,axiom,
! [A] :
( ( epsilon_transitive(A)
& epsilon_connected(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
tff(f_204,negated_conjecture,
~ ! [A] :
~ ! [B] :
( ordinal(B)
=> in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_ordinal1) ).
tff(c_410,plain,
! [A_60] :
( ordinal('#skF_16'(A_60))
| in('#skF_17'(A_60),A_60) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_130,plain,
! [C_16,A_11] :
( ordinal(C_16)
| ~ in(C_16,'#skF_15'(A_11)) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_592,plain,
! [A_78] :
( ordinal('#skF_17'('#skF_15'(A_78)))
| ordinal('#skF_16'('#skF_15'(A_78))) ),
inference(resolution,[status(thm)],[c_410,c_130]) ).
tff(c_8,plain,
! [A_4] :
( epsilon_transitive(A_4)
| ~ ordinal(A_4) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_635,plain,
! [A_82] :
( epsilon_transitive('#skF_16'('#skF_15'(A_82)))
| ordinal('#skF_17'('#skF_15'(A_82))) ),
inference(resolution,[status(thm)],[c_592,c_8]) ).
tff(c_317,plain,
! [A_51] :
( ordinal('#skF_16'(A_51))
| ~ ordinal('#skF_17'(A_51)) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_325,plain,
! [A_51] :
( epsilon_transitive('#skF_16'(A_51))
| ~ ordinal('#skF_17'(A_51)) ),
inference(resolution,[status(thm)],[c_317,c_8]) ).
tff(c_649,plain,
! [A_82] : epsilon_transitive('#skF_16'('#skF_15'(A_82))),
inference(resolution,[status(thm)],[c_635,c_325]) ).
tff(c_6,plain,
! [A_4] :
( epsilon_connected(A_4)
| ~ ordinal(A_4) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_618,plain,
! [A_81] :
( epsilon_connected('#skF_16'('#skF_15'(A_81)))
| ordinal('#skF_17'('#skF_15'(A_81))) ),
inference(resolution,[status(thm)],[c_592,c_6]) ).
tff(c_324,plain,
! [A_51] :
( epsilon_connected('#skF_16'(A_51))
| ~ ordinal('#skF_17'(A_51)) ),
inference(resolution,[status(thm)],[c_317,c_6]) ).
tff(c_631,plain,
! [A_81] : epsilon_connected('#skF_16'('#skF_15'(A_81))),
inference(resolution,[status(thm)],[c_618,c_324]) ).
tff(c_18,plain,
! [A_7] :
( ordinal(A_7)
| ~ epsilon_connected(A_7)
| ~ epsilon_transitive(A_7) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_146,plain,
! [B_24] :
( in(B_24,'#skF_18')
| ~ ordinal(B_24) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_554,plain,
! [C_73,A_74] :
( in(C_73,'#skF_15'(A_74))
| ~ ordinal(C_73)
| ~ in(C_73,A_74) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_138,plain,
! [A_21] :
( ~ in('#skF_16'(A_21),A_21)
| ~ ordinal('#skF_17'(A_21)) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_1106,plain,
! [A_110] :
( ~ ordinal('#skF_17'('#skF_15'(A_110)))
| ~ ordinal('#skF_16'('#skF_15'(A_110)))
| ~ in('#skF_16'('#skF_15'(A_110)),A_110) ),
inference(resolution,[status(thm)],[c_554,c_138]) ).
tff(c_1129,plain,
( ~ ordinal('#skF_17'('#skF_15'('#skF_18')))
| ~ ordinal('#skF_16'('#skF_15'('#skF_18'))) ),
inference(resolution,[status(thm)],[c_146,c_1106]) ).
tff(c_1138,plain,
~ ordinal('#skF_16'('#skF_15'('#skF_18'))),
inference(splitLeft,[status(thm)],[c_1129]) ).
tff(c_1153,plain,
( ~ epsilon_connected('#skF_16'('#skF_15'('#skF_18')))
| ~ epsilon_transitive('#skF_16'('#skF_15'('#skF_18'))) ),
inference(resolution,[status(thm)],[c_18,c_1138]) ).
tff(c_1164,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_649,c_631,c_1153]) ).
tff(c_1165,plain,
~ ordinal('#skF_17'('#skF_15'('#skF_18'))),
inference(splitRight,[status(thm)],[c_1129]) ).
tff(c_1166,plain,
ordinal('#skF_16'('#skF_15'('#skF_18'))),
inference(splitRight,[status(thm)],[c_1129]) ).
tff(c_142,plain,
! [A_21] :
( ~ in('#skF_16'(A_21),A_21)
| in('#skF_17'(A_21),A_21) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_1199,plain,
! [A_114] :
( in('#skF_17'('#skF_15'(A_114)),'#skF_15'(A_114))
| ~ ordinal('#skF_16'('#skF_15'(A_114)))
| ~ in('#skF_16'('#skF_15'(A_114)),A_114) ),
inference(resolution,[status(thm)],[c_554,c_142]) ).
tff(c_3897,plain,
! [A_172] :
( ordinal('#skF_17'('#skF_15'(A_172)))
| ~ ordinal('#skF_16'('#skF_15'(A_172)))
| ~ in('#skF_16'('#skF_15'(A_172)),A_172) ),
inference(resolution,[status(thm)],[c_1199,c_130]) ).
tff(c_3933,plain,
( ordinal('#skF_17'('#skF_15'('#skF_18')))
| ~ ordinal('#skF_16'('#skF_15'('#skF_18'))) ),
inference(resolution,[status(thm)],[c_146,c_3897]) ).
tff(c_3940,plain,
ordinal('#skF_17'('#skF_15'('#skF_18'))),
inference(demodulation,[status(thm),theory(equality)],[c_1166,c_3933]) ).
tff(c_3942,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1165,c_3940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM405+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.13 % 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
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 12:09:28 EDT 2025
% 0.12/0.34 % CPUTime :
% 6.89/2.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.89/2.65
% 6.89/2.65 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------