%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM388+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 : n011.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 07:55:48 PM UTC 2025
% Result : Theorem 5.75s 2.71s
% Output : CNFRefutation 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 52 ( 21 ~; 17 |; 4 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-1 aty)
% Number of variables : 32 ( 32 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_2 > #skF_11 > #skF_15 > #skF_1 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #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_2',type,
'#skF_2': $i > $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(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('#skF_16',type,
'#skF_16': $i ).
tff(ordinal,type,
ordinal: $i > $o ).
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_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(powerset,type,
powerset: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_151,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(C,A)
& in(A,B) )
=> in(C,B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_ordinal1) ).
tff(f_187,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
tff(f_161,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
tff(f_41,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
tff(f_70,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
tff(f_165,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
tff(f_171,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
tff(c_94,plain,
in('#skF_14','#skF_15'),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_214,plain,
! [B_45,A_46] :
( ~ empty(B_45)
| ~ in(A_46,B_45) ),
inference(cnfTransformation,[status(thm)],[f_187]) ).
tff(c_222,plain,
~ empty('#skF_15'),
inference(resolution,[status(thm)],[c_94,c_214]) ).
tff(c_335,plain,
! [A_67,B_68] :
( in(A_67,B_68)
| empty(B_68)
| ~ element(A_67,B_68) ),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_92,plain,
~ in('#skF_16','#skF_15'),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_356,plain,
( empty('#skF_15')
| ~ element('#skF_16','#skF_15') ),
inference(resolution,[status(thm)],[c_335,c_92]) ).
tff(c_367,plain,
~ element('#skF_16','#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_222,c_356]) ).
tff(c_100,plain,
ordinal('#skF_15'),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_178,plain,
! [A_42] :
( epsilon_transitive(A_42)
| ~ ordinal(A_42) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_190,plain,
epsilon_transitive('#skF_15'),
inference(resolution,[status(thm)],[c_100,c_178]) ).
tff(c_20,plain,
! [B_11,A_8] :
( subset(B_11,A_8)
| ~ in(B_11,A_8)
| ~ epsilon_transitive(A_8) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_96,plain,
in('#skF_16','#skF_14'),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_110,plain,
! [A_24,B_25] :
( element(A_24,powerset(B_25))
| ~ subset(A_24,B_25) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_383,plain,
! [A_72,C_73,B_74] :
( element(A_72,C_73)
| ~ element(B_74,powerset(C_73))
| ~ in(A_72,B_74) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_490,plain,
! [A_91,B_92,A_93] :
( element(A_91,B_92)
| ~ in(A_91,A_93)
| ~ subset(A_93,B_92) ),
inference(resolution,[status(thm)],[c_110,c_383]) ).
tff(c_503,plain,
! [B_94] :
( element('#skF_16',B_94)
| ~ subset('#skF_14',B_94) ),
inference(resolution,[status(thm)],[c_96,c_490]) ).
tff(c_527,plain,
! [A_96] :
( element('#skF_16',A_96)
| ~ in('#skF_14',A_96)
| ~ epsilon_transitive(A_96) ),
inference(resolution,[status(thm)],[c_20,c_503]) ).
tff(c_534,plain,
( element('#skF_16','#skF_15')
| ~ epsilon_transitive('#skF_15') ),
inference(resolution,[status(thm)],[c_94,c_527]) ).
tff(c_538,plain,
element('#skF_16','#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_190,c_534]) ).
tff(c_540,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_367,c_538]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM388+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.13 % 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
% 0.12/0.35 % Computer : n011.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Apr 8 12:05:48 EDT 2025
% 0.12/0.35 % CPUTime :
% 5.75/2.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.00/2.72
% 6.00/2.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------