%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU113+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 : n026.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 08:52:47 PM UTC 2025
% Result : Theorem 5.16s 2.21s
% Output : CNFRefutation 5.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 1 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 40 ( 14 ~; 15 |; 4 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation > preboolean > ordinal > one_to_one > natural > function > finite > epsilon_transitive > epsilon_connected > empty > diff_closed > cup_closed > cap_closed > #nlpp > powerset > finite_subsets > empty_set > #skF_9 > #skF_7 > #skF_4 > #skF_11 > #skF_3 > #skF_14 > #skF_5 > #skF_10 > #skF_6 > #skF_8 > #skF_13 > #skF_2 > #skF_12 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(cup_closed,type,
cup_closed: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(finite_subsets,type,
finite_subsets: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(finite,type,
finite: $i > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $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('#skF_10',type,
'#skF_10': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(preboolean,type,
preboolean: $i > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(diff_closed,type,
diff_closed: $i > $o ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(cap_closed,type,
cap_closed: $i > $o ).
tff(natural,type,
natural: $i > $o ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_65,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
tff(f_103,axiom,
! [A] :
( ~ empty(finite_subsets(A))
& cup_closed(finite_subsets(A))
& diff_closed(finite_subsets(A))
& preboolean(finite_subsets(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finsub_1) ).
tff(f_76,axiom,
! [A,B] :
( preboolean(B)
=> ( ( B = finite_subsets(A) )
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
tff(f_93,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
tff(f_200,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
tff(f_196,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
tff(f_190,negated_conjecture,
~ ! [A] : subset(finite_subsets(A),powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
tff(c_330,plain,
! [A_117,B_118] :
( in('#skF_1'(A_117,B_118),A_117)
| subset(A_117,B_118) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_62,plain,
! [A_26] : preboolean(finite_subsets(A_26)),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_38,plain,
! [C_20,A_16] :
( subset(C_20,A_16)
| ~ in(C_20,finite_subsets(A_16))
| ~ preboolean(finite_subsets(A_16)) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_145,plain,
! [C_20,A_16] :
( subset(C_20,A_16)
| ~ in(C_20,finite_subsets(A_16)) ),
inference(demodulation,[status(thm),theory(equality)],[c_62,c_38]) ).
tff(c_347,plain,
! [A_16,B_118] :
( subset('#skF_1'(finite_subsets(A_16),B_118),A_16)
| subset(finite_subsets(A_16),B_118) ),
inference(resolution,[status(thm)],[c_330,c_145]) ).
tff(c_52,plain,
! [A_25] : ~ empty(powerset(A_25)),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_132,plain,
! [A_43,B_44] :
( element(A_43,powerset(B_44))
| ~ subset(A_43,B_44) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_128,plain,
! [A_41,B_42] :
( in(A_41,B_42)
| empty(B_42)
| ~ element(A_41,B_42) ),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_416,plain,
! [A_128,B_129] :
( ~ in('#skF_1'(A_128,B_129),B_129)
| subset(A_128,B_129) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_998,plain,
! [A_194,B_195] :
( subset(A_194,B_195)
| empty(B_195)
| ~ element('#skF_1'(A_194,B_195),B_195) ),
inference(resolution,[status(thm)],[c_128,c_416]) ).
tff(c_1010,plain,
! [A_194,B_44] :
( subset(A_194,powerset(B_44))
| empty(powerset(B_44))
| ~ subset('#skF_1'(A_194,powerset(B_44)),B_44) ),
inference(resolution,[status(thm)],[c_132,c_998]) ).
tff(c_1104,plain,
! [A_210,B_211] :
( subset(A_210,powerset(B_211))
| ~ subset('#skF_1'(A_210,powerset(B_211)),B_211) ),
inference(negUnitSimplification,[status(thm)],[c_52,c_1010]) ).
tff(c_1119,plain,
! [A_16] : subset(finite_subsets(A_16),powerset(A_16)),
inference(resolution,[status(thm)],[c_347,c_1104]) ).
tff(c_126,plain,
~ subset(finite_subsets('#skF_14'),powerset('#skF_14')),
inference(cnfTransformation,[status(thm)],[f_190]) ).
tff(c_1123,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1119,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU113+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.13 % 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
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 22:04:08 EDT 2025
% 0.14/0.34 % CPUTime :
% 5.16/2.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.16/2.21
% 5.16/2.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------