%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU112+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 : n029.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 4.55s 2.03s
% Output : CNFRefutation 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 4 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 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 > set_union2 > #nlpp > powerset > finite_subsets > empty_set > #skF_9 > #skF_7 > #skF_4 > #skF_11 > #skF_1 > #skF_5 > #skF_10 > #skF_2 > #skF_3 > #skF_8 > #skF_6 > #skF_12
%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('#skF_1',type,
'#skF_1': $i > $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(ordinal,type,
ordinal: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
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_2',type,
'#skF_2': $i ).
tff(diff_closed,type,
diff_closed: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(set_union2,type,
set_union2: ( $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_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_60,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_234,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
tff(f_197,axiom,
! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
tff(f_248,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(C,B) )
=> subset(set_union2(A,C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
tff(f_200,negated_conjecture,
~ ! [A,B] : subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finsub_1) ).
tff(c_306,plain,
! [B_105,A_106] : ( set_union2(B_105,A_106) = set_union2(A_106,B_105) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_132,plain,
! [A_57,B_58] : subset(A_57,set_union2(A_57,B_58)),
inference(cnfTransformation,[status(thm)],[f_234]) ).
tff(c_327,plain,
! [A_106,B_105] : subset(A_106,set_union2(B_105,A_106)),
inference(superposition,[status(thm),theory(equality)],[c_306,c_132]) ).
tff(c_114,plain,
! [A_42,B_43] :
( subset(finite_subsets(A_42),finite_subsets(B_43))
| ~ subset(A_42,B_43) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_771,plain,
! [A_170,C_171,B_172] :
( subset(set_union2(A_170,C_171),B_172)
| ~ subset(C_171,B_172)
| ~ subset(A_170,B_172) ),
inference(cnfTransformation,[status(thm)],[f_248]) ).
tff(c_16,plain,
! [B_12,A_11] : ( set_union2(B_12,A_11) = set_union2(A_11,B_12) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_116,plain,
~ subset(set_union2(finite_subsets('#skF_11'),finite_subsets('#skF_12')),finite_subsets(set_union2('#skF_11','#skF_12'))),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_138,plain,
~ subset(set_union2(finite_subsets('#skF_12'),finite_subsets('#skF_11')),finite_subsets(set_union2('#skF_12','#skF_11'))),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_116]) ).
tff(c_794,plain,
( ~ subset(finite_subsets('#skF_11'),finite_subsets(set_union2('#skF_12','#skF_11')))
| ~ subset(finite_subsets('#skF_12'),finite_subsets(set_union2('#skF_12','#skF_11'))) ),
inference(resolution,[status(thm)],[c_771,c_138]) ).
tff(c_826,plain,
~ subset(finite_subsets('#skF_12'),finite_subsets(set_union2('#skF_12','#skF_11'))),
inference(splitLeft,[status(thm)],[c_794]) ).
tff(c_829,plain,
~ subset('#skF_12',set_union2('#skF_12','#skF_11')),
inference(resolution,[status(thm)],[c_114,c_826]) ).
tff(c_833,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_132,c_829]) ).
tff(c_834,plain,
~ subset(finite_subsets('#skF_11'),finite_subsets(set_union2('#skF_12','#skF_11'))),
inference(splitRight,[status(thm)],[c_794]) ).
tff(c_838,plain,
~ subset('#skF_11',set_union2('#skF_12','#skF_11')),
inference(resolution,[status(thm)],[c_114,c_834]) ).
tff(c_842,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_327,c_838]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU112+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % 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 : n029.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 22:04:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.55/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.55/2.03
% 4.55/2.03 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------