%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU143+2 : TPTP v9.0.0. Released v3.3.0.
% 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 : n003.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 08:52:54 PM UTC 2025
% Result : Theorem 5.63s 2.62s
% Output : CNFRefutation 5.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 0 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 4 con; 0-3 aty)
% Number of variables : 8 ( 8 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > disjoint > empty > unordered_pair > set_union2 > set_intersection2 > set_difference > #nlpp > singleton > empty_set > #skF_6 > #skF_15 > #skF_17 > #skF_12 > #skF_4 > #skF_14 > #skF_18 > #skF_19 > #skF_13 > #skF_5 > #skF_8 > #skF_11 > #skF_7 > #skF_9 > #skF_3 > #skF_2 > #skF_1 > #skF_16 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_61,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_141,negated_conjecture,
~ ! [A] : ( singleton(A) != empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
tff(f_55,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
tff(c_30,plain,
! [B_21] : ~ in(B_21,empty_set),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_146,plain,
singleton('#skF_13') = empty_set,
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_248,plain,
! [C_142] : in(C_142,singleton(C_142)),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_251,plain,
in('#skF_13',empty_set),
inference(superposition,[status(thm),theory(equality)],[c_146,c_248]) ).
tff(c_253,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU143+2 : TPTP v9.0.0. Released v3.3.0.
% 0.00/0.11 % 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
% 0.10/0.30 % Computer : n003.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Apr 8 22:07:33 EDT 2025
% 0.10/0.31 % CPUTime :
% 5.63/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.63/2.63
% 5.63/2.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------