%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU154+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/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 : 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 08:52:58 PM UTC 2025
% Result : Theorem 16.87s 6.01s
% Output : CNFRefutation 16.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 22 ( 9 ~; 5 |; 5 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 5 con; 0-3 aty)
% Number of variables : 17 ( 16 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > disjoint > empty > unordered_pair > set_union2 > set_intersection2 > set_difference > #nlpp > singleton > powerset > empty_set > #skF_13 > #skF_22 > #skF_18 > #skF_17 > #skF_6 > #skF_15 > #skF_20 > #skF_12 > #skF_16 > #skF_19 > #skF_10 > #skF_11 > #skF_7 > #skF_9 > #skF_14 > #skF_3 > #skF_2 > #skF_8 > #skF_1 > #skF_21 > #skF_5 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i ) > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_17',type,
'#skF_17': $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_20',type,
'#skF_20': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $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_14',type,
'#skF_14': ( $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(powerset,type,
powerset: $i > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_162,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
tff(f_274,lemma,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] :
~ ( in(C,A)
& in(C,B) ) )
& ~ ( ? [C] :
( in(C,A)
& in(C,B) )
& disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
tff(f_55,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
tff(c_166,plain,
~ disjoint(singleton('#skF_15'),'#skF_16'),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_168,plain,
~ in('#skF_15','#skF_16'),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_4008,plain,
! [A_423,B_424] :
( in('#skF_21'(A_423,B_424),A_423)
| disjoint(A_423,B_424) ),
inference(cnfTransformation,[status(thm)],[f_274]) ).
tff(c_18,plain,
! [C_17,A_13] :
( ( C_17 = A_13 )
| ~ in(C_17,singleton(A_13)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_34303,plain,
! [A_53461,B_53462] :
( ( '#skF_21'(singleton(A_53461),B_53462) = A_53461 )
| disjoint(singleton(A_53461),B_53462) ),
inference(resolution,[status(thm)],[c_4008,c_18]) ).
tff(c_34353,plain,
'#skF_21'(singleton('#skF_15'),'#skF_16') = '#skF_15',
inference(resolution,[status(thm)],[c_34303,c_166]) ).
tff(c_238,plain,
! [A_123,B_124] :
( in('#skF_21'(A_123,B_124),B_124)
| disjoint(A_123,B_124) ),
inference(cnfTransformation,[status(thm)],[f_274]) ).
tff(c_34367,plain,
( in('#skF_15','#skF_16')
| disjoint(singleton('#skF_15'),'#skF_16') ),
inference(superposition,[status(thm),theory(equality)],[c_34353,c_238]) ).
tff(c_34377,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_166,c_168,c_34367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU154+2 : TPTP v9.0.0. Released v3.3.0.
% 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
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 22:09:03 EDT 2025
% 0.13/0.34 % CPUTime :
% 16.87/6.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.87/6.01
% 16.87/6.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------