%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU230+3 : 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 : n016.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 08:53:18 PM UTC 2025
% Result : Theorem 5.24s 2.31s
% Output : CNFRefutation 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 12 ( 5 ~; 3 |; 0 &)
% ( 4 <=>; 0 =>; 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 : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 16 ( 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > element > relation_non_empty > relation_empty_yielding > relation > one_to_one > function > empty > set_union2 > #nlpp > succ > singleton > empty_set > #skF_5 > #skF_11 > #skF_15 > #skF_4 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(singleton,type,
singleton: $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(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
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(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $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_3',type,
'#skF_3': ( $i * $i * $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(succ,type,
succ: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_62,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_55,axiom,
! [A] : ( succ(A) = set_union2(A,singleton(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
tff(f_71,axiom,
! [A,B,C] :
( ( C = set_union2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
tff(f_155,negated_conjecture,
~ ! [A] : in(A,succ(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
tff(c_20,plain,
! [C_13] : in(C_13,singleton(C_13)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_16,plain,
! [A_8] : ( set_union2(A_8,singleton(A_8)) = succ(A_8) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_405,plain,
! [D_71,B_72,A_73] :
( ~ in(D_71,B_72)
| in(D_71,set_union2(A_73,B_72)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_1540,plain,
! [D_157,A_158] :
( ~ in(D_157,singleton(A_158))
| in(D_157,succ(A_158)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_405]) ).
tff(c_116,plain,
~ in('#skF_16',succ('#skF_16')),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_1615,plain,
~ in('#skF_16',singleton('#skF_16')),
inference(resolution,[status(thm)],[c_1540,c_116]) ).
tff(c_1642,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_20,c_1615]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU230+3 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % 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
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 8 22:25:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 5.24/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.24/2.31
% 5.24/2.31 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------