%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET873+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/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 : n028.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 08:39:29 PM UTC 2025
% Result : Theorem 3.11s 1.79s
% Output : CNFRefutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 5 ~; 3 |; 0 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > set_union2 > #nlpp > singleton > #skF_5 > #skF_6 > #skF_3 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_4',type,
'#skF_4': $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(f_70,negated_conjecture,
~ ! [A,B] :
( ( set_union2(singleton(A),singleton(B)) = singleton(A) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
tff(f_65,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_33,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_58,axiom,
! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).
tff(f_40,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
tff(c_32,plain,
'#skF_5' != '#skF_6',
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_30,plain,
! [A_18] : subset(A_18,A_18),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_34,plain,
set_union2(singleton('#skF_5'),singleton('#skF_6')) = singleton('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_4,plain,
! [B_4,A_3] : ( set_union2(B_4,A_3) = set_union2(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_90,plain,
set_union2(singleton('#skF_6'),singleton('#skF_5')) = singleton('#skF_5'),
inference(superposition,[status(thm),theory(equality)],[c_34,c_4]) ).
tff(c_24,plain,
! [A_16,B_17] :
( in(A_16,B_17)
| ~ subset(set_union2(singleton(A_16),B_17),B_17) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_154,plain,
( in('#skF_6',singleton('#skF_5'))
| ~ subset(singleton('#skF_5'),singleton('#skF_5')) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_24]) ).
tff(c_164,plain,
in('#skF_6',singleton('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_154]) ).
tff(c_6,plain,
! [C_9,A_5] :
( ( C_9 = A_5 )
| ~ in(C_9,singleton(A_5)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_170,plain,
'#skF_5' = '#skF_6',
inference(resolution,[status(thm)],[c_164,c_6]) ).
tff(c_176,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET873+1 : TPTP v9.0.0. Released v3.2.0.
% 0.10/0.11 % 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
% 0.11/0.31 % Computer : n028.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Apr 8 21:48:34 EDT 2025
% 0.11/0.31 % CPUTime :
% 3.11/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.11/1.80
% 3.11/1.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------