%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET949+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 : n005.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 08:39:39 PM UTC 2025
% Result : Theorem 3.93s 2.07s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 5 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 12 ( 6 ~; 1 |; 3 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-4 aty)
% Number of variables : 18 ( 16 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_1 > #skF_11 > #skF_4 > #skF_7 > #skF_10 > #skF_2 > #skF_6 > #skF_9 > #skF_8 > #skF_5 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(f_45,axiom,
! [A,B,C] :
( ( C = cartesian_product2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& ( D = ordered_pair(E,F) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
tff(f_63,negated_conjecture,
~ ! [A,B,C] :
~ ( in(A,cartesian_product2(B,C))
& ! [D,E] : ( ordered_pair(D,E) != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_zfmisc_1) ).
tff(c_571,plain,
! [A_96,B_97,D_98] :
( ( ordered_pair('#skF_5'(A_96,B_97,cartesian_product2(A_96,B_97),D_98),'#skF_6'(A_96,B_97,cartesian_product2(A_96,B_97),D_98)) = D_98 )
| ~ in(D_98,cartesian_product2(A_96,B_97)) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_38,plain,
! [D_45,E_46] : ( ordered_pair(D_45,E_46) != '#skF_9' ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_605,plain,
! [A_96,B_97] : ~ in('#skF_9',cartesian_product2(A_96,B_97)),
inference(superposition,[status(thm),theory(equality)],[c_571,c_38]) ).
tff(c_40,plain,
in('#skF_9',cartesian_product2('#skF_10','#skF_11')),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_607,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_605,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET949+1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % 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
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 21:51:42 EDT 2025
% 0.14/0.34 % CPUTime :
% 3.93/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.93/2.08
% 3.93/2.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------