%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU123+1 : 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 : n021.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 08:52:49 PM UTC 2025
% Result : Theorem 2.50s 1.63s
% Output : CNFRefutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 4 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 11 ( 10 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > #nlpp > empty_set > #skF_2 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(in,type,
in: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(f_41,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_57,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_53,negated_conjecture,
~ ! [A] :
( subset(A,empty_set)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
tff(f_48,axiom,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
tff(f_37,axiom,
! [A,B] :
( ( A = B )
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
tff(c_14,plain,
empty('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_35,plain,
! [A_15] :
( ( empty_set = A_15 )
| ~ empty(A_15) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_44,plain,
empty_set = '#skF_1',
inference(resolution,[status(thm)],[c_14,c_35]) ).
tff(c_22,plain,
empty_set != '#skF_3',
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_49,plain,
'#skF_3' != '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_44,c_22]) ).
tff(c_20,plain,
! [A_7] : subset(empty_set,A_7),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_46,plain,
! [A_7] : subset('#skF_1',A_7),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_20]) ).
tff(c_24,plain,
subset('#skF_3',empty_set),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_47,plain,
subset('#skF_3','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_24]) ).
tff(c_68,plain,
! [B_24,A_25] :
( ( B_24 = A_25 )
| ~ subset(B_24,A_25)
| ~ subset(A_25,B_24) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_72,plain,
( ( '#skF_3' = '#skF_1' )
| ~ subset('#skF_1','#skF_3') ),
inference(resolution,[status(thm)],[c_47,c_68]) ).
tff(c_78,plain,
'#skF_3' = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_46,c_72]) ).
tff(c_80,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_49,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU123+1 : 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
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 22:05:14 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.50/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.75/1.63
% 2.75/1.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------