%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET604+3 : TPTP v9.0.0. Released v2.2.0.
% 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 : n032.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 08:38:51 PM UTC 2025
% Result : Theorem 2.77s 1.70s
% Output : CNFRefutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > difference > #nlpp > empty_set > #skF_2 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_29,axiom,
! [B] : subset(empty_set,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_subset) ).
tff(f_34,axiom,
! [B,C] :
( ( difference(B,C) = empty_set )
<=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_empty_set) ).
tff(f_75,negated_conjecture,
~ ! [B] : ( difference(empty_set,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_no_difference_with_empty_set) ).
tff(c_2,plain,
! [B_1] : subset(empty_set,B_1),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_52,plain,
! [B_28,C_29] :
( ( difference(B_28,C_29) = empty_set )
| ~ subset(B_28,C_29) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_63,plain,
! [B_1] : ( difference(empty_set,B_1) = empty_set ),
inference(resolution,[status(thm)],[c_2,c_52]) ).
tff(c_34,plain,
difference(empty_set,'#skF_3') != empty_set,
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_83,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_63,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.08 % Problem : SET604+3 : TPTP v9.0.0. Released v2.2.0.
% 0.05/0.09 % 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
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Tue Apr 8 21:17:45 EDT 2025
% 0.08/0.28 % CPUTime :
% 2.77/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.77/1.70
% 2.77/1.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------