%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET063+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/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 : n007.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 08:37:45 PM UTC 2025
% Result : Theorem 2.71s 1.71s
% Output : CNFRefutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 3 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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; 2 con; 0-2 aty)
% Number of variables : 7 ( 7 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > #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('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_64,negated_conjecture,
~ ! [B] :
( subset(B,empty_set)
=> ( B = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_of_empty_set_is_empty_set) ).
tff(f_29,axiom,
! [B] : subset(empty_set,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_subset) ).
tff(f_48,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
tff(c_24,plain,
empty_set != '#skF_3',
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_2,plain,
! [B_1] : subset(empty_set,B_1),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_26,plain,
subset('#skF_3',empty_set),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_54,plain,
! [C_23,B_24] :
( ( C_23 = B_24 )
| ~ subset(C_23,B_24)
| ~ subset(B_24,C_23) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_58,plain,
( ( empty_set = '#skF_3' )
| ~ subset(empty_set,'#skF_3') ),
inference(resolution,[status(thm)],[c_26,c_54]) ).
tff(c_67,plain,
empty_set = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_2,c_58]) ).
tff(c_69,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET063+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 19:55:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.71/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.71/1.72
% 2.71/1.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------