%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET639+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 : n003.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 08:38:58 PM UTC 2025
% Result : Theorem 2.97s 1.73s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 7 ( 3 ~; 1 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > intersection > #nlpp > empty_set > #skF_2 > #skF_3 > #skF_5 > #skF_6 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_86,negated_conjecture,
~ ! [B,C] :
( ( subset(B,C)
& ( intersection(C,B) = empty_set ) )
=> ( B = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th121) ).
tff(f_60,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_31,axiom,
! [B,C] :
( subset(B,C)
=> ( intersection(B,C) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_intersection) ).
tff(c_44,plain,
empty_set != '#skF_5',
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_24,plain,
! [C_15,B_14] : ( intersection(C_15,B_14) = intersection(B_14,C_15) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_48,plain,
subset('#skF_5','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_101,plain,
! [B_33,C_34] :
( ( intersection(B_33,C_34) = B_33 )
| ~ subset(B_33,C_34) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_108,plain,
intersection('#skF_5','#skF_6') = '#skF_5',
inference(resolution,[status(thm)],[c_48,c_101]) ).
tff(c_123,plain,
intersection('#skF_6','#skF_5') = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_24,c_108]) ).
tff(c_46,plain,
intersection('#skF_6','#skF_5') = empty_set,
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_135,plain,
empty_set = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_123,c_46]) ).
tff(c_137,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET639+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n003.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 21:21:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.97/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.97/1.74
% 2.97/1.74 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------