%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET622+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 : n002.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 08:38:54 PM UTC 2025
% Result : Theorem 5.74s 2.43s
% Output : CNFRefutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > symmetric_difference > intersection > difference > #nlpp > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(symmetric_difference,type,
symmetric_difference: ( $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('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_37,axiom,
! [B,C] : ( symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).
tff(f_34,axiom,
! [B,C,D] : ( difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union2) ).
tff(f_75,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_31,axiom,
! [B,C,D] : ( intersection(intersection(B,C),D) = intersection(B,intersection(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).
tff(f_72,axiom,
! [B,C] : ( union(B,C) = union(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
tff(f_78,axiom,
! [B,C] : ( symmetric_difference(B,C) = symmetric_difference(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
tff(f_101,negated_conjecture,
~ ! [B,C,D] : ( difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th98) ).
tff(c_6,plain,
! [B_7,C_8] : ( difference(union(B_7,C_8),intersection(B_7,C_8)) = symmetric_difference(B_7,C_8) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_4,plain,
! [B_4,C_5,D_6] : ( union(difference(B_4,C_5),intersection(B_4,D_6)) = difference(B_4,difference(C_5,D_6)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_36,plain,
! [C_25,B_24] : ( intersection(C_25,B_24) = intersection(B_24,C_25) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_278,plain,
! [B_75,C_76,D_77] : ( intersection(intersection(B_75,C_76),D_77) = intersection(B_75,intersection(C_76,D_77)) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_319,plain,
! [B_75,C_76,B_24] : ( intersection(B_75,intersection(C_76,B_24)) = intersection(B_24,intersection(B_75,C_76)) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_278]) ).
tff(c_34,plain,
! [C_23,B_22] : ( union(C_23,B_22) = union(B_22,C_23) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_38,plain,
! [C_27,B_26] : ( symmetric_difference(C_27,B_26) = symmetric_difference(B_26,C_27) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_60,plain,
union(difference('#skF_4',union('#skF_5','#skF_6')),intersection(intersection('#skF_4','#skF_5'),'#skF_6')) != difference('#skF_4',symmetric_difference('#skF_5','#skF_6')),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_61,plain,
union(difference('#skF_4',union('#skF_5','#skF_6')),intersection(intersection('#skF_4','#skF_5'),'#skF_6')) != difference('#skF_4',symmetric_difference('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_60]) ).
tff(c_62,plain,
union(difference('#skF_4',union('#skF_5','#skF_6')),intersection('#skF_6',intersection('#skF_4','#skF_5'))) != difference('#skF_4',symmetric_difference('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_61]) ).
tff(c_63,plain,
union(difference('#skF_4',union('#skF_6','#skF_5')),intersection('#skF_6',intersection('#skF_4','#skF_5'))) != difference('#skF_4',symmetric_difference('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_62]) ).
tff(c_441,plain,
union(difference('#skF_4',union('#skF_6','#skF_5')),intersection('#skF_4',intersection('#skF_5','#skF_6'))) != difference('#skF_4',symmetric_difference('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_319,c_63]) ).
tff(c_442,plain,
union(difference('#skF_4',union('#skF_6','#skF_5')),intersection('#skF_4',intersection('#skF_6','#skF_5'))) != difference('#skF_4',symmetric_difference('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_441]) ).
tff(c_2069,plain,
difference('#skF_4',difference(union('#skF_6','#skF_5'),intersection('#skF_6','#skF_5'))) != difference('#skF_4',symmetric_difference('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_442]) ).
tff(c_2072,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET622+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/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 : n002.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 21:20:32 EDT 2025
% 0.14/0.35 % CPUTime :
% 5.74/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.74/2.44
% 5.74/2.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------