%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET620+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 : n025.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 10.18s 3.46s
% Output : CNFRefutation 10.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% 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 : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > symmetric_difference > intersection > difference > #nlpp > #skF_3 > #skF_5 > #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_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_74,axiom,
! [B,C] : ( symmetric_difference(B,C) = symmetric_difference(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
tff(f_68,axiom,
! [B,C] : ( union(B,C) = union(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
tff(f_30,axiom,
! [B,C] : ( symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
tff(f_71,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_33,axiom,
! [B,C] : ( difference(B,intersection(B,C)) = difference(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_into_intersection) ).
tff(f_36,axiom,
! [B,C,D] : ( difference(union(B,C),D) = union(difference(B,D),difference(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_distributes_over_union) ).
tff(f_97,negated_conjecture,
~ ! [B,C] : ( symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th96) ).
tff(c_36,plain,
! [C_24,B_23] : ( symmetric_difference(C_24,B_23) = symmetric_difference(B_23,C_24) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_32,plain,
! [C_20,B_19] : ( union(C_20,B_19) = union(B_19,C_20) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_2,plain,
! [B_1,C_2] : ( union(difference(B_1,C_2),difference(C_2,B_1)) = symmetric_difference(B_1,C_2) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_34,plain,
! [C_22,B_21] : ( intersection(C_22,B_21) = intersection(B_21,C_22) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_182,plain,
! [B_51,C_52] : ( difference(B_51,intersection(B_51,C_52)) = difference(B_51,C_52) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_191,plain,
! [B_21,C_22] : ( difference(B_21,intersection(C_22,B_21)) = difference(B_21,C_22) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_182]) ).
tff(c_4,plain,
! [B_3,C_4] : ( difference(B_3,intersection(B_3,C_4)) = difference(B_3,C_4) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_700,plain,
! [B_117,D_118,C_119] : ( union(difference(B_117,D_118),difference(C_119,D_118)) = difference(union(B_117,C_119),D_118) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_8395,plain,
! [B_366,B_367,C_368] : ( union(difference(B_366,intersection(B_367,C_368)),difference(B_367,C_368)) = difference(union(B_366,B_367),intersection(B_367,C_368)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_700]) ).
tff(c_8605,plain,
! [B_21,C_22] : ( union(difference(B_21,C_22),difference(C_22,B_21)) = difference(union(B_21,C_22),intersection(C_22,B_21)) ),
inference(superposition,[status(thm),theory(equality)],[c_191,c_8395]) ).
tff(c_12077,plain,
! [B_456,C_457] : ( difference(union(B_456,C_457),intersection(C_457,B_456)) = symmetric_difference(B_456,C_457) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8605]) ).
tff(c_12282,plain,
! [C_20,B_19] : ( difference(union(C_20,B_19),intersection(C_20,B_19)) = symmetric_difference(B_19,C_20) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_12077]) ).
tff(c_58,plain,
difference(union('#skF_4','#skF_5'),intersection('#skF_4','#skF_5')) != symmetric_difference('#skF_4','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_12503,plain,
symmetric_difference('#skF_5','#skF_4') != symmetric_difference('#skF_4','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_12282,c_58]) ).
tff(c_12506,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_12503]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET620+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
% 0.13/0.34 % Computer : n025.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 21:20:20 EDT 2025
% 0.13/0.34 % CPUTime :
% 10.18/3.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.18/3.46
% 10.18/3.46 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------