%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET013+4 : 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 : n028.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 08:37:27 PM UTC 2025
% Result : Theorem 125.72s 108.20s
% Output : CNFRefutation 125.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 33 ( 13 ~; 14 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > equal_set > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_3 > #skF_5 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(equal_set,type,
equal_set: ( $i * $i ) > $o ).
tff(power_set,type,
power_set: $i > $i ).
tff(product,type,
product: $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(sum,type,
sum: $i > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $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(empty_set,type,
empty_set: $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_56,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
tff(f_72,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,A)
& member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
tff(f_62,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
tff(f_117,negated_conjecture,
~ ! [A,B] : equal_set(intersection(A,B),intersection(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI06) ).
tff(c_100,plain,
! [A_68,B_69] :
( member('#skF_1'(A_68,B_69),A_68)
| subset(A_68,B_69) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_20,plain,
! [X_10,B_12,A_11] :
( member(X_10,B_12)
| ~ member(X_10,intersection(A_11,B_12)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_131,plain,
! [A_11,B_12,B_69] :
( member('#skF_1'(intersection(A_11,B_12),B_69),B_12)
| subset(intersection(A_11,B_12),B_69) ),
inference(resolution,[status(thm)],[c_100,c_20]) ).
tff(c_22,plain,
! [X_10,A_11,B_12] :
( member(X_10,A_11)
| ~ member(X_10,intersection(A_11,B_12)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_132,plain,
! [A_11,B_12,B_69] :
( member('#skF_1'(intersection(A_11,B_12),B_69),A_11)
| subset(intersection(A_11,B_12),B_69) ),
inference(resolution,[status(thm)],[c_100,c_22]) ).
tff(c_866,plain,
! [X_143,A_144,B_145] :
( member(X_143,intersection(A_144,B_145))
| ~ member(X_143,B_145)
| ~ member(X_143,A_144) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_4,plain,
! [A_1,B_2] :
( ~ member('#skF_1'(A_1,B_2),B_2)
| subset(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_19114,plain,
! [A_822,A_823,B_824] :
( subset(A_822,intersection(A_823,B_824))
| ~ member('#skF_1'(A_822,intersection(A_823,B_824)),B_824)
| ~ member('#skF_1'(A_822,intersection(A_823,B_824)),A_823) ),
inference(resolution,[status(thm)],[c_866,c_4]) ).
tff(c_218484,plain,
! [A_3359,B_3360,A_3361] :
( ~ member('#skF_1'(intersection(A_3359,B_3360),intersection(A_3361,A_3359)),A_3361)
| subset(intersection(A_3359,B_3360),intersection(A_3361,A_3359)) ),
inference(resolution,[status(thm)],[c_132,c_19114]) ).
tff(c_219676,plain,
! [A_11,B_12] : subset(intersection(A_11,B_12),intersection(B_12,A_11)),
inference(resolution,[status(thm)],[c_131,c_218484]) ).
tff(c_219720,plain,
! [A_3362,B_3363] : subset(intersection(A_3362,B_3363),intersection(B_3363,A_3362)),
inference(resolution,[status(thm)],[c_131,c_218484]) ).
tff(c_8,plain,
! [A_6,B_7] :
( equal_set(A_6,B_7)
| ~ subset(B_7,A_6)
| ~ subset(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_219754,plain,
! [B_3363,A_3362] :
( equal_set(intersection(B_3363,A_3362),intersection(A_3362,B_3363))
| ~ subset(intersection(B_3363,A_3362),intersection(A_3362,B_3363)) ),
inference(resolution,[status(thm)],[c_219720,c_8]) ).
tff(c_219773,plain,
! [B_3363,A_3362] : equal_set(intersection(B_3363,A_3362),intersection(A_3362,B_3363)),
inference(demodulation,[status(thm),theory(equality)],[c_219676,c_219754]) ).
tff(c_60,plain,
~ equal_set(intersection('#skF_4','#skF_5'),intersection('#skF_5','#skF_4')),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_219828,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_219773,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET013+4 : TPTP v9.0.0. Released v2.2.0.
% 0.02/0.09 % 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
% 0.09/0.29 % Computer : n028.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue Apr 8 19:40:34 EDT 2025
% 0.09/0.29 % CPUTime :
% 125.72/108.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 125.82/108.21
% 125.82/108.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------