%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET696+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/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 : n021.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 08:39:06 PM UTC 2025
% Result : Theorem 173.85s 156.61s
% Output : CNFRefutation 173.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 13 ~; 10 |; 3 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 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 ( 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/sandbox/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/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
tff(f_88,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( member(B,E)
& ~ member(B,A) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
tff(f_81,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
tff(f_62,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
tff(f_119,negated_conjecture,
~ ! [A,E] :
( subset(A,E)
=> equal_set(intersection(difference(E,A),A),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI28) ).
tff(c_102,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_133,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_102,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_8582,plain,
! [A_463,B_464,B_465] :
( member('#skF_1'(intersection(A_463,B_464),B_465),A_463)
| subset(intersection(A_463,B_464),B_465) ),
inference(resolution,[status(thm)],[c_102,c_22]) ).
tff(c_34,plain,
! [B_17,A_18,E_19] :
( ~ member(B_17,A_18)
| ~ member(B_17,difference(E_19,A_18)) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_296537,plain,
! [E_3694,A_3695,B_3696,B_3697] :
( ~ member('#skF_1'(intersection(difference(E_3694,A_3695),B_3696),B_3697),A_3695)
| subset(intersection(difference(E_3694,A_3695),B_3696),B_3697) ),
inference(resolution,[status(thm)],[c_8582,c_34]) ).
tff(c_297914,plain,
! [E_3701,B_3702,B_3703] : subset(intersection(difference(E_3701,B_3702),B_3702),B_3703),
inference(resolution,[status(thm)],[c_133,c_296537]) ).
tff(c_30,plain,
! [X_16] : ~ member(X_16,empty_set),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_137,plain,
! [B_69] : subset(empty_set,B_69),
inference(resolution,[status(thm)],[c_102,c_30]) ).
tff(c_189,plain,
! [A_79,B_80] :
( equal_set(A_79,B_80)
| ~ subset(B_80,A_79)
| ~ subset(A_79,B_80) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_203,plain,
! [B_69] :
( equal_set(B_69,empty_set)
| ~ subset(B_69,empty_set) ),
inference(resolution,[status(thm)],[c_137,c_189]) ).
tff(c_298128,plain,
! [E_3701,B_3702] : equal_set(intersection(difference(E_3701,B_3702),B_3702),empty_set),
inference(resolution,[status(thm)],[c_297914,c_203]) ).
tff(c_60,plain,
~ equal_set(intersection(difference('#skF_5','#skF_4'),'#skF_4'),empty_set),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_298291,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_298128,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET696+4 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.13 % 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 : n021.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 21:26:14 EDT 2025
% 0.13/0.34 % CPUTime :
% 173.85/156.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 173.85/156.61
% 173.85/156.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------