%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET002+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 : 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 08:37:24 PM UTC 2025
% Result : Theorem 23.50s 11.85s
% Output : CNFRefutation 23.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 41 ( 16 ~; 20 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 13 ( 13 usr; 2 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_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(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_78,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,A)
| member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).
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_117,negated_conjecture,
~ ! [A] : equal_set(union(A,A),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI14) ).
tff(c_6,plain,
! [A_1,B_2] :
( member('#skF_1'(A_1,B_2),A_1)
| subset(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_85,plain,
! [X_53,A_54,B_55] :
( ~ member(X_53,A_54)
| member(X_53,union(A_54,B_55)) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
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_7589,plain,
! [A_427,A_428,B_429] :
( subset(A_427,union(A_428,B_429))
| ~ member('#skF_1'(A_427,union(A_428,B_429)),A_428) ),
inference(resolution,[status(thm)],[c_85,c_4]) ).
tff(c_7800,plain,
! [A_1,B_429] : subset(A_1,union(A_1,B_429)),
inference(resolution,[status(thm)],[c_6,c_7589]) ).
tff(c_848,plain,
! [X_140,B_141,A_142] :
( member(X_140,B_141)
| member(X_140,A_142)
| ~ member(X_140,union(A_142,B_141)) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_18992,plain,
! [A_827,B_828,B_829] :
( member('#skF_1'(union(A_827,B_828),B_829),B_828)
| member('#skF_1'(union(A_827,B_828),B_829),A_827)
| subset(union(A_827,B_828),B_829) ),
inference(resolution,[status(thm)],[c_6,c_848]) ).
tff(c_41077,plain,
! [A_1279,B_1280] :
( member('#skF_1'(union(A_1279,B_1280),A_1279),B_1280)
| subset(union(A_1279,B_1280),A_1279) ),
inference(resolution,[status(thm)],[c_18992,c_4]) ).
tff(c_41383,plain,
! [B_1281] : subset(union(B_1281,B_1281),B_1281),
inference(resolution,[status(thm)],[c_41077,c_4]) ).
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_41419,plain,
! [B_1281] :
( equal_set(B_1281,union(B_1281,B_1281))
| ~ subset(B_1281,union(B_1281,B_1281)) ),
inference(resolution,[status(thm)],[c_41383,c_8]) ).
tff(c_41729,plain,
! [B_1286] : equal_set(B_1286,union(B_1286,B_1286)),
inference(demodulation,[status(thm),theory(equality)],[c_7800,c_41419]) ).
tff(c_10,plain,
! [B_7,A_6] :
( subset(B_7,A_6)
| ~ equal_set(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_12,plain,
! [A_6,B_7] :
( subset(A_6,B_7)
| ~ equal_set(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_268,plain,
! [A_92,B_93] :
( equal_set(A_92,B_93)
| ~ subset(B_93,A_92)
| ~ subset(A_92,B_93) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_2671,plain,
! [B_238,A_239] :
( equal_set(B_238,A_239)
| ~ subset(B_238,A_239)
| ~ equal_set(A_239,B_238) ),
inference(resolution,[status(thm)],[c_12,c_268]) ).
tff(c_2761,plain,
! [B_7,A_6] :
( equal_set(B_7,A_6)
| ~ equal_set(A_6,B_7) ),
inference(resolution,[status(thm)],[c_10,c_2671]) ).
tff(c_41773,plain,
! [B_1286] : equal_set(union(B_1286,B_1286),B_1286),
inference(resolution,[status(thm)],[c_41729,c_2761]) ).
tff(c_60,plain,
~ equal_set(union('#skF_4','#skF_4'),'#skF_4'),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_42614,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_41773,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET002+4 : TPTP v9.0.0. Released v2.2.0.
% 0.02/0.11 % 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
% 0.10/0.32 % Computer : n002.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue Apr 8 19:38:47 EDT 2025
% 0.10/0.32 % CPUTime :
% 23.50/11.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.50/11.86
% 23.50/11.86 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------