%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU129+2 : TPTP v9.0.0. Released v3.3.0.
% 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 : n016.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 08:52:51 PM UTC 2025
% Result : Theorem 7.95s 3.05s
% Output : CNFRefutation 7.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 8 |; 2 &)
% ( 0 <=>; 4 =>; 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 40 ( 40 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > disjoint > empty > set_union2 > set_intersection2 > #nlpp > empty_set > #skF_11 > #skF_6 > #skF_1 > #skF_7 > #skF_13 > #skF_10 > #skF_12 > #skF_5 > #skF_2 > #skF_9 > #skF_8 > #skF_3 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_35,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(f_111,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
tff(f_130,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
tff(f_125,lemma,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
tff(f_109,lemma,
! [A,B] :
( subset(A,B)
=> ( set_union2(A,B) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
tff(f_181,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
tff(f_117,lemma,
! [A,B,C] :
( ( subset(A,B)
& subset(A,C) )
=> subset(A,set_intersection2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
tff(c_6,plain,
! [B_6,A_5] : ( set_intersection2(B_6,A_5) = set_intersection2(A_5,B_6) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_445,plain,
! [B_109,A_110] : ( set_intersection2(B_109,A_110) = set_intersection2(A_110,B_109) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_90,plain,
! [A_46,B_47] : subset(set_intersection2(A_46,B_47),A_46),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_468,plain,
! [B_109,A_110] : subset(set_intersection2(B_109,A_110),A_110),
inference(superposition,[status(thm),theory(equality)],[c_445,c_90]) ).
tff(c_100,plain,
subset('#skF_9','#skF_10'),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_2378,plain,
! [A_229,C_230,B_231] :
( subset(A_229,C_230)
| ~ subset(B_231,C_230)
| ~ subset(A_229,B_231) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_2403,plain,
! [A_232] :
( subset(A_232,'#skF_10')
| ~ subset(A_232,'#skF_9') ),
inference(resolution,[status(thm)],[c_100,c_2378]) ).
tff(c_88,plain,
! [A_44,B_45] :
( ( set_union2(A_44,B_45) = B_45 )
| ~ subset(A_44,B_45) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_2418,plain,
! [A_233] :
( ( set_union2(A_233,'#skF_10') = '#skF_10' )
| ~ subset(A_233,'#skF_9') ),
inference(resolution,[status(thm)],[c_2403,c_88]) ).
tff(c_2445,plain,
! [B_234] : ( set_union2(set_intersection2(B_234,'#skF_9'),'#skF_10') = '#skF_10' ),
inference(resolution,[status(thm)],[c_468,c_2418]) ).
tff(c_122,plain,
! [A_71,B_72] : subset(A_71,set_union2(A_71,B_72)),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_2544,plain,
! [B_235] : subset(set_intersection2(B_235,'#skF_9'),'#skF_10'),
inference(superposition,[status(thm),theory(equality)],[c_2445,c_122]) ).
tff(c_2569,plain,
! [A_5] : subset(set_intersection2('#skF_9',A_5),'#skF_10'),
inference(superposition,[status(thm),theory(equality)],[c_6,c_2544]) ).
tff(c_3315,plain,
! [A_257,B_258,C_259] :
( subset(A_257,set_intersection2(B_258,C_259))
| ~ subset(A_257,C_259)
| ~ subset(A_257,B_258) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_98,plain,
~ subset(set_intersection2('#skF_9','#skF_11'),set_intersection2('#skF_10','#skF_11')),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_3333,plain,
( ~ subset(set_intersection2('#skF_9','#skF_11'),'#skF_11')
| ~ subset(set_intersection2('#skF_9','#skF_11'),'#skF_10') ),
inference(resolution,[status(thm)],[c_3315,c_98]) ).
tff(c_3364,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2569,c_468,c_3333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU129+2 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.13 % 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
% 0.13/0.34 % Computer : n016.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 22:05:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 7.95/3.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.95/3.06
% 7.95/3.06 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------