%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET196+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 : n022.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 08:38:13 PM UTC 2025
% Result : Theorem 3.14s 1.79s
% Output : CNFRefutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 4 ~; 4 |; 1 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > intersection > #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('#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('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_44,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_41,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(f_33,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
tff(f_59,negated_conjecture,
~ ! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_is_subset) ).
tff(c_14,plain,
! [C_10,B_9] : ( intersection(C_10,B_9) = intersection(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_12,plain,
! [B_4,C_5] :
( member('#skF_1'(B_4,C_5),B_4)
| subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_85,plain,
! [D_27,C_28,B_29] :
( member(D_27,C_28)
| ~ member(D_27,intersection(B_29,C_28)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_208,plain,
! [B_47,C_48,C_49] :
( member('#skF_1'(intersection(B_47,C_48),C_49),C_48)
| subset(intersection(B_47,C_48),C_49) ),
inference(resolution,[status(thm)],[c_12,c_85]) ).
tff(c_10,plain,
! [B_4,C_5] :
( ~ member('#skF_1'(B_4,C_5),C_5)
| subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_233,plain,
! [B_50,C_51] : subset(intersection(B_50,C_51),C_51),
inference(resolution,[status(thm)],[c_208,c_10]) ).
tff(c_236,plain,
! [C_10,B_9] : subset(intersection(C_10,B_9),C_10),
inference(superposition,[status(thm),theory(equality)],[c_14,c_233]) ).
tff(c_30,plain,
~ subset(intersection('#skF_4','#skF_5'),'#skF_4'),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_242,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_236,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET196+3 : TPTP v9.0.0. Released v2.2.0.
% 0.02/0.12 % 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
% 0.11/0.33 % Computer : n022.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Apr 8 20:18:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 3.14/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.14/1.79
% 3.14/1.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------