%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET146+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/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 : n014.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 08:38:06 PM UTC 2025
% Result : Theorem 3.18s 1.88s
% Output : CNFRefutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 13 ~; 10 |; 2 &)
% ( 4 <=>; 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > intersection > #nlpp > empty_set > #skF_2 > #skF_3 > #skF_5 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
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(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_47,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_65,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
tff(f_33,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
tff(f_37,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_55,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
tff(f_44,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
tff(f_77,negated_conjecture,
~ ! [B] : ( intersection(B,empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th61) ).
tff(c_16,plain,
! [C_8,B_7] : ( intersection(C_8,B_7) = intersection(B_7,C_8) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_28,plain,
! [B_15] :
( empty(B_15)
| member('#skF_2'(B_15),B_15) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_164,plain,
! [D_45,B_46,C_47] :
( member(D_45,B_46)
| ~ member(D_45,intersection(B_46,C_47)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_261,plain,
! [B_60,C_61] :
( member('#skF_2'(intersection(B_60,C_61)),B_60)
| empty(intersection(B_60,C_61)) ),
inference(resolution,[status(thm)],[c_28,c_164]) ).
tff(c_8,plain,
! [B_4] : ~ member(B_4,empty_set),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_317,plain,
! [C_65] : empty(intersection(empty_set,C_65)),
inference(resolution,[status(thm)],[c_261,c_8]) ).
tff(c_333,plain,
! [C_66] : empty(intersection(C_66,empty_set)),
inference(superposition,[status(thm),theory(equality)],[c_16,c_317]) ).
tff(c_104,plain,
! [B_36,C_37] :
( member('#skF_1'(B_36,C_37),B_36)
| subset(B_36,C_37) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_26,plain,
! [C_18,B_15] :
( ~ member(C_18,B_15)
| ~ empty(B_15) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_123,plain,
! [B_36,C_37] :
( ~ empty(B_36)
| subset(B_36,C_37) ),
inference(resolution,[status(thm)],[c_104,c_26]) ).
tff(c_124,plain,
! [C_37] : subset(empty_set,C_37),
inference(resolution,[status(thm)],[c_104,c_8]) ).
tff(c_127,plain,
! [C_41,B_42] :
( ( C_41 = B_42 )
| ~ subset(C_41,B_42)
| ~ subset(B_42,C_41) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_140,plain,
! [C_43] :
( ( empty_set = C_43 )
| ~ subset(C_43,empty_set) ),
inference(resolution,[status(thm)],[c_124,c_127]) ).
tff(c_153,plain,
! [B_36] :
( ( empty_set = B_36 )
| ~ empty(B_36) ),
inference(resolution,[status(thm)],[c_123,c_140]) ).
tff(c_348,plain,
! [C_66] : ( intersection(C_66,empty_set) = empty_set ),
inference(resolution,[status(thm)],[c_333,c_153]) ).
tff(c_42,plain,
intersection('#skF_5',empty_set) != empty_set,
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_404,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_348,c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET146+3 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.13 % 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 : n014.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 20:11:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.18/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.18/1.88
% 3.18/1.88 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------