%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET629+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 : n031.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 08:38:56 PM UTC 2025
% Result : Theorem 3.72s 1.79s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 7 |; 3 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 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 : 44 ( 43 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ member > intersect > disjoint > intersection > difference > #nlpp > #skF_3 > #skF_5 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(intersect,type,
intersect: ( $i * $i ) > $o ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
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,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
tff(f_59,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_50,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
tff(f_34,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_42,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
tff(f_76,negated_conjecture,
~ ! [B,C] : disjoint(intersection(B,C),difference(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_and_difference_disjoint) ).
tff(c_22,plain,
! [B_12,C_13] :
( disjoint(B_12,C_13)
| intersect(B_12,C_13) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_24,plain,
! [C_15,B_14] : ( intersection(C_15,B_14) = intersection(B_14,C_15) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_130,plain,
! [B_49,C_50] :
( member('#skF_1'(B_49,C_50),B_49)
| ~ intersect(B_49,C_50) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_6,plain,
! [D_3,B_1,C_2] :
( member(D_3,B_1)
| ~ member(D_3,intersection(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_700,plain,
! [B_120,C_121,C_122] :
( member('#skF_1'(intersection(B_120,C_121),C_122),B_120)
| ~ intersect(intersection(B_120,C_121),C_122) ),
inference(resolution,[status(thm)],[c_130,c_6]) ).
tff(c_95,plain,
! [B_41,C_42] :
( member('#skF_1'(B_41,C_42),C_42)
| ~ intersect(B_41,C_42) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_10,plain,
! [D_6,C_5,B_4] :
( ~ member(D_6,C_5)
| ~ member(D_6,difference(B_4,C_5)) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_104,plain,
! [B_41,B_4,C_5] :
( ~ member('#skF_1'(B_41,difference(B_4,C_5)),C_5)
| ~ intersect(B_41,difference(B_4,C_5)) ),
inference(resolution,[status(thm)],[c_95,c_10]) ).
tff(c_743,plain,
! [B_123,C_124,B_125] : ~ intersect(intersection(B_123,C_124),difference(B_125,B_123)),
inference(resolution,[status(thm)],[c_700,c_104]) ).
tff(c_768,plain,
! [C_129,B_130,B_131] : ~ intersect(intersection(C_129,B_130),difference(B_131,B_130)),
inference(superposition,[status(thm),theory(equality)],[c_24,c_743]) ).
tff(c_782,plain,
! [C_129,B_130,B_131] : disjoint(intersection(C_129,B_130),difference(B_131,B_130)),
inference(resolution,[status(thm)],[c_22,c_768]) ).
tff(c_40,plain,
~ disjoint(intersection('#skF_4','#skF_5'),difference('#skF_4','#skF_5')),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_797,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_782,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET629+3 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.08 % 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
% 0.07/0.26 % Computer : n031.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Apr 8 21:21:07 EDT 2025
% 0.07/0.26 % CPUTime :
% 3.72/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.72/1.79
% 3.72/1.79 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------