%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET173+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 : n011.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 08:38:11 PM UTC 2025
% Result : Theorem 7.49s 2.85s
% Output : CNFRefutation 7.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 20 ~; 22 |; 2 &)
% ( 4 <=>; 1 =>; 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 71 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > 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(union,type,
union: ( $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_50,axiom,
! [B,C] : ( union(B,C) = union(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
tff(f_61,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,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
tff(f_53,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_40,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_47,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
tff(f_76,negated_conjecture,
~ ! [B,C] : ( intersection(B,union(B,C)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_absorbtion_for_intersection) ).
tff(c_20,plain,
! [C_10,B_9] : ( union(C_10,B_9) = union(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_28,plain,
! [B_13,C_14] :
( member('#skF_1'(B_13,C_14),B_13)
| subset(B_13,C_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_165,plain,
! [D_44,C_45,B_46] :
( ~ member(D_44,C_45)
| member(D_44,union(B_46,C_45)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_26,plain,
! [B_13,C_14] :
( ~ member('#skF_1'(B_13,C_14),C_14)
| subset(B_13,C_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_410,plain,
! [B_78,B_79,C_80] :
( subset(B_78,union(B_79,C_80))
| ~ member('#skF_1'(B_78,union(B_79,C_80)),C_80) ),
inference(resolution,[status(thm)],[c_165,c_26]) ).
tff(c_442,plain,
! [B_81,B_82] : subset(B_81,union(B_82,B_81)),
inference(resolution,[status(thm)],[c_28,c_410]) ).
tff(c_453,plain,
! [C_10,B_9] : subset(C_10,union(C_10,B_9)),
inference(superposition,[status(thm),theory(equality)],[c_20,c_442]) ).
tff(c_22,plain,
! [C_12,B_11] : ( intersection(C_12,B_11) = intersection(B_11,C_12) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_134,plain,
! [D_37,B_38,C_39] :
( member(D_37,B_38)
| ~ member(D_37,intersection(B_38,C_39)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_517,plain,
! [B_91,C_92,C_93] :
( member('#skF_1'(intersection(B_91,C_92),C_93),B_91)
| subset(intersection(B_91,C_92),C_93) ),
inference(resolution,[status(thm)],[c_28,c_134]) ).
tff(c_557,plain,
! [B_94,C_95] : subset(intersection(B_94,C_95),B_94),
inference(resolution,[status(thm)],[c_517,c_26]) ).
tff(c_562,plain,
! [C_12,B_11] : subset(intersection(C_12,B_11),B_11),
inference(superposition,[status(thm),theory(equality)],[c_22,c_557]) ).
tff(c_177,plain,
! [D_47,C_48,B_49] :
( member(D_47,C_48)
| ~ member(D_47,B_49)
| ~ subset(B_49,C_48) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_185,plain,
! [B_13,C_14,C_48] :
( member('#skF_1'(B_13,C_14),C_48)
| ~ subset(B_13,C_48)
| subset(B_13,C_14) ),
inference(resolution,[status(thm)],[c_28,c_177]) ).
tff(c_187,plain,
! [D_50,B_51,C_52] :
( member(D_50,intersection(B_51,C_52))
| ~ member(D_50,C_52)
| ~ member(D_50,B_51) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_3752,plain,
! [B_337,B_338,C_339] :
( subset(B_337,intersection(B_338,C_339))
| ~ member('#skF_1'(B_337,intersection(B_338,C_339)),C_339)
| ~ member('#skF_1'(B_337,intersection(B_338,C_339)),B_338) ),
inference(resolution,[status(thm)],[c_187,c_26]) ).
tff(c_3849,plain,
! [B_340,B_341] :
( ~ member('#skF_1'(B_340,intersection(B_341,B_340)),B_341)
| subset(B_340,intersection(B_341,B_340)) ),
inference(resolution,[status(thm)],[c_28,c_3752]) ).
tff(c_4365,plain,
! [B_346,C_347] :
( ~ subset(B_346,C_347)
| subset(B_346,intersection(C_347,B_346)) ),
inference(resolution,[status(thm)],[c_185,c_3849]) ).
tff(c_14,plain,
! [C_8,B_7] :
( ( C_8 = B_7 )
| ~ subset(C_8,B_7)
| ~ subset(B_7,C_8) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_4439,plain,
! [C_347,B_346] :
( ( intersection(C_347,B_346) = B_346 )
| ~ subset(intersection(C_347,B_346),B_346)
| ~ subset(B_346,C_347) ),
inference(resolution,[status(thm)],[c_4365,c_14]) ).
tff(c_4657,plain,
! [C_351,B_352] :
( ( intersection(C_351,B_352) = B_352 )
| ~ subset(B_352,C_351) ),
inference(demodulation,[status(thm),theory(equality)],[c_562,c_4439]) ).
tff(c_4708,plain,
! [C_353,B_354] : ( intersection(union(C_353,B_354),C_353) = C_353 ),
inference(resolution,[status(thm)],[c_453,c_4657]) ).
tff(c_4854,plain,
! [C_353,B_354] : ( intersection(C_353,union(C_353,B_354)) = C_353 ),
inference(superposition,[status(thm),theory(equality)],[c_4708,c_22]) ).
tff(c_44,plain,
intersection('#skF_4',union('#skF_4','#skF_5')) != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_5122,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4854,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET173+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.13 % 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
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 20:15:18 EDT 2025
% 0.14/0.34 % CPUTime :
% 7.49/2.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.49/2.86
% 7.49/2.86 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------