%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET183+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 : n029.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 08:38:12 PM UTC 2025
% Result : Theorem 6.27s 2.81s
% Output : CNFRefutation 6.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 26 ~; 28 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 63 ( 63 !; 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_71,negated_conjecture,
~ ! [B,C] :
( subset(B,C)
=> ( intersection(B,C) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_intersection) ).
tff(f_57,axiom,
! [B] : subset(B,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
tff(f_44,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
tff(f_54,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_36,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).
tff(f_51,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
tff(c_38,plain,
intersection('#skF_4','#skF_5') != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_24,plain,
! [B_15] : subset(B_15,B_15),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_40,plain,
subset('#skF_4','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_14,plain,
! [B_6,C_7] :
( member('#skF_1'(B_6,C_7),B_6)
| subset(B_6,C_7) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_143,plain,
! [D_40,C_41,B_42] :
( member(D_40,C_41)
| ~ member(D_40,B_42)
| ~ subset(B_42,C_41) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_198,plain,
! [B_54,C_55,C_56] :
( member('#skF_1'(B_54,C_55),C_56)
| ~ subset(B_54,C_56)
| subset(B_54,C_55) ),
inference(resolution,[status(thm)],[c_14,c_143]) ).
tff(c_10,plain,
! [D_10,C_7,B_6] :
( member(D_10,C_7)
| ~ member(D_10,B_6)
| ~ subset(B_6,C_7) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_435,plain,
! [B_89,C_90,C_91,C_92] :
( member('#skF_1'(B_89,C_90),C_91)
| ~ subset(C_92,C_91)
| ~ subset(B_89,C_92)
| subset(B_89,C_90) ),
inference(resolution,[status(thm)],[c_198,c_10]) ).
tff(c_447,plain,
! [B_89,C_90] :
( member('#skF_1'(B_89,C_90),'#skF_5')
| ~ subset(B_89,'#skF_4')
| subset(B_89,C_90) ),
inference(resolution,[status(thm)],[c_40,c_435]) ).
tff(c_161,plain,
! [D_47,B_48,C_49] :
( member(D_47,intersection(B_48,C_49))
| ~ member(D_47,C_49)
| ~ member(D_47,B_48) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_12,plain,
! [B_6,C_7] :
( ~ member('#skF_1'(B_6,C_7),C_7)
| subset(B_6,C_7) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1718,plain,
! [B_212,B_213,C_214] :
( subset(B_212,intersection(B_213,C_214))
| ~ member('#skF_1'(B_212,intersection(B_213,C_214)),C_214)
| ~ member('#skF_1'(B_212,intersection(B_213,C_214)),B_213) ),
inference(resolution,[status(thm)],[c_161,c_12]) ).
tff(c_1783,plain,
! [B_215,B_216] :
( ~ member('#skF_1'(B_215,intersection(B_216,B_215)),B_216)
| subset(B_215,intersection(B_216,B_215)) ),
inference(resolution,[status(thm)],[c_14,c_1718]) ).
tff(c_2163,plain,
! [B_219] :
( ~ subset(B_219,'#skF_4')
| subset(B_219,intersection('#skF_5',B_219)) ),
inference(resolution,[status(thm)],[c_447,c_1783]) ).
tff(c_45,plain,
! [C_24,B_25] : ( intersection(C_24,B_25) = intersection(B_25,C_24) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_8,plain,
! [B_4,C_5] : subset(intersection(B_4,C_5),B_4),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_97,plain,
! [C_28,B_29] : subset(intersection(C_28,B_29),B_29),
inference(superposition,[status(thm),theory(equality)],[c_45,c_8]) ).
tff(c_16,plain,
! [C_12,B_11] :
( ( C_12 = B_11 )
| ~ subset(C_12,B_11)
| ~ subset(B_11,C_12) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_106,plain,
! [C_28,B_29] :
( ( intersection(C_28,B_29) = B_29 )
| ~ subset(B_29,intersection(C_28,B_29)) ),
inference(resolution,[status(thm)],[c_97,c_16]) ).
tff(c_2449,plain,
! [B_225] :
( ( intersection('#skF_5',B_225) = B_225 )
| ~ subset(B_225,'#skF_4') ),
inference(resolution,[status(thm)],[c_2163,c_106]) ).
tff(c_2474,plain,
intersection('#skF_5','#skF_4') = '#skF_4',
inference(resolution,[status(thm)],[c_24,c_2449]) ).
tff(c_22,plain,
! [C_14,B_13] : ( intersection(C_14,B_13) = intersection(B_13,C_14) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_84,plain,
! [C_26,B_27] :
( ( C_26 = B_27 )
| ~ subset(C_26,B_27)
| ~ subset(B_27,C_26) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_147,plain,
! [B_43,C_44] :
( ( intersection(B_43,C_44) = B_43 )
| ~ subset(B_43,intersection(B_43,C_44)) ),
inference(resolution,[status(thm)],[c_8,c_84]) ).
tff(c_150,plain,
! [B_13,C_14] :
( ( intersection(B_13,C_14) = B_13 )
| ~ subset(B_13,intersection(C_14,B_13)) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_147]) ).
tff(c_2603,plain,
( ( intersection('#skF_4','#skF_5') = '#skF_4' )
| ~ subset('#skF_4','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_2474,c_150]) ).
tff(c_2673,plain,
intersection('#skF_4','#skF_5') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_24,c_2603]) ).
tff(c_2675,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_2673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SET183+3 : TPTP v9.0.0. Released v2.2.0.
% 0.05/0.09 % 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
% 0.09/0.28 % Computer : n029.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Tue Apr 8 20:16:49 EDT 2025
% 0.09/0.28 % CPUTime :
% 6.27/2.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.27/2.82
% 6.27/2.82 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------