%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET584+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 : n024.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 08:38:46 PM UTC 2025
% Result : Theorem 30.49s 15.69s
% Output : CNFRefutation 30.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 74 ( 29 ~; 41 |; 0 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 3 con; 0-2 aty)
% Number of variables : 85 ( 85 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > #nlpp > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
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_6',type,
'#skF_6': $i ).
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_42,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(f_34,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_62,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(union(B,D),union(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th33) ).
tff(f_45,axiom,
! [B,C] : ( union(B,C) = union(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
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_42]) ).
tff(c_110,plain,
! [D_33,C_34,B_35] :
( member(D_33,C_34)
| member(D_33,B_35)
| ~ member(D_33,union(B_35,C_34)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_129,plain,
! [B_35,C_34,C_5] :
( member('#skF_1'(union(B_35,C_34),C_5),C_34)
| member('#skF_1'(union(B_35,C_34),C_5),B_35)
| subset(union(B_35,C_34),C_5) ),
inference(resolution,[status(thm)],[c_12,c_110]) ).
tff(c_1947,plain,
! [C_179,C_180] :
( subset(union(C_179,C_179),C_180)
| member('#skF_1'(union(C_179,C_179),C_180),C_179) ),
inference(factorization,[status(thm),theory(equality)],[c_129]) ).
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_42]) ).
tff(c_1994,plain,
! [C_179] : subset(union(C_179,C_179),C_179),
inference(resolution,[status(thm)],[c_1947,c_10]) ).
tff(c_32,plain,
subset('#skF_4','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_100,plain,
! [D_30,C_31,B_32] :
( member(D_30,C_31)
| ~ member(D_30,B_32)
| ~ subset(B_32,C_31) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_182,plain,
! [B_49,C_50,C_51] :
( member('#skF_1'(B_49,C_50),C_51)
| ~ subset(B_49,C_51)
| subset(B_49,C_50) ),
inference(resolution,[status(thm)],[c_12,c_100]) ).
tff(c_8,plain,
! [D_8,C_5,B_4] :
( member(D_8,C_5)
| ~ member(D_8,B_4)
| ~ subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_3284,plain,
! [B_239,C_240,C_241,C_242] :
( member('#skF_1'(B_239,C_240),C_241)
| ~ subset(C_242,C_241)
| ~ subset(B_239,C_242)
| subset(B_239,C_240) ),
inference(resolution,[status(thm)],[c_182,c_8]) ).
tff(c_3324,plain,
! [B_243,C_244] :
( member('#skF_1'(B_243,C_244),'#skF_5')
| ~ subset(B_243,'#skF_4')
| subset(B_243,C_244) ),
inference(resolution,[status(thm)],[c_32,c_3284]) ).
tff(c_3365,plain,
! [B_245] :
( ~ subset(B_245,'#skF_4')
| subset(B_245,'#skF_5') ),
inference(resolution,[status(thm)],[c_3324,c_10]) ).
tff(c_4,plain,
! [D_3,C_2,B_1] :
( ~ member(D_3,C_2)
| member(D_3,union(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_108,plain,
! [D_3,C_31,B_1,C_2] :
( member(D_3,C_31)
| ~ subset(union(B_1,C_2),C_31)
| ~ member(D_3,C_2) ),
inference(resolution,[status(thm)],[c_4,c_100]) ).
tff(c_3601,plain,
! [D_253,C_254,B_255] :
( member(D_253,'#skF_5')
| ~ member(D_253,C_254)
| ~ subset(union(B_255,C_254),'#skF_4') ),
inference(resolution,[status(thm)],[c_3365,c_108]) ).
tff(c_28121,plain,
! [B_996,C_997,B_998] :
( member('#skF_1'(B_996,C_997),'#skF_5')
| ~ subset(union(B_998,B_996),'#skF_4')
| subset(B_996,C_997) ),
inference(resolution,[status(thm)],[c_12,c_3601]) ).
tff(c_28130,plain,
! [C_999] :
( member('#skF_1'('#skF_4',C_999),'#skF_5')
| subset('#skF_4',C_999) ),
inference(resolution,[status(thm)],[c_1994,c_28121]) ).
tff(c_76,plain,
! [D_24,C_25,B_26] :
( ~ member(D_24,C_25)
| member(D_24,union(B_26,C_25)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_87,plain,
! [B_4,B_26,C_25] :
( subset(B_4,union(B_26,C_25))
| ~ member('#skF_1'(B_4,union(B_26,C_25)),C_25) ),
inference(resolution,[status(thm)],[c_76,c_10]) ).
tff(c_28217,plain,
! [B_26] : subset('#skF_4',union(B_26,'#skF_5')),
inference(resolution,[status(thm)],[c_28130,c_87]) ).
tff(c_14,plain,
! [C_10,B_9] : ( union(C_10,B_9) = union(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_1840,plain,
! [B_176,C_177,C_178] :
( member('#skF_1'(union(B_176,C_177),C_178),C_177)
| member('#skF_1'(union(B_176,C_177),C_178),B_176)
| subset(union(B_176,C_177),C_178) ),
inference(resolution,[status(thm)],[c_12,c_110]) ).
tff(c_21679,plain,
! [B_847,C_848,C_849,C_850] :
( member('#skF_1'(union(B_847,C_848),C_849),C_850)
| ~ subset(C_848,C_850)
| member('#skF_1'(union(B_847,C_848),C_849),B_847)
| subset(union(B_847,C_848),C_849) ),
inference(resolution,[status(thm)],[c_1840,c_8]) ).
tff(c_63537,plain,
! [C_1685,C_1686,B_1687] :
( ~ subset(C_1685,C_1686)
| member('#skF_1'(union(B_1687,C_1685),C_1686),B_1687)
| subset(union(B_1687,C_1685),C_1686) ),
inference(resolution,[status(thm)],[c_21679,c_10]) ).
tff(c_88,plain,
! [D_27,B_28,C_29] :
( ~ member(D_27,B_28)
| member(D_27,union(B_28,C_29)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_99,plain,
! [B_4,B_28,C_29] :
( subset(B_4,union(B_28,C_29))
| ~ member('#skF_1'(B_4,union(B_28,C_29)),B_28) ),
inference(resolution,[status(thm)],[c_88,c_10]) ).
tff(c_64217,plain,
! [C_1692,B_1693,C_1694] :
( ~ subset(C_1692,union(B_1693,C_1694))
| subset(union(B_1693,C_1692),union(B_1693,C_1694)) ),
inference(resolution,[status(thm)],[c_63537,c_99]) ).
tff(c_64505,plain,
! [C_1698,B_1699,C_1700] :
( ~ subset(C_1698,union(B_1699,C_1700))
| subset(union(C_1698,B_1699),union(B_1699,C_1700)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_64217]) ).
tff(c_30,plain,
~ subset(union('#skF_4','#skF_6'),union('#skF_5','#skF_6')),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_33,plain,
~ subset(union('#skF_4','#skF_6'),union('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_30]) ).
tff(c_64594,plain,
~ subset('#skF_4',union('#skF_6','#skF_5')),
inference(resolution,[status(thm)],[c_64505,c_33]) ).
tff(c_64652,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28217,c_64594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET584+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % 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
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 21:15:51 EDT 2025
% 0.12/0.34 % CPUTime :
% 30.49/15.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.49/15.70
% 30.49/15.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------