TSTP Solution File: SET934+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET934+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n004.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 : Tue Aug 22 10:57:22 EDT 2023
% Result : Theorem 276.33s 227.71s
% Output : CNFRefutation 276.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 68 ( 17 unt; 14 typ; 0 def)
% Number of atoms : 118 ( 21 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 96 ( 32 ~; 56 |; 1 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 10 >; 10 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 135 (; 135 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > set_union2 > #nlpp > powerset > #skF_4 > #skF_7 > #skF_6 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1 > #skF_5
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff(f_33,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_56,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
tff(f_40,axiom,
! [A,B] :
( ( B = powerset(A) )
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
tff(f_85,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
tff(f_83,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
tff(f_70,axiom,
! [A,B] : ( set_union2(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
tff(f_49,axiom,
! [A,B,C] :
( ( C = set_union2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
tff(f_88,negated_conjecture,
~ ! [A,B] : subset(set_union2(powerset(A),powerset(B)),powerset(set_union2(A,B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
tff(c_4,plain,
! [B_4,A_3] : ( set_union2(B_4,A_3) = set_union2(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_215,plain,
! [A_62,B_63] :
( in('#skF_5'(A_62,B_63),A_62)
| subset(A_62,B_63) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_6,plain,
! [C_9,A_5] :
( subset(C_9,A_5)
| ~ in(C_9,powerset(A_5)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_228,plain,
! [A_5,B_63] :
( subset('#skF_5'(powerset(A_5),B_63),A_5)
| subset(powerset(A_5),B_63) ),
inference(resolution,[status(thm)],[c_215,c_6]) ).
tff(c_56,plain,
! [A_32,B_33] : subset(A_32,set_union2(A_32,B_33)),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_280,plain,
! [A_70,C_71,B_72] :
( subset(A_70,C_71)
| ~ subset(B_72,C_71)
| ~ subset(A_70,B_72) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_288,plain,
! [A_70,A_32,B_33] :
( subset(A_70,set_union2(A_32,B_33))
| ~ subset(A_70,A_32) ),
inference(resolution,[status(thm)],[c_56,c_280]) ).
tff(c_8,plain,
! [C_9,A_5] :
( in(C_9,powerset(A_5))
| ~ subset(C_9,A_5) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_199,plain,
! [A_60,B_61] :
( ~ in('#skF_5'(A_60,B_61),B_61)
| subset(A_60,B_61) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_1334,plain,
! [A_180,A_181] :
( subset(A_180,powerset(A_181))
| ~ subset('#skF_5'(A_180,powerset(A_181)),A_181) ),
inference(resolution,[status(thm)],[c_8,c_199]) ).
tff(c_22003,plain,
! [A_984,A_985,B_986] :
( subset(A_984,powerset(set_union2(A_985,B_986)))
| ~ subset('#skF_5'(A_984,powerset(set_union2(A_985,B_986))),A_985) ),
inference(resolution,[status(thm)],[c_288,c_1334]) ).
tff(c_22050,plain,
! [A_5,B_986] : subset(powerset(A_5),powerset(set_union2(A_5,B_986))),
inference(resolution,[status(thm)],[c_228,c_22003]) ).
tff(c_46,plain,
! [A_25] : ( set_union2(A_25,A_25) = A_25 ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_34,plain,
! [A_10,B_11,C_12] :
( in('#skF_3'(A_10,B_11,C_12),B_11)
| in('#skF_3'(A_10,B_11,C_12),A_10)
| in('#skF_4'(A_10,B_11,C_12),C_12)
| ( set_union2(A_10,B_11) = C_12 ) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_960,plain,
! [A_144,B_145,C_146] :
( in('#skF_3'(A_144,B_145,C_146),B_145)
| in('#skF_3'(A_144,B_145,C_146),A_144)
| ~ in('#skF_4'(A_144,B_145,C_146),A_144)
| ( set_union2(A_144,B_145) = C_146 ) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_4840,plain,
! [C_370,B_371] :
( in('#skF_3'(C_370,B_371,C_370),B_371)
| in('#skF_3'(C_370,B_371,C_370),C_370)
| ( set_union2(C_370,B_371) = C_370 ) ),
inference(resolution,[status(thm)],[c_34,c_960]) ).
tff(c_36,plain,
! [C_20,B_17,A_16] :
( in(C_20,B_17)
| ~ in(C_20,A_16)
| ~ subset(A_16,B_17) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_4890,plain,
! [C_370,B_371,B_17] :
( in('#skF_3'(C_370,B_371,C_370),B_17)
| ~ subset(B_371,B_17)
| in('#skF_3'(C_370,B_371,C_370),C_370)
| ( set_union2(C_370,B_371) = C_370 ) ),
inference(resolution,[status(thm)],[c_4840,c_36]) ).
tff(c_249458,plain,
! [B_4250,C_4251] :
( ~ subset(B_4250,C_4251)
| ( set_union2(C_4251,B_4250) = C_4251 )
| in('#skF_3'(C_4251,B_4250,C_4251),C_4251) ),
inference(factorization,[status(thm),theory(equality)],[c_4890]) ).
tff(c_807,plain,
! [A_132,B_133,C_134] :
( ~ in('#skF_3'(A_132,B_133,C_134),C_134)
| in('#skF_4'(A_132,B_133,C_134),C_134)
| ( set_union2(A_132,B_133) = C_134 ) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_18,plain,
! [D_15,B_11,A_10] :
( in(D_15,B_11)
| in(D_15,A_10)
| ~ in(D_15,set_union2(A_10,B_11)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_15466,plain,
! [A_809,B_810,A_811,B_812] :
( in('#skF_4'(A_809,B_810,set_union2(A_811,B_812)),B_812)
| in('#skF_4'(A_809,B_810,set_union2(A_811,B_812)),A_811)
| ~ in('#skF_3'(A_809,B_810,set_union2(A_811,B_812)),set_union2(A_811,B_812))
| ( set_union2(A_811,B_812) = set_union2(A_809,B_810) ) ),
inference(resolution,[status(thm)],[c_807,c_18]) ).
tff(c_15598,plain,
! [A_809,B_810,A_3,B_4] :
( in('#skF_4'(A_809,B_810,set_union2(A_3,B_4)),B_4)
| in('#skF_4'(A_809,B_810,set_union2(A_3,B_4)),A_3)
| ~ in('#skF_3'(A_809,B_810,set_union2(A_3,B_4)),set_union2(B_4,A_3))
| ( set_union2(A_809,B_810) = set_union2(A_3,B_4) ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_15466]) ).
tff(c_249466,plain,
! [A_3,B_4250] :
( in('#skF_4'(set_union2(A_3,A_3),B_4250,set_union2(A_3,A_3)),A_3)
| ~ subset(B_4250,set_union2(A_3,A_3))
| ( set_union2(set_union2(A_3,A_3),B_4250) = set_union2(A_3,A_3) ) ),
inference(resolution,[status(thm)],[c_249458,c_15598]) ).
tff(c_292595,plain,
! [A_4837,B_4838] :
( in('#skF_4'(A_4837,B_4838,A_4837),A_4837)
| ~ subset(B_4838,A_4837)
| ( set_union2(A_4837,B_4838) = A_4837 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_46,c_46,c_46,c_46,c_46,c_249466]) ).
tff(c_28,plain,
! [A_10,B_11,C_12] :
( ~ in('#skF_3'(A_10,B_11,C_12),C_12)
| ~ in('#skF_4'(A_10,B_11,C_12),A_10)
| ( set_union2(A_10,B_11) = C_12 ) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_249596,plain,
! [C_4251,B_4250] :
( ~ in('#skF_4'(C_4251,B_4250,C_4251),C_4251)
| ~ subset(B_4250,C_4251)
| ( set_union2(C_4251,B_4250) = C_4251 ) ),
inference(resolution,[status(thm)],[c_249458,c_28]) ).
tff(c_292767,plain,
! [B_4839,A_4840] :
( ~ subset(B_4839,A_4840)
| ( set_union2(A_4840,B_4839) = A_4840 ) ),
inference(resolution,[status(thm)],[c_292595,c_249596]) ).
tff(c_426051,plain,
! [A_5019,B_5020] : ( set_union2(powerset(set_union2(A_5019,B_5020)),powerset(A_5019)) = powerset(set_union2(A_5019,B_5020)) ),
inference(resolution,[status(thm)],[c_22050,c_292767]) ).
tff(c_431105,plain,
! [A_3,B_4] : ( set_union2(powerset(set_union2(A_3,B_4)),powerset(B_4)) = powerset(set_union2(B_4,A_3)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_426051]) ).
tff(c_40,plain,
! [A_16,B_17] :
( in('#skF_5'(A_16,B_17),A_16)
| subset(A_16,B_17) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_408,plain,
! [D_91,B_92,A_93] :
( in(D_91,B_92)
| in(D_91,A_93)
| ~ in(D_91,set_union2(A_93,B_92)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_7501,plain,
! [A_489,B_490,B_491] :
( in('#skF_5'(set_union2(A_489,B_490),B_491),B_490)
| in('#skF_5'(set_union2(A_489,B_490),B_491),A_489)
| subset(set_union2(A_489,B_490),B_491) ),
inference(resolution,[status(thm)],[c_40,c_408]) ).
tff(c_20,plain,
! [D_15,B_11,A_10] :
( ~ in(D_15,B_11)
| in(D_15,set_union2(A_10,B_11)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_212,plain,
! [A_60,A_10,B_11] :
( subset(A_60,set_union2(A_10,B_11))
| ~ in('#skF_5'(A_60,set_union2(A_10,B_11)),B_11) ),
inference(resolution,[status(thm)],[c_20,c_199]) ).
tff(c_7586,plain,
! [A_489,B_490,A_10] :
( in('#skF_5'(set_union2(A_489,B_490),set_union2(A_10,B_490)),A_489)
| subset(set_union2(A_489,B_490),set_union2(A_10,B_490)) ),
inference(resolution,[status(thm)],[c_7501,c_212]) ).
tff(c_22,plain,
! [D_15,A_10,B_11] :
( ~ in(D_15,A_10)
| in(D_15,set_union2(A_10,B_11)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_3596,plain,
! [A_311,A_312,B_313] :
( subset(A_311,set_union2(A_312,B_313))
| ~ in('#skF_5'(A_311,set_union2(A_312,B_313)),A_312) ),
inference(resolution,[status(thm)],[c_22,c_199]) ).
tff(c_27077,plain,
! [A_1070,A_1071,B_1072,B_1073] :
( subset(A_1070,set_union2(set_union2(A_1071,B_1072),B_1073))
| ~ in('#skF_5'(A_1070,set_union2(set_union2(A_1071,B_1072),B_1073)),A_1071) ),
inference(resolution,[status(thm)],[c_22,c_3596]) ).
tff(c_27213,plain,
! [A_1074,B_1075,B_1076] : subset(set_union2(A_1074,B_1075),set_union2(set_union2(A_1074,B_1076),B_1075)),
inference(resolution,[status(thm)],[c_7586,c_27077]) ).
tff(c_27457,plain,
! [A_1080,B_1081,B_1082] : subset(set_union2(A_1080,B_1081),set_union2(set_union2(B_1082,A_1080),B_1081)),
inference(superposition,[status(thm),theory(equality)],[c_4,c_27213]) ).
tff(c_27530,plain,
! [A_3,B_4,B_1082] : subset(set_union2(A_3,B_4),set_union2(set_union2(B_1082,B_4),A_3)),
inference(superposition,[status(thm),theory(equality)],[c_4,c_27457]) ).
tff(c_608679,plain,
! [A_5486,A_5487,B_5488] : subset(set_union2(A_5486,powerset(A_5487)),set_union2(powerset(set_union2(A_5487,B_5488)),A_5486)),
inference(superposition,[status(thm),theory(equality)],[c_426051,c_27530]) ).
tff(c_609036,plain,
! [B_4,A_3] : subset(set_union2(powerset(B_4),powerset(A_3)),powerset(set_union2(B_4,A_3))),
inference(superposition,[status(thm),theory(equality)],[c_431105,c_608679]) ).
tff(c_58,plain,
~ subset(set_union2(powerset('#skF_8'),powerset('#skF_9')),powerset(set_union2('#skF_8','#skF_9'))),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_609354,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_609036,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET934+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % 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 : n004.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 : Thu Aug 3 16:58:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 276.33/227.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 276.33/227.73
% 276.33/227.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 276.55/227.78
% 276.55/227.78 Inference rules
% 276.55/227.78 ----------------------
% 276.55/227.78 #Ref : 0
% 276.55/227.78 #Sup : 151753
% 276.55/227.78 #Fact : 354
% 276.55/227.78 #Define : 0
% 276.55/227.78 #Split : 0
% 276.55/227.78 #Chain : 0
% 276.55/227.78 #Close : 0
% 276.55/227.78
% 276.55/227.78 Ordering : KBO
% 276.55/227.78
% 276.55/227.78 Simplification rules
% 276.55/227.78 ----------------------
% 276.55/227.78 #Subsume : 40846
% 276.55/227.78 #Demod : 56212
% 276.55/227.78 #Tautology : 19926
% 276.55/227.78 #SimpNegUnit : 0
% 276.55/227.78 #BackRed : 39
% 276.55/227.78
% 276.55/227.78 #Partial instantiations: 0
% 276.55/227.78 #Strategies tried : 1
% 276.55/227.78
% 276.55/227.78 Timing (in seconds)
% 276.55/227.78 ----------------------
% 276.55/227.78 Preprocessing : 0.50
% 276.55/227.78 Parsing : 0.26
% 276.55/227.78 CNF conversion : 0.04
% 276.55/227.78 Main loop : 226.18
% 276.55/227.78 Inferencing : 11.05
% 276.55/227.78 Reduction : 99.20
% 276.55/227.79 Demodulation : 68.29
% 276.55/227.79 BG Simplification : 0.94
% 276.55/227.79 Subsumption : 95.41
% 276.55/227.79 Abstraction : 1.24
% 276.55/227.79 MUC search : 0.00
% 276.55/227.79 Cooper : 0.00
% 276.55/227.79 Total : 226.76
% 276.55/227.79 Index Insertion : 0.00
% 276.55/227.79 Index Deletion : 0.00
% 276.55/227.79 Index Matching : 0.00
% 276.55/227.79 BG Taut test : 0.00
%------------------------------------------------------------------------------