TSTP Solution File: SET587+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET587+3 : TPTP v8.1.2. 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 : n014.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 10:56:37 EDT 2023
% Result : Theorem 6.67s 2.62s
% Output : CNFRefutation 6.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 82 ( 22 unt; 15 typ; 0 def)
% Number of atoms : 130 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 116 ( 53 ~; 55 |; 2 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 10 >; 8 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 91 (; 91 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > difference > #nlpp > empty_set > #skF_7 > #skF_3 > #skF_10 > #skF_9 > #skF_8 > #skF_2 > #skF_1 > #skF_5 > #skF_6 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $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('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_86,negated_conjecture,
~ ! [B,C] :
( ( difference(B,C) = empty_set )
<=> subset(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_empty_set) ).
tff(f_55,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(f_47,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_43,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
tff(f_80,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
tff(f_62,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
tff(c_50,plain,
( subset('#skF_7','#skF_8')
| ~ subset('#skF_9','#skF_10') ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_70,plain,
~ subset('#skF_9','#skF_10'),
inference(splitLeft,[status(thm)],[c_50]) ).
tff(c_22,plain,
! [B_8,C_9] :
( member('#skF_3'(B_8,C_9),B_8)
| subset(B_8,C_9) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_16,plain,
! [B_7] : ~ member(B_7,empty_set),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_54,plain,
( subset('#skF_7','#skF_8')
| ( difference('#skF_9','#skF_10') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_71,plain,
difference('#skF_9','#skF_10') = empty_set,
inference(splitLeft,[status(thm)],[c_54]) ).
tff(c_213,plain,
! [D_56,B_57,C_58] :
( member(D_56,difference(B_57,C_58))
| member(D_56,C_58)
| ~ member(D_56,B_57) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_231,plain,
! [D_56] :
( member(D_56,empty_set)
| member(D_56,'#skF_10')
| ~ member(D_56,'#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_71,c_213]) ).
tff(c_256,plain,
! [D_60] :
( member(D_60,'#skF_10')
| ~ member(D_60,'#skF_9') ),
inference(negUnitSimplification,[status(thm)],[c_16,c_231]) ).
tff(c_20,plain,
! [B_8,C_9] :
( ~ member('#skF_3'(B_8,C_9),C_9)
| subset(B_8,C_9) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_270,plain,
! [B_61] :
( subset(B_61,'#skF_10')
| ~ member('#skF_3'(B_61,'#skF_10'),'#skF_9') ),
inference(resolution,[status(thm)],[c_256,c_20]) ).
tff(c_274,plain,
subset('#skF_9','#skF_10'),
inference(resolution,[status(thm)],[c_22,c_270]) ).
tff(c_278,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_70,c_70,c_274]) ).
tff(c_280,plain,
difference('#skF_9','#skF_10') != empty_set,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_52,plain,
( ( difference('#skF_7','#skF_8') != empty_set )
| ( difference('#skF_9','#skF_10') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_281,plain,
difference('#skF_7','#skF_8') != empty_set,
inference(negUnitSimplification,[status(thm)],[c_280,c_52]) ).
tff(c_306,plain,
! [B_72,C_73] :
( member('#skF_3'(B_72,C_73),B_72)
| subset(B_72,C_73) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_14,plain,
! [D_6,B_4,C_5] :
( member(D_6,B_4)
| ~ member(D_6,difference(B_4,C_5)) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_1512,plain,
! [B_177,C_178,C_179] :
( member('#skF_3'(difference(B_177,C_178),C_179),B_177)
| subset(difference(B_177,C_178),C_179) ),
inference(resolution,[status(thm)],[c_306,c_14]) ).
tff(c_1553,plain,
! [B_177,C_178] : subset(difference(B_177,C_178),B_177),
inference(resolution,[status(thm)],[c_1512,c_20]) ).
tff(c_279,plain,
subset('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_46,plain,
! [B_21] :
( empty(B_21)
| member('#skF_6'(B_21),B_21) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_348,plain,
! [D_77,C_78,B_79] :
( member(D_77,C_78)
| ~ member(D_77,B_79)
| ~ subset(B_79,C_78) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_422,plain,
! [B_89,C_90] :
( member('#skF_6'(B_89),C_90)
| ~ subset(B_89,C_90)
| empty(B_89) ),
inference(resolution,[status(thm)],[c_46,c_348]) ).
tff(c_18,plain,
! [D_12,C_9,B_8] :
( member(D_12,C_9)
| ~ member(D_12,B_8)
| ~ subset(B_8,C_9) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_2599,plain,
! [B_241,C_242,C_243] :
( member('#skF_6'(B_241),C_242)
| ~ subset(C_243,C_242)
| ~ subset(B_241,C_243)
| empty(B_241) ),
inference(resolution,[status(thm)],[c_422,c_18]) ).
tff(c_2621,plain,
! [B_244] :
( member('#skF_6'(B_244),'#skF_8')
| ~ subset(B_244,'#skF_7')
| empty(B_244) ),
inference(resolution,[status(thm)],[c_279,c_2599]) ).
tff(c_289,plain,
! [D_67,C_68,B_69] :
( ~ member(D_67,C_68)
| ~ member(D_67,difference(B_69,C_68)) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_294,plain,
! [B_69,C_68] :
( ~ member('#skF_6'(difference(B_69,C_68)),C_68)
| empty(difference(B_69,C_68)) ),
inference(resolution,[status(thm)],[c_46,c_289]) ).
tff(c_2637,plain,
! [B_245] :
( ~ subset(difference(B_245,'#skF_8'),'#skF_7')
| empty(difference(B_245,'#skF_8')) ),
inference(resolution,[status(thm)],[c_2621,c_294]) ).
tff(c_2675,plain,
empty(difference('#skF_7','#skF_8')),
inference(resolution,[status(thm)],[c_1553,c_2637]) ).
tff(c_44,plain,
! [C_24,B_21] :
( ~ member(C_24,B_21)
| ~ empty(B_21) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_330,plain,
! [B_72,C_73] :
( ~ empty(B_72)
| subset(B_72,C_73) ),
inference(resolution,[status(thm)],[c_306,c_44]) ).
tff(c_332,plain,
! [C_74] : subset(empty_set,C_74),
inference(resolution,[status(thm)],[c_306,c_16]) ).
tff(c_24,plain,
! [C_14,B_13] :
( ( C_14 = B_13 )
| ~ subset(C_14,B_13)
| ~ subset(B_13,C_14) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_355,plain,
! [C_80] :
( ( empty_set = C_80 )
| ~ subset(C_80,empty_set) ),
inference(resolution,[status(thm)],[c_332,c_24]) ).
tff(c_368,plain,
! [B_72] :
( ( empty_set = B_72 )
| ~ empty(B_72) ),
inference(resolution,[status(thm)],[c_330,c_355]) ).
tff(c_2701,plain,
difference('#skF_7','#skF_8') = empty_set,
inference(resolution,[status(thm)],[c_2675,c_368]) ).
tff(c_2712,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_281,c_2701]) ).
tff(c_2714,plain,
subset('#skF_9','#skF_10'),
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_48,plain,
( ( difference('#skF_7','#skF_8') != empty_set )
| ~ subset('#skF_9','#skF_10') ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_2716,plain,
difference('#skF_7','#skF_8') != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_2714,c_48]) ).
tff(c_2731,plain,
! [B_254,C_255] :
( member('#skF_3'(B_254,C_255),B_254)
| subset(B_254,C_255) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_4462,plain,
! [B_395,C_396,C_397] :
( member('#skF_3'(difference(B_395,C_396),C_397),B_395)
| subset(difference(B_395,C_396),C_397) ),
inference(resolution,[status(thm)],[c_2731,c_14]) ).
tff(c_4508,plain,
! [B_395,C_396] : subset(difference(B_395,C_396),B_395),
inference(resolution,[status(thm)],[c_4462,c_20]) ).
tff(c_2713,plain,
subset('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_2778,plain,
! [D_261,C_262,B_263] :
( member(D_261,C_262)
| ~ member(D_261,B_263)
| ~ subset(B_263,C_262) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_2866,plain,
! [B_273,C_274] :
( member('#skF_6'(B_273),C_274)
| ~ subset(B_273,C_274)
| empty(B_273) ),
inference(resolution,[status(thm)],[c_46,c_2778]) ).
tff(c_5551,plain,
! [B_456,C_457,C_458] :
( member('#skF_6'(B_456),C_457)
| ~ subset(C_458,C_457)
| ~ subset(B_456,C_458)
| empty(B_456) ),
inference(resolution,[status(thm)],[c_2866,c_18]) ).
tff(c_5595,plain,
! [B_460] :
( member('#skF_6'(B_460),'#skF_8')
| ~ subset(B_460,'#skF_7')
| empty(B_460) ),
inference(resolution,[status(thm)],[c_2713,c_5551]) ).
tff(c_2718,plain,
! [D_246,C_247,B_248] :
( ~ member(D_246,C_247)
| ~ member(D_246,difference(B_248,C_247)) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_2723,plain,
! [B_248,C_247] :
( ~ member('#skF_6'(difference(B_248,C_247)),C_247)
| empty(difference(B_248,C_247)) ),
inference(resolution,[status(thm)],[c_46,c_2718]) ).
tff(c_5970,plain,
! [B_466] :
( ~ subset(difference(B_466,'#skF_8'),'#skF_7')
| empty(difference(B_466,'#skF_8')) ),
inference(resolution,[status(thm)],[c_5595,c_2723]) ).
tff(c_6011,plain,
empty(difference('#skF_7','#skF_8')),
inference(resolution,[status(thm)],[c_4508,c_5970]) ).
tff(c_2755,plain,
! [B_254,C_255] :
( ~ empty(B_254)
| subset(B_254,C_255) ),
inference(resolution,[status(thm)],[c_2731,c_44]) ).
tff(c_2756,plain,
! [C_255] : subset(empty_set,C_255),
inference(resolution,[status(thm)],[c_2731,c_16]) ).
tff(c_2759,plain,
! [C_259,B_260] :
( ( C_259 = B_260 )
| ~ subset(C_259,B_260)
| ~ subset(B_260,C_259) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_2795,plain,
! [C_264] :
( ( empty_set = C_264 )
| ~ subset(C_264,empty_set) ),
inference(resolution,[status(thm)],[c_2756,c_2759]) ).
tff(c_2808,plain,
! [B_254] :
( ( empty_set = B_254 )
| ~ empty(B_254) ),
inference(resolution,[status(thm)],[c_2755,c_2795]) ).
tff(c_6039,plain,
difference('#skF_7','#skF_8') = empty_set,
inference(resolution,[status(thm)],[c_6011,c_2808]) ).
tff(c_6050,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2716,c_6039]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15 % 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
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 16:03:03 EDT 2023
% 0.15/0.36 % CPUTime :
% 6.67/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.67/2.62
% 6.67/2.62 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.67/2.66
% 6.67/2.66 Inference rules
% 6.67/2.66 ----------------------
% 6.67/2.66 #Ref : 0
% 6.67/2.66 #Sup : 1413
% 6.67/2.66 #Fact : 0
% 6.67/2.66 #Define : 0
% 6.67/2.66 #Split : 6
% 6.67/2.66 #Chain : 0
% 6.67/2.66 #Close : 0
% 6.67/2.66
% 6.67/2.66 Ordering : KBO
% 6.67/2.66
% 6.67/2.66 Simplification rules
% 6.67/2.66 ----------------------
% 6.67/2.66 #Subsume : 547
% 6.67/2.66 #Demod : 524
% 6.67/2.66 #Tautology : 368
% 6.67/2.66 #SimpNegUnit : 31
% 6.67/2.66 #BackRed : 5
% 6.67/2.66
% 6.67/2.66 #Partial instantiations: 0
% 6.67/2.66 #Strategies tried : 1
% 6.67/2.66
% 6.67/2.66 Timing (in seconds)
% 6.67/2.66 ----------------------
% 6.67/2.66 Preprocessing : 0.49
% 6.67/2.66 Parsing : 0.25
% 6.67/2.66 CNF conversion : 0.04
% 6.67/2.66 Main loop : 1.08
% 6.67/2.66 Inferencing : 0.43
% 6.67/2.66 Reduction : 0.27
% 6.67/2.66 Demodulation : 0.18
% 6.67/2.66 BG Simplification : 0.04
% 6.67/2.66 Subsumption : 0.26
% 6.67/2.66 Abstraction : 0.04
% 6.67/2.66 MUC search : 0.00
% 6.67/2.66 Cooper : 0.00
% 6.67/2.66 Total : 1.62
% 6.67/2.66 Index Insertion : 0.00
% 6.67/2.66 Index Deletion : 0.00
% 6.67/2.66 Index Matching : 0.00
% 6.67/2.66 BG Taut test : 0.00
%------------------------------------------------------------------------------