TSTP Solution File: SEU210+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n010.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 10:58:01 EDT 2023
% Result : Theorem 86.56s 72.37s
% Output : CNFRefutation 86.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 41
% Syntax : Number of formulae : 107 ( 30 unt; 27 typ; 0 def)
% Number of atoms : 175 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 159 ( 64 ~; 72 |; 9 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 20 >; 14 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-3 aty)
% Number of variables : 109 (; 103 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation > empty > unordered_pair > relation_inverse_image > ordered_pair > #nlpp > singleton > relation_rng > powerset > empty_set > #skF_13 > #skF_15 > #skF_8 > #skF_7 > #skF_3 > #skF_10 > #skF_14 > #skF_5 > #skF_9 > #skF_11 > #skF_2 > #skF_1 > #skF_6 > #skF_12 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff(relation,type,
relation: $i > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(relation_inverse_image,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_106,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_174,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_143,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ~ ( ( A != empty_set )
& subset(A,relation_rng(B))
& ( relation_inverse_image(B,A) = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
tff(f_153,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
tff(f_44,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
tff(f_104,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( element(B,powerset(A))
& ~ empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
tff(f_163,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
tff(f_157,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
tff(f_61,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
tff(f_147,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
tff(f_116,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
tff(f_170,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
tff(f_55,axiom,
! [A] :
( relation(A)
=> ! [B] :
( ( B = relation_rng(A) )
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
tff(f_132,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,relation_rng(C))
& in(ordered_pair(A,D),C)
& in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
tff(c_74,plain,
empty('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_132,plain,
! [A_99] :
( ( empty_set = A_99 )
| ~ empty(A_99) ),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_146,plain,
empty_set = '#skF_9',
inference(resolution,[status(thm)],[c_74,c_132]) ).
tff(c_100,plain,
empty_set != '#skF_14',
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_154,plain,
'#skF_14' != '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_146,c_100]) ).
tff(c_98,plain,
subset('#skF_14',relation_rng('#skF_15')),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_106,plain,
! [A_77,B_78] :
( in(A_77,B_78)
| empty(B_78)
| ~ element(A_77,B_78) ),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_397,plain,
! [C_144,B_145,A_146] :
( in(C_144,B_145)
| ~ in(C_144,A_146)
| ~ subset(A_146,B_145) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_2306,plain,
! [A_294,B_295,B_296] :
( in(A_294,B_295)
| ~ subset(B_296,B_295)
| empty(B_296)
| ~ element(A_294,B_296) ),
inference(resolution,[status(thm)],[c_106,c_397]) ).
tff(c_2348,plain,
! [A_294] :
( in(A_294,relation_rng('#skF_15'))
| empty('#skF_14')
| ~ element(A_294,'#skF_14') ),
inference(resolution,[status(thm)],[c_98,c_2306]) ).
tff(c_2384,plain,
empty('#skF_14'),
inference(splitLeft,[status(thm)],[c_2348]) ).
tff(c_116,plain,
! [A_87] :
( ( empty_set = A_87 )
| ~ empty(A_87) ),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_150,plain,
! [A_87] :
( ( A_87 = '#skF_9' )
| ~ empty(A_87) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_116]) ).
tff(c_2402,plain,
'#skF_14' = '#skF_9',
inference(resolution,[status(thm)],[c_2384,c_150]) ).
tff(c_2413,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_154,c_2402]) ).
tff(c_2415,plain,
~ empty('#skF_14'),
inference(splitRight,[status(thm)],[c_2348]) ).
tff(c_12,plain,
! [A_6,B_7] :
( in('#skF_1'(A_6,B_7),A_6)
| subset(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_72,plain,
! [A_63] :
( element('#skF_8'(A_63),powerset(A_63))
| empty(A_63) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_504,plain,
! [A_164,C_165,B_166] :
( element(A_164,C_165)
| ~ element(B_166,powerset(C_165))
| ~ in(A_164,B_166) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_568,plain,
! [A_175,A_176] :
( element(A_175,A_176)
| ~ in(A_175,'#skF_8'(A_176))
| empty(A_176) ),
inference(resolution,[status(thm)],[c_72,c_504]) ).
tff(c_40741,plain,
! [A_931,B_932] :
( element('#skF_1'('#skF_8'(A_931),B_932),A_931)
| empty(A_931)
| subset('#skF_8'(A_931),B_932) ),
inference(resolution,[status(thm)],[c_12,c_568]) ).
tff(c_2564,plain,
! [A_301] :
( in(A_301,relation_rng('#skF_15'))
| ~ element(A_301,'#skF_14') ),
inference(splitRight,[status(thm)],[c_2348]) ).
tff(c_10,plain,
! [A_6,B_7] :
( ~ in('#skF_1'(A_6,B_7),B_7)
| subset(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_2617,plain,
! [A_6] :
( subset(A_6,relation_rng('#skF_15'))
| ~ element('#skF_1'(A_6,relation_rng('#skF_15')),'#skF_14') ),
inference(resolution,[status(thm)],[c_2564,c_10]) ).
tff(c_40764,plain,
( empty('#skF_14')
| subset('#skF_8'('#skF_14'),relation_rng('#skF_15')) ),
inference(resolution,[status(thm)],[c_40741,c_2617]) ).
tff(c_40791,plain,
subset('#skF_8'('#skF_14'),relation_rng('#skF_15')),
inference(negUnitSimplification,[status(thm)],[c_2415,c_40764]) ).
tff(c_110,plain,
! [A_79,B_80] :
( element(A_79,powerset(B_80))
| ~ subset(A_79,B_80) ),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_561,plain,
! [A_172,B_173,A_174] :
( element(A_172,B_173)
| ~ in(A_172,A_174)
| ~ subset(A_174,B_173) ),
inference(resolution,[status(thm)],[c_110,c_504]) ).
tff(c_567,plain,
! [A_77,B_173,B_78] :
( element(A_77,B_173)
| ~ subset(B_78,B_173)
| empty(B_78)
| ~ element(A_77,B_78) ),
inference(resolution,[status(thm)],[c_106,c_561]) ).
tff(c_40840,plain,
! [A_77] :
( element(A_77,relation_rng('#skF_15'))
| empty('#skF_8'('#skF_14'))
| ~ element(A_77,'#skF_8'('#skF_14')) ),
inference(resolution,[status(thm)],[c_40791,c_567]) ).
tff(c_40853,plain,
empty('#skF_8'('#skF_14')),
inference(splitLeft,[status(thm)],[c_40840]) ).
tff(c_70,plain,
! [A_63] :
( ~ empty('#skF_8'(A_63))
| empty(A_63) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_40907,plain,
empty('#skF_14'),
inference(resolution,[status(thm)],[c_40853,c_70]) ).
tff(c_40939,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2415,c_40907]) ).
tff(c_40941,plain,
~ empty('#skF_8'('#skF_14')),
inference(splitRight,[status(thm)],[c_40840]) ).
tff(c_44,plain,
! [A_53] : element('#skF_6'(A_53),A_53),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_317,plain,
! [A_125,B_126] :
( subset(A_125,B_126)
| ~ element(A_125,powerset(B_126)) ),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_331,plain,
! [A_63] :
( subset('#skF_8'(A_63),A_63)
| empty(A_63) ),
inference(resolution,[status(thm)],[c_72,c_317]) ).
tff(c_30635,plain,
! [A_856,A_857] :
( in(A_856,A_857)
| empty('#skF_8'(A_857))
| ~ element(A_856,'#skF_8'(A_857))
| empty(A_857) ),
inference(resolution,[status(thm)],[c_331,c_2306]) ).
tff(c_33094,plain,
! [A_870] :
( in('#skF_6'('#skF_8'(A_870)),A_870)
| empty('#skF_8'(A_870))
| empty(A_870) ),
inference(resolution,[status(thm)],[c_44,c_30635]) ).
tff(c_104,plain,
! [A_75,B_76] :
( element(A_75,B_76)
| ~ in(A_75,B_76) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_33253,plain,
! [A_870] :
( element('#skF_6'('#skF_8'(A_870)),A_870)
| empty('#skF_8'(A_870))
| empty(A_870) ),
inference(resolution,[status(thm)],[c_33094,c_104]) ).
tff(c_2414,plain,
! [A_294] :
( in(A_294,relation_rng('#skF_15'))
| ~ element(A_294,'#skF_14') ),
inference(splitRight,[status(thm)],[c_2348]) ).
tff(c_80,plain,
! [A_65] : empty('#skF_11'(A_65)),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_145,plain,
! [A_65] : ( '#skF_11'(A_65) = empty_set ),
inference(resolution,[status(thm)],[c_80,c_132]) ).
tff(c_169,plain,
! [A_65] : ( '#skF_11'(A_65) = '#skF_9' ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_145]) ).
tff(c_82,plain,
! [A_65] : element('#skF_11'(A_65),powerset(A_65)),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_192,plain,
! [A_65] : element('#skF_9',powerset(A_65)),
inference(demodulation,[status(thm),theory(equality)],[c_169,c_82]) ).
tff(c_453,plain,
! [C_153,B_154,A_155] :
( ~ empty(C_153)
| ~ element(B_154,powerset(C_153))
| ~ in(A_155,B_154) ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_469,plain,
! [A_65,A_155] :
( ~ empty(A_65)
| ~ in(A_155,'#skF_9') ),
inference(resolution,[status(thm)],[c_192,c_453]) ).
tff(c_471,plain,
! [A_155] : ~ in(A_155,'#skF_9'),
inference(splitLeft,[status(thm)],[c_469]) ).
tff(c_102,plain,
relation('#skF_15'),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_96,plain,
relation_inverse_image('#skF_15','#skF_14') = empty_set,
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_151,plain,
relation_inverse_image('#skF_15','#skF_14') = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_146,c_96]) ).
tff(c_14,plain,
! [A_11,C_47] :
( in(ordered_pair('#skF_5'(A_11,relation_rng(A_11),C_47),C_47),A_11)
| ~ in(C_47,relation_rng(A_11))
| ~ relation(A_11) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_1220,plain,
! [A_232,C_233,B_234,D_235] :
( in(A_232,relation_inverse_image(C_233,B_234))
| ~ in(D_235,B_234)
| ~ in(ordered_pair(A_232,D_235),C_233)
| ~ in(D_235,relation_rng(C_233))
| ~ relation(C_233) ),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_14145,plain,
! [A_608,C_609,B_610,A_611] :
( in(A_608,relation_inverse_image(C_609,B_610))
| ~ in(ordered_pair(A_608,A_611),C_609)
| ~ in(A_611,relation_rng(C_609))
| ~ relation(C_609)
| empty(B_610)
| ~ element(A_611,B_610) ),
inference(resolution,[status(thm)],[c_106,c_1220]) ).
tff(c_394882,plain,
! [A_2749,C_2750,B_2751] :
( in('#skF_5'(A_2749,relation_rng(A_2749),C_2750),relation_inverse_image(A_2749,B_2751))
| empty(B_2751)
| ~ element(C_2750,B_2751)
| ~ in(C_2750,relation_rng(A_2749))
| ~ relation(A_2749) ),
inference(resolution,[status(thm)],[c_14,c_14145]) ).
tff(c_395507,plain,
! [C_2750] :
( in('#skF_5'('#skF_15',relation_rng('#skF_15'),C_2750),'#skF_9')
| empty('#skF_14')
| ~ element(C_2750,'#skF_14')
| ~ in(C_2750,relation_rng('#skF_15'))
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_151,c_394882]) ).
tff(c_395623,plain,
! [C_2750] :
( in('#skF_5'('#skF_15',relation_rng('#skF_15'),C_2750),'#skF_9')
| empty('#skF_14')
| ~ element(C_2750,'#skF_14')
| ~ in(C_2750,relation_rng('#skF_15')) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_395507]) ).
tff(c_395625,plain,
! [C_2752] :
( ~ element(C_2752,'#skF_14')
| ~ in(C_2752,relation_rng('#skF_15')) ),
inference(negUnitSimplification,[status(thm)],[c_2415,c_471,c_395623]) ).
tff(c_395914,plain,
! [A_2753] : ~ element(A_2753,'#skF_14'),
inference(resolution,[status(thm)],[c_2414,c_395625]) ).
tff(c_395978,plain,
( empty('#skF_8'('#skF_14'))
| empty('#skF_14') ),
inference(resolution,[status(thm)],[c_33253,c_395914]) ).
tff(c_396055,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2415,c_40941,c_395978]) ).
tff(c_396056,plain,
! [A_65] : ~ empty(A_65),
inference(splitRight,[status(thm)],[c_469]) ).
tff(c_396065,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_396056,c_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % 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
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 11:30:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 86.56/72.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 86.56/72.38
% 86.56/72.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 86.56/72.42
% 86.56/72.42 Inference rules
% 86.56/72.42 ----------------------
% 86.56/72.42 #Ref : 0
% 86.56/72.42 #Sup : 108575
% 86.56/72.42 #Fact : 0
% 86.56/72.42 #Define : 0
% 86.56/72.42 #Split : 99
% 86.56/72.42 #Chain : 0
% 86.56/72.42 #Close : 0
% 86.56/72.42
% 86.56/72.42 Ordering : KBO
% 86.56/72.42
% 86.56/72.42 Simplification rules
% 86.56/72.42 ----------------------
% 86.56/72.42 #Subsume : 53113
% 86.56/72.42 #Demod : 54239
% 86.56/72.42 #Tautology : 24155
% 86.56/72.42 #SimpNegUnit : 5534
% 86.56/72.42 #BackRed : 1691
% 86.56/72.42
% 86.56/72.42 #Partial instantiations: 0
% 86.56/72.42 #Strategies tried : 1
% 86.56/72.42
% 86.56/72.42 Timing (in seconds)
% 86.56/72.42 ----------------------
% 86.56/72.42 Preprocessing : 0.58
% 86.56/72.42 Parsing : 0.29
% 86.56/72.42 CNF conversion : 0.05
% 86.56/72.42 Main loop : 70.74
% 86.56/72.42 Inferencing : 6.03
% 86.56/72.42 Reduction : 18.48
% 86.56/72.42 Demodulation : 12.67
% 86.56/72.42 BG Simplification : 0.38
% 86.56/72.42 Subsumption : 40.49
% 86.56/72.42 Abstraction : 0.68
% 86.56/72.42 MUC search : 0.00
% 86.56/72.42 Cooper : 0.00
% 86.56/72.42 Total : 71.39
% 86.56/72.42 Index Insertion : 0.00
% 86.56/72.42 Index Deletion : 0.00
% 86.56/72.42 Index Matching : 0.00
% 86.56/72.42 BG Taut test : 0.00
%------------------------------------------------------------------------------