TSTP Solution File: SEU243+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU243+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/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 : Tue Aug 22 10:58:09 EDT 2023
% Result : Theorem 7.66s 3.10s
% Output : CNFRefutation 7.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 33
% Syntax : Number of formulae : 81 ( 16 unt; 28 typ; 0 def)
% Number of atoms : 158 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 189 ( 84 ~; 90 |; 8 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 21 >; 11 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 57 (; 56 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > is_well_founded_in > in > element > disjoint > well_founded_relation > relation > one_to_one > function > empty > set_union2 > fiber > #nlpp > relation_rng > relation_field > relation_dom > powerset > empty_set > #skF_5 > #skF_2 > #skF_11 > #skF_4 > #skF_7 > #skF_3 > #skF_10 > #skF_6 > #skF_9 > #skF_8 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation_field,type,
relation_field: $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $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(well_founded_relation,type,
well_founded_relation: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(is_well_founded_in,type,
is_well_founded_in: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(set_union2,type,
set_union2: ( $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(fiber,type,
fiber: ( $i * $i ) > $i ).
tff(f_170,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
tff(f_119,axiom,
? [A] :
( relation(A)
& empty(A)
& function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
tff(f_174,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_84,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_well_founded_in(A,B)
<=> ! [C] :
~ ( subset(C,B)
& ( C != empty_set )
& ! [D] :
~ ( in(D,C)
& disjoint(fiber(A,D),C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_wellord1) ).
tff(f_66,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> ! [B] :
~ ( subset(B,relation_field(A))
& ( B != empty_set )
& ! [C] :
~ ( in(C,B)
& disjoint(fiber(A,C),B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
tff(c_100,plain,
relation('#skF_11'),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_70,plain,
empty('#skF_8'),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_2147,plain,
! [A_328] :
( ( empty_set = A_328 )
| ~ empty(A_328) ),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_2158,plain,
empty_set = '#skF_8',
inference(resolution,[status(thm)],[c_70,c_2147]) ).
tff(c_30,plain,
! [A_18,B_32] :
( ( '#skF_3'(A_18,B_32) != empty_set )
| is_well_founded_in(A_18,B_32)
| ~ relation(A_18) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_2407,plain,
! [A_359,B_360] :
( ( '#skF_3'(A_359,B_360) != '#skF_8' )
| is_well_founded_in(A_359,B_360)
| ~ relation(A_359) ),
inference(demodulation,[status(thm),theory(equality)],[c_2158,c_30]) ).
tff(c_102,plain,
( ~ is_well_founded_in('#skF_11',relation_field('#skF_11'))
| ~ well_founded_relation('#skF_11') ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_115,plain,
~ well_founded_relation('#skF_11'),
inference(splitLeft,[status(thm)],[c_102]) ).
tff(c_118,plain,
! [A_76] :
( ( empty_set = A_76 )
| ~ empty(A_76) ),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_129,plain,
empty_set = '#skF_8',
inference(resolution,[status(thm)],[c_70,c_118]) ).
tff(c_16,plain,
! [A_7] :
( ( '#skF_2'(A_7) != empty_set )
| well_founded_relation(A_7)
| ~ relation(A_7) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_340,plain,
! [A_103] :
( ( '#skF_2'(A_103) != '#skF_8' )
| well_founded_relation(A_103)
| ~ relation(A_103) ),
inference(demodulation,[status(thm),theory(equality)],[c_129,c_16]) ).
tff(c_343,plain,
( ( '#skF_2'('#skF_11') != '#skF_8' )
| ~ relation('#skF_11') ),
inference(resolution,[status(thm)],[c_340,c_115]) ).
tff(c_346,plain,
'#skF_2'('#skF_11') != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_100,c_343]) ).
tff(c_108,plain,
( well_founded_relation('#skF_11')
| is_well_founded_in('#skF_11',relation_field('#skF_11')) ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_144,plain,
is_well_founded_in('#skF_11',relation_field('#skF_11')),
inference(negUnitSimplification,[status(thm)],[c_115,c_108]) ).
tff(c_18,plain,
! [A_7] :
( subset('#skF_2'(A_7),relation_field(A_7))
| well_founded_relation(A_7)
| ~ relation(A_7) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_26,plain,
! [A_18,B_32,C_41] :
( in('#skF_4'(A_18,B_32,C_41),C_41)
| ( empty_set = C_41 )
| ~ subset(C_41,B_32)
| ~ is_well_founded_in(A_18,B_32)
| ~ relation(A_18) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_623,plain,
! [A_18,B_32,C_41] :
( in('#skF_4'(A_18,B_32,C_41),C_41)
| ( C_41 = '#skF_8' )
| ~ subset(C_41,B_32)
| ~ is_well_founded_in(A_18,B_32)
| ~ relation(A_18) ),
inference(demodulation,[status(thm),theory(equality)],[c_129,c_26]) ).
tff(c_24,plain,
! [A_18,B_32,C_41] :
( disjoint(fiber(A_18,'#skF_4'(A_18,B_32,C_41)),C_41)
| ( empty_set = C_41 )
| ~ subset(C_41,B_32)
| ~ is_well_founded_in(A_18,B_32)
| ~ relation(A_18) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_874,plain,
! [A_180,B_181,C_182] :
( disjoint(fiber(A_180,'#skF_4'(A_180,B_181,C_182)),C_182)
| ( C_182 = '#skF_8' )
| ~ subset(C_182,B_181)
| ~ is_well_founded_in(A_180,B_181)
| ~ relation(A_180) ),
inference(demodulation,[status(thm),theory(equality)],[c_129,c_24]) ).
tff(c_14,plain,
! [A_7,C_17] :
( ~ disjoint(fiber(A_7,C_17),'#skF_2'(A_7))
| ~ in(C_17,'#skF_2'(A_7))
| well_founded_relation(A_7)
| ~ relation(A_7) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_2030,plain,
! [A_315,B_316] :
( ~ in('#skF_4'(A_315,B_316,'#skF_2'(A_315)),'#skF_2'(A_315))
| well_founded_relation(A_315)
| ( '#skF_2'(A_315) = '#skF_8' )
| ~ subset('#skF_2'(A_315),B_316)
| ~ is_well_founded_in(A_315,B_316)
| ~ relation(A_315) ),
inference(resolution,[status(thm)],[c_874,c_14]) ).
tff(c_2040,plain,
! [A_317,B_318] :
( well_founded_relation(A_317)
| ( '#skF_2'(A_317) = '#skF_8' )
| ~ subset('#skF_2'(A_317),B_318)
| ~ is_well_founded_in(A_317,B_318)
| ~ relation(A_317) ),
inference(resolution,[status(thm)],[c_623,c_2030]) ).
tff(c_2050,plain,
! [A_319] :
( ( '#skF_2'(A_319) = '#skF_8' )
| ~ is_well_founded_in(A_319,relation_field(A_319))
| well_founded_relation(A_319)
| ~ relation(A_319) ),
inference(resolution,[status(thm)],[c_18,c_2040]) ).
tff(c_2065,plain,
( ( '#skF_2'('#skF_11') = '#skF_8' )
| well_founded_relation('#skF_11')
| ~ relation('#skF_11') ),
inference(resolution,[status(thm)],[c_144,c_2050]) ).
tff(c_2071,plain,
( ( '#skF_2'('#skF_11') = '#skF_8' )
| well_founded_relation('#skF_11') ),
inference(demodulation,[status(thm),theory(equality)],[c_100,c_2065]) ).
tff(c_2073,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_115,c_346,c_2071]) ).
tff(c_2074,plain,
~ is_well_founded_in('#skF_11',relation_field('#skF_11')),
inference(splitRight,[status(thm)],[c_102]) ).
tff(c_2076,plain,
is_well_founded_in('#skF_11',relation_field('#skF_11')),
inference(splitLeft,[status(thm)],[c_108]) ).
tff(c_2141,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2074,c_2076]) ).
tff(c_2143,plain,
~ is_well_founded_in('#skF_11',relation_field('#skF_11')),
inference(splitRight,[status(thm)],[c_108]) ).
tff(c_2410,plain,
( ( '#skF_3'('#skF_11',relation_field('#skF_11')) != '#skF_8' )
| ~ relation('#skF_11') ),
inference(resolution,[status(thm)],[c_2407,c_2143]) ).
tff(c_2413,plain,
'#skF_3'('#skF_11',relation_field('#skF_11')) != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_100,c_2410]) ).
tff(c_2075,plain,
well_founded_relation('#skF_11'),
inference(splitRight,[status(thm)],[c_102]) ).
tff(c_32,plain,
! [A_18,B_32] :
( subset('#skF_3'(A_18,B_32),B_32)
| is_well_founded_in(A_18,B_32)
| ~ relation(A_18) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_22,plain,
! [A_7,B_14] :
( in('#skF_1'(A_7,B_14),B_14)
| ( empty_set = B_14 )
| ~ subset(B_14,relation_field(A_7))
| ~ well_founded_relation(A_7)
| ~ relation(A_7) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_2561,plain,
! [A_401,B_402] :
( in('#skF_1'(A_401,B_402),B_402)
| ( B_402 = '#skF_8' )
| ~ subset(B_402,relation_field(A_401))
| ~ well_founded_relation(A_401)
| ~ relation(A_401) ),
inference(demodulation,[status(thm),theory(equality)],[c_2158,c_22]) ).
tff(c_5443,plain,
! [A_596,A_597] :
( in('#skF_1'(A_596,'#skF_3'(A_597,relation_field(A_596))),'#skF_3'(A_597,relation_field(A_596)))
| ( '#skF_3'(A_597,relation_field(A_596)) = '#skF_8' )
| ~ well_founded_relation(A_596)
| ~ relation(A_596)
| is_well_founded_in(A_597,relation_field(A_596))
| ~ relation(A_597) ),
inference(resolution,[status(thm)],[c_32,c_2561]) ).
tff(c_20,plain,
! [A_7,B_14] :
( disjoint(fiber(A_7,'#skF_1'(A_7,B_14)),B_14)
| ( empty_set = B_14 )
| ~ subset(B_14,relation_field(A_7))
| ~ well_founded_relation(A_7)
| ~ relation(A_7) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_2667,plain,
! [A_7,B_14] :
( disjoint(fiber(A_7,'#skF_1'(A_7,B_14)),B_14)
| ( B_14 = '#skF_8' )
| ~ subset(B_14,relation_field(A_7))
| ~ well_founded_relation(A_7)
| ~ relation(A_7) ),
inference(demodulation,[status(thm),theory(equality)],[c_2158,c_20]) ).
tff(c_2790,plain,
! [A_418,D_419,B_420] :
( ~ disjoint(fiber(A_418,D_419),'#skF_3'(A_418,B_420))
| ~ in(D_419,'#skF_3'(A_418,B_420))
| is_well_founded_in(A_418,B_420)
| ~ relation(A_418) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_2795,plain,
! [A_7,B_420] :
( ~ in('#skF_1'(A_7,'#skF_3'(A_7,B_420)),'#skF_3'(A_7,B_420))
| is_well_founded_in(A_7,B_420)
| ( '#skF_3'(A_7,B_420) = '#skF_8' )
| ~ subset('#skF_3'(A_7,B_420),relation_field(A_7))
| ~ well_founded_relation(A_7)
| ~ relation(A_7) ),
inference(resolution,[status(thm)],[c_2667,c_2790]) ).
tff(c_6679,plain,
! [A_639] :
( ~ subset('#skF_3'(A_639,relation_field(A_639)),relation_field(A_639))
| ( '#skF_3'(A_639,relation_field(A_639)) = '#skF_8' )
| ~ well_founded_relation(A_639)
| is_well_founded_in(A_639,relation_field(A_639))
| ~ relation(A_639) ),
inference(resolution,[status(thm)],[c_5443,c_2795]) ).
tff(c_6694,plain,
! [A_640] :
( ( '#skF_3'(A_640,relation_field(A_640)) = '#skF_8' )
| ~ well_founded_relation(A_640)
| is_well_founded_in(A_640,relation_field(A_640))
| ~ relation(A_640) ),
inference(resolution,[status(thm)],[c_32,c_6679]) ).
tff(c_6703,plain,
( ( '#skF_3'('#skF_11',relation_field('#skF_11')) = '#skF_8' )
| ~ well_founded_relation('#skF_11')
| ~ relation('#skF_11') ),
inference(resolution,[status(thm)],[c_6694,c_2143]) ).
tff(c_6708,plain,
'#skF_3'('#skF_11',relation_field('#skF_11')) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_100,c_2075,c_6703]) ).
tff(c_6710,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2413,c_6708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU243+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % 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
% 0.15/0.36 % Computer : n029.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 12:11:07 EDT 2023
% 0.15/0.36 % CPUTime :
% 7.66/3.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.66/3.11
% 7.66/3.11 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.66/3.14
% 7.66/3.14 Inference rules
% 7.66/3.14 ----------------------
% 7.66/3.14 #Ref : 0
% 7.66/3.14 #Sup : 1773
% 7.66/3.14 #Fact : 0
% 7.66/3.14 #Define : 0
% 7.66/3.14 #Split : 17
% 7.66/3.14 #Chain : 0
% 7.66/3.14 #Close : 0
% 7.66/3.14
% 7.66/3.14 Ordering : KBO
% 7.66/3.14
% 7.66/3.14 Simplification rules
% 7.66/3.14 ----------------------
% 7.66/3.14 #Subsume : 1359
% 7.66/3.14 #Demod : 102
% 7.66/3.14 #Tautology : 185
% 7.66/3.14 #SimpNegUnit : 194
% 7.66/3.14 #BackRed : 116
% 7.66/3.14
% 7.66/3.14 #Partial instantiations: 0
% 7.66/3.14 #Strategies tried : 1
% 7.66/3.14
% 7.66/3.14 Timing (in seconds)
% 7.66/3.14 ----------------------
% 7.66/3.14 Preprocessing : 0.56
% 7.66/3.14 Parsing : 0.30
% 7.66/3.15 CNF conversion : 0.05
% 7.66/3.15 Main loop : 1.47
% 7.66/3.15 Inferencing : 0.54
% 7.66/3.15 Reduction : 0.41
% 7.66/3.15 Demodulation : 0.28
% 7.66/3.15 BG Simplification : 0.04
% 7.66/3.15 Subsumption : 0.37
% 7.66/3.15 Abstraction : 0.05
% 7.66/3.15 MUC search : 0.00
% 7.66/3.15 Cooper : 0.00
% 7.66/3.15 Total : 2.09
% 7.66/3.15 Index Insertion : 0.00
% 7.66/3.15 Index Deletion : 0.00
% 7.66/3.15 Index Matching : 0.00
% 7.66/3.15 BG Taut test : 0.00
%------------------------------------------------------------------------------