TSTP Solution File: NUM394+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM394+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 : 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 10:51:35 EDT 2023
% Result : Theorem 4.79s 2.13s
% Output : CNFRefutation 4.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 41
% Syntax : Number of formulae : 87 ( 16 unt; 30 typ; 0 def)
% Number of atoms : 143 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 157 ( 71 ~; 64 |; 10 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 16 >; 4 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-1 aty)
% Number of variables : 67 (; 66 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > ordinal_subset > in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_2 > #skF_11 > #skF_15 > #skF_1 > #skF_7 > #skF_10 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(relation_non_empty,type,
relation_non_empty: $i > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
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_7',type,
'#skF_7': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
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_4',type,
'#skF_4': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(ordinal_subset,type,
ordinal_subset: ( $i * $i ) > $o ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_187,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( ordinal_subset(A,B)
| in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_ordinal1) ).
tff(f_156,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ordinal_subset(A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
tff(f_100,axiom,
? [A] :
( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
tff(f_71,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
| ordinal_subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
tff(f_150,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
tff(f_177,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(A,B)
& ( A != B )
& ~ in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
tff(f_197,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
tff(f_210,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
tff(f_203,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
tff(f_193,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
tff(f_31,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
tff(c_110,plain,
ordinal('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_187]) ).
tff(c_96,plain,
! [A_18,B_19] :
( ordinal_subset(A_18,A_18)
| ~ ordinal(B_19)
| ~ ordinal(A_18) ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_249,plain,
! [B_19] : ~ ordinal(B_19),
inference(splitLeft,[status(thm)],[c_96]) ).
tff(c_46,plain,
ordinal('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_254,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_249,c_46]) ).
tff(c_255,plain,
! [A_18] :
( ordinal_subset(A_18,A_18)
| ~ ordinal(A_18) ),
inference(splitRight,[status(thm)],[c_96]) ).
tff(c_108,plain,
ordinal('#skF_15'),
inference(cnfTransformation,[status(thm)],[f_187]) ).
tff(c_20,plain,
! [B_9,A_8] :
( ordinal_subset(B_9,A_8)
| ordinal_subset(A_8,B_9)
| ~ ordinal(B_9)
| ~ ordinal(A_8) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_94,plain,
! [A_16,B_17] :
( subset(A_16,B_17)
| ~ ordinal_subset(A_16,B_17)
| ~ ordinal(B_17)
| ~ ordinal(A_16) ),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_525,plain,
! [B_109,A_110] :
( in(B_109,A_110)
| ( B_109 = A_110 )
| in(A_110,B_109)
| ~ ordinal(B_109)
| ~ ordinal(A_110) ),
inference(cnfTransformation,[status(thm)],[f_177]) ).
tff(c_104,plain,
~ in('#skF_15','#skF_14'),
inference(cnfTransformation,[status(thm)],[f_187]) ).
tff(c_553,plain,
( ( '#skF_15' = '#skF_14' )
| in('#skF_14','#skF_15')
| ~ ordinal('#skF_15')
| ~ ordinal('#skF_14') ),
inference(resolution,[status(thm)],[c_525,c_104]) ).
tff(c_592,plain,
( ( '#skF_15' = '#skF_14' )
| in('#skF_14','#skF_15') ),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_108,c_553]) ).
tff(c_604,plain,
in('#skF_14','#skF_15'),
inference(splitLeft,[status(thm)],[c_592]) ).
tff(c_116,plain,
! [A_30,B_31] :
( element(A_30,powerset(B_31))
| ~ subset(A_30,B_31) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_349,plain,
! [C_76,B_77,A_78] :
( ~ empty(C_76)
| ~ element(B_77,powerset(C_76))
| ~ in(A_78,B_77) ),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_358,plain,
! [B_31,A_78,A_30] :
( ~ empty(B_31)
| ~ in(A_78,A_30)
| ~ subset(A_30,B_31) ),
inference(resolution,[status(thm)],[c_116,c_349]) ).
tff(c_670,plain,
! [B_113] :
( ~ empty(B_113)
| ~ subset('#skF_15',B_113) ),
inference(resolution,[status(thm)],[c_604,c_358]) ).
tff(c_674,plain,
! [B_17] :
( ~ empty(B_17)
| ~ ordinal_subset('#skF_15',B_17)
| ~ ordinal(B_17)
| ~ ordinal('#skF_15') ),
inference(resolution,[status(thm)],[c_94,c_670]) ).
tff(c_707,plain,
! [B_115] :
( ~ empty(B_115)
| ~ ordinal_subset('#skF_15',B_115)
| ~ ordinal(B_115) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_674]) ).
tff(c_711,plain,
! [A_8] :
( ~ empty(A_8)
| ordinal_subset(A_8,'#skF_15')
| ~ ordinal('#skF_15')
| ~ ordinal(A_8) ),
inference(resolution,[status(thm)],[c_20,c_707]) ).
tff(c_756,plain,
! [A_117] :
( ~ empty(A_117)
| ordinal_subset(A_117,'#skF_15')
| ~ ordinal(A_117) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_711]) ).
tff(c_106,plain,
~ ordinal_subset('#skF_14','#skF_15'),
inference(cnfTransformation,[status(thm)],[f_187]) ).
tff(c_763,plain,
( ~ empty('#skF_14')
| ~ ordinal('#skF_14') ),
inference(resolution,[status(thm)],[c_756,c_106]) ).
tff(c_769,plain,
~ empty('#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_763]) ).
tff(c_460,plain,
! [A_99,C_100,B_101] :
( element(A_99,C_100)
| ~ element(B_101,powerset(C_100))
| ~ in(A_99,B_101) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_469,plain,
! [A_99,B_31,A_30] :
( element(A_99,B_31)
| ~ in(A_99,A_30)
| ~ subset(A_30,B_31) ),
inference(resolution,[status(thm)],[c_116,c_460]) ).
tff(c_688,plain,
! [B_114] :
( element('#skF_14',B_114)
| ~ subset('#skF_15',B_114) ),
inference(resolution,[status(thm)],[c_604,c_469]) ).
tff(c_692,plain,
! [B_17] :
( element('#skF_14',B_17)
| ~ ordinal_subset('#skF_15',B_17)
| ~ ordinal(B_17)
| ~ ordinal('#skF_15') ),
inference(resolution,[status(thm)],[c_94,c_688]) ).
tff(c_770,plain,
! [B_118] :
( element('#skF_14',B_118)
| ~ ordinal_subset('#skF_15',B_118)
| ~ ordinal(B_118) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_692]) ).
tff(c_778,plain,
! [A_8] :
( element('#skF_14',A_8)
| ordinal_subset(A_8,'#skF_15')
| ~ ordinal('#skF_15')
| ~ ordinal(A_8) ),
inference(resolution,[status(thm)],[c_20,c_770]) ).
tff(c_799,plain,
! [A_119] :
( element('#skF_14',A_119)
| ordinal_subset(A_119,'#skF_15')
| ~ ordinal(A_119) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_778]) ).
tff(c_810,plain,
( element('#skF_14','#skF_14')
| ~ ordinal('#skF_14') ),
inference(resolution,[status(thm)],[c_799,c_106]) ).
tff(c_819,plain,
element('#skF_14','#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_810]) ).
tff(c_112,plain,
! [A_28,B_29] :
( in(A_28,B_29)
| empty(B_29)
| ~ element(A_28,B_29) ),
inference(cnfTransformation,[status(thm)],[f_193]) ).
tff(c_283,plain,
! [A_73,B_74] :
( in(A_73,B_74)
| empty(B_74)
| ~ element(A_73,B_74) ),
inference(cnfTransformation,[status(thm)],[f_193]) ).
tff(c_2,plain,
! [B_2,A_1] :
( ~ in(B_2,A_1)
| ~ in(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_399,plain,
! [B_87,A_88] :
( ~ in(B_87,A_88)
| empty(B_87)
| ~ element(A_88,B_87) ),
inference(resolution,[status(thm)],[c_283,c_2]) ).
tff(c_882,plain,
! [A_127,B_128] :
( empty(A_127)
| ~ element(B_128,A_127)
| empty(B_128)
| ~ element(A_127,B_128) ),
inference(resolution,[status(thm)],[c_112,c_399]) ).
tff(c_886,plain,
( empty('#skF_14')
| ~ element('#skF_14','#skF_14') ),
inference(resolution,[status(thm)],[c_819,c_882]) ).
tff(c_900,plain,
empty('#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_886]) ).
tff(c_902,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_769,c_900]) ).
tff(c_903,plain,
'#skF_15' = '#skF_14',
inference(splitRight,[status(thm)],[c_592]) ).
tff(c_908,plain,
~ ordinal_subset('#skF_14','#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_903,c_106]) ).
tff(c_929,plain,
~ ordinal('#skF_14'),
inference(resolution,[status(thm)],[c_255,c_908]) ).
tff(c_933,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_110,c_929]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM394+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % 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
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 15:06:14 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.79/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.79/2.14
% 4.79/2.14 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.79/2.17
% 4.79/2.17 Inference rules
% 4.79/2.17 ----------------------
% 4.79/2.17 #Ref : 0
% 4.79/2.17 #Sup : 154
% 4.79/2.17 #Fact : 4
% 4.79/2.17 #Define : 0
% 4.79/2.17 #Split : 6
% 4.79/2.17 #Chain : 0
% 4.79/2.17 #Close : 0
% 4.79/2.17
% 4.79/2.17 Ordering : KBO
% 4.79/2.17
% 4.79/2.17 Simplification rules
% 4.79/2.17 ----------------------
% 4.79/2.17 #Subsume : 36
% 4.79/2.17 #Demod : 71
% 4.79/2.17 #Tautology : 45
% 4.79/2.17 #SimpNegUnit : 5
% 4.79/2.17 #BackRed : 21
% 4.79/2.17
% 4.79/2.17 #Partial instantiations: 0
% 4.79/2.17 #Strategies tried : 1
% 4.79/2.17
% 4.79/2.17 Timing (in seconds)
% 4.79/2.17 ----------------------
% 4.79/2.18 Preprocessing : 0.54
% 4.79/2.18 Parsing : 0.29
% 4.79/2.18 CNF conversion : 0.05
% 4.79/2.18 Main loop : 0.55
% 4.79/2.18 Inferencing : 0.21
% 4.79/2.18 Reduction : 0.15
% 4.79/2.18 Demodulation : 0.10
% 4.79/2.18 BG Simplification : 0.03
% 4.79/2.18 Subsumption : 0.11
% 4.79/2.18 Abstraction : 0.02
% 4.79/2.18 MUC search : 0.00
% 4.79/2.18 Cooper : 0.00
% 4.79/2.18 Total : 1.15
% 4.79/2.18 Index Insertion : 0.00
% 4.79/2.18 Index Deletion : 0.00
% 4.79/2.18 Index Matching : 0.00
% 4.79/2.18 BG Taut test : 0.00
%------------------------------------------------------------------------------