TSTP Solution File: SEU008+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU008+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/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 : n027.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 10:57:29 EDT 2023
% Result : Theorem 12.08s 4.04s
% Output : CNFRefutation 12.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 35
% Syntax : Number of formulae : 58 ( 14 unt; 29 typ; 0 def)
% Number of atoms : 72 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 74 ( 31 ~; 26 |; 7 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 19 >; 11 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-3 aty)
% Number of variables : 41 (; 41 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > function > empty > set_intersection2 > relation_composition > apply > #nlpp > relation_dom > powerset > identity_relation > empty_set > #skF_9 > #skF_1 > #skF_11 > #skF_15 > #skF_7 > #skF_10 > #skF_12 > #skF_14 > #skF_5 > #skF_13 > #skF_2 > #skF_8 > #skF_4 > #skF_3 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(element,type,
element: ( $i * $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('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
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(identity_relation,type,
identity_relation: $i > $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(relation_composition,type,
relation_composition: ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_41,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(f_212,negated_conjecture,
~ ! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(B,set_intersection2(relation_dom(C),A))
=> ( apply(C,B) = apply(relation_composition(identity_relation(A),C),B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_1) ).
tff(f_50,axiom,
! [A,B,C] :
( ( C = set_intersection2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
tff(f_100,axiom,
! [A] :
( relation(identity_relation(A))
& function(identity_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
tff(f_203,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( ( B = identity_relation(A) )
<=> ( ( relation_dom(B) = A )
& ! [C] :
( in(C,A)
=> ( apply(B,C) = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
tff(f_182,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(B))
=> ( apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
tff(c_8,plain,
! [B_6,A_5] : ( set_intersection2(B_6,A_5) = set_intersection2(A_5,B_6) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_122,plain,
in('#skF_14',set_intersection2(relation_dom('#skF_15'),'#skF_13')),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_153,plain,
in('#skF_14',set_intersection2('#skF_13',relation_dom('#skF_15'))),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_122]) ).
tff(c_720,plain,
! [D_122,A_123,B_124] :
( in(D_122,A_123)
| ~ in(D_122,set_intersection2(A_123,B_124)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_744,plain,
in('#skF_14','#skF_13'),
inference(resolution,[status(thm)],[c_153,c_720]) ).
tff(c_54,plain,
! [A_25] : relation(identity_relation(A_25)),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_56,plain,
! [A_25] : function(identity_relation(A_25)),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_116,plain,
! [A_47,C_51] :
( ( apply(identity_relation(A_47),C_51) = C_51 )
| ~ in(C_51,A_47)
| ~ function(identity_relation(A_47))
| ~ relation(identity_relation(A_47)) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_144,plain,
! [A_47,C_51] :
( ( apply(identity_relation(A_47),C_51) = C_51 )
| ~ in(C_51,A_47)
| ~ relation(identity_relation(A_47)) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_116]) ).
tff(c_148,plain,
! [A_47,C_51] :
( ( apply(identity_relation(A_47),C_51) = C_51 )
| ~ in(C_51,A_47) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_144]) ).
tff(c_126,plain,
relation('#skF_15'),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_124,plain,
function('#skF_15'),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_118,plain,
! [A_47] :
( ( relation_dom(identity_relation(A_47)) = A_47 )
| ~ function(identity_relation(A_47))
| ~ relation(identity_relation(A_47)) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_142,plain,
! [A_47] :
( ( relation_dom(identity_relation(A_47)) = A_47 )
| ~ relation(identity_relation(A_47)) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_118]) ).
tff(c_146,plain,
! [A_47] : ( relation_dom(identity_relation(A_47)) = A_47 ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_142]) ).
tff(c_6000,plain,
! [B_290,C_291,A_292] :
( ( apply(relation_composition(B_290,C_291),A_292) = apply(C_291,apply(B_290,A_292)) )
| ~ in(A_292,relation_dom(B_290))
| ~ function(C_291)
| ~ relation(C_291)
| ~ function(B_290)
| ~ relation(B_290) ),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_6035,plain,
! [A_47,C_291,A_292] :
( ( apply(relation_composition(identity_relation(A_47),C_291),A_292) = apply(C_291,apply(identity_relation(A_47),A_292)) )
| ~ in(A_292,A_47)
| ~ function(C_291)
| ~ relation(C_291)
| ~ function(identity_relation(A_47))
| ~ relation(identity_relation(A_47)) ),
inference(superposition,[status(thm),theory(equality)],[c_146,c_6000]) ).
tff(c_18135,plain,
! [A_573,C_574,A_575] :
( ( apply(relation_composition(identity_relation(A_573),C_574),A_575) = apply(C_574,apply(identity_relation(A_573),A_575)) )
| ~ in(A_575,A_573)
| ~ function(C_574)
| ~ relation(C_574) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_56,c_6035]) ).
tff(c_120,plain,
apply(relation_composition(identity_relation('#skF_13'),'#skF_15'),'#skF_14') != apply('#skF_15','#skF_14'),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_18153,plain,
( ( apply('#skF_15',apply(identity_relation('#skF_13'),'#skF_14')) != apply('#skF_15','#skF_14') )
| ~ in('#skF_14','#skF_13')
| ~ function('#skF_15')
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_18135,c_120]) ).
tff(c_18222,plain,
apply('#skF_15',apply(identity_relation('#skF_13'),'#skF_14')) != apply('#skF_15','#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_124,c_744,c_18153]) ).
tff(c_18241,plain,
~ in('#skF_14','#skF_13'),
inference(superposition,[status(thm),theory(equality)],[c_148,c_18222]) ).
tff(c_18245,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_744,c_18241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU008+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/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
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 12:24:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 12.08/4.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.19/4.04
% 12.19/4.04 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.19/4.07
% 12.19/4.07 Inference rules
% 12.19/4.07 ----------------------
% 12.19/4.07 #Ref : 0
% 12.19/4.07 #Sup : 4407
% 12.19/4.07 #Fact : 0
% 12.19/4.07 #Define : 0
% 12.19/4.07 #Split : 7
% 12.19/4.07 #Chain : 0
% 12.19/4.07 #Close : 0
% 12.19/4.07
% 12.19/4.07 Ordering : KBO
% 12.19/4.07
% 12.19/4.07 Simplification rules
% 12.19/4.07 ----------------------
% 12.19/4.07 #Subsume : 1126
% 12.19/4.07 #Demod : 3577
% 12.19/4.07 #Tautology : 2238
% 12.19/4.07 #SimpNegUnit : 38
% 12.19/4.07 #BackRed : 9
% 12.19/4.07
% 12.19/4.07 #Partial instantiations: 0
% 12.19/4.07 #Strategies tried : 1
% 12.19/4.07
% 12.19/4.07 Timing (in seconds)
% 12.19/4.07 ----------------------
% 12.19/4.07 Preprocessing : 0.59
% 12.19/4.07 Parsing : 0.30
% 12.19/4.07 CNF conversion : 0.05
% 12.19/4.07 Main loop : 2.43
% 12.19/4.07 Inferencing : 0.68
% 12.19/4.07 Reduction : 0.85
% 12.19/4.07 Demodulation : 0.62
% 12.19/4.07 BG Simplification : 0.07
% 12.19/4.07 Subsumption : 0.68
% 12.19/4.07 Abstraction : 0.07
% 12.19/4.07 MUC search : 0.00
% 12.19/4.07 Cooper : 0.00
% 12.19/4.07 Total : 3.07
% 12.19/4.08 Index Insertion : 0.00
% 12.19/4.08 Index Deletion : 0.00
% 12.19/4.08 Index Matching : 0.00
% 12.19/4.08 BG Taut test : 0.00
%------------------------------------------------------------------------------