TSTP Solution File: DAT097_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : DAT097_1 : TPTP v8.1.2. Released v6.1.0.
% 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 : n032.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 10:37:09 EDT 2023
% Result : Theorem 8.44s 3.16s
% Output : CNFRefutation 8.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 50 ( 21 unt; 16 typ; 0 def)
% Number of atoms : 53 ( 33 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 25 ( 6 ~; 11 |; 4 &)
% ( 2 <=>; 1 =>; 1 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 92 ( 5 atm; 14 fun; 27 num; 46 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 25 ( 14 >; 11 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 86 (; 82 !; 4 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
%$ inRange > in > count > cons > append > #nlpp > tail > length > head > nil > #skF_4 > #skF_1 > #skF_2 > #skF_6 > #skF_3 > #skF_5
%Foreground sorts:
tff(list,type,
list: $tType ).
%Background operators:
%Foreground operators:
tff(inRange,type,
inRange: ( $int * list ) > $o ).
tff(tail,type,
tail: list > list ).
tff(nil,type,
nil: list ).
tff(head,type,
head: list > $int ).
tff(length,type,
length: list > $int ).
tff('#skF_4',type,
'#skF_4': ( $int * list ) > list ).
tff(append,type,
append: ( list * list ) > list ).
tff(count,type,
count: ( $int * list ) > $int ).
tff(cons,type,
cons: ( $int * list ) > list ).
tff(in,type,
in: ( $int * list ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $int * list ) > $int ).
tff('#skF_2',type,
'#skF_2': ( $int * list ) > list ).
tff('#skF_6',type,
'#skF_6': ( $int * list ) > list ).
tff('#skF_3',type,
'#skF_3': ( $int * list ) > $int ).
tff('#skF_5',type,
'#skF_5': ( $int * list ) > $int ).
tff(f_75,axiom,
! [Ka: $int] : ( count(Ka,nil) = 0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).
tff(f_84,axiom,
! [Ka: $int,Ha: $int,T: list,Na: $int] :
( ( count(Ka,cons(Ha,T)) = $sum(count(Ka,T),1) )
<= ( Ka = Ha ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_4) ).
tff(f_89,axiom,
! [Ia: $int,K: list,L: list] : ( append(cons(Ia,K),L) = cons(Ia,append(K,L)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_7) ).
tff(f_54,axiom,
! [Xa: $int,L: list] :
( in(Xa,L)
<=> ( ? [Ha: $int,T: list] :
( ( L = cons(Ha,T) )
& ( Xa = Ha ) )
| ? [Ha: $int,T: list] :
( ( L = cons(Ha,T) )
& in(Xa,T) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_conv) ).
tff(f_104,negated_conjecture,
~ ~ ! [Ma: $int,Na: $int,K: list,L: list,L1: list] :
( ( in(Na,L)
& ~ in(Ma,K)
& ( L1 = append(L,cons(Ma,K)) ) )
=> ( count(Na,L1) = count(Na,L) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(f_93,axiom,
! [Na: $int,L: list] :
( in(Na,L)
<=> $greater(count(Na,L),0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_8) ).
tff(f_87,axiom,
! [L: list] : ( append(nil,L) = L ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_6) ).
tff(c_63,plain,
! [K_32a: $int] : ( count(K_32a,nil) = 0 ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_43,plain,
! [H_38a: $int,T_39: list] : ( count(H_38a,cons(H_38a,T_39)) = $sum(count(H_38a,T_39),1) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_61,plain,
! [H_38a: $int,T_39: list] : ( count(H_38a,cons(H_38a,T_39)) = $sum(1,count(H_38a,T_39)) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_43]) ).
tff(c_60,plain,
! [I_42a: $int,K_43: list,L_44: list] : ( cons(I_42a,append(K_43,L_44)) = append(cons(I_42a,K_43),L_44) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_442,plain,
! [H_106a: $int,T_107: list] : ( count(H_106a,cons(H_106a,T_107)) = $sum(1,count(H_106a,T_107)) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_43]) ).
tff(c_469,plain,
! [I_42a: $int,K_43: list,L_44: list] : ( count(I_42a,append(cons(I_42a,K_43),L_44)) = $sum(1,count(I_42a,append(K_43,L_44))) ),
inference(superposition,[status(thm),theory(equality)],[c_60,c_442]) ).
tff(c_72,plain,
! [H_18a: $int,T_19: list] : in(H_18a,cons(H_18a,T_19)),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_130,plain,
! [N_66a: $int,L_67: list,M_68a: $int,K_69: list] :
( ( count(N_66a,append(L_67,cons(M_68a,K_69))) = count(N_66a,L_67) )
| in(M_68a,K_69)
| ~ in(N_66a,L_67) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_138,plain,
! [H_18a: $int,T_19: list,M_68a: $int,K_69: list] :
( ( count(H_18a,append(cons(H_18a,T_19),cons(M_68a,K_69))) = count(H_18a,cons(H_18a,T_19)) )
| in(M_68a,K_69) ),
inference(resolution,[status(thm)],[c_72,c_130]) ).
tff(c_440,plain,
! [H_18a: $int,T_19: list,M_68a: $int,K_69: list] :
( ( count(H_18a,append(cons(H_18a,T_19),cons(M_68a,K_69))) = $sum(1,count(H_18a,T_19)) )
| in(M_68a,K_69) ),
inference(demodulation,[status(thm),theory(equality)],[c_61,c_138]) ).
tff(c_5918,plain,
! [H_18a: $int,T_19: list,M_68a: $int,K_69: list] :
( ( $sum(1,count(H_18a,append(T_19,cons(M_68a,K_69)))) = $sum(1,count(H_18a,T_19)) )
| in(M_68a,K_69) ),
inference(demodulation,[status(thm),theory(equality)],[c_469,c_440]) ).
tff(c_5921,plain,
! [H_391a: $int,T_392: list,M_393a: $int,K_394: list] :
( ( count(H_391a,append(T_392,cons(M_393a,K_394))) = count(H_391a,T_392) )
| in(M_393a,K_394) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5918]) ).
tff(c_50,plain,
! [N_45a: $int,L_46: list] :
( $greater(count(N_45a,L_46),0)
| ~ in(N_45a,L_46) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_59,plain,
! [N_45a: $int,L_46: list] :
( $less(0,count(N_45a,L_46))
| ~ in(N_45a,L_46) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_50]) ).
tff(c_7717,plain,
! [M_422a: $int,K_423: list,H_424a: $int,T_425: list] :
( $less(0,count(M_422a,K_423))
| ( count(H_424a,append(T_425,cons(M_422a,K_423))) = count(H_424a,T_425) ) ),
inference(resolution,[status(thm)],[c_5921,c_59]) ).
tff(c_7868,plain,
! [H_424a: $int,T_425: list,K_32a: $int] :
( $less(0,0)
| ( count(H_424a,append(T_425,cons(K_32a,nil))) = count(H_424a,T_425) ) ),
inference(superposition,[status(thm),theory(equality)],[c_63,c_7717]) ).
tff(c_7959,plain,
! [H_426a: $int,T_427: list,K_428a: $int] : ( count(H_426a,append(T_427,cons(K_428a,nil))) = count(H_426a,T_427) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7868]) ).
tff(c_46,plain,
! [L_41: list] : ( append(nil,L_41) = L_41 ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_254,plain,
! [I_92a: $int,K_93: list,L_94: list] : ( cons(I_92a,append(K_93,L_94)) = append(cons(I_92a,K_93),L_94) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_306,plain,
! [I_92a: $int,L_41: list] : ( cons(I_92a,L_41) = append(cons(I_92a,nil),L_41) ),
inference(superposition,[status(thm),theory(equality)],[c_46,c_254]) ).
tff(c_468,plain,
! [I_92a: $int,L_41: list] : ( count(I_92a,append(cons(I_92a,nil),L_41)) = $sum(1,count(I_92a,L_41)) ),
inference(superposition,[status(thm),theory(equality)],[c_306,c_442]) ).
tff(c_7998,plain,
! [H_426a: $int,K_428a: $int] : ( count(H_426a,cons(H_426a,nil)) = $sum(1,count(H_426a,cons(K_428a,nil))) ),
inference(superposition,[status(thm),theory(equality)],[c_7959,c_468]) ).
tff(c_8075,plain,
! [H_426a: $int,K_428a: $int] : ( $sum(1,count(H_426a,cons(K_428a,nil))) = $sum(1,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_63,c_61,c_7998]) ).
tff(c_8166,plain,
! [H_431a: $int,K_432a: $int] : ( count(H_431a,cons(K_432a,nil)) = 0 ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8075]) ).
tff(c_8183,plain,
! [K_432a: $int] : ( $sum(1,count(K_432a,nil)) = 0 ),
inference(superposition,[status(thm),theory(equality)],[c_8166,c_61]) ).
tff(c_8209,plain,
$sum(1,0) = 0,
inference(demodulation,[status(thm),theory(equality)],[c_63,c_8183]) ).
tff(c_8212,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT097_1 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.11 % 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
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Thu Aug 3 13:16:06 EDT 2023
% 0.11/0.30 % CPUTime :
% 8.44/3.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.78/3.16
% 8.78/3.16 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.89/3.19
% 8.89/3.19 Inference rules
% 8.89/3.19 ----------------------
% 8.89/3.19 #Ref : 0
% 8.89/3.19 #Sup : 1752
% 8.89/3.19 #Fact : 0
% 8.89/3.19 #Define : 0
% 8.89/3.19 #Split : 0
% 8.89/3.19 #Chain : 0
% 8.89/3.19 #Close : 0
% 8.89/3.19
% 8.89/3.19 Ordering : LPO
% 8.89/3.19
% 8.89/3.19 Simplification rules
% 8.89/3.19 ----------------------
% 8.89/3.19 #Subsume : 229
% 8.89/3.19 #Demod : 2105
% 8.89/3.19 #Tautology : 712
% 8.89/3.19 #SimpNegUnit : 24
% 8.89/3.19 #BackRed : 12
% 8.89/3.19
% 8.89/3.19 #Partial instantiations: 0
% 8.89/3.19 #Strategies tried : 1
% 8.89/3.19
% 8.89/3.19 Timing (in seconds)
% 8.89/3.19 ----------------------
% 8.89/3.19 Preprocessing : 0.58
% 8.89/3.19 Parsing : 0.30
% 8.89/3.19 CNF conversion : 0.04
% 8.89/3.19 Main loop : 1.69
% 8.89/3.19 Inferencing : 0.45
% 8.89/3.19 Reduction : 0.73
% 8.89/3.20 Demodulation : 0.62
% 8.89/3.20 BG Simplification : 0.15
% 8.89/3.20 Subsumption : 0.27
% 8.89/3.20 Abstraction : 0.10
% 8.89/3.20 MUC search : 0.00
% 8.89/3.20 Cooper : 0.00
% 8.89/3.20 Total : 2.32
% 8.89/3.20 Index Insertion : 0.00
% 8.89/3.20 Index Deletion : 0.00
% 8.89/3.20 Index Matching : 0.00
% 8.89/3.20 BG Taut test : 0.00
%------------------------------------------------------------------------------