TSTP Solution File: ALG211+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n019.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 10:32:21 EDT 2023
% Result : Theorem 3.26s 1.87s
% Output : CNFRefutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 38 ( 9 unt; 11 typ; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 59 ( 27 ~; 19 |; 6 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 44 (; 40 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ lin_ind_subset > basis_of > a_vector_subspace_of > a_subset_of > a_vector_space > union > #nlpp > vec_to_class > #skF_1 > #skF_2 > #skF_3 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a_vector_subspace_of,type,
a_vector_subspace_of: ( $i * $i ) > $o ).
tff(a_vector_space,type,
a_vector_space: $i > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(lin_ind_subset,type,
lin_ind_subset: ( $i * $i ) > $o ).
tff(vec_to_class,type,
vec_to_class: $i > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(basis_of,type,
basis_of: ( $i * $i ) > $o ).
tff(a_subset_of,type,
a_subset_of: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_72,negated_conjecture,
~ ! [W,V] :
( ( a_vector_subspace_of(W,V)
& a_vector_space(V) )
=> ? [E,F] :
( basis_of(union(E,F),V)
& basis_of(E,W) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_3) ).
tff(f_48,axiom,
! [A] :
( a_vector_space(A)
=> ? [B] : basis_of(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_remark_63_a) ).
tff(f_53,axiom,
! [A,B] :
( a_vector_subspace_of(A,B)
=> a_vector_space(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_a) ).
tff(f_32,axiom,
! [B,V] :
( basis_of(B,V)
=> ( lin_ind_subset(B,V)
& a_subset_of(B,vec_to_class(V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',basis_of) ).
tff(f_62,axiom,
! [W,V,E] :
( ( a_vector_subspace_of(W,V)
& a_subset_of(E,vec_to_class(W)) )
=> ( lin_ind_subset(E,W)
<=> lin_ind_subset(E,V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_2) ).
tff(f_42,axiom,
! [S,T,V] :
( ( lin_ind_subset(S,V)
& basis_of(T,V) )
=> ? [U] :
( a_subset_of(U,T)
& basis_of(union(S,U),V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_2_5) ).
tff(c_20,plain,
a_vector_space('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_10,plain,
! [A_7] :
( basis_of('#skF_2'(A_7),A_7)
| ~ a_vector_space(A_7) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_22,plain,
a_vector_subspace_of('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_23,plain,
! [A_18,B_19] :
( a_vector_space(A_18)
| ~ a_vector_subspace_of(A_18,B_19) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_27,plain,
a_vector_space('#skF_3'),
inference(resolution,[status(thm)],[c_22,c_23]) ).
tff(c_4,plain,
! [B_1,V_2] :
( lin_ind_subset(B_1,V_2)
| ~ basis_of(B_1,V_2) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_2,plain,
! [B_1,V_2] :
( a_subset_of(B_1,vec_to_class(V_2))
| ~ basis_of(B_1,V_2) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_33,plain,
! [E_30,V_31,W_32] :
( lin_ind_subset(E_30,V_31)
| ~ lin_ind_subset(E_30,W_32)
| ~ a_subset_of(E_30,vec_to_class(W_32))
| ~ a_vector_subspace_of(W_32,V_31) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_41,plain,
! [B_33,V_34,V_35] :
( lin_ind_subset(B_33,V_34)
| ~ lin_ind_subset(B_33,V_35)
| ~ a_vector_subspace_of(V_35,V_34)
| ~ basis_of(B_33,V_35) ),
inference(resolution,[status(thm)],[c_2,c_33]) ).
tff(c_45,plain,
! [B_36,V_37,V_38] :
( lin_ind_subset(B_36,V_37)
| ~ a_vector_subspace_of(V_38,V_37)
| ~ basis_of(B_36,V_38) ),
inference(resolution,[status(thm)],[c_4,c_41]) ).
tff(c_48,plain,
! [B_36] :
( lin_ind_subset(B_36,'#skF_4')
| ~ basis_of(B_36,'#skF_3') ),
inference(resolution,[status(thm)],[c_22,c_45]) ).
tff(c_65,plain,
! [S_46,T_47,V_48] :
( basis_of(union(S_46,'#skF_1'(S_46,T_47,V_48)),V_48)
| ~ basis_of(T_47,V_48)
| ~ lin_ind_subset(S_46,V_48) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_18,plain,
! [E_16,F_17] :
( ~ basis_of(E_16,'#skF_3')
| ~ basis_of(union(E_16,F_17),'#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_70,plain,
! [S_46,T_47] :
( ~ basis_of(S_46,'#skF_3')
| ~ basis_of(T_47,'#skF_4')
| ~ lin_ind_subset(S_46,'#skF_4') ),
inference(resolution,[status(thm)],[c_65,c_18]) ).
tff(c_72,plain,
! [S_49] :
( ~ basis_of(S_49,'#skF_3')
| ~ lin_ind_subset(S_49,'#skF_4') ),
inference(splitLeft,[status(thm)],[c_70]) ).
tff(c_82,plain,
! [B_50] : ~ basis_of(B_50,'#skF_3'),
inference(resolution,[status(thm)],[c_48,c_72]) ).
tff(c_90,plain,
~ a_vector_space('#skF_3'),
inference(resolution,[status(thm)],[c_10,c_82]) ).
tff(c_95,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_27,c_90]) ).
tff(c_97,plain,
! [T_51] : ~ basis_of(T_51,'#skF_4'),
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_105,plain,
~ a_vector_space('#skF_4'),
inference(resolution,[status(thm)],[c_10,c_97]) ).
tff(c_110,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_20,c_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 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
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 20:19:17 EDT 2023
% 0.14/0.36 % CPUTime :
% 3.26/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.26/1.87
% 3.26/1.87 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.34/1.91
% 3.34/1.91 Inference rules
% 3.34/1.91 ----------------------
% 3.34/1.91 #Ref : 0
% 3.34/1.91 #Sup : 16
% 3.34/1.91 #Fact : 0
% 3.34/1.91 #Define : 0
% 3.34/1.91 #Split : 1
% 3.34/1.91 #Chain : 0
% 3.34/1.91 #Close : 0
% 3.34/1.91
% 3.34/1.91 Ordering : KBO
% 3.34/1.91
% 3.34/1.91 Simplification rules
% 3.34/1.91 ----------------------
% 3.34/1.91 #Subsume : 8
% 3.34/1.91 #Demod : 2
% 3.34/1.91 #Tautology : 0
% 3.34/1.91 #SimpNegUnit : 0
% 3.34/1.91 #BackRed : 0
% 3.34/1.91
% 3.34/1.91 #Partial instantiations: 0
% 3.34/1.91 #Strategies tried : 1
% 3.34/1.91
% 3.34/1.91 Timing (in seconds)
% 3.34/1.91 ----------------------
% 3.34/1.91 Preprocessing : 0.44
% 3.34/1.91 Parsing : 0.25
% 3.34/1.91 CNF conversion : 0.03
% 3.34/1.91 Main loop : 0.30
% 3.34/1.91 Inferencing : 0.13
% 3.34/1.91 Reduction : 0.06
% 3.34/1.92 Demodulation : 0.04
% 3.34/1.92 BG Simplification : 0.02
% 3.34/1.92 Subsumption : 0.06
% 3.34/1.92 Abstraction : 0.01
% 3.34/1.92 MUC search : 0.00
% 3.34/1.92 Cooper : 0.00
% 3.34/1.92 Total : 0.80
% 3.34/1.92 Index Insertion : 0.00
% 3.34/1.92 Index Deletion : 0.00
% 3.34/1.92 Index Matching : 0.00
% 3.34/1.92 BG Taut test : 0.00
%------------------------------------------------------------------------------