TSTP Solution File: ALG211+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 : Wed Aug 30 16:06:39 EDT 2023
% Result : Theorem 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 40 ( 5 unt; 11 typ; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 89 ( 37 ~; 31 |; 13 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 58 ( 6 sgn; 28 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
basis_of: ( $i * $i ) > $o ).
tff(decl_23,type,
lin_ind_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
vec_to_class: $i > $i ).
tff(decl_25,type,
a_subset_of: ( $i * $i ) > $o ).
tff(decl_26,type,
union: ( $i * $i ) > $i ).
tff(decl_27,type,
a_vector_space: $i > $o ).
tff(decl_28,type,
a_vector_subspace_of: ( $i * $i ) > $o ).
tff(decl_29,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
esk2_1: $i > $i ).
tff(decl_31,type,
esk3_0: $i ).
tff(decl_32,type,
esk4_0: $i ).
fof(bg_2_4_3,conjecture,
! [X7,X2] :
( ( a_vector_subspace_of(X7,X2)
& a_vector_space(X2) )
=> ? [X8,X9] :
( basis_of(union(X8,X9),X2)
& basis_of(X8,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_3) ).
fof(bg_2_4_2,axiom,
! [X7,X2,X8] :
( ( a_vector_subspace_of(X7,X2)
& a_subset_of(X8,vec_to_class(X7)) )
=> ( lin_ind_subset(X8,X7)
<=> lin_ind_subset(X8,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).
fof(basis_of,axiom,
! [X1,X2] :
( basis_of(X1,X2)
=> ( lin_ind_subset(X1,X2)
& a_subset_of(X1,vec_to_class(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_of) ).
fof(bg_2_2_5,axiom,
! [X3,X4,X2] :
( ( lin_ind_subset(X3,X2)
& basis_of(X4,X2) )
=> ? [X5] :
( a_subset_of(X5,X4)
& basis_of(union(X3,X5),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_2_5) ).
fof(bg_2_4_a,axiom,
! [X6,X1] :
( a_vector_subspace_of(X6,X1)
=> a_vector_space(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_a) ).
fof(bg_remark_63_a,axiom,
! [X6] :
( a_vector_space(X6)
=> ? [X1] : basis_of(X1,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_remark_63_a) ).
fof(c_0_6,negated_conjecture,
~ ! [X7,X2] :
( ( a_vector_subspace_of(X7,X2)
& a_vector_space(X2) )
=> ? [X8,X9] :
( basis_of(union(X8,X9),X2)
& basis_of(X8,X7) ) ),
inference(assume_negation,[status(cth)],[bg_2_4_3]) ).
fof(c_0_7,plain,
! [X20,X21,X22] :
( ( ~ lin_ind_subset(X22,X20)
| lin_ind_subset(X22,X21)
| ~ a_vector_subspace_of(X20,X21)
| ~ a_subset_of(X22,vec_to_class(X20)) )
& ( ~ lin_ind_subset(X22,X21)
| lin_ind_subset(X22,X20)
| ~ a_vector_subspace_of(X20,X21)
| ~ a_subset_of(X22,vec_to_class(X20)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_2])])]) ).
fof(c_0_8,plain,
! [X10,X11] :
( ( lin_ind_subset(X10,X11)
| ~ basis_of(X10,X11) )
& ( a_subset_of(X10,vec_to_class(X11))
| ~ basis_of(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[basis_of])])]) ).
fof(c_0_9,negated_conjecture,
! [X25,X26] :
( a_vector_subspace_of(esk3_0,esk4_0)
& a_vector_space(esk4_0)
& ( ~ basis_of(union(X25,X26),esk4_0)
| ~ basis_of(X25,esk3_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_10,plain,
! [X12,X13,X14] :
( ( a_subset_of(esk1_3(X12,X13,X14),X13)
| ~ lin_ind_subset(X12,X14)
| ~ basis_of(X13,X14) )
& ( basis_of(union(X12,esk1_3(X12,X13,X14)),X14)
| ~ lin_ind_subset(X12,X14)
| ~ basis_of(X13,X14) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_2_5])])])]) ).
cnf(c_0_11,plain,
( lin_ind_subset(X1,X3)
| ~ lin_ind_subset(X1,X2)
| ~ a_vector_subspace_of(X2,X3)
| ~ a_subset_of(X1,vec_to_class(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( a_subset_of(X1,vec_to_class(X2))
| ~ basis_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( lin_ind_subset(X1,X2)
| ~ basis_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( ~ basis_of(union(X1,X2),esk4_0)
| ~ basis_of(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( basis_of(union(X1,esk1_3(X1,X2,X3)),X3)
| ~ lin_ind_subset(X1,X3)
| ~ basis_of(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( lin_ind_subset(X1,X2)
| ~ a_vector_subspace_of(X3,X2)
| ~ basis_of(X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_17,negated_conjecture,
a_vector_subspace_of(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_18,plain,
! [X18,X19] :
( ~ a_vector_subspace_of(X18,X19)
| a_vector_space(X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_a])]) ).
cnf(c_0_19,negated_conjecture,
( ~ lin_ind_subset(X1,esk4_0)
| ~ basis_of(X1,esk3_0)
| ~ basis_of(X2,esk4_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( lin_ind_subset(X1,esk4_0)
| ~ basis_of(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,plain,
! [X16] :
( ~ a_vector_space(X16)
| basis_of(esk2_1(X16),X16) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_remark_63_a])])]) ).
cnf(c_0_22,plain,
( a_vector_space(X1)
| ~ a_vector_subspace_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ basis_of(X1,esk3_0)
| ~ basis_of(X2,esk4_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( basis_of(esk2_1(X1),X1)
| ~ a_vector_space(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
a_vector_space(esk3_0),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
~ basis_of(X1,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_27,negated_conjecture,
a_vector_space(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 03:32:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.58 % Total time : 0.007000 s
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58 % Total time : 0.009000 s
%------------------------------------------------------------------------------