TSTP Solution File: ALG211+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 : 600s
% DateTime : Thu Jul 14 18:03:00 EDT 2022
% Result : Theorem 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 19 ( 7 unt; 0 nHn; 19 RR)
% Number of literals : 37 ( 0 equ; 23 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
a_vector_space(skc2),
file('ALG211+1.p',unknown),
[] ).
cnf(2,axiom,
a_vector_subspace_of(skc3,skc2),
file('ALG211+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ a_vector_subspace_of(u,v)
| a_vector_space(u) ),
file('ALG211+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ basis_of(u,v)
| lin_ind_subset(u,v) ),
file('ALG211+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ a_vector_space(u)
| basis_of(skf3(u),u) ),
file('ALG211+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ basis_of(u,v)
| a_subset_of(u,vec_to_class(v)) ),
file('ALG211+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ basis_of(u,skc3)
| ~ basis_of(union(u,v),skc2) ),
file('ALG211+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ basis_of(u,v)
| ~ lin_ind_subset(w,v)
| basis_of(union(w,skf2(u,v,w)),v) ),
file('ALG211+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ a_vector_subspace_of(u,v)
| ~ lin_ind_subset(w,u)
| ~ a_subset_of(w,vec_to_class(u))
| lin_ind_subset(w,v) ),
file('ALG211+1.p',unknown),
[] ).
cnf(12,plain,
basis_of(skf3(skc2),skc2),
inference(res,[status(thm),theory(equality)],[1,5]),
[iquote('0:Res:1.0,5.0')] ).
cnf(13,plain,
a_vector_space(skc3),
inference(res,[status(thm),theory(equality)],[2,3]),
[iquote('0:Res:2.0,3.0')] ).
cnf(15,plain,
( ~ lin_ind_subset(u,skc3)
| ~ a_subset_of(u,vec_to_class(skc3))
| lin_ind_subset(u,skc2) ),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.1')] ).
cnf(22,plain,
( ~ basis_of(u,skc3)
| ~ lin_ind_subset(u,skc3)
| lin_ind_subset(u,skc2) ),
inference(res,[status(thm),theory(equality)],[6,15]),
[iquote('0:Res:6.1,15.1')] ).
cnf(23,plain,
( ~ basis_of(u,skc3)
| lin_ind_subset(u,skc2) ),
inference(mrr,[status(thm)],[22,4]),
[iquote('0:MRR:22.1,4.1')] ).
cnf(42,plain,
( ~ basis_of(u,skc2)
| ~ lin_ind_subset(v,skc2)
| ~ basis_of(v,skc3) ),
inference(res,[status(thm),theory(equality)],[9,7]),
[iquote('0:Res:9.2,7.1')] ).
cnf(43,plain,
( ~ basis_of(u,skc2)
| ~ basis_of(v,skc3) ),
inference(mrr,[status(thm)],[42,23]),
[iquote('0:MRR:42.1,23.1')] ).
cnf(45,plain,
~ basis_of(u,skc3),
inference(res,[status(thm),theory(equality)],[12,43]),
[iquote('0:Res:12.0,43.0')] ).
cnf(48,plain,
~ a_vector_space(skc3),
inference(res,[status(thm),theory(equality)],[5,45]),
[iquote('0:Res:5.1,45.0')] ).
cnf(50,plain,
$false,
inference(ssi,[status(thm)],[48,13]),
[iquote('0:SSi:48.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 06:41:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 29 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.18/0.42 SPASS allocated 97645 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.02 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.00 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 3, length 19 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : bg_2_4_3 bg_2_4_a basis_of bg_remark_63_a bg_2_2_5 bg_2_4_2
% 0.18/0.42
%------------------------------------------------------------------------------