TSTP Solution File: ALG211+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 Jul 27 12:46:18 EDT 2022
% Result : Theorem 1.66s 1.88s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 10 unt; 0 nHn; 17 RR)
% Number of literals : 27 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% 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 : 15 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ basis_of(A,B)
| lin_ind_subset(A,B) ),
file('ALG211+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ basis_of(A,B)
| a_subset_of(A,vec_to_class(B)) ),
file('ALG211+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ lin_ind_subset(A,B)
| ~ basis_of(C,B)
| basis_of(union(A,dollar_f1(A,C,B)),B) ),
file('ALG211+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ a_vector_space(A)
| basis_of(dollar_f2(A),A) ),
file('ALG211+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ a_vector_subspace_of(A,B)
| a_vector_space(A) ),
file('ALG211+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ a_vector_subspace_of(A,B)
| ~ a_subset_of(C,vec_to_class(A))
| ~ lin_ind_subset(C,A)
| lin_ind_subset(C,B) ),
file('ALG211+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ basis_of(union(A,B),dollar_c1)
| ~ basis_of(A,dollar_c2) ),
file('ALG211+1.p',unknown),
[] ).
cnf(10,axiom,
a_vector_subspace_of(dollar_c2,dollar_c1),
file('ALG211+1.p',unknown),
[] ).
cnf(11,axiom,
a_vector_space(dollar_c1),
file('ALG211+1.p',unknown),
[] ).
cnf(12,plain,
a_vector_space(dollar_c2),
inference(hyper,[status(thm)],[10,6]),
[iquote('hyper,10,6')] ).
cnf(13,plain,
basis_of(dollar_f2(dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[11,5]),
[iquote('hyper,11,5')] ).
cnf(14,plain,
basis_of(dollar_f2(dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[12,5]),
[iquote('hyper,12,5')] ).
cnf(17,plain,
a_subset_of(dollar_f2(dollar_c2),vec_to_class(dollar_c2)),
inference(hyper,[status(thm)],[14,2]),
[iquote('hyper,14,2')] ).
cnf(18,plain,
lin_ind_subset(dollar_f2(dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[14,1]),
[iquote('hyper,14,1')] ).
cnf(23,plain,
lin_ind_subset(dollar_f2(dollar_c2),dollar_c1),
inference(hyper,[status(thm)],[17,7,10,18]),
[iquote('hyper,17,7,10,18')] ).
cnf(24,plain,
basis_of(union(dollar_f2(dollar_c2),dollar_f1(dollar_f2(dollar_c2),dollar_f2(dollar_c1),dollar_c1)),dollar_c1),
inference(hyper,[status(thm)],[23,4,13]),
[iquote('hyper,23,4,13')] ).
cnf(36,plain,
$false,
inference(hyper,[status(thm)],[24,9,14]),
[iquote('hyper,24,9,14')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n008.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 : Wed Jul 27 03:44:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.66/1.88 ----- Otter 3.3f, August 2004 -----
% 1.66/1.88 The process was started by sandbox on n008.cluster.edu,
% 1.66/1.88 Wed Jul 27 03:44:38 2022
% 1.66/1.88 The command was "./otter". The process ID is 31193.
% 1.66/1.88
% 1.66/1.88 set(prolog_style_variables).
% 1.66/1.88 set(auto).
% 1.66/1.88 dependent: set(auto1).
% 1.66/1.88 dependent: set(process_input).
% 1.66/1.88 dependent: clear(print_kept).
% 1.66/1.88 dependent: clear(print_new_demod).
% 1.66/1.88 dependent: clear(print_back_demod).
% 1.66/1.88 dependent: clear(print_back_sub).
% 1.66/1.88 dependent: set(control_memory).
% 1.66/1.88 dependent: assign(max_mem, 12000).
% 1.66/1.88 dependent: assign(pick_given_ratio, 4).
% 1.66/1.88 dependent: assign(stats_level, 1).
% 1.66/1.88 dependent: assign(max_seconds, 10800).
% 1.66/1.88 clear(print_given).
% 1.66/1.88
% 1.66/1.88 formula_list(usable).
% 1.66/1.88 all B V (basis_of(B,V)->lin_ind_subset(B,V)&a_subset_of(B,vec_to_class(V))).
% 1.66/1.88 all S T V (lin_ind_subset(S,V)&basis_of(T,V)-> (exists U (a_subset_of(U,T)&basis_of(union(S,U),V)))).
% 1.66/1.88 all A (a_vector_space(A)-> (exists B basis_of(B,A))).
% 1.66/1.88 all A B (a_vector_subspace_of(A,B)->a_vector_space(A)).
% 1.66/1.88 all 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))).
% 1.66/1.88 -(all W V (a_vector_subspace_of(W,V)&a_vector_space(V)-> (exists E F (basis_of(union(E,F),V)&basis_of(E,W))))).
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 -------> usable clausifies to:
% 1.66/1.88
% 1.66/1.88 list(usable).
% 1.66/1.88 0 [] -basis_of(B,V)|lin_ind_subset(B,V).
% 1.66/1.88 0 [] -basis_of(B,V)|a_subset_of(B,vec_to_class(V)).
% 1.66/1.88 0 [] -lin_ind_subset(S,V)| -basis_of(T,V)|a_subset_of($f1(S,T,V),T).
% 1.66/1.88 0 [] -lin_ind_subset(S,V)| -basis_of(T,V)|basis_of(union(S,$f1(S,T,V)),V).
% 1.66/1.88 0 [] -a_vector_space(A)|basis_of($f2(A),A).
% 1.66/1.88 0 [] -a_vector_subspace_of(A,B)|a_vector_space(A).
% 1.66/1.88 0 [] -a_vector_subspace_of(W,V)| -a_subset_of(E,vec_to_class(W))| -lin_ind_subset(E,W)|lin_ind_subset(E,V).
% 1.66/1.88 0 [] -a_vector_subspace_of(W,V)| -a_subset_of(E,vec_to_class(W))|lin_ind_subset(E,W)| -lin_ind_subset(E,V).
% 1.66/1.88 0 [] a_vector_subspace_of($c2,$c1).
% 1.66/1.88 0 [] a_vector_space($c1).
% 1.66/1.88 0 [] -basis_of(union(E,F),$c1)| -basis_of(E,$c2).
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.66/1.88
% 1.66/1.88 This is a Horn set without equality. The strategy will
% 1.66/1.88 be hyperresolution, with satellites in sos and nuclei
% 1.66/1.88 in usable.
% 1.66/1.88
% 1.66/1.88 dependent: set(hyper_res).
% 1.66/1.88 dependent: clear(order_hyper).
% 1.66/1.88
% 1.66/1.88 ------------> process usable:
% 1.66/1.88 ** KEPT (pick-wt=6): 1 [] -basis_of(A,B)|lin_ind_subset(A,B).
% 1.66/1.88 ** KEPT (pick-wt=7): 2 [] -basis_of(A,B)|a_subset_of(A,vec_to_class(B)).
% 1.66/1.88 ** KEPT (pick-wt=12): 3 [] -lin_ind_subset(A,B)| -basis_of(C,B)|a_subset_of($f1(A,C,B),C).
% 1.66/1.88 ** KEPT (pick-wt=14): 4 [] -lin_ind_subset(A,B)| -basis_of(C,B)|basis_of(union(A,$f1(A,C,B)),B).
% 1.66/1.88 ** KEPT (pick-wt=6): 5 [] -a_vector_space(A)|basis_of($f2(A),A).
% 1.66/1.88 ** KEPT (pick-wt=5): 6 [] -a_vector_subspace_of(A,B)|a_vector_space(A).
% 1.66/1.88 ** KEPT (pick-wt=13): 7 [] -a_vector_subspace_of(A,B)| -a_subset_of(C,vec_to_class(A))| -lin_ind_subset(C,A)|lin_ind_subset(C,B).
% 1.66/1.88 ** KEPT (pick-wt=13): 8 [] -a_vector_subspace_of(A,B)| -a_subset_of(C,vec_to_class(A))|lin_ind_subset(C,A)| -lin_ind_subset(C,B).
% 1.66/1.88 ** KEPT (pick-wt=8): 9 [] -basis_of(union(A,B),$c1)| -basis_of(A,$c2).
% 1.66/1.88
% 1.66/1.88 ------------> process sos:
% 1.66/1.88 ** KEPT (pick-wt=3): 10 [] a_vector_subspace_of($c2,$c1).
% 1.66/1.88 ** KEPT (pick-wt=2): 11 [] a_vector_space($c1).
% 1.66/1.88
% 1.66/1.88 ======= end of input processing =======
% 1.66/1.88
% 1.66/1.88 =========== start of search ===========
% 1.66/1.88
% 1.66/1.88 -------- PROOF --------
% 1.66/1.88
% 1.66/1.88 -----> EMPTY CLAUSE at 0.00 sec ----> 36 [hyper,24,9,14] $F.
% 1.66/1.88
% 1.66/1.88 Length of proof is 7. Level of proof is 5.
% 1.66/1.88
% 1.66/1.88 ---------------- PROOF ----------------
% 1.66/1.88 % SZS status Theorem
% 1.66/1.88 % SZS output start Refutation
% See solution above
% 1.66/1.88 ------------ end of proof -------------
% 1.66/1.88
% 1.66/1.88
% 1.66/1.88 Search stopped by max_proofs option.
% 1.66/1.88
% 1.66/1.88
% 1.66/1.88 Search stopped by max_proofs option.
% 1.66/1.88
% 1.66/1.88 ============ end of search ============
% 1.66/1.88
% 1.66/1.88 -------------- statistics -------------
% 1.66/1.88 clauses given 16
% 1.66/1.88 clauses generated 26
% 1.66/1.88 clauses kept 35
% 1.66/1.88 clauses forward subsumed 1
% 1.66/1.88 clauses back subsumed 0
% 1.66/1.88 Kbytes malloced 976
% 1.66/1.88
% 1.66/1.88 ----------- times (seconds) -----------
% 1.66/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.88 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.66/1.88
% 1.66/1.88 That finishes the proof of the theorem.
% 1.66/1.88
% 1.66/1.88 Process 31193 finished Wed Jul 27 03:44:40 2022
% 1.66/1.88 Otter interrupted
% 1.66/1.88 PROOF FOUND
%------------------------------------------------------------------------------