TSTP Solution File: SYN084+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 13:23:32 EDT 2022
% Result : Theorem 1.67s 1.89s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 24 ( 8 unt; 12 nHn; 21 RR)
% Number of literals : 52 ( 0 equ; 15 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( big_p(A)
| big_p(f(f(A)))
| ~ big_p(a)
| big_p(B)
| big_p(f(f(B))) ),
file('SYN084+1.p',unknown),
[] ).
cnf(2,plain,
( big_p(A)
| big_p(f(f(A)))
| ~ big_p(a) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[1])])]),
[iquote('copy,1,factor_simp,factor_simp')] ).
cnf(3,axiom,
( ~ big_p(f(A))
| big_p(f(f(A)))
| ~ big_p(a)
| ~ big_p(f(B))
| big_p(f(f(B))) ),
file('SYN084+1.p',unknown),
[] ).
cnf(4,plain,
( ~ big_p(f(A))
| big_p(f(f(A)))
| ~ big_p(a) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[3])])]),
[iquote('copy,3,factor_simp,factor_simp')] ).
cnf(5,axiom,
( ~ big_p(dollar_c1)
| big_p(f(dollar_c1))
| ~ big_p(dollar_c2)
| big_p(f(dollar_c2)) ),
file('SYN084+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ big_p(dollar_c1)
| big_p(f(dollar_c1))
| ~ big_p(f(f(dollar_c2))) ),
file('SYN084+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ big_p(f(f(dollar_c1)))
| ~ big_p(dollar_c2)
| big_p(f(dollar_c2)) ),
file('SYN084+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ big_p(f(f(dollar_c1)))
| ~ big_p(f(f(dollar_c2))) ),
file('SYN084+1.p',unknown),
[] ).
cnf(9,axiom,
big_p(a),
file('SYN084+1.p',unknown),
[] ).
cnf(10,plain,
( big_p(A)
| big_p(f(f(A))) ),
inference(hyper,[status(thm)],[9,2]),
[iquote('hyper,9,2')] ).
cnf(22,plain,
( big_p(dollar_c2)
| big_p(dollar_c1) ),
inference(hyper,[status(thm)],[10,8,10]),
[iquote('hyper,10,8,10')] ).
cnf(24,plain,
( big_p(dollar_c1)
| big_p(f(dollar_c2)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[22,7,10])]),
[iquote('hyper,22,7,10,factor_simp')] ).
cnf(25,plain,
( big_p(dollar_c2)
| big_p(f(dollar_c1)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[22,6,10])]),
[iquote('hyper,22,6,10,factor_simp')] ).
cnf(28,plain,
( big_p(dollar_c1)
| big_p(f(f(dollar_c2))) ),
inference(hyper,[status(thm)],[24,4,9]),
[iquote('hyper,24,4,9')] ).
cnf(29,plain,
( big_p(f(dollar_c1))
| big_p(f(dollar_c2)) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[25,5,24])])]),
[iquote('hyper,25,5,24,factor_simp,factor_simp')] ).
cnf(31,plain,
( big_p(dollar_c2)
| big_p(f(f(dollar_c1))) ),
inference(hyper,[status(thm)],[25,4,9]),
[iquote('hyper,25,4,9')] ).
cnf(35,plain,
big_p(dollar_c1),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[28,8,10])]),
[iquote('hyper,28,8,10,factor_simp')] ).
cnf(37,plain,
( big_p(f(dollar_c2))
| big_p(f(f(dollar_c1))) ),
inference(hyper,[status(thm)],[29,4,9]),
[iquote('hyper,29,4,9')] ).
cnf(40,plain,
big_p(dollar_c2),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[31,8,10])]),
[iquote('hyper,31,8,10,factor_simp')] ).
cnf(55,plain,
big_p(f(dollar_c2)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[37,7,40])]),
[iquote('hyper,37,7,40,factor_simp')] ).
cnf(58,plain,
big_p(f(f(dollar_c2))),
inference(hyper,[status(thm)],[55,4,9]),
[iquote('hyper,55,4,9')] ).
cnf(68,plain,
big_p(f(dollar_c1)),
inference(hyper,[status(thm)],[58,6,35]),
[iquote('hyper,58,6,35')] ).
cnf(70,plain,
big_p(f(f(dollar_c1))),
inference(hyper,[status(thm)],[68,4,9]),
[iquote('hyper,68,4,9')] ).
cnf(71,plain,
$false,
inference(hyper,[status(thm)],[70,8,58]),
[iquote('hyper,70,8,58')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:57:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.89 ----- Otter 3.3f, August 2004 -----
% 1.67/1.89 The process was started by sandbox on n005.cluster.edu,
% 1.67/1.89 Wed Jul 27 10:57:35 2022
% 1.67/1.89 The command was "./otter". The process ID is 12229.
% 1.67/1.89
% 1.67/1.89 set(prolog_style_variables).
% 1.67/1.89 set(auto).
% 1.67/1.89 dependent: set(auto1).
% 1.67/1.89 dependent: set(process_input).
% 1.67/1.89 dependent: clear(print_kept).
% 1.67/1.89 dependent: clear(print_new_demod).
% 1.67/1.89 dependent: clear(print_back_demod).
% 1.67/1.89 dependent: clear(print_back_sub).
% 1.67/1.89 dependent: set(control_memory).
% 1.67/1.89 dependent: assign(max_mem, 12000).
% 1.67/1.89 dependent: assign(pick_given_ratio, 4).
% 1.67/1.89 dependent: assign(stats_level, 1).
% 1.67/1.89 dependent: assign(max_seconds, 10800).
% 1.67/1.89 clear(print_given).
% 1.67/1.89
% 1.67/1.89 formula_list(usable).
% 1.67/1.89 -((all X (big_p(a)& (big_p(X)->big_p(f(X)))->big_p(f(f(X)))))<-> (all X1 ((-big_p(a)|big_p(X1)|big_p(f(f(X1))))& (-big_p(a)| -big_p(f(X1))|big_p(f(f(X1))))))).
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 -------> usable clausifies to:
% 1.67/1.89
% 1.67/1.89 list(usable).
% 1.67/1.89 0 [] big_p(X)|big_p(f(f(X)))| -big_p(a)|big_p(X1)|big_p(f(f(X1))).
% 1.67/1.89 0 [] big_p(X)|big_p(f(f(X)))| -big_p(a)| -big_p(f(X1))|big_p(f(f(X1))).
% 1.67/1.89 0 [] -big_p(f(X))|big_p(f(f(X)))| -big_p(a)|big_p(X1)|big_p(f(f(X1))).
% 1.67/1.89 0 [] -big_p(f(X))|big_p(f(f(X)))| -big_p(a)| -big_p(f(X1))|big_p(f(f(X1))).
% 1.67/1.89 0 [] big_p(a).
% 1.67/1.89 0 [] -big_p($c1)|big_p(f($c1))| -big_p($c2)|big_p(f($c2)).
% 1.67/1.89 0 [] -big_p($c1)|big_p(f($c1))| -big_p(f(f($c2))).
% 1.67/1.89 0 [] -big_p(f(f($c1)))| -big_p($c2)|big_p(f($c2)).
% 1.67/1.89 0 [] -big_p(f(f($c1)))| -big_p(f(f($c2))).
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.67/1.89
% 1.67/1.89 This is a non-Horn set without equality. The strategy will
% 1.67/1.89 be ordered hyper_res, unit deletion, and factoring, with
% 1.67/1.89 satellites in sos and with nuclei in usable.
% 1.67/1.89
% 1.67/1.89 dependent: set(hyper_res).
% 1.67/1.89 dependent: set(factor).
% 1.67/1.89 dependent: set(unit_deletion).
% 1.67/1.89
% 1.67/1.89 ------------> process usable:
% 1.67/1.89 ** KEPT (pick-wt=8): 2 [copy,1,factor_simp,factor_simp] big_p(A)|big_p(f(f(A)))| -big_p(a).
% 1.67/1.89 Following clause subsumed by 2 during input processing: 0 [] big_p(A)|big_p(f(f(A)))| -big_p(a)| -big_p(f(B))|big_p(f(f(B))).
% 1.67/1.89 Following clause subsumed by 2 during input processing: 0 [] -big_p(f(A))|big_p(f(f(A)))| -big_p(a)|big_p(B)|big_p(f(f(B))).
% 1.67/1.89 ** KEPT (pick-wt=9): 4 [copy,3,factor_simp,factor_simp] -big_p(f(A))|big_p(f(f(A)))| -big_p(a).
% 1.67/1.89 ** KEPT (pick-wt=10): 5 [] -big_p($c1)|big_p(f($c1))| -big_p($c2)|big_p(f($c2)).
% 1.67/1.89 ** KEPT (pick-wt=9): 6 [] -big_p($c1)|big_p(f($c1))| -big_p(f(f($c2))).
% 1.67/1.89 ** KEPT (pick-wt=9): 7 [] -big_p(f(f($c1)))| -big_p($c2)|big_p(f($c2)).
% 1.67/1.89 ** KEPT (pick-wt=8): 8 [] -big_p(f(f($c1)))| -big_p(f(f($c2))).
% 1.67/1.89
% 1.67/1.89 ------------> process sos:
% 1.67/1.89 ** KEPT (pick-wt=2): 9 [] big_p(a).
% 1.67/1.89
% 1.67/1.89 ======= end of input processing =======
% 1.67/1.89
% 1.67/1.89 =========== start of search ===========
% 1.67/1.89
% 1.67/1.89 -------- PROOF --------
% 1.67/1.89
% 1.67/1.89 -----> EMPTY CLAUSE at 0.00 sec ----> 71 [hyper,70,8,58] $F.
% 1.67/1.89
% 1.67/1.89 Length of proof is 16. Level of proof is 10.
% 1.67/1.89
% 1.67/1.89 ---------------- PROOF ----------------
% 1.67/1.89 % SZS status Theorem
% 1.67/1.89 % SZS output start Refutation
% See solution above
% 1.67/1.89 ------------ end of proof -------------
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89 ============ end of search ============
% 1.67/1.89
% 1.67/1.89 -------------- statistics -------------
% 1.67/1.89 clauses given 19
% 1.67/1.89 clauses generated 161
% 1.67/1.89 clauses kept 68
% 1.67/1.89 clauses forward subsumed 101
% 1.67/1.89 clauses back subsumed 57
% 1.67/1.89 Kbytes malloced 976
% 1.67/1.89
% 1.67/1.89 ----------- times (seconds) -----------
% 1.67/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.67/1.89
% 1.67/1.89 That finishes the proof of the theorem.
% 1.67/1.89
% 1.67/1.89 Process 12229 finished Wed Jul 27 10:57:37 2022
% 1.67/1.89 Otter interrupted
% 1.67/1.89 PROOF FOUND
%------------------------------------------------------------------------------