TSTP Solution File: SYN328+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN328+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 13:24:15 EDT 2022
% Result : Theorem 1.98s 2.16s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 12 unt; 14 nHn; 8 RR)
% Number of literals : 59 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 31 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ big_g(dollar_f2(A))
| big_f(A) ),
file('SYN328+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ big_f(dollar_f2(A))
| big_g(dollar_f2(A))
| ~ big_f(A) ),
file('SYN328+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ big_h(dollar_f2(A))
| big_g(A) ),
file('SYN328+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ big_f(dollar_f2(A))
| big_h(dollar_f2(A))
| ~ big_g(A) ),
file('SYN328+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ big_f(dollar_f2(A))
| big_g(dollar_f2(A))
| big_h(A) ),
file('SYN328+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ big_h(dollar_f2(A))
| big_h(A) ),
file('SYN328+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ big_f(dollar_f1(A))
| ~ big_g(dollar_f1(A))
| ~ big_h(dollar_f1(A)) ),
file('SYN328+1.p',unknown),
[] ).
cnf(10,axiom,
( big_f(dollar_f2(A))
| big_f(A) ),
file('SYN328+1.p',unknown),
[] ).
cnf(11,axiom,
( big_f(dollar_f2(A))
| big_g(A) ),
file('SYN328+1.p',unknown),
[] ).
cnf(12,plain,
( big_f(A)
| big_g(dollar_f2(A))
| big_h(A) ),
inference(hyper,[status(thm)],[10,5]),
[iquote('hyper,10,5')] ).
cnf(13,plain,
( big_f(dollar_f2(dollar_f2(A)))
| big_f(A) ),
inference(hyper,[status(thm)],[11,1]),
[iquote('hyper,11,1')] ).
cnf(20,plain,
( big_f(dollar_f2(A))
| big_g(dollar_f2(dollar_f2(A)))
| big_h(A) ),
inference(hyper,[status(thm)],[12,6]),
[iquote('hyper,12,6')] ).
cnf(22,plain,
( big_f(dollar_f2(dollar_f1(A)))
| big_g(dollar_f2(dollar_f2(dollar_f1(A)))) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[20,9,10,11])])]),
[iquote('hyper,20,9,10,11,factor_simp,factor_simp')] ).
cnf(24,plain,
( big_f(dollar_f2(dollar_f2(A)))
| big_g(dollar_f2(dollar_f2(dollar_f2(A))))
| big_g(A) ),
inference(hyper,[status(thm)],[20,3]),
[iquote('hyper,20,3')] ).
cnf(27,plain,
big_f(dollar_f2(dollar_f1(A))),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[22,1])]),
[iquote('hyper,22,1,factor_simp')] ).
cnf(36,plain,
( big_f(dollar_f2(dollar_f2(A)))
| big_g(A) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[24,1])]),
[iquote('hyper,24,1,factor_simp')] ).
cnf(41,plain,
( big_f(dollar_f2(dollar_f2(A)))
| big_h(dollar_f2(A)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[36,4,10])]),
[iquote('hyper,36,4,10,factor_simp')] ).
cnf(42,plain,
( big_f(dollar_f2(dollar_f2(dollar_f2(A))))
| big_f(A) ),
inference(hyper,[status(thm)],[36,1]),
[iquote('hyper,36,1')] ).
cnf(44,plain,
( big_f(dollar_f2(dollar_f2(A)))
| big_h(A) ),
inference(hyper,[status(thm)],[41,6]),
[iquote('hyper,41,6')] ).
cnf(47,plain,
big_f(dollar_f2(dollar_f2(dollar_f1(A)))),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[44,9,13,36])])]),
[iquote('hyper,44,9,13,36,factor_simp,factor_simp')] ).
cnf(48,plain,
( big_f(dollar_f2(dollar_f2(dollar_f2(A))))
| big_h(A) ),
inference(hyper,[status(thm)],[44,6]),
[iquote('hyper,44,6')] ).
cnf(49,plain,
( big_f(dollar_f2(dollar_f2(dollar_f2(A))))
| big_g(A) ),
inference(hyper,[status(thm)],[44,3]),
[iquote('hyper,44,3')] ).
cnf(51,plain,
big_g(dollar_f2(dollar_f2(dollar_f1(A)))),
inference(hyper,[status(thm)],[47,2,27]),
[iquote('hyper,47,2,27')] ).
cnf(59,plain,
big_f(dollar_f2(dollar_f2(dollar_f2(dollar_f1(A))))),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[49,9,42,48])])]),
[iquote('hyper,49,9,42,48,factor_simp,factor_simp')] ).
cnf(62,plain,
big_h(dollar_f2(dollar_f2(dollar_f2(dollar_f1(A))))),
inference(hyper,[status(thm)],[59,4,51]),
[iquote('hyper,59,4,51')] ).
cnf(64,plain,
big_h(dollar_f2(dollar_f2(dollar_f1(A)))),
inference(hyper,[status(thm)],[62,6]),
[iquote('hyper,62,6')] ).
cnf(66,plain,
big_h(dollar_f2(dollar_f1(A))),
inference(hyper,[status(thm)],[64,6]),
[iquote('hyper,64,6')] ).
cnf(67,plain,
big_g(dollar_f2(dollar_f1(A))),
inference(hyper,[status(thm)],[64,3]),
[iquote('hyper,64,3')] ).
cnf(68,plain,
big_h(dollar_f1(A)),
inference(hyper,[status(thm)],[66,6]),
[iquote('hyper,66,6')] ).
cnf(69,plain,
big_g(dollar_f1(A)),
inference(hyper,[status(thm)],[66,3]),
[iquote('hyper,66,3')] ).
cnf(70,plain,
big_f(dollar_f1(A)),
inference(hyper,[status(thm)],[67,1]),
[iquote('hyper,67,1')] ).
cnf(71,plain,
$false,
inference(hyper,[status(thm)],[70,9,69,68]),
[iquote('hyper,70,9,69,68')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN328+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 11:37:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.16 ----- Otter 3.3f, August 2004 -----
% 1.98/2.16 The process was started by sandbox2 on n026.cluster.edu,
% 1.98/2.16 Wed Jul 27 11:37:39 2022
% 1.98/2.16 The command was "./otter". The process ID is 31009.
% 1.98/2.16
% 1.98/2.16 set(prolog_style_variables).
% 1.98/2.16 set(auto).
% 1.98/2.16 dependent: set(auto1).
% 1.98/2.16 dependent: set(process_input).
% 1.98/2.16 dependent: clear(print_kept).
% 1.98/2.16 dependent: clear(print_new_demod).
% 1.98/2.16 dependent: clear(print_back_demod).
% 1.98/2.16 dependent: clear(print_back_sub).
% 1.98/2.16 dependent: set(control_memory).
% 1.98/2.16 dependent: assign(max_mem, 12000).
% 1.98/2.16 dependent: assign(pick_given_ratio, 4).
% 1.98/2.16 dependent: assign(stats_level, 1).
% 1.98/2.16 dependent: assign(max_seconds, 10800).
% 1.98/2.16 clear(print_given).
% 1.98/2.16
% 1.98/2.16 formula_list(usable).
% 1.98/2.16 -(exists X all Y Z (((big_f(Y)->big_g(Y))<->big_f(X))-> (((big_f(Y)->big_h(Y))<->big_g(X))-> ((((big_f(Y)->big_g(Y))->big_h(Y))<->big_h(X))->big_f(Z)&big_g(Z)&big_h(Z))))).
% 1.98/2.16 end_of_list.
% 1.98/2.16
% 1.98/2.16 -------> usable clausifies to:
% 1.98/2.16
% 1.98/2.16 list(usable).
% 1.98/2.16 0 [] big_f($f2(X))|big_f(X).
% 1.98/2.16 0 [] -big_g($f2(X))|big_f(X).
% 1.98/2.16 0 [] -big_f($f2(X))|big_g($f2(X))| -big_f(X).
% 1.98/2.16 0 [] big_f($f2(X))|big_g(X).
% 1.98/2.16 0 [] -big_h($f2(X))|big_g(X).
% 1.98/2.16 0 [] -big_f($f2(X))|big_h($f2(X))| -big_g(X).
% 1.98/2.16 0 [] -big_f($f2(X))|big_g($f2(X))|big_h(X).
% 1.98/2.16 0 [] -big_h($f2(X))|big_h(X).
% 1.98/2.16 0 [] big_f($f2(X))|big_h($f2(X))| -big_h(X).
% 1.98/2.16 0 [] -big_g($f2(X))|big_h($f2(X))| -big_h(X).
% 1.98/2.16 0 [] -big_f($f1(X))| -big_g($f1(X))| -big_h($f1(X)).
% 1.98/2.16 end_of_list.
% 1.98/2.16
% 1.98/2.16 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.98/2.16
% 1.98/2.16 This is a non-Horn set without equality. The strategy will
% 1.98/2.16 be ordered hyper_res, unit deletion, and factoring, with
% 1.98/2.16 satellites in sos and with nuclei in usable.
% 1.98/2.16
% 1.98/2.16 dependent: set(hyper_res).
% 1.98/2.16 dependent: set(factor).
% 1.98/2.16 dependent: set(unit_deletion).
% 1.98/2.16
% 1.98/2.16 ------------> process usable:
% 1.98/2.16 ** KEPT (pick-wt=5): 1 [] -big_g($f2(A))|big_f(A).
% 1.98/2.16 ** KEPT (pick-wt=8): 2 [] -big_f($f2(A))|big_g($f2(A))| -big_f(A).
% 1.98/2.16 ** KEPT (pick-wt=5): 3 [] -big_h($f2(A))|big_g(A).
% 1.98/2.16 ** KEPT (pick-wt=8): 4 [] -big_f($f2(A))|big_h($f2(A))| -big_g(A).
% 1.98/2.16 ** KEPT (pick-wt=8): 5 [] -big_f($f2(A))|big_g($f2(A))|big_h(A).
% 1.98/2.16 ** KEPT (pick-wt=5): 6 [] -big_h($f2(A))|big_h(A).
% 1.98/2.16 ** KEPT (pick-wt=8): 7 [] big_f($f2(A))|big_h($f2(A))| -big_h(A).
% 1.98/2.16 ** KEPT (pick-wt=8): 8 [] -big_g($f2(A))|big_h($f2(A))| -big_h(A).
% 1.98/2.16 ** KEPT (pick-wt=9): 9 [] -big_f($f1(A))| -big_g($f1(A))| -big_h($f1(A)).
% 1.98/2.16
% 1.98/2.16 ------------> process sos:
% 1.98/2.16 ** KEPT (pick-wt=5): 10 [] big_f($f2(A))|big_f(A).
% 1.98/2.16 ** KEPT (pick-wt=5): 11 [] big_f($f2(A))|big_g(A).
% 1.98/2.16
% 1.98/2.16 ======= end of input processing =======
% 1.98/2.16
% 1.98/2.16 =========== start of search ===========
% 1.98/2.16
% 1.98/2.16 -------- PROOF --------
% 1.98/2.16
% 1.98/2.16 -----> EMPTY CLAUSE at 0.01 sec ----> 71 [hyper,70,9,69,68] $F.
% 1.98/2.16
% 1.98/2.16 Length of proof is 22. Level of proof is 12.
% 1.98/2.16
% 1.98/2.16 ---------------- PROOF ----------------
% 1.98/2.16 % SZS status Theorem
% 1.98/2.16 % SZS output start Refutation
% See solution above
% 1.98/2.16 ------------ end of proof -------------
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Search stopped by max_proofs option.
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Search stopped by max_proofs option.
% 1.98/2.16
% 1.98/2.16 ============ end of search ============
% 1.98/2.16
% 1.98/2.16 -------------- statistics -------------
% 1.98/2.16 clauses given 33
% 1.98/2.16 clauses generated 394
% 1.98/2.16 clauses kept 70
% 1.98/2.16 clauses forward subsumed 334
% 1.98/2.16 clauses back subsumed 30
% 1.98/2.16 Kbytes malloced 976
% 1.98/2.16
% 1.98/2.16 ----------- times (seconds) -----------
% 1.98/2.16 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.98/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.16 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.16
% 1.98/2.16 That finishes the proof of the theorem.
% 1.98/2.16
% 1.98/2.16 Process 31009 finished Wed Jul 27 11:37:41 2022
% 1.98/2.16 Otter interrupted
% 1.98/2.16 PROOF FOUND
%------------------------------------------------------------------------------