TSTP Solution File: SYN068+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN068+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 13:23:29 EDT 2022
% Result : Theorem 1.56s 1.77s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 5 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ big_f(A)
| big_g(dollar_f2(A)) ),
file('SYN068+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ big_f(A)
| ~ big_h(A,dollar_f2(A)) ),
file('SYN068+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ big_g(A)
| big_h(dollar_c1,A) ),
file('SYN068+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ big_j(A)
| big_f(A) ),
file('SYN068+1.p',unknown),
[] ).
cnf(7,axiom,
big_j(dollar_c1),
file('SYN068+1.p',unknown),
[] ).
cnf(8,plain,
big_f(dollar_c1),
inference(hyper,[status(thm)],[7,6]),
[iquote('hyper,7,6')] ).
cnf(9,plain,
big_g(dollar_f2(dollar_c1)),
inference(hyper,[status(thm)],[8,3]),
[iquote('hyper,8,3')] ).
cnf(12,plain,
big_h(dollar_c1,dollar_f2(dollar_c1)),
inference(hyper,[status(thm)],[9,5]),
[iquote('hyper,9,5')] ).
cnf(13,plain,
$false,
inference(hyper,[status(thm)],[12,4,8]),
[iquote('hyper,12,4,8')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN068+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 11:00:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.56/1.77 ----- Otter 3.3f, August 2004 -----
% 1.56/1.77 The process was started by sandbox on n007.cluster.edu,
% 1.56/1.77 Wed Jul 27 11:00:16 2022
% 1.56/1.77 The command was "./otter". The process ID is 17848.
% 1.56/1.77
% 1.56/1.77 set(prolog_style_variables).
% 1.56/1.77 set(auto).
% 1.56/1.77 dependent: set(auto1).
% 1.56/1.77 dependent: set(process_input).
% 1.56/1.77 dependent: clear(print_kept).
% 1.56/1.77 dependent: clear(print_new_demod).
% 1.56/1.77 dependent: clear(print_back_demod).
% 1.56/1.77 dependent: clear(print_back_sub).
% 1.56/1.77 dependent: set(control_memory).
% 1.56/1.77 dependent: assign(max_mem, 12000).
% 1.56/1.77 dependent: assign(pick_given_ratio, 4).
% 1.56/1.77 dependent: assign(stats_level, 1).
% 1.56/1.77 dependent: assign(max_seconds, 10800).
% 1.56/1.77 clear(print_given).
% 1.56/1.77
% 1.56/1.77 formula_list(usable).
% 1.56/1.77 all X (big_f(X)-> (exists Y (big_g(Y)&big_h(X,Y)))& (exists Y1 (big_g(Y1)& -big_h(X,Y1)))).
% 1.56/1.77 exists X (big_j(X)& (all Y (big_g(Y)->big_h(X,Y)))).
% 1.56/1.77 -(exists X (big_j(X)& -big_f(X))).
% 1.56/1.77 end_of_list.
% 1.56/1.77
% 1.56/1.77 -------> usable clausifies to:
% 1.56/1.77
% 1.56/1.77 list(usable).
% 1.56/1.77 0 [] -big_f(X)|big_g($f1(X)).
% 1.56/1.77 0 [] -big_f(X)|big_h(X,$f1(X)).
% 1.56/1.77 0 [] -big_f(X)|big_g($f2(X)).
% 1.56/1.77 0 [] -big_f(X)| -big_h(X,$f2(X)).
% 1.56/1.77 0 [] big_j($c1).
% 1.56/1.77 0 [] -big_g(Y)|big_h($c1,Y).
% 1.56/1.77 0 [] -big_j(X)|big_f(X).
% 1.56/1.77 end_of_list.
% 1.56/1.77
% 1.56/1.77 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=2.
% 1.56/1.77
% 1.56/1.77 This is a Horn set without equality. The strategy will
% 1.56/1.77 be hyperresolution, with satellites in sos and nuclei
% 1.56/1.77 in usable.
% 1.56/1.77
% 1.56/1.77 dependent: set(hyper_res).
% 1.56/1.77 dependent: clear(order_hyper).
% 1.56/1.77
% 1.56/1.77 ------------> process usable:
% 1.56/1.77 ** KEPT (pick-wt=5): 1 [] -big_f(A)|big_g($f1(A)).
% 1.56/1.77 ** KEPT (pick-wt=6): 2 [] -big_f(A)|big_h(A,$f1(A)).
% 1.56/1.77 ** KEPT (pick-wt=5): 3 [] -big_f(A)|big_g($f2(A)).
% 1.56/1.77 ** KEPT (pick-wt=6): 4 [] -big_f(A)| -big_h(A,$f2(A)).
% 1.56/1.77 ** KEPT (pick-wt=5): 5 [] -big_g(A)|big_h($c1,A).
% 1.56/1.77 ** KEPT (pick-wt=4): 6 [] -big_j(A)|big_f(A).
% 1.56/1.77
% 1.56/1.77 ------------> process sos:
% 1.56/1.77 ** KEPT (pick-wt=2): 7 [] big_j($c1).
% 1.56/1.77
% 1.56/1.77 ======= end of input processing =======
% 1.56/1.77
% 1.56/1.77 =========== start of search ===========
% 1.56/1.77
% 1.56/1.77 -------- PROOF --------
% 1.56/1.77
% 1.56/1.77 -----> EMPTY CLAUSE at 0.00 sec ----> 13 [hyper,12,4,8] $F.
% 1.56/1.77
% 1.56/1.77 Length of proof is 3. Level of proof is 3.
% 1.56/1.77
% 1.56/1.77 ---------------- PROOF ----------------
% 1.56/1.77 % SZS status Theorem
% 1.56/1.77 % SZS output start Refutation
% See solution above
% 1.56/1.77 ------------ end of proof -------------
% 1.56/1.77
% 1.56/1.77
% 1.56/1.77 Search stopped by max_proofs option.
% 1.56/1.77
% 1.56/1.77
% 1.56/1.77 Search stopped by max_proofs option.
% 1.56/1.77
% 1.56/1.77 ============ end of search ============
% 1.56/1.77
% 1.56/1.77 -------------- statistics -------------
% 1.56/1.77 clauses given 6
% 1.56/1.77 clauses generated 7
% 1.56/1.77 clauses kept 12
% 1.56/1.77 clauses forward subsumed 1
% 1.56/1.77 clauses back subsumed 0
% 1.56/1.77 Kbytes malloced 976
% 1.56/1.77
% 1.56/1.77 ----------- times (seconds) -----------
% 1.56/1.77 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.56/1.77 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.56/1.77 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.56/1.77
% 1.56/1.77 That finishes the proof of the theorem.
% 1.56/1.77
% 1.56/1.77 Process 17848 finished Wed Jul 27 11:00:17 2022
% 1.56/1.77 Otter interrupted
% 1.56/1.77 PROOF FOUND
%------------------------------------------------------------------------------