TSTP Solution File: SYN069+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN069+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 1.79s 2.03s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 7 unt; 2 nHn; 11 RR)
% Number of literals : 27 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 12 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ big_f(A)
| big_g(dollar_f1(A))
| big_g(B) ),
file('SYN069+1.p',unknown),
[] ).
cnf(2,plain,
( ~ big_f(A)
| big_g(dollar_f1(A)) ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,factor_simp')] ).
cnf(4,axiom,
( ~ big_f(A)
| big_h(A,dollar_f1(A))
| big_h(A,B) ),
file('SYN069+1.p',unknown),
[] ).
cnf(5,plain,
( ~ big_f(A)
| big_h(A,dollar_f1(A)) ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,factor_simp')] ).
cnf(8,axiom,
( ~ big_f(A)
| ~ big_j(A,dollar_f1(A))
| big_k(B) ),
file('SYN069+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ big_l(A)
| ~ big_k(A) ),
file('SYN069+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ big_h(dollar_c1,A)
| big_l(A) ),
file('SYN069+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ big_g(A)
| ~ big_h(dollar_c1,A)
| big_j(dollar_c1,A) ),
file('SYN069+1.p',unknown),
[] ).
cnf(14,axiom,
big_f(dollar_c1),
file('SYN069+1.p',unknown),
[] ).
cnf(17,plain,
big_h(dollar_c1,dollar_f1(dollar_c1)),
inference(hyper,[status(thm)],[14,5]),
[iquote('hyper,14,5')] ).
cnf(18,plain,
big_g(dollar_f1(dollar_c1)),
inference(hyper,[status(thm)],[14,2]),
[iquote('hyper,14,2')] ).
cnf(21,plain,
big_j(dollar_c1,dollar_f1(dollar_c1)),
inference(hyper,[status(thm)],[17,11,18]),
[iquote('hyper,17,11,18')] ).
cnf(22,plain,
big_l(dollar_f1(dollar_c1)),
inference(hyper,[status(thm)],[17,10]),
[iquote('hyper,17,10')] ).
cnf(23,plain,
big_k(A),
inference(hyper,[status(thm)],[21,8,14]),
[iquote('hyper,21,8,14')] ).
cnf(26,plain,
$false,
inference(hyper,[status(thm)],[23,9,22]),
[iquote('hyper,23,9,22')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN069+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 11:17:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.79/2.03 ----- Otter 3.3f, August 2004 -----
% 1.79/2.03 The process was started by sandbox2 on n015.cluster.edu,
% 1.79/2.03 Wed Jul 27 11:17:27 2022
% 1.79/2.03 The command was "./otter". The process ID is 17680.
% 1.79/2.03
% 1.79/2.03 set(prolog_style_variables).
% 1.79/2.03 set(auto).
% 1.79/2.03 dependent: set(auto1).
% 1.79/2.03 dependent: set(process_input).
% 1.79/2.03 dependent: clear(print_kept).
% 1.79/2.03 dependent: clear(print_new_demod).
% 1.79/2.03 dependent: clear(print_back_demod).
% 1.79/2.03 dependent: clear(print_back_sub).
% 1.79/2.03 dependent: set(control_memory).
% 1.79/2.03 dependent: assign(max_mem, 12000).
% 1.79/2.03 dependent: assign(pick_given_ratio, 4).
% 1.79/2.03 dependent: assign(stats_level, 1).
% 1.79/2.03 dependent: assign(max_seconds, 10800).
% 1.79/2.03 clear(print_given).
% 1.79/2.03
% 1.79/2.03 formula_list(usable).
% 1.79/2.03 all X (big_f(X)& (all Y (big_g(Y)&big_h(X,Y)->big_j(X,Y)))-> (all Y1 (big_g(Y1)&big_h(X,Y1)&big_k(Y1)))).
% 1.79/2.03 -(exists Y (big_l(Y)&big_k(Y))).
% 1.79/2.03 exists X (big_f(X)& (all Y (big_h(X,Y)->big_l(Y)))& (all Y1 (big_g(Y1)&big_h(X,Y1)->big_j(X,Y1)))).
% 1.79/2.03 -(exists X (big_f(X)& -(exists Y (big_g(Y)&big_h(X,Y))))).
% 1.79/2.03 end_of_list.
% 1.79/2.03
% 1.79/2.03 -------> usable clausifies to:
% 1.79/2.03
% 1.79/2.03 list(usable).
% 1.79/2.03 0 [] -big_f(X)|big_g($f1(X))|big_g(Y1).
% 1.79/2.03 0 [] -big_f(X)|big_g($f1(X))|big_h(X,Y1).
% 1.79/2.03 0 [] -big_f(X)|big_g($f1(X))|big_k(Y1).
% 1.79/2.03 0 [] -big_f(X)|big_h(X,$f1(X))|big_g(Y1).
% 1.79/2.03 0 [] -big_f(X)|big_h(X,$f1(X))|big_h(X,Y1).
% 1.79/2.03 0 [] -big_f(X)|big_h(X,$f1(X))|big_k(Y1).
% 1.79/2.03 0 [] -big_f(X)| -big_j(X,$f1(X))|big_g(Y1).
% 1.79/2.03 0 [] -big_f(X)| -big_j(X,$f1(X))|big_h(X,Y1).
% 1.79/2.03 0 [] -big_f(X)| -big_j(X,$f1(X))|big_k(Y1).
% 1.79/2.03 0 [] -big_l(Y)| -big_k(Y).
% 1.79/2.03 0 [] big_f($c1).
% 1.79/2.03 0 [] -big_h($c1,Y)|big_l(Y).
% 1.79/2.03 0 [] -big_g(Y1)| -big_h($c1,Y1)|big_j($c1,Y1).
% 1.79/2.03 0 [] -big_f(X)|big_g($f2(X)).
% 1.79/2.03 0 [] -big_f(X)|big_h(X,$f2(X)).
% 1.79/2.03 end_of_list.
% 1.79/2.03
% 1.79/2.03 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.79/2.03
% 1.79/2.03 This is a non-Horn set without equality. The strategy will
% 1.79/2.03 be ordered hyper_res, unit deletion, and factoring, with
% 1.79/2.03 satellites in sos and with nuclei in usable.
% 1.79/2.03
% 1.79/2.03 dependent: set(hyper_res).
% 1.79/2.03 dependent: set(factor).
% 1.79/2.03 dependent: set(unit_deletion).
% 1.79/2.03
% 1.79/2.03 ------------> process usable:
% 1.79/2.03 ** KEPT (pick-wt=5): 2 [copy,1,factor_simp] -big_f(A)|big_g($f1(A)).
% 1.79/2.03 Following clause subsumed by 2 during input processing: 0 [] -big_f(A)|big_g($f1(A))|big_h(A,B).
% 1.79/2.03 Following clause subsumed by 2 during input processing: 0 [] -big_f(A)|big_g($f1(A))|big_k(B).
% 1.79/2.03 ** KEPT (pick-wt=8): 3 [] -big_f(A)|big_h(A,$f1(A))|big_g(B).
% 1.79/2.03 ** KEPT (pick-wt=6): 5 [copy,4,factor_simp] -big_f(A)|big_h(A,$f1(A)).
% 1.79/2.03 Following clause subsumed by 5 during input processing: 0 [] -big_f(A)|big_h(A,$f1(A))|big_k(B).
% 1.79/2.03 ** KEPT (pick-wt=8): 6 [] -big_f(A)| -big_j(A,$f1(A))|big_g(B).
% 1.79/2.03 ** KEPT (pick-wt=9): 7 [] -big_f(A)| -big_j(A,$f1(A))|big_h(A,B).
% 1.79/2.03 ** KEPT (pick-wt=8): 8 [] -big_f(A)| -big_j(A,$f1(A))|big_k(B).
% 1.79/2.03 ** KEPT (pick-wt=4): 9 [] -big_l(A)| -big_k(A).
% 1.79/2.03 ** KEPT (pick-wt=5): 10 [] -big_h($c1,A)|big_l(A).
% 1.79/2.03 ** KEPT (pick-wt=8): 11 [] -big_g(A)| -big_h($c1,A)|big_j($c1,A).
% 1.79/2.03 ** KEPT (pick-wt=5): 12 [] -big_f(A)|big_g($f2(A)).
% 1.79/2.03 ** KEPT (pick-wt=6): 13 [] -big_f(A)|big_h(A,$f2(A)).
% 1.79/2.03 5 back subsumes 3.
% 1.79/2.03
% 1.79/2.03 ------------> process sos:
% 1.79/2.03 ** KEPT (pick-wt=2): 14 [] big_f($c1).
% 1.79/2.03
% 1.79/2.03 ======= end of input processing =======
% 1.79/2.03
% 1.79/2.03 =========== start of search ===========
% 1.79/2.03
% 1.79/2.03 -------- PROOF --------
% 1.79/2.03
% 1.79/2.03 -----> EMPTY CLAUSE at 0.00 sec ----> 26 [hyper,23,9,22] $F.
% 1.79/2.03
% 1.79/2.03 Length of proof is 7. Level of proof is 4.
% 1.79/2.03
% 1.79/2.03 ---------------- PROOF ----------------
% 1.79/2.03 % SZS status Theorem
% 1.79/2.03 % SZS output start Refutation
% See solution above
% 1.79/2.03 ------------ end of proof -------------
% 1.79/2.03
% 1.79/2.03
% 1.79/2.03 Search stopped by max_proofs option.
% 1.79/2.03
% 1.79/2.03
% 1.79/2.03 Search stopped by max_proofs option.
% 1.79/2.03
% 1.79/2.03 ============ end of search ============
% 1.79/2.03
% 1.79/2.03 -------------- statistics -------------
% 1.79/2.03 clauses given 10
% 1.79/2.03 clauses generated 12
% 1.79/2.03 clauses kept 23
% 1.79/2.03 clauses forward subsumed 3
% 1.79/2.03 clauses back subsumed 9
% 1.79/2.03 Kbytes malloced 976
% 1.79/2.03
% 1.79/2.03 ----------- times (seconds) -----------
% 1.79/2.03 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/2.03 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/2.03 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.79/2.03
% 1.79/2.03 That finishes the proof of the theorem.
% 1.79/2.03
% 1.79/2.03 Process 17680 finished Wed Jul 27 11:17:28 2022
% 1.79/2.03 Otter interrupted
% 1.79/2.03 PROOF FOUND
%------------------------------------------------------------------------------