TSTP Solution File: SYN354+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN354+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:24:20 EDT 2022
% Result : Theorem 1.87s 2.08s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 3 unt; 3 nHn; 10 RR)
% Number of literals : 24 ( 0 equ; 12 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( big_g(dollar_c1,dollar_f1(A,B))
| big_g(B,dollar_f1(A,B))
| ~ big_f(A,B)
| big_f(dollar_c1,B) ),
file('SYN354+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ big_g(dollar_c1,dollar_f1(A,B))
| ~ big_g(B,dollar_f1(A,B))
| ~ big_f(A,B)
| big_f(dollar_c1,B) ),
file('SYN354+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ big_f(dollar_c2,A)
| ~ big_f(dollar_c1,A)
| ~ big_f(A,B) ),
file('SYN354+1.p',unknown),
[] ).
cnf(6,plain,
( big_g(dollar_c1,dollar_f1(A,dollar_c1))
| ~ big_f(A,dollar_c1)
| big_f(dollar_c1,dollar_c1) ),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.1.2')] ).
cnf(7,plain,
( ~ big_g(dollar_c1,dollar_f1(A,dollar_c1))
| ~ big_f(A,dollar_c1)
| big_f(dollar_c1,dollar_c1) ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.1.2')] ).
cnf(9,plain,
( ~ big_f(dollar_c2,dollar_c1)
| ~ big_f(dollar_c1,dollar_c1) ),
inference(factor,[status(thm)],[5]),
[iquote('factor,5.2.3')] ).
cnf(10,axiom,
big_f(dollar_c2,dollar_c1),
file('SYN354+1.p',unknown),
[] ).
cnf(12,plain,
( big_g(dollar_c1,dollar_f1(dollar_c2,dollar_c1))
| big_f(dollar_c1,dollar_c1) ),
inference(hyper,[status(thm)],[10,6]),
[iquote('hyper,10,6')] ).
cnf(13,plain,
big_f(dollar_c1,dollar_c1),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[12,7,10])]),
[iquote('hyper,12,7,10,factor_simp')] ).
cnf(14,plain,
$false,
inference(hyper,[status(thm)],[13,9,10]),
[iquote('hyper,13,9,10')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SYN354+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 11:46:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.87/2.08 ----- Otter 3.3f, August 2004 -----
% 1.87/2.08 The process was started by sandbox2 on n023.cluster.edu,
% 1.87/2.08 Wed Jul 27 11:46:33 2022
% 1.87/2.08 The command was "./otter". The process ID is 29167.
% 1.87/2.08
% 1.87/2.08 set(prolog_style_variables).
% 1.87/2.08 set(auto).
% 1.87/2.08 dependent: set(auto1).
% 1.87/2.08 dependent: set(process_input).
% 1.87/2.08 dependent: clear(print_kept).
% 1.87/2.08 dependent: clear(print_new_demod).
% 1.87/2.08 dependent: clear(print_back_demod).
% 1.87/2.08 dependent: clear(print_back_sub).
% 1.87/2.08 dependent: set(control_memory).
% 1.87/2.08 dependent: assign(max_mem, 12000).
% 1.87/2.08 dependent: assign(pick_given_ratio, 4).
% 1.87/2.08 dependent: assign(stats_level, 1).
% 1.87/2.08 dependent: assign(max_seconds, 10800).
% 1.87/2.08 clear(print_given).
% 1.87/2.08
% 1.87/2.08 formula_list(usable).
% 1.87/2.08 -(all X1 X2 exists Y1 Y2 all Z (big_f(X1,X2)-> (big_g(X1,X2)-> (((big_g(X2,Z)<->big_g(Y2,Z))-> (big_f(Y1,Y2)->big_f(X2,Y2)))-> ((big_g(X2,Z)<->big_g(Y1,Z))->big_f(X1,Y1)&big_f(X2,Y1)&big_f(Y1,Y2)))))).
% 1.87/2.08 end_of_list.
% 1.87/2.08
% 1.87/2.08 -------> usable clausifies to:
% 1.87/2.08
% 1.87/2.08 list(usable).
% 1.87/2.08 0 [] big_f($c2,$c1).
% 1.87/2.08 0 [] big_g($c2,$c1).
% 1.87/2.08 0 [] big_g($c1,$f1(Y1,Y2))|big_g(Y2,$f1(Y1,Y2))| -big_f(Y1,Y2)|big_f($c1,Y2).
% 1.87/2.08 0 [] -big_g($c1,$f1(Y1,Y2))| -big_g(Y2,$f1(Y1,Y2))| -big_f(Y1,Y2)|big_f($c1,Y2).
% 1.87/2.08 0 [] -big_g($c1,$f1(Y1,Y2))|big_g(Y1,$f1(Y1,Y2)).
% 1.87/2.08 0 [] big_g($c1,$f1(Y1,Y2))| -big_g(Y1,$f1(Y1,Y2)).
% 1.87/2.08 0 [] -big_f($c2,Y1)| -big_f($c1,Y1)| -big_f(Y1,Y2).
% 1.87/2.08 end_of_list.
% 1.87/2.08
% 1.87/2.08 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.87/2.08
% 1.87/2.08 This is a non-Horn set without equality. The strategy will
% 1.87/2.08 be ordered hyper_res, unit deletion, and factoring, with
% 1.87/2.08 satellites in sos and with nuclei in usable.
% 1.87/2.08
% 1.87/2.08 dependent: set(hyper_res).
% 1.87/2.08 dependent: set(factor).
% 1.87/2.08 dependent: set(unit_deletion).
% 1.87/2.08
% 1.87/2.08 ------------> process usable:
% 1.87/2.08 ** KEPT (pick-wt=16): 1 [] big_g($c1,$f1(A,B))|big_g(B,$f1(A,B))| -big_f(A,B)|big_f($c1,B).
% 1.87/2.08 ** KEPT (pick-wt=16): 2 [] -big_g($c1,$f1(A,B))| -big_g(B,$f1(A,B))| -big_f(A,B)|big_f($c1,B).
% 1.87/2.08 ** KEPT (pick-wt=10): 3 [] -big_g($c1,$f1(A,B))|big_g(A,$f1(A,B)).
% 1.87/2.08 ** KEPT (pick-wt=10): 4 [] big_g($c1,$f1(A,B))| -big_g(A,$f1(A,B)).
% 1.87/2.08 ** KEPT (pick-wt=9): 5 [] -big_f($c2,A)| -big_f($c1,A)| -big_f(A,B).
% 1.87/2.08
% 1.87/2.08 ------------> process sos:
% 1.87/2.08 ** KEPT (pick-wt=3): 10 [] big_f($c2,$c1).
% 1.87/2.08 ** KEPT (pick-wt=3): 11 [] big_g($c2,$c1).
% 1.87/2.08
% 1.87/2.08 ======= end of input processing =======
% 1.87/2.08
% 1.87/2.08 =========== start of search ===========
% 1.87/2.08
% 1.87/2.08 -------- PROOF --------
% 1.87/2.08
% 1.87/2.08 -----> EMPTY CLAUSE at 0.00 sec ----> 14 [hyper,13,9,10] $F.
% 1.87/2.08
% 1.87/2.08 Length of proof is 5. Level of proof is 3.
% 1.87/2.08
% 1.87/2.08 ---------------- PROOF ----------------
% 1.87/2.08 % SZS status Theorem
% 1.87/2.08 % SZS output start Refutation
% See solution above
% 1.87/2.08 ------------ end of proof -------------
% 1.87/2.08
% 1.87/2.08
% 1.87/2.08 Search stopped by max_proofs option.
% 1.87/2.08
% 1.87/2.08
% 1.87/2.08 Search stopped by max_proofs option.
% 1.87/2.08
% 1.87/2.08 ============ end of search ============
% 1.87/2.08
% 1.87/2.08 -------------- statistics -------------
% 1.87/2.08 clauses given 4
% 1.87/2.08 clauses generated 11
% 1.87/2.08 clauses kept 13
% 1.87/2.08 clauses forward subsumed 4
% 1.87/2.08 clauses back subsumed 3
% 1.87/2.08 Kbytes malloced 976
% 1.87/2.08
% 1.87/2.08 ----------- times (seconds) -----------
% 1.87/2.08 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.08 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.87/2.08
% 1.87/2.08 That finishes the proof of the theorem.
% 1.87/2.08
% 1.87/2.08 Process 29167 finished Wed Jul 27 11:46:35 2022
% 1.87/2.08 Otter interrupted
% 1.87/2.08 PROOF FOUND
%------------------------------------------------------------------------------