TSTP Solution File: SYN332+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN332+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:24:16 EDT 2022
% Result : Theorem 2.04s 2.23s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 3 unt; 6 nHn; 8 RR)
% Number of literals : 30 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 25 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ big_f(A,dollar_f1(A,B))
| big_f(dollar_f1(A,B),A) ),
file('SYN332+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ big_f(A,dollar_f1(A,B))
| big_f(B,dollar_f1(A,B)) ),
file('SYN332+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ big_f(A,B)
| big_f(B,A)
| ~ big_f(dollar_f1(B,A),dollar_f1(B,A)) ),
file('SYN332+1.p',unknown),
[] ).
cnf(10,axiom,
( big_f(A,B)
| big_f(B,A)
| ~ big_f(dollar_f1(A,B),B) ),
file('SYN332+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ big_f(A,B)
| ~ big_f(B,A)
| ~ big_f(dollar_f1(A,B),B) ),
file('SYN332+1.p',unknown),
[] ).
cnf(13,plain,
( big_f(A,A)
| ~ big_f(dollar_f1(A,A),A) ),
inference(factor,[status(thm)],[10]),
[iquote('factor,10.1.2')] ).
cnf(14,plain,
( ~ big_f(A,A)
| ~ big_f(dollar_f1(A,A),A) ),
inference(factor,[status(thm)],[11]),
[iquote('factor,11.1.2')] ).
cnf(15,axiom,
( big_f(A,B)
| big_f(A,dollar_f1(A,B)) ),
file('SYN332+1.p',unknown),
[] ).
cnf(31,plain,
( big_f(A,B)
| big_f(B,dollar_f1(A,B)) ),
inference(hyper,[status(thm)],[15,4]),
[iquote('hyper,15,4')] ).
cnf(32,plain,
( big_f(A,B)
| big_f(dollar_f1(A,B),A) ),
inference(hyper,[status(thm)],[15,2]),
[iquote('hyper,15,2')] ).
cnf(213,plain,
big_f(A,A),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[32,13])]),
[iquote('hyper,32,13,factor_simp')] ).
cnf(250,plain,
( big_f(dollar_f1(A,B),B)
| big_f(A,B) ),
inference(hyper,[status(thm)],[213,7,31]),
[iquote('hyper,213,7,31')] ).
cnf(798,plain,
( big_f(A,B)
| big_f(B,A) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[250,10])]),
[iquote('hyper,250,10,factor_simp')] ).
cnf(1057,plain,
big_f(A,B),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[798,7,213])]),
[iquote('hyper,798,7,213,factor_simp')] ).
cnf(1058,plain,
$false,
inference(hyper,[status(thm)],[1057,14,1057]),
[iquote('hyper,1057,14,1057')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN332+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 11:22:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.04/2.23 ----- Otter 3.3f, August 2004 -----
% 2.04/2.23 The process was started by sandbox2 on n022.cluster.edu,
% 2.04/2.23 Wed Jul 27 11:22:20 2022
% 2.04/2.23 The command was "./otter". The process ID is 18813.
% 2.04/2.23
% 2.04/2.23 set(prolog_style_variables).
% 2.04/2.23 set(auto).
% 2.04/2.23 dependent: set(auto1).
% 2.04/2.23 dependent: set(process_input).
% 2.04/2.23 dependent: clear(print_kept).
% 2.04/2.23 dependent: clear(print_new_demod).
% 2.04/2.23 dependent: clear(print_back_demod).
% 2.04/2.23 dependent: clear(print_back_sub).
% 2.04/2.23 dependent: set(control_memory).
% 2.04/2.23 dependent: assign(max_mem, 12000).
% 2.04/2.23 dependent: assign(pick_given_ratio, 4).
% 2.04/2.23 dependent: assign(stats_level, 1).
% 2.04/2.23 dependent: assign(max_seconds, 10800).
% 2.04/2.23 clear(print_given).
% 2.04/2.23
% 2.04/2.23 formula_list(usable).
% 2.04/2.23 -(exists X Y all Z (-(big_f(X,Y)&big_f(Y,X)<->big_f(X,Z))-> ((big_f(X,Z)<->big_f(Z,X))-> ((big_f(X,Z)<->big_f(Y,Z))-> (((big_f(Y,X)->big_f(X,Y))<->big_f(Z,Z))-> ((big_f(X,Y)<->big_f(Y,X))<->big_f(Z,Y))))))).
% 2.04/2.23 end_of_list.
% 2.04/2.23
% 2.04/2.23 -------> usable clausifies to:
% 2.04/2.23
% 2.04/2.23 list(usable).
% 2.04/2.23 0 [] big_f(X,Y)|big_f(X,$f1(X,Y)).
% 2.04/2.23 0 [] big_f(Y,X)|big_f(X,$f1(X,Y)).
% 2.04/2.23 0 [] -big_f(X,Y)| -big_f(Y,X)| -big_f(X,$f1(X,Y)).
% 2.04/2.23 0 [] -big_f(X,$f1(X,Y))|big_f($f1(X,Y),X).
% 2.04/2.23 0 [] big_f(X,$f1(X,Y))| -big_f($f1(X,Y),X).
% 2.04/2.23 0 [] -big_f(X,$f1(X,Y))|big_f(Y,$f1(X,Y)).
% 2.04/2.23 0 [] big_f(X,$f1(X,Y))| -big_f(Y,$f1(X,Y)).
% 2.04/2.23 0 [] big_f(Y,X)|big_f($f1(X,Y),$f1(X,Y)).
% 2.04/2.23 0 [] -big_f(X,Y)|big_f($f1(X,Y),$f1(X,Y)).
% 2.04/2.23 0 [] -big_f(Y,X)|big_f(X,Y)| -big_f($f1(X,Y),$f1(X,Y)).
% 2.04/2.23 0 [] -big_f(X,Y)|big_f(Y,X)|big_f($f1(X,Y),Y).
% 2.04/2.23 0 [] big_f(X,Y)| -big_f(Y,X)|big_f($f1(X,Y),Y).
% 2.04/2.23 0 [] big_f(X,Y)|big_f(Y,X)| -big_f($f1(X,Y),Y).
% 2.04/2.23 0 [] -big_f(X,Y)| -big_f(Y,X)| -big_f($f1(X,Y),Y).
% 2.04/2.23 end_of_list.
% 2.04/2.23
% 2.04/2.23 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 2.04/2.23
% 2.04/2.23 This is a non-Horn set without equality. The strategy will
% 2.04/2.23 be ordered hyper_res, unit deletion, and factoring, with
% 2.04/2.23 satellites in sos and with nuclei in usable.
% 2.04/2.23
% 2.04/2.23 dependent: set(hyper_res).
% 2.04/2.23 dependent: set(factor).
% 2.04/2.23 dependent: set(unit_deletion).
% 2.04/2.23
% 2.04/2.23 ------------> process usable:
% 2.04/2.23 ** KEPT (pick-wt=11): 1 [] -big_f(A,B)| -big_f(B,A)| -big_f(A,$f1(A,B)).
% 2.04/2.23 ** KEPT (pick-wt=10): 2 [] -big_f(A,$f1(A,B))|big_f($f1(A,B),A).
% 2.04/2.23 ** KEPT (pick-wt=10): 3 [] big_f(A,$f1(A,B))| -big_f($f1(A,B),A).
% 2.04/2.23 ** KEPT (pick-wt=10): 4 [] -big_f(A,$f1(A,B))|big_f(B,$f1(A,B)).
% 2.04/2.23 ** KEPT (pick-wt=10): 5 [] big_f(A,$f1(A,B))| -big_f(B,$f1(A,B)).
% 2.04/2.23 ** KEPT (pick-wt=10): 6 [] -big_f(A,B)|big_f($f1(A,B),$f1(A,B)).
% 2.04/2.23 ** KEPT (pick-wt=13): 7 [] -big_f(A,B)|big_f(B,A)| -big_f($f1(B,A),$f1(B,A)).
% 2.04/2.23 ** KEPT (pick-wt=11): 8 [] -big_f(A,B)|big_f(B,A)|big_f($f1(A,B),B).
% 2.04/2.23 ** KEPT (pick-wt=11): 9 [] big_f(A,B)| -big_f(B,A)|big_f($f1(A,B),B).
% 2.04/2.23 ** KEPT (pick-wt=11): 10 [] big_f(A,B)|big_f(B,A)| -big_f($f1(A,B),B).
% 2.04/2.23 ** KEPT (pick-wt=11): 11 [] -big_f(A,B)| -big_f(B,A)| -big_f($f1(A,B),B).
% 2.04/2.23
% 2.04/2.23 ------------> process sos:
% 2.04/2.23 ** KEPT (pick-wt=8): 15 [] big_f(A,B)|big_f(A,$f1(A,B)).
% 2.04/2.23 ** KEPT (pick-wt=8): 16 [] big_f(A,B)|big_f(B,$f1(B,A)).
% 2.04/2.23 ** KEPT (pick-wt=10): 17 [] big_f(A,B)|big_f($f1(B,A),$f1(B,A)).
% 2.04/2.23
% 2.04/2.23 ======= end of input processing =======
% 2.04/2.23
% 2.04/2.23 =========== start of search ===========
% 2.04/2.23
% 2.04/2.23 -------- PROOF --------
% 2.04/2.23
% 2.04/2.23 -----> EMPTY CLAUSE at 0.39 sec ----> 1058 [hyper,1057,14,1057] $F.
% 2.04/2.23
% 2.04/2.23 Length of proof is 8. Level of proof is 5.
% 2.04/2.23
% 2.04/2.23 ---------------- PROOF ----------------
% 2.04/2.23 % SZS status Theorem
% 2.04/2.23 % SZS output start Refutation
% See solution above
% 2.04/2.23 ------------ end of proof -------------
% 2.04/2.23
% 2.04/2.23
% 2.04/2.23 Search stopped by max_proofs option.
% 2.04/2.23
% 2.04/2.23
% 2.04/2.23 Search stopped by max_proofs option.
% 2.04/2.23
% 2.04/2.23 ============ end of search ============
% 2.04/2.23
% 2.04/2.23 -------------- statistics -------------
% 2.04/2.23 clauses given 16
% 2.04/2.23 clauses generated 13236
% 2.04/2.23 clauses kept 1057
% 2.04/2.23 clauses forward subsumed 12192
% 2.04/2.23 clauses back subsumed 1052
% 2.04/2.23 Kbytes malloced 976
% 2.04/2.23
% 2.04/2.23 ----------- times (seconds) -----------
% 2.04/2.23 user CPU time 0.39 (0 hr, 0 min, 0 sec)
% 2.04/2.23 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.04/2.23 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.04/2.23
% 2.04/2.23 That finishes the proof of the theorem.
% 2.04/2.23
% 2.04/2.23 Process 18813 finished Wed Jul 27 11:22:22 2022
% 2.04/2.23 Otter interrupted
% 2.04/2.23 PROOF FOUND
%------------------------------------------------------------------------------