TSTP Solution File: SYN334+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN334+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 13:24:16 EDT 2022
% Result : Theorem 1.96s 2.16s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 3 unt; 8 nHn; 6 RR)
% Number of literals : 33 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ big_f(A,B)
| ~ big_f(A,dollar_f1(A,B))
| big_g(B,dollar_f1(A,B)) ),
file('SYN334+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ big_f(A,B)
| big_f(A,dollar_f1(A,B))
| ~ big_g(B,dollar_f1(A,B)) ),
file('SYN334+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ big_f(A,B)
| ~ big_f(dollar_f1(A,B),dollar_f1(A,B))
| big_g(dollar_f1(A,B),dollar_f1(A,B)) ),
file('SYN334+1.p',unknown),
[] ).
cnf(4,axiom,
( big_f(A,B)
| ~ big_g(dollar_f1(A,B),dollar_f1(A,B)) ),
file('SYN334+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ big_g(A,B)
| ~ big_g(dollar_f1(A,B),dollar_f1(A,B)) ),
file('SYN334+1.p',unknown),
[] ).
cnf(6,axiom,
( big_f(A,B)
| big_f(dollar_f1(A,B),dollar_f1(A,B)) ),
file('SYN334+1.p',unknown),
[] ).
cnf(7,axiom,
( big_g(A,B)
| big_g(dollar_f1(A,B),dollar_f1(A,B)) ),
file('SYN334+1.p',unknown),
[] ).
cnf(15,plain,
( big_g(A,B)
| big_f(A,B) ),
inference(hyper,[status(thm)],[7,4]),
[iquote('hyper,7,4')] ).
cnf(18,plain,
( big_f(A,dollar_f1(B,A))
| big_f(B,dollar_f1(B,A))
| big_f(dollar_f1(B,A),dollar_f1(B,A)) ),
inference(hyper,[status(thm)],[15,2,6]),
[iquote('hyper,15,2,6')] ).
cnf(19,plain,
( big_f(A,dollar_f1(A,A))
| big_f(dollar_f1(A,A),dollar_f1(A,A)) ),
inference(factor,[status(thm)],[18]),
[iquote('factor,18.1.2')] ).
cnf(25,plain,
( big_f(dollar_f1(A,A),dollar_f1(A,A))
| big_g(A,dollar_f1(A,A)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[19,1,6])]),
[iquote('hyper,19,1,6,factor_simp')] ).
cnf(31,plain,
( big_f(dollar_f1(A,A),dollar_f1(A,A))
| big_f(dollar_f1(A,dollar_f1(A,A)),dollar_f1(A,dollar_f1(A,A))) ),
inference(hyper,[status(thm)],[25,5,15]),
[iquote('hyper,25,5,15')] ).
cnf(131,plain,
( big_f(dollar_f1(A,A),dollar_f1(A,A))
| big_g(dollar_f1(A,dollar_f1(A,A)),dollar_f1(A,dollar_f1(A,A))) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[31,3,19])]),
[iquote('hyper,31,3,19,factor_simp')] ).
cnf(139,plain,
big_f(dollar_f1(A,A),dollar_f1(A,A)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[131,5,25])]),
[iquote('hyper,131,5,25,factor_simp')] ).
cnf(140,plain,
big_g(dollar_f1(dollar_f1(A,A),dollar_f1(A,A)),dollar_f1(dollar_f1(A,A),dollar_f1(A,A))),
inference(hyper,[status(thm)],[139,3,139]),
[iquote('hyper,139,3,139')] ).
cnf(154,plain,
$false,
inference(hyper,[status(thm)],[140,5,140]),
[iquote('hyper,140,5,140')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN334+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 11:31:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.96/2.16 ----- Otter 3.3f, August 2004 -----
% 1.96/2.16 The process was started by sandbox2 on n023.cluster.edu,
% 1.96/2.16 Wed Jul 27 11:31:18 2022
% 1.96/2.16 The command was "./otter". The process ID is 9921.
% 1.96/2.16
% 1.96/2.16 set(prolog_style_variables).
% 1.96/2.16 set(auto).
% 1.96/2.16 dependent: set(auto1).
% 1.96/2.16 dependent: set(process_input).
% 1.96/2.16 dependent: clear(print_kept).
% 1.96/2.16 dependent: clear(print_new_demod).
% 1.96/2.16 dependent: clear(print_back_demod).
% 1.96/2.16 dependent: clear(print_back_sub).
% 1.96/2.16 dependent: set(control_memory).
% 1.96/2.16 dependent: assign(max_mem, 12000).
% 1.96/2.16 dependent: assign(pick_given_ratio, 4).
% 1.96/2.16 dependent: assign(stats_level, 1).
% 1.96/2.16 dependent: assign(max_seconds, 10800).
% 1.96/2.16 clear(print_given).
% 1.96/2.16
% 1.96/2.16 formula_list(usable).
% 1.96/2.16 -(exists X Y all Z ((big_f(X,Y)-> (big_f(X,Z)<->big_g(Y,Z)))-> ((big_f(X,Y)<-> (big_f(Z,Z)->big_g(Z,Z)))-> (big_g(X,Y)<->big_g(Z,Z))))).
% 1.96/2.16 end_of_list.
% 1.96/2.16
% 1.96/2.16 -------> usable clausifies to:
% 1.96/2.16
% 1.96/2.16 list(usable).
% 1.96/2.16 0 [] -big_f(X,Y)| -big_f(X,$f1(X,Y))|big_g(Y,$f1(X,Y)).
% 1.96/2.16 0 [] -big_f(X,Y)|big_f(X,$f1(X,Y))| -big_g(Y,$f1(X,Y)).
% 1.96/2.16 0 [] -big_f(X,Y)| -big_f($f1(X,Y),$f1(X,Y))|big_g($f1(X,Y),$f1(X,Y)).
% 1.96/2.16 0 [] big_f(X,Y)|big_f($f1(X,Y),$f1(X,Y)).
% 1.96/2.16 0 [] big_f(X,Y)| -big_g($f1(X,Y),$f1(X,Y)).
% 1.96/2.16 0 [] big_g(X,Y)|big_g($f1(X,Y),$f1(X,Y)).
% 1.96/2.16 0 [] -big_g(X,Y)| -big_g($f1(X,Y),$f1(X,Y)).
% 1.96/2.16 end_of_list.
% 1.96/2.16
% 1.96/2.16 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.96/2.16
% 1.96/2.16 This is a non-Horn set without equality. The strategy will
% 1.96/2.16 be ordered hyper_res, unit deletion, and factoring, with
% 1.96/2.16 satellites in sos and with nuclei in usable.
% 1.96/2.16
% 1.96/2.16 dependent: set(hyper_res).
% 1.96/2.16 dependent: set(factor).
% 1.96/2.16 dependent: set(unit_deletion).
% 1.96/2.16
% 1.96/2.16 ------------> process usable:
% 1.96/2.16 ** KEPT (pick-wt=13): 1 [] -big_f(A,B)| -big_f(A,$f1(A,B))|big_g(B,$f1(A,B)).
% 1.96/2.16 ** KEPT (pick-wt=13): 2 [] -big_f(A,B)|big_f(A,$f1(A,B))| -big_g(B,$f1(A,B)).
% 1.96/2.16 ** KEPT (pick-wt=17): 3 [] -big_f(A,B)| -big_f($f1(A,B),$f1(A,B))|big_g($f1(A,B),$f1(A,B)).
% 1.96/2.16 ** KEPT (pick-wt=10): 4 [] big_f(A,B)| -big_g($f1(A,B),$f1(A,B)).
% 1.96/2.16 ** KEPT (pick-wt=10): 5 [] -big_g(A,B)| -big_g($f1(A,B),$f1(A,B)).
% 1.96/2.16
% 1.96/2.16 ------------> process sos:
% 1.96/2.16 ** KEPT (pick-wt=10): 6 [] big_f(A,B)|big_f($f1(A,B),$f1(A,B)).
% 1.96/2.16 ** KEPT (pick-wt=10): 7 [] big_g(A,B)|big_g($f1(A,B),$f1(A,B)).
% 1.96/2.16
% 1.96/2.16 ======= end of input processing =======
% 1.96/2.16
% 1.96/2.16 =========== start of search ===========
% 1.96/2.16
% 1.96/2.16 -------- PROOF --------
% 1.96/2.16
% 1.96/2.16 -----> EMPTY CLAUSE at 0.03 sec ----> 154 [hyper,140,5,140] $F.
% 1.96/2.16
% 1.96/2.16 Length of proof is 8. Level of proof is 8.
% 1.96/2.16
% 1.96/2.16 ---------------- PROOF ----------------
% 1.96/2.16 % SZS status Theorem
% 1.96/2.16 % SZS output start Refutation
% See solution above
% 1.96/2.16 ------------ end of proof -------------
% 1.96/2.16
% 1.96/2.16
% 1.96/2.16 Search stopped by max_proofs option.
% 1.96/2.16
% 1.96/2.16
% 1.96/2.16 Search stopped by max_proofs option.
% 1.96/2.16
% 1.96/2.16 ============ end of search ============
% 1.96/2.16
% 1.96/2.16 -------------- statistics -------------
% 1.96/2.16 clauses given 23
% 1.96/2.16 clauses generated 442
% 1.96/2.16 clauses kept 153
% 1.96/2.16 clauses forward subsumed 295
% 1.96/2.16 clauses back subsumed 105
% 1.96/2.16 Kbytes malloced 2929
% 1.96/2.16
% 1.96/2.16 ----------- times (seconds) -----------
% 1.96/2.16 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.96/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.16 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.96/2.16
% 1.96/2.16 That finishes the proof of the theorem.
% 1.96/2.16
% 1.96/2.16 Process 9921 finished Wed Jul 27 11:31:20 2022
% 1.96/2.16 Otter interrupted
% 1.96/2.16 PROOF FOUND
%------------------------------------------------------------------------------