TSTP Solution File: SYN078+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:23:31 EDT 2022
% Result : Theorem 1.67s 1.86s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 8 unt; 7 nHn; 20 RR)
% Number of literals : 40 ( 9 equ; 13 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ big_p(A)
| B != f(A)
| big_p(B)
| ~ big_p(C)
| big_p(f(C)) ),
file('SYN078+1.p',unknown),
[] ).
cnf(2,axiom,
( big_p(dollar_c1)
| ~ big_p(f(dollar_c3)) ),
file('SYN078+1.p',unknown),
[] ).
cnf(3,axiom,
( dollar_c2 = f(dollar_c1)
| ~ big_p(f(dollar_c3)) ),
file('SYN078+1.p',unknown),
[] ).
cnf(4,plain,
( f(dollar_c1) = dollar_c2
| ~ big_p(f(dollar_c3)) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(5,axiom,
( ~ big_p(dollar_c2)
| big_p(dollar_c3) ),
file('SYN078+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ big_p(dollar_c2)
| ~ big_p(f(dollar_c3)) ),
file('SYN078+1.p',unknown),
[] ).
cnf(7,plain,
( ~ big_p(A)
| B != f(A)
| big_p(B)
| big_p(f(A)) ),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.1.4')] ).
cnf(9,plain,
( ~ big_p(A)
| f(A) != f(A)
| big_p(f(A)) ),
inference(factor,[status(thm)],[7]),
[iquote('factor,7.3.4')] ).
cnf(10,axiom,
A = A,
file('SYN078+1.p',unknown),
[] ).
cnf(11,axiom,
( big_p(dollar_c1)
| big_p(dollar_c3) ),
file('SYN078+1.p',unknown),
[] ).
cnf(12,axiom,
( dollar_c2 = f(dollar_c1)
| big_p(dollar_c3) ),
file('SYN078+1.p',unknown),
[] ).
cnf(13,plain,
( f(dollar_c1) = dollar_c2
| big_p(dollar_c3) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.1')] ).
cnf(15,plain,
( big_p(dollar_c1)
| big_p(f(dollar_c3)) ),
inference(hyper,[status(thm)],[11,9,10]),
[iquote('hyper,11,9,10')] ).
cnf(21,plain,
big_p(dollar_c1),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[15,2])]),
[iquote('hyper,15,2,factor_simp')] ).
cnf(22,plain,
big_p(f(dollar_c1)),
inference(hyper,[status(thm)],[21,9,10]),
[iquote('hyper,21,9,10')] ).
cnf(26,plain,
( big_p(dollar_c2)
| big_p(dollar_c3) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[13,9]),21,10]),
[iquote('para_from,13.1.1,9.3.1,unit_del,21,10')] ).
cnf(30,plain,
big_p(dollar_c3),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[26,5])]),
[iquote('hyper,26,5,factor_simp')] ).
cnf(32,plain,
big_p(f(dollar_c3)),
inference(hyper,[status(thm)],[30,9,10]),
[iquote('hyper,30,9,10')] ).
cnf(35,plain,
f(dollar_c1) = dollar_c2,
inference(hyper,[status(thm)],[32,4]),
[iquote('hyper,32,4')] ).
cnf(37,plain,
big_p(dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[22]),35]),
[iquote('back_demod,22,demod,35')] ).
cnf(39,plain,
$false,
inference(hyper,[status(thm)],[37,6,32]),
[iquote('hyper,37,6,32')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:59:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.86 ----- Otter 3.3f, August 2004 -----
% 1.67/1.86 The process was started by sandbox2 on n018.cluster.edu,
% 1.67/1.86 Wed Jul 27 10:59:31 2022
% 1.67/1.86 The command was "./otter". The process ID is 28527.
% 1.67/1.86
% 1.67/1.86 set(prolog_style_variables).
% 1.67/1.86 set(auto).
% 1.67/1.86 dependent: set(auto1).
% 1.67/1.86 dependent: set(process_input).
% 1.67/1.86 dependent: clear(print_kept).
% 1.67/1.86 dependent: clear(print_new_demod).
% 1.67/1.86 dependent: clear(print_back_demod).
% 1.67/1.86 dependent: clear(print_back_sub).
% 1.67/1.86 dependent: set(control_memory).
% 1.67/1.86 dependent: assign(max_mem, 12000).
% 1.67/1.86 dependent: assign(pick_given_ratio, 4).
% 1.67/1.86 dependent: assign(stats_level, 1).
% 1.67/1.86 dependent: assign(max_seconds, 10800).
% 1.67/1.86 clear(print_given).
% 1.67/1.86
% 1.67/1.86 formula_list(usable).
% 1.67/1.86 all A (A=A).
% 1.67/1.86 -((all X ((exists Y (big_p(Y)&X=f(Y)))->big_p(X)))<-> (all U (big_p(U)->big_p(f(U))))).
% 1.67/1.86 end_of_list.
% 1.67/1.86
% 1.67/1.86 -------> usable clausifies to:
% 1.67/1.86
% 1.67/1.86 list(usable).
% 1.67/1.86 0 [] A=A.
% 1.67/1.86 0 [] -big_p(Y)|X!=f(Y)|big_p(X)| -big_p(U)|big_p(f(U)).
% 1.67/1.86 0 [] big_p($c1)|big_p($c3).
% 1.67/1.86 0 [] big_p($c1)| -big_p(f($c3)).
% 1.67/1.86 0 [] $c2=f($c1)|big_p($c3).
% 1.67/1.86 0 [] $c2=f($c1)| -big_p(f($c3)).
% 1.67/1.86 0 [] -big_p($c2)|big_p($c3).
% 1.67/1.86 0 [] -big_p($c2)| -big_p(f($c3)).
% 1.67/1.86 end_of_list.
% 1.67/1.86
% 1.67/1.86 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.67/1.86
% 1.67/1.86 This ia a non-Horn set with equality. The strategy will be
% 1.67/1.86 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.67/1.86 deletion, with positive clauses in sos and nonpositive
% 1.67/1.86 clauses in usable.
% 1.67/1.86
% 1.67/1.86 dependent: set(knuth_bendix).
% 1.67/1.86 dependent: set(anl_eq).
% 1.67/1.86 dependent: set(para_from).
% 1.67/1.86 dependent: set(para_into).
% 1.67/1.86 dependent: clear(para_from_right).
% 1.67/1.86 dependent: clear(para_into_right).
% 1.67/1.86 dependent: set(para_from_vars).
% 1.67/1.86 dependent: set(eq_units_both_ways).
% 1.67/1.86 dependent: set(dynamic_demod_all).
% 1.67/1.86 dependent: set(dynamic_demod).
% 1.67/1.86 dependent: set(order_eq).
% 1.67/1.86 dependent: set(back_demod).
% 1.67/1.86 dependent: set(lrpo).
% 1.67/1.86 dependent: set(hyper_res).
% 1.67/1.86 dependent: set(unit_deletion).
% 1.67/1.86 dependent: set(factor).
% 1.67/1.86
% 1.67/1.86 ------------> process usable:
% 1.67/1.86 ** KEPT (pick-wt=13): 1 [] -big_p(A)|B!=f(A)|big_p(B)| -big_p(C)|big_p(f(C)).
% 1.67/1.86 ** KEPT (pick-wt=5): 2 [] big_p($c1)| -big_p(f($c3)).
% 1.67/1.86 ** KEPT (pick-wt=7): 4 [copy,3,flip.1] f($c1)=$c2| -big_p(f($c3)).
% 1.67/1.86 ** KEPT (pick-wt=4): 5 [] -big_p($c2)|big_p($c3).
% 1.67/1.86 ** KEPT (pick-wt=5): 6 [] -big_p($c2)| -big_p(f($c3)).
% 1.67/1.86
% 1.67/1.86 ------------> process sos:
% 1.67/1.86 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.67/1.86 ** KEPT (pick-wt=4): 11 [] big_p($c1)|big_p($c3).
% 1.67/1.86 ** KEPT (pick-wt=6): 13 [copy,12,flip.1] f($c1)=$c2|big_p($c3).
% 1.67/1.86 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.67/1.86
% 1.67/1.86 ======= end of input processing =======
% 1.67/1.86
% 1.67/1.86 =========== start of search ===========
% 1.67/1.86
% 1.67/1.86 -------- PROOF --------
% 1.67/1.86
% 1.67/1.86 -----> EMPTY CLAUSE at 0.00 sec ----> 39 [hyper,37,6,32] $F.
% 1.67/1.86
% 1.67/1.86 Length of proof is 12. Level of proof is 9.
% 1.67/1.86
% 1.67/1.86 ---------------- PROOF ----------------
% 1.67/1.86 % SZS status Theorem
% 1.67/1.86 % SZS output start Refutation
% See solution above
% 1.67/1.86 ------------ end of proof -------------
% 1.67/1.86
% 1.67/1.86
% 1.67/1.86 Search stopped by max_proofs option.
% 1.67/1.86
% 1.67/1.86
% 1.67/1.86 Search stopped by max_proofs option.
% 1.67/1.86
% 1.67/1.86 ============ end of search ============
% 1.67/1.86
% 1.67/1.86 -------------- statistics -------------
% 1.67/1.86 clauses given 12
% 1.67/1.86 clauses generated 195
% 1.67/1.86 clauses kept 35
% 1.67/1.86 clauses forward subsumed 171
% 1.67/1.86 clauses back subsumed 18
% 1.67/1.86 Kbytes malloced 976
% 1.67/1.86
% 1.67/1.86 ----------- times (seconds) -----------
% 1.67/1.86 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.86 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.86 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.67/1.86
% 1.67/1.86 That finishes the proof of the theorem.
% 1.67/1.86
% 1.67/1.86 Process 28527 finished Wed Jul 27 10:59:33 2022
% 1.67/1.86 Otter interrupted
% 1.67/1.86 PROOF FOUND
%------------------------------------------------------------------------------