TSTP Solution File: COM007+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COM007+2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 12:48:21 EDT 2022
% Result : Theorem 1.69s 1.92s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 13 unt; 3 nHn; 21 RR)
% Number of literals : 39 ( 5 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ reflexive_rewrite(b,A)
| ~ reflexive_rewrite(c,A)
| goal ),
file('COM007+2.p',unknown),
[] ).
cnf(2,axiom,
( A != B
| reflexive_rewrite(A,B) ),
file('COM007+2.p',unknown),
[] ).
cnf(3,axiom,
( ~ rewrite(A,B)
| reflexive_rewrite(A,B) ),
file('COM007+2.p',unknown),
[] ).
cnf(4,axiom,
( ~ reflexive_rewrite(A,B)
| A = B
| rewrite(A,B) ),
file('COM007+2.p',unknown),
[] ).
cnf(5,axiom,
( ~ rewrite(A,B)
| ~ rewrite(A,C)
| rewrite(B,dollar_f1(A,B,C)) ),
file('COM007+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ rewrite(A,B)
| ~ rewrite(A,C)
| rewrite(C,dollar_f1(A,B,C)) ),
file('COM007+2.p',unknown),
[] ).
cnf(7,axiom,
~ goal,
file('COM007+2.p',unknown),
[] ).
cnf(9,axiom,
A = A,
file('COM007+2.p',unknown),
[] ).
cnf(10,axiom,
reflexive_rewrite(a,b),
file('COM007+2.p',unknown),
[] ).
cnf(11,axiom,
reflexive_rewrite(a,c),
file('COM007+2.p',unknown),
[] ).
cnf(12,plain,
reflexive_rewrite(A,A),
inference(hyper,[status(thm)],[9,2]),
[iquote('hyper,9,2')] ).
cnf(13,plain,
( b = a
| rewrite(a,b) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[10,4])]),
[iquote('hyper,10,4,flip.1')] ).
cnf(16,plain,
( c = a
| rewrite(a,c) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[11,4])]),
[iquote('hyper,11,4,flip.1')] ).
cnf(23,plain,
( ~ reflexive_rewrite(a,A)
| ~ reflexive_rewrite(c,A)
| rewrite(a,b) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[13,1]),7]),
[iquote('para_from,13.1.1,1.1.1,unit_del,7')] ).
cnf(38,plain,
( ~ reflexive_rewrite(b,A)
| ~ reflexive_rewrite(a,A)
| rewrite(a,c) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[16,1]),7]),
[iquote('para_from,16.1.1,1.2.1,unit_del,7')] ).
cnf(134,plain,
rewrite(a,b),
inference(hyper,[status(thm)],[23,11,12]),
[iquote('hyper,23,11,12')] ).
cnf(178,plain,
rewrite(a,c),
inference(hyper,[status(thm)],[38,12,10]),
[iquote('hyper,38,12,10')] ).
cnf(180,plain,
rewrite(c,dollar_f1(a,b,c)),
inference(hyper,[status(thm)],[178,6,134]),
[iquote('hyper,178,6,134')] ).
cnf(182,plain,
rewrite(b,dollar_f1(a,b,c)),
inference(hyper,[status(thm)],[178,5,134]),
[iquote('hyper,178,5,134')] ).
cnf(202,plain,
reflexive_rewrite(c,dollar_f1(a,b,c)),
inference(hyper,[status(thm)],[180,3]),
[iquote('hyper,180,3')] ).
cnf(228,plain,
reflexive_rewrite(b,dollar_f1(a,b,c)),
inference(hyper,[status(thm)],[182,3]),
[iquote('hyper,182,3')] ).
cnf(266,plain,
goal,
inference(hyper,[status(thm)],[228,1,202]),
[iquote('hyper,228,1,202')] ).
cnf(267,plain,
$false,
inference(binary,[status(thm)],[266,7]),
[iquote('binary,266.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COM007+2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 06:43:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.92 ----- Otter 3.3f, August 2004 -----
% 1.69/1.92 The process was started by sandbox on n028.cluster.edu,
% 1.69/1.92 Wed Jul 27 06:43:33 2022
% 1.69/1.92 The command was "./otter". The process ID is 25266.
% 1.69/1.92
% 1.69/1.92 set(prolog_style_variables).
% 1.69/1.92 set(auto).
% 1.69/1.92 dependent: set(auto1).
% 1.69/1.92 dependent: set(process_input).
% 1.69/1.92 dependent: clear(print_kept).
% 1.69/1.92 dependent: clear(print_new_demod).
% 1.69/1.92 dependent: clear(print_back_demod).
% 1.69/1.92 dependent: clear(print_back_sub).
% 1.69/1.92 dependent: set(control_memory).
% 1.69/1.92 dependent: assign(max_mem, 12000).
% 1.69/1.92 dependent: assign(pick_given_ratio, 4).
% 1.69/1.92 dependent: assign(stats_level, 1).
% 1.69/1.92 dependent: assign(max_seconds, 10800).
% 1.69/1.92 clear(print_given).
% 1.69/1.92
% 1.69/1.92 formula_list(usable).
% 1.69/1.92 all A (A=A).
% 1.69/1.92 reflexive_rewrite(a,b).
% 1.69/1.92 reflexive_rewrite(a,c).
% 1.69/1.92 all A (reflexive_rewrite(b,A)&reflexive_rewrite(c,A)->goal).
% 1.69/1.92 all A B (A=B->reflexive_rewrite(A,B)).
% 1.69/1.92 all A B (rewrite(A,B)->reflexive_rewrite(A,B)).
% 1.69/1.92 all A B (reflexive_rewrite(A,B)->A=B|rewrite(A,B)).
% 1.69/1.92 all A B C (rewrite(A,B)&rewrite(A,C)-> (exists D (rewrite(B,D)&rewrite(C,D)))).
% 1.69/1.92 -goal.
% 1.69/1.92 end_of_list.
% 1.69/1.92
% 1.69/1.92 -------> usable clausifies to:
% 1.69/1.92
% 1.69/1.92 list(usable).
% 1.69/1.92 0 [] A=A.
% 1.69/1.92 0 [] reflexive_rewrite(a,b).
% 1.69/1.92 0 [] reflexive_rewrite(a,c).
% 1.69/1.92 0 [] -reflexive_rewrite(b,A)| -reflexive_rewrite(c,A)|goal.
% 1.69/1.92 0 [] A!=B|reflexive_rewrite(A,B).
% 1.69/1.92 0 [] -rewrite(A,B)|reflexive_rewrite(A,B).
% 1.69/1.92 0 [] -reflexive_rewrite(A,B)|A=B|rewrite(A,B).
% 1.69/1.92 0 [] -rewrite(A,B)| -rewrite(A,C)|rewrite(B,$f1(A,B,C)).
% 1.69/1.92 0 [] -rewrite(A,B)| -rewrite(A,C)|rewrite(C,$f1(A,B,C)).
% 1.69/1.92 0 [] -goal.
% 1.69/1.92 end_of_list.
% 1.69/1.92
% 1.69/1.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.69/1.92
% 1.69/1.92 This ia a non-Horn set with equality. The strategy will be
% 1.69/1.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.69/1.92 deletion, with positive clauses in sos and nonpositive
% 1.69/1.92 clauses in usable.
% 1.69/1.92
% 1.69/1.92 dependent: set(knuth_bendix).
% 1.69/1.92 dependent: set(anl_eq).
% 1.69/1.92 dependent: set(para_from).
% 1.69/1.92 dependent: set(para_into).
% 1.69/1.92 dependent: clear(para_from_right).
% 1.69/1.92 dependent: clear(para_into_right).
% 1.69/1.92 dependent: set(para_from_vars).
% 1.69/1.92 dependent: set(eq_units_both_ways).
% 1.69/1.92 dependent: set(dynamic_demod_all).
% 1.69/1.92 dependent: set(dynamic_demod).
% 1.69/1.92 dependent: set(order_eq).
% 1.69/1.92 dependent: set(back_demod).
% 1.69/1.92 dependent: set(lrpo).
% 1.69/1.92 dependent: set(hyper_res).
% 1.69/1.92 dependent: set(unit_deletion).
% 1.69/1.92 dependent: set(factor).
% 1.69/1.92
% 1.69/1.92 ------------> process usable:
% 1.69/1.92 ** KEPT (pick-wt=7): 1 [] -reflexive_rewrite(b,A)| -reflexive_rewrite(c,A)|goal.
% 1.69/1.92 ** KEPT (pick-wt=6): 2 [] A!=B|reflexive_rewrite(A,B).
% 1.69/1.92 ** KEPT (pick-wt=6): 3 [] -rewrite(A,B)|reflexive_rewrite(A,B).
% 1.69/1.92 ** KEPT (pick-wt=9): 4 [] -reflexive_rewrite(A,B)|A=B|rewrite(A,B).
% 1.69/1.92 ** KEPT (pick-wt=12): 5 [] -rewrite(A,B)| -rewrite(A,C)|rewrite(B,$f1(A,B,C)).
% 1.69/1.92 ** KEPT (pick-wt=12): 6 [] -rewrite(A,B)| -rewrite(A,C)|rewrite(C,$f1(A,B,C)).
% 1.69/1.92 ** KEPT (pick-wt=1): 7 [] -goal.
% 1.69/1.92
% 1.69/1.92 ------------> process sos:
% 1.69/1.92 ** KEPT (pick-wt=3): 9 [] A=A.
% 1.69/1.92 ** KEPT (pick-wt=3): 10 [] reflexive_rewrite(a,b).
% 1.69/1.92 ** KEPT (pick-wt=3): 11 [] reflexive_rewrite(a,c).
% 1.69/1.92 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 1.69/1.92
% 1.69/1.92 ======= end of input processing =======
% 1.69/1.92
% 1.69/1.92 =========== start of search ===========
% 1.69/1.92
% 1.69/1.92 -------- PROOF --------
% 1.69/1.92
% 1.69/1.92 ----> UNIT CONFLICT at 0.01 sec ----> 267 [binary,266.1,7.1] $F.
% 1.69/1.92
% 1.69/1.92 Length of proof is 12. Level of proof is 6.
% 1.69/1.92
% 1.69/1.92 ---------------- PROOF ----------------
% 1.69/1.92 % SZS status Theorem
% 1.69/1.92 % SZS output start Refutation
% See solution above
% 1.69/1.92 ------------ end of proof -------------
% 1.69/1.92
% 1.69/1.92
% 1.69/1.92 Search stopped by max_proofs option.
% 1.69/1.92
% 1.69/1.92
% 1.69/1.92 Search stopped by max_proofs option.
% 1.69/1.92
% 1.69/1.92 ============ end of search ============
% 1.69/1.92
% 1.69/1.92 -------------- statistics -------------
% 1.69/1.92 clauses given 35
% 1.69/1.92 clauses generated 598
% 1.69/1.92 clauses kept 266
% 1.69/1.92 clauses forward subsumed 335
% 1.69/1.92 clauses back subsumed 131
% 1.69/1.92 Kbytes malloced 976
% 1.69/1.92
% 1.69/1.92 ----------- times (seconds) -----------
% 1.69/1.92 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.69/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.92 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.69/1.92
% 1.69/1.92 That finishes the proof of the theorem.
% 1.69/1.92
% 1.69/1.92 Process 25266 finished Wed Jul 27 06:43:35 2022
% 1.69/1.92 Otter interrupted
% 1.69/1.92 PROOF FOUND
%------------------------------------------------------------------------------