TSTP Solution File: CAT018-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT018-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 12:47:50 EDT 2022
% Result : Unsatisfiable 1.83s 2.02s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 17 ( 12 unt; 0 nHn; 15 RR)
% Number of literals : 29 ( 0 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ defined(A,B)
| product(A,B,compose(A,B)) ),
file('CAT018-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ defined(C,D)
| defined(B,D) ),
file('CAT018-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ defined(C,D)
| defined(A,E) ),
file('CAT018-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(A,B,C)
| ~ product(D,A,E)
| ~ defined(D,C)
| defined(E,B) ),
file('CAT018-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ defined(A,B)
| ~ defined(B,C)
| ~ identity_map(B)
| defined(A,C) ),
file('CAT018-1.p',unknown),
[] ).
cnf(13,axiom,
~ defined(a,compose(b,c)),
file('CAT018-1.p',unknown),
[] ).
cnf(15,axiom,
identity_map(domain(A)),
file('CAT018-1.p',unknown),
[] ).
cnf(19,axiom,
product(A,domain(A),A),
file('CAT018-1.p',unknown),
[] ).
cnf(21,axiom,
defined(a,b),
file('CAT018-1.p',unknown),
[] ).
cnf(22,axiom,
defined(b,c),
file('CAT018-1.p',unknown),
[] ).
cnf(25,plain,
product(a,b,compose(a,b)),
inference(hyper,[status(thm)],[21,1]),
[iquote('hyper,21,1')] ).
cnf(28,plain,
product(b,c,compose(b,c)),
inference(hyper,[status(thm)],[22,1]),
[iquote('hyper,22,1')] ).
cnf(44,plain,
defined(domain(b),c),
inference(hyper,[status(thm)],[19,3,22]),
[iquote('hyper,19,3,22')] ).
cnf(192,plain,
defined(compose(a,b),domain(b)),
inference(hyper,[status(thm)],[25,7,19,21]),
[iquote('hyper,25,7,19,21')] ).
cnf(730,plain,
defined(compose(a,b),c),
inference(hyper,[status(thm)],[192,9,44,15]),
[iquote('hyper,192,9,44,15')] ).
cnf(740,plain,
defined(a,compose(b,c)),
inference(hyper,[status(thm)],[730,4,25,28]),
[iquote('hyper,730,4,25,28')] ).
cnf(741,plain,
$false,
inference(binary,[status(thm)],[740,13]),
[iquote('binary,740.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 01:55:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.83/2.01 ----- Otter 3.3f, August 2004 -----
% 1.83/2.01 The process was started by sandbox on n014.cluster.edu,
% 1.83/2.01 Wed Jul 27 01:55:24 2022
% 1.83/2.01 The command was "./otter". The process ID is 32745.
% 1.83/2.01
% 1.83/2.01 set(prolog_style_variables).
% 1.83/2.01 set(auto).
% 1.83/2.01 dependent: set(auto1).
% 1.83/2.01 dependent: set(process_input).
% 1.83/2.01 dependent: clear(print_kept).
% 1.83/2.01 dependent: clear(print_new_demod).
% 1.83/2.01 dependent: clear(print_back_demod).
% 1.83/2.01 dependent: clear(print_back_sub).
% 1.83/2.01 dependent: set(control_memory).
% 1.83/2.01 dependent: assign(max_mem, 12000).
% 1.83/2.01 dependent: assign(pick_given_ratio, 4).
% 1.83/2.01 dependent: assign(stats_level, 1).
% 1.83/2.01 dependent: assign(max_seconds, 10800).
% 1.83/2.01 clear(print_given).
% 1.83/2.01
% 1.83/2.01 list(usable).
% 1.83/2.01 0 [] A=A.
% 1.83/2.01 0 [] -defined(X,Y)|product(X,Y,compose(X,Y)).
% 1.83/2.01 0 [] -product(X,Y,Z)|defined(X,Y).
% 1.83/2.01 0 [] -product(X,Y,Xy)| -defined(Xy,Z)|defined(Y,Z).
% 1.83/2.01 0 [] -product(X,Y,Xy)| -product(Y,Z,Yz)| -defined(Xy,Z)|defined(X,Yz).
% 1.83/2.01 0 [] -product(X,Y,Xy)| -product(Xy,Z,Xyz)| -product(Y,Z,Yz)|product(X,Yz,Xyz).
% 1.83/2.01 0 [] -product(Y,Z,Yz)| -defined(X,Yz)|defined(X,Y).
% 1.83/2.01 0 [] -product(Y,Z,Yz)| -product(X,Y,Xy)| -defined(X,Yz)|defined(Xy,Z).
% 1.83/2.02 0 [] -product(Y,Z,Yz)| -product(X,Yz,Xyz)| -product(X,Y,Xy)|product(Xy,Z,Xyz).
% 1.83/2.02 0 [] -defined(X,Y)| -defined(Y,Z)| -identity_map(Y)|defined(X,Z).
% 1.83/2.02 0 [] identity_map(domain(X)).
% 1.83/2.02 0 [] identity_map(codomain(X)).
% 1.83/2.02 0 [] defined(X,domain(X)).
% 1.83/2.02 0 [] defined(codomain(X),X).
% 1.83/2.02 0 [] product(X,domain(X),X).
% 1.83/2.02 0 [] product(codomain(X),X,X).
% 1.83/2.02 0 [] -defined(X,Y)| -identity_map(X)|product(X,Y,Y).
% 1.83/2.02 0 [] -defined(X,Y)| -identity_map(Y)|product(X,Y,X).
% 1.83/2.02 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.83/2.02 0 [] defined(a,b).
% 1.83/2.02 0 [] defined(b,c).
% 1.83/2.02 0 [] -defined(a,compose(b,c)).
% 1.83/2.02 end_of_list.
% 1.83/2.02
% 1.83/2.02 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.83/2.02
% 1.83/2.02 This is a Horn set with equality. The strategy will be
% 1.83/2.02 Knuth-Bendix and hyper_res, with positive clauses in
% 1.83/2.02 sos and nonpositive clauses in usable.
% 1.83/2.02
% 1.83/2.02 dependent: set(knuth_bendix).
% 1.83/2.02 dependent: set(anl_eq).
% 1.83/2.02 dependent: set(para_from).
% 1.83/2.02 dependent: set(para_into).
% 1.83/2.02 dependent: clear(para_from_right).
% 1.83/2.02 dependent: clear(para_into_right).
% 1.83/2.02 dependent: set(para_from_vars).
% 1.83/2.02 dependent: set(eq_units_both_ways).
% 1.83/2.02 dependent: set(dynamic_demod_all).
% 1.83/2.02 dependent: set(dynamic_demod).
% 1.83/2.02 dependent: set(order_eq).
% 1.83/2.02 dependent: set(back_demod).
% 1.83/2.02 dependent: set(lrpo).
% 1.83/2.02 dependent: set(hyper_res).
% 1.83/2.02 dependent: clear(order_hyper).
% 1.83/2.02
% 1.83/2.02 ------------> process usable:
% 1.83/2.02 ** KEPT (pick-wt=9): 1 [] -defined(A,B)|product(A,B,compose(A,B)).
% 1.83/2.02 ** KEPT (pick-wt=7): 2 [] -product(A,B,C)|defined(A,B).
% 1.83/2.02 ** KEPT (pick-wt=10): 3 [] -product(A,B,C)| -defined(C,D)|defined(B,D).
% 1.83/2.02 ** KEPT (pick-wt=14): 4 [] -product(A,B,C)| -product(B,D,E)| -defined(C,D)|defined(A,E).
% 1.83/2.02 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(C,D,E)| -product(B,D,F)|product(A,F,E).
% 1.83/2.02 ** KEPT (pick-wt=10): 6 [] -product(A,B,C)| -defined(D,C)|defined(D,A).
% 1.83/2.02 ** KEPT (pick-wt=14): 7 [] -product(A,B,C)| -product(D,A,E)| -defined(D,C)|defined(E,B).
% 1.83/2.02 ** KEPT (pick-wt=16): 8 [] -product(A,B,C)| -product(D,C,E)| -product(D,A,F)|product(F,B,E).
% 1.83/2.02 ** KEPT (pick-wt=11): 9 [] -defined(A,B)| -defined(B,C)| -identity_map(B)|defined(A,C).
% 1.83/2.02 ** KEPT (pick-wt=9): 10 [] -defined(A,B)| -identity_map(A)|product(A,B,B).
% 1.83/2.02 ** KEPT (pick-wt=9): 11 [] -defined(A,B)| -identity_map(B)|product(A,B,A).
% 1.83/2.02 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.83/2.02 ** KEPT (pick-wt=5): 13 [] -defined(a,compose(b,c)).
% 1.83/2.02
% 1.83/2.02 ------------> process sos:
% 1.83/2.02 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.83/2.02 ** KEPT (pick-wt=3): 15 [] identity_map(domain(A)).
% 1.83/2.02 ** KEPT (pick-wt=3): 16 [] identity_map(codomain(A)).
% 1.83/2.02 ** KEPT (pick-wt=4): 17 [] defined(A,domain(A)).
% 1.83/2.02 ** KEPT (pick-wt=4): 18 [] defined(codomain(A),A).
% 1.83/2.02 ** KEPT (pick-wt=5): 19 [] product(A,domain(A),A).
% 1.83/2.02 ** KEPT (pick-wt=5): 20 [] product(codomain(A),A,A).
% 1.83/2.02 ** KEPT (pick-wt=3): 21 [] defined(a,b).
% 1.83/2.02 ** KEPT (pick-wt=3): 22 [] defined(b,c).
% 1.83/2.02 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.83/2.02
% 1.83/2.02 ======= end of input processing =======
% 1.83/2.02
% 1.83/2.02 =========== start of search ===========
% 1.83/2.02
% 1.83/2.02 -------- PROOF --------
% 1.83/2.02
% 1.83/2.02 ----> UNIT CONFLICT at 0.04 sec ----> 741 [binary,740.1,13.1] $F.
% 1.83/2.02
% 1.83/2.02 Length of proof is 6. Level of proof is 4.
% 1.83/2.02
% 1.83/2.02 ---------------- PROOF ----------------
% 1.83/2.02 % SZS status Unsatisfiable
% 1.83/2.02 % SZS output start Refutation
% See solution above
% 1.83/2.02 ------------ end of proof -------------
% 1.83/2.02
% 1.83/2.02
% 1.83/2.02 Search stopped by max_proofs option.
% 1.83/2.02
% 1.83/2.02
% 1.83/2.02 Search stopped by max_proofs option.
% 1.83/2.02
% 1.83/2.02 ============ end of search ============
% 1.83/2.02
% 1.83/2.02 -------------- statistics -------------
% 1.83/2.02 clauses given 68
% 1.83/2.02 clauses generated 1788
% 1.83/2.02 clauses kept 737
% 1.83/2.02 clauses forward subsumed 1445
% 1.83/2.02 clauses back subsumed 6
% 1.83/2.02 Kbytes malloced 2929
% 1.83/2.02
% 1.83/2.02 ----------- times (seconds) -----------
% 1.83/2.02 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.83/2.02 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.83/2.02 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.83/2.02
% 1.83/2.02 That finishes the proof of the theorem.
% 1.83/2.02
% 1.83/2.02 Process 32745 finished Wed Jul 27 01:55:26 2022
% 1.83/2.02 Otter interrupted
% 1.83/2.02 PROOF FOUND
%------------------------------------------------------------------------------