%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:47:47 EDT 2022
% Result : Unsatisfiable 2.01s 2.19s
% Output : Refutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 17 ( 11 unt; 0 nHn; 15 RR)
% Number of literals : 29 ( 3 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ defined(A,B)
| product(A,B,compose(A,B)) ),
file('CAT009-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ defined(C,D)
| defined(B,D) ),
file('CAT009-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(A,B,C)
| ~ product(D,A,E)
| ~ defined(D,C)
| defined(E,B) ),
file('CAT009-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
file('CAT009-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ defined(A,B)
| ~ identity_map(B)
| product(A,B,A) ),
file('CAT009-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('CAT009-1.p',unknown),
[] ).
cnf(13,axiom,
domain(compose(b,a)) != domain(a),
file('CAT009-1.p',unknown),
[] ).
cnf(15,axiom,
identity_map(domain(A)),
file('CAT009-1.p',unknown),
[] ).
cnf(19,axiom,
product(A,domain(A),A),
file('CAT009-1.p',unknown),
[] ).
cnf(21,axiom,
defined(b,a),
file('CAT009-1.p',unknown),
[] ).
cnf(24,plain,
product(b,a,compose(b,a)),
inference(hyper,[status(thm)],[21,1]),
[iquote('hyper,21,1')] ).
cnf(153,plain,
defined(compose(b,a),domain(a)),
inference(hyper,[status(thm)],[24,7,19,21]),
[iquote('hyper,24,7,19,21')] ).
cnf(425,plain,
defined(domain(compose(b,a)),domain(a)),
inference(hyper,[status(thm)],[153,3,19]),
[iquote('hyper,153,3,19')] ).
cnf(548,plain,
product(domain(compose(b,a)),domain(a),domain(compose(b,a))),
inference(hyper,[status(thm)],[425,11,15]),
[iquote('hyper,425,11,15')] ).
cnf(549,plain,
product(domain(compose(b,a)),domain(a),domain(a)),
inference(hyper,[status(thm)],[425,10,15]),
[iquote('hyper,425,10,15')] ).
cnf(653,plain,
domain(compose(b,a)) = domain(a),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[548,12,549])]),
[iquote('hyper,548,12,549,flip.1')] ).
cnf(655,plain,
$false,
inference(binary,[status(thm)],[653,13]),
[iquote('binary,653.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n026.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 02:12:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.01/2.19 ----- Otter 3.3f, August 2004 -----
% 2.01/2.19 The process was started by sandbox on n026.cluster.edu,
% 2.01/2.19 Wed Jul 27 02:12:39 2022
% 2.01/2.19 The command was "./otter". The process ID is 31325.
% 2.01/2.19
% 2.01/2.19 set(prolog_style_variables).
% 2.01/2.19 set(auto).
% 2.01/2.19 dependent: set(auto1).
% 2.01/2.19 dependent: set(process_input).
% 2.01/2.19 dependent: clear(print_kept).
% 2.01/2.19 dependent: clear(print_new_demod).
% 2.01/2.19 dependent: clear(print_back_demod).
% 2.01/2.19 dependent: clear(print_back_sub).
% 2.01/2.19 dependent: set(control_memory).
% 2.01/2.19 dependent: assign(max_mem, 12000).
% 2.01/2.19 dependent: assign(pick_given_ratio, 4).
% 2.01/2.19 dependent: assign(stats_level, 1).
% 2.01/2.19 dependent: assign(max_seconds, 10800).
% 2.01/2.19 clear(print_given).
% 2.01/2.19
% 2.01/2.19 list(usable).
% 2.01/2.19 0 [] A=A.
% 2.01/2.19 0 [] -defined(X,Y)|product(X,Y,compose(X,Y)).
% 2.01/2.19 0 [] -product(X,Y,Z)|defined(X,Y).
% 2.01/2.19 0 [] -product(X,Y,Xy)| -defined(Xy,Z)|defined(Y,Z).
% 2.01/2.19 0 [] -product(X,Y,Xy)| -product(Y,Z,Yz)| -defined(Xy,Z)|defined(X,Yz).
% 2.01/2.19 0 [] -product(X,Y,Xy)| -product(Xy,Z,Xyz)| -product(Y,Z,Yz)|product(X,Yz,Xyz).
% 2.01/2.19 0 [] -product(Y,Z,Yz)| -defined(X,Yz)|defined(X,Y).
% 2.01/2.19 0 [] -product(Y,Z,Yz)| -product(X,Y,Xy)| -defined(X,Yz)|defined(Xy,Z).
% 2.01/2.19 0 [] -product(Y,Z,Yz)| -product(X,Yz,Xyz)| -product(X,Y,Xy)|product(Xy,Z,Xyz).
% 2.01/2.19 0 [] -defined(X,Y)| -defined(Y,Z)| -identity_map(Y)|defined(X,Z).
% 2.01/2.19 0 [] identity_map(domain(X)).
% 2.01/2.19 0 [] identity_map(codomain(X)).
% 2.01/2.19 0 [] defined(X,domain(X)).
% 2.01/2.19 0 [] defined(codomain(X),X).
% 2.01/2.19 0 [] product(X,domain(X),X).
% 2.01/2.19 0 [] product(codomain(X),X,X).
% 2.01/2.19 0 [] -defined(X,Y)| -identity_map(X)|product(X,Y,Y).
% 2.01/2.19 0 [] -defined(X,Y)| -identity_map(Y)|product(X,Y,X).
% 2.01/2.19 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 2.01/2.19 0 [] defined(b,a).
% 2.01/2.19 0 [] domain(compose(b,a))!=domain(a).
% 2.01/2.19 end_of_list.
% 2.01/2.19
% 2.01/2.19 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 2.01/2.19
% 2.01/2.19 This is a Horn set with equality. The strategy will be
% 2.01/2.19 Knuth-Bendix and hyper_res, with positive clauses in
% 2.01/2.19 sos and nonpositive clauses in usable.
% 2.01/2.19
% 2.01/2.19 dependent: set(knuth_bendix).
% 2.01/2.19 dependent: set(anl_eq).
% 2.01/2.19 dependent: set(para_from).
% 2.01/2.19 dependent: set(para_into).
% 2.01/2.19 dependent: clear(para_from_right).
% 2.01/2.19 dependent: clear(para_into_right).
% 2.01/2.19 dependent: set(para_from_vars).
% 2.01/2.19 dependent: set(eq_units_both_ways).
% 2.01/2.19 dependent: set(dynamic_demod_all).
% 2.01/2.19 dependent: set(dynamic_demod).
% 2.01/2.19 dependent: set(order_eq).
% 2.01/2.19 dependent: set(back_demod).
% 2.01/2.19 dependent: set(lrpo).
% 2.01/2.19 dependent: set(hyper_res).
% 2.01/2.19 dependent: clear(order_hyper).
% 2.01/2.19
% 2.01/2.19 ------------> process usable:
% 2.01/2.19 ** KEPT (pick-wt=9): 1 [] -defined(A,B)|product(A,B,compose(A,B)).
% 2.01/2.19 ** KEPT (pick-wt=7): 2 [] -product(A,B,C)|defined(A,B).
% 2.01/2.19 ** KEPT (pick-wt=10): 3 [] -product(A,B,C)| -defined(C,D)|defined(B,D).
% 2.01/2.19 ** KEPT (pick-wt=14): 4 [] -product(A,B,C)| -product(B,D,E)| -defined(C,D)|defined(A,E).
% 2.01/2.19 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(C,D,E)| -product(B,D,F)|product(A,F,E).
% 2.01/2.19 ** KEPT (pick-wt=10): 6 [] -product(A,B,C)| -defined(D,C)|defined(D,A).
% 2.01/2.19 ** KEPT (pick-wt=14): 7 [] -product(A,B,C)| -product(D,A,E)| -defined(D,C)|defined(E,B).
% 2.01/2.19 ** KEPT (pick-wt=16): 8 [] -product(A,B,C)| -product(D,C,E)| -product(D,A,F)|product(F,B,E).
% 2.01/2.19 ** KEPT (pick-wt=11): 9 [] -defined(A,B)| -defined(B,C)| -identity_map(B)|defined(A,C).
% 2.01/2.19 ** KEPT (pick-wt=9): 10 [] -defined(A,B)| -identity_map(A)|product(A,B,B).
% 2.01/2.19 ** KEPT (pick-wt=9): 11 [] -defined(A,B)| -identity_map(B)|product(A,B,A).
% 2.01/2.19 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 2.01/2.19 ** KEPT (pick-wt=7): 13 [] domain(compose(b,a))!=domain(a).
% 2.01/2.19
% 2.01/2.19 ------------> process sos:
% 2.01/2.19 ** KEPT (pick-wt=3): 14 [] A=A.
% 2.01/2.19 ** KEPT (pick-wt=3): 15 [] identity_map(domain(A)).
% 2.01/2.19 ** KEPT (pick-wt=3): 16 [] identity_map(codomain(A)).
% 2.01/2.19 ** KEPT (pick-wt=4): 17 [] defined(A,domain(A)).
% 2.01/2.19 ** KEPT (pick-wt=4): 18 [] defined(codomain(A),A).
% 2.01/2.19 ** KEPT (pick-wt=5): 19 [] product(A,domain(A),A).
% 2.01/2.19 ** KEPT (pick-wt=5): 20 [] product(codomain(A),A,A).
% 2.01/2.19 ** KEPT (pick-wt=3): 21 [] defined(b,a).
% 2.01/2.19 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 2.01/2.19
% 2.01/2.19 ======= end of input processing =======
% 2.01/2.19
% 2.01/2.19 =========== start of search ===========
% 2.01/2.19
% 2.01/2.19 -------- PROOF --------
% 2.01/2.19
% 2.01/2.19 ----> UNIT CONFLICT at 0.04 sec ----> 655 [binary,653.1,13.1] $F.
% 2.01/2.19
% 2.01/2.19 Length of proof is 6. Level of proof is 5.
% 2.01/2.19
% 2.01/2.19 ---------------- PROOF ----------------
% 2.01/2.19 % SZS status Unsatisfiable
% 2.01/2.19 % SZS output start Refutation
% See solution above
% 2.01/2.19 ------------ end of proof -------------
% 2.01/2.19
% 2.01/2.19
% 2.01/2.19 Search stopped by max_proofs option.
% 2.01/2.19
% 2.01/2.19
% 2.01/2.19 Search stopped by max_proofs option.
% 2.01/2.19
% 2.01/2.19 ============ end of search ============
% 2.01/2.19
% 2.01/2.19 -------------- statistics -------------
% 2.01/2.19 clauses given 89
% 2.01/2.19 clauses generated 2255
% 2.01/2.19 clauses kept 643
% 2.01/2.19 clauses forward subsumed 2021
% 2.01/2.19 clauses back subsumed 12
% 2.01/2.19 Kbytes malloced 1953
% 2.01/2.19
% 2.01/2.19 ----------- times (seconds) -----------
% 2.01/2.19 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 2.01/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.01/2.19 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 2.01/2.19
% 2.01/2.19 That finishes the proof of the theorem.
% 2.01/2.19
% 2.01/2.19 Process 31325 finished Wed Jul 27 02:12:40 2022
% 2.01/2.19 Otter interrupted
% 2.01/2.19 PROOF FOUND
%------------------------------------------------------------------------------