%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT008-1 : TPTP v8.1.0. Released v1.0.0.
% 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 12:47:47 EDT 2022
% Result : Unsatisfiable 1.82s 2.01s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of clauses : 17 ( 12 unt; 0 nHn; 13 RR)
% Number of literals : 27 ( 3 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 20 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ product(A,B,C)
| ~ defined(C,D)
| defined(B,D) ),
file('CAT008-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(A,B,C)
| ~ defined(D,C)
| defined(D,A) ),
file('CAT008-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
file('CAT008-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ defined(A,B)
| ~ identity_map(B)
| product(A,B,A) ),
file('CAT008-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('CAT008-1.p',unknown),
[] ).
cnf(13,axiom,
domain(a) != codomain(b),
file('CAT008-1.p',unknown),
[] ).
cnf(15,axiom,
identity_map(domain(A)),
file('CAT008-1.p',unknown),
[] ).
cnf(16,axiom,
identity_map(codomain(A)),
file('CAT008-1.p',unknown),
[] ).
cnf(19,axiom,
product(A,domain(A),A),
file('CAT008-1.p',unknown),
[] ).
cnf(20,axiom,
product(codomain(A),A,A),
file('CAT008-1.p',unknown),
[] ).
cnf(21,axiom,
defined(a,b),
file('CAT008-1.p',unknown),
[] ).
cnf(40,plain,
defined(domain(a),b),
inference(hyper,[status(thm)],[19,3,21]),
[iquote('hyper,19,3,21')] ).
cnf(51,plain,
defined(domain(a),codomain(b)),
inference(hyper,[status(thm)],[20,6,40]),
[iquote('hyper,20,6,40')] ).
cnf(140,plain,
product(domain(a),codomain(b),domain(a)),
inference(hyper,[status(thm)],[51,11,16]),
[iquote('hyper,51,11,16')] ).
cnf(141,plain,
product(domain(a),codomain(b),codomain(b)),
inference(hyper,[status(thm)],[51,10,15]),
[iquote('hyper,51,10,15')] ).
cnf(521,plain,
domain(a) = codomain(b),
inference(hyper,[status(thm)],[141,12,140]),
[iquote('hyper,141,12,140')] ).
cnf(523,plain,
$false,
inference(binary,[status(thm)],[521,13]),
[iquote('binary,521.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : CAT008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n028.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 02:11:18 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.82/2.01 ----- Otter 3.3f, August 2004 -----
% 1.82/2.01 The process was started by sandbox on n028.cluster.edu,
% 1.82/2.01 Wed Jul 27 02:11:18 2022
% 1.82/2.01 The command was "./otter". The process ID is 22878.
% 1.82/2.01
% 1.82/2.01 set(prolog_style_variables).
% 1.82/2.01 set(auto).
% 1.82/2.01 dependent: set(auto1).
% 1.82/2.01 dependent: set(process_input).
% 1.82/2.01 dependent: clear(print_kept).
% 1.82/2.01 dependent: clear(print_new_demod).
% 1.82/2.01 dependent: clear(print_back_demod).
% 1.82/2.01 dependent: clear(print_back_sub).
% 1.82/2.01 dependent: set(control_memory).
% 1.82/2.01 dependent: assign(max_mem, 12000).
% 1.82/2.01 dependent: assign(pick_given_ratio, 4).
% 1.82/2.01 dependent: assign(stats_level, 1).
% 1.82/2.01 dependent: assign(max_seconds, 10800).
% 1.82/2.01 clear(print_given).
% 1.82/2.01
% 1.82/2.01 list(usable).
% 1.82/2.01 0 [] A=A.
% 1.82/2.01 0 [] -defined(X,Y)|product(X,Y,compose(X,Y)).
% 1.82/2.01 0 [] -product(X,Y,Z)|defined(X,Y).
% 1.82/2.01 0 [] -product(X,Y,Xy)| -defined(Xy,Z)|defined(Y,Z).
% 1.82/2.01 0 [] -product(X,Y,Xy)| -product(Y,Z,Yz)| -defined(Xy,Z)|defined(X,Yz).
% 1.82/2.01 0 [] -product(X,Y,Xy)| -product(Xy,Z,Xyz)| -product(Y,Z,Yz)|product(X,Yz,Xyz).
% 1.82/2.01 0 [] -product(Y,Z,Yz)| -defined(X,Yz)|defined(X,Y).
% 1.82/2.01 0 [] -product(Y,Z,Yz)| -product(X,Y,Xy)| -defined(X,Yz)|defined(Xy,Z).
% 1.82/2.01 0 [] -product(Y,Z,Yz)| -product(X,Yz,Xyz)| -product(X,Y,Xy)|product(Xy,Z,Xyz).
% 1.82/2.01 0 [] -defined(X,Y)| -defined(Y,Z)| -identity_map(Y)|defined(X,Z).
% 1.82/2.01 0 [] identity_map(domain(X)).
% 1.82/2.01 0 [] identity_map(codomain(X)).
% 1.82/2.01 0 [] defined(X,domain(X)).
% 1.82/2.01 0 [] defined(codomain(X),X).
% 1.82/2.01 0 [] product(X,domain(X),X).
% 1.82/2.01 0 [] product(codomain(X),X,X).
% 1.82/2.01 0 [] -defined(X,Y)| -identity_map(X)|product(X,Y,Y).
% 1.82/2.01 0 [] -defined(X,Y)| -identity_map(Y)|product(X,Y,X).
% 1.82/2.01 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.82/2.01 0 [] defined(a,b).
% 1.82/2.01 0 [] domain(a)!=codomain(b).
% 1.82/2.01 end_of_list.
% 1.82/2.01
% 1.82/2.01 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.82/2.01
% 1.82/2.01 This is a Horn set with equality. The strategy will be
% 1.82/2.01 Knuth-Bendix and hyper_res, with positive clauses in
% 1.82/2.01 sos and nonpositive clauses in usable.
% 1.82/2.01
% 1.82/2.01 dependent: set(knuth_bendix).
% 1.82/2.01 dependent: set(anl_eq).
% 1.82/2.01 dependent: set(para_from).
% 1.82/2.01 dependent: set(para_into).
% 1.82/2.01 dependent: clear(para_from_right).
% 1.82/2.01 dependent: clear(para_into_right).
% 1.82/2.01 dependent: set(para_from_vars).
% 1.82/2.01 dependent: set(eq_units_both_ways).
% 1.82/2.01 dependent: set(dynamic_demod_all).
% 1.82/2.01 dependent: set(dynamic_demod).
% 1.82/2.01 dependent: set(order_eq).
% 1.82/2.01 dependent: set(back_demod).
% 1.82/2.01 dependent: set(lrpo).
% 1.82/2.01 dependent: set(hyper_res).
% 1.82/2.01 dependent: clear(order_hyper).
% 1.82/2.01
% 1.82/2.01 ------------> process usable:
% 1.82/2.01 ** KEPT (pick-wt=9): 1 [] -defined(A,B)|product(A,B,compose(A,B)).
% 1.82/2.01 ** KEPT (pick-wt=7): 2 [] -product(A,B,C)|defined(A,B).
% 1.82/2.01 ** KEPT (pick-wt=10): 3 [] -product(A,B,C)| -defined(C,D)|defined(B,D).
% 1.82/2.01 ** KEPT (pick-wt=14): 4 [] -product(A,B,C)| -product(B,D,E)| -defined(C,D)|defined(A,E).
% 1.82/2.01 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(C,D,E)| -product(B,D,F)|product(A,F,E).
% 1.82/2.01 ** KEPT (pick-wt=10): 6 [] -product(A,B,C)| -defined(D,C)|defined(D,A).
% 1.82/2.01 ** KEPT (pick-wt=14): 7 [] -product(A,B,C)| -product(D,A,E)| -defined(D,C)|defined(E,B).
% 1.82/2.01 ** KEPT (pick-wt=16): 8 [] -product(A,B,C)| -product(D,C,E)| -product(D,A,F)|product(F,B,E).
% 1.82/2.01 ** KEPT (pick-wt=11): 9 [] -defined(A,B)| -defined(B,C)| -identity_map(B)|defined(A,C).
% 1.82/2.01 ** KEPT (pick-wt=9): 10 [] -defined(A,B)| -identity_map(A)|product(A,B,B).
% 1.82/2.01 ** KEPT (pick-wt=9): 11 [] -defined(A,B)| -identity_map(B)|product(A,B,A).
% 1.82/2.01 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.82/2.01 ** KEPT (pick-wt=5): 13 [] domain(a)!=codomain(b).
% 1.82/2.01
% 1.82/2.01 ------------> process sos:
% 1.82/2.01 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.82/2.01 ** KEPT (pick-wt=3): 15 [] identity_map(domain(A)).
% 1.82/2.01 ** KEPT (pick-wt=3): 16 [] identity_map(codomain(A)).
% 1.82/2.01 ** KEPT (pick-wt=4): 17 [] defined(A,domain(A)).
% 1.82/2.01 ** KEPT (pick-wt=4): 18 [] defined(codomain(A),A).
% 1.82/2.01 ** KEPT (pick-wt=5): 19 [] product(A,domain(A),A).
% 1.82/2.01 ** KEPT (pick-wt=5): 20 [] product(codomain(A),A,A).
% 1.82/2.01 ** KEPT (pick-wt=3): 21 [] defined(a,b).
% 1.82/2.01 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.82/2.01
% 1.82/2.01 ======= end of input processing =======
% 1.82/2.01
% 1.82/2.01 =========== start of search ===========
% 1.82/2.01
% 1.82/2.01 -------- PROOF --------
% 1.82/2.01
% 1.82/2.01 ----> UNIT CONFLICT at 0.03 sec ----> 523 [binary,521.1,13.1] $F.
% 1.82/2.01
% 1.82/2.01 Length of proof is 5. Level of proof is 4.
% 1.82/2.01
% 1.82/2.01 ---------------- PROOF ----------------
% 1.82/2.01 % SZS status Unsatisfiable
% 1.82/2.01 % SZS output start Refutation
% See solution above
% 1.82/2.01 ------------ end of proof -------------
% 1.82/2.01
% 1.82/2.01
% 1.82/2.01 Search stopped by max_proofs option.
% 1.82/2.01
% 1.82/2.01
% 1.82/2.01 Search stopped by max_proofs option.
% 1.82/2.01
% 1.82/2.01 ============ end of search ============
% 1.82/2.01
% 1.82/2.01 -------------- statistics -------------
% 1.82/2.01 clauses given 65
% 1.82/2.01 clauses generated 1632
% 1.82/2.01 clauses kept 514
% 1.82/2.01 clauses forward subsumed 1490
% 1.82/2.01 clauses back subsumed 5
% 1.82/2.01 Kbytes malloced 1953
% 1.82/2.01
% 1.82/2.01 ----------- times (seconds) -----------
% 1.82/2.01 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.82/2.01 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.01 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/2.01
% 1.82/2.01 That finishes the proof of the theorem.
% 1.82/2.01
% 1.82/2.01 Process 22878 finished Wed Jul 27 02:11:20 2022
% 1.82/2.01 Otter interrupted
% 1.82/2.01 PROOF FOUND
%------------------------------------------------------------------------------