TSTP Solution File: CAT007-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 12:47:46 EDT 2022
% Result : Unsatisfiable 1.71s 1.94s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 8 unt; 0 nHn; 6 RR)
% Number of literals : 12 ( 1 equ; 4 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 6 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
( ~ defined(A,B)
| ~ defined(B,C)
| ~ identity_map(B)
| defined(A,C) ),
file('CAT007-1.p',unknown),
[] ).
cnf(13,axiom,
~ defined(a,b),
file('CAT007-1.p',unknown),
[] ).
cnf(16,axiom,
identity_map(codomain(A)),
file('CAT007-1.p',unknown),
[] ).
cnf(17,axiom,
defined(A,domain(A)),
file('CAT007-1.p',unknown),
[] ).
cnf(18,axiom,
defined(codomain(A),A),
file('CAT007-1.p',unknown),
[] ).
cnf(21,axiom,
domain(a) = codomain(b),
file('CAT007-1.p',unknown),
[] ).
cnf(47,plain,
defined(a,codomain(b)),
inference(para_from,[status(thm),theory(equality)],[21,17]),
[iquote('para_from,21.1.1,17.1.2')] ).
cnf(48,plain,
defined(a,b),
inference(hyper,[status(thm)],[47,9,18,16]),
[iquote('hyper,47,9,18,16')] ).
cnf(49,plain,
$false,
inference(binary,[status(thm)],[48,13]),
[iquote('binary,48.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n016.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 02:22:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.94 ----- Otter 3.3f, August 2004 -----
% 1.71/1.94 The process was started by sandbox on n016.cluster.edu,
% 1.71/1.94 Wed Jul 27 02:22:22 2022
% 1.71/1.94 The command was "./otter". The process ID is 3686.
% 1.71/1.94
% 1.71/1.94 set(prolog_style_variables).
% 1.71/1.94 set(auto).
% 1.71/1.94 dependent: set(auto1).
% 1.71/1.94 dependent: set(process_input).
% 1.71/1.94 dependent: clear(print_kept).
% 1.71/1.94 dependent: clear(print_new_demod).
% 1.71/1.94 dependent: clear(print_back_demod).
% 1.71/1.94 dependent: clear(print_back_sub).
% 1.71/1.94 dependent: set(control_memory).
% 1.71/1.94 dependent: assign(max_mem, 12000).
% 1.71/1.94 dependent: assign(pick_given_ratio, 4).
% 1.71/1.94 dependent: assign(stats_level, 1).
% 1.71/1.94 dependent: assign(max_seconds, 10800).
% 1.71/1.94 clear(print_given).
% 1.71/1.94
% 1.71/1.94 list(usable).
% 1.71/1.94 0 [] A=A.
% 1.71/1.94 0 [] -defined(X,Y)|product(X,Y,compose(X,Y)).
% 1.71/1.94 0 [] -product(X,Y,Z)|defined(X,Y).
% 1.71/1.94 0 [] -product(X,Y,Xy)| -defined(Xy,Z)|defined(Y,Z).
% 1.71/1.94 0 [] -product(X,Y,Xy)| -product(Y,Z,Yz)| -defined(Xy,Z)|defined(X,Yz).
% 1.71/1.94 0 [] -product(X,Y,Xy)| -product(Xy,Z,Xyz)| -product(Y,Z,Yz)|product(X,Yz,Xyz).
% 1.71/1.94 0 [] -product(Y,Z,Yz)| -defined(X,Yz)|defined(X,Y).
% 1.71/1.94 0 [] -product(Y,Z,Yz)| -product(X,Y,Xy)| -defined(X,Yz)|defined(Xy,Z).
% 1.71/1.94 0 [] -product(Y,Z,Yz)| -product(X,Yz,Xyz)| -product(X,Y,Xy)|product(Xy,Z,Xyz).
% 1.71/1.94 0 [] -defined(X,Y)| -defined(Y,Z)| -identity_map(Y)|defined(X,Z).
% 1.71/1.94 0 [] identity_map(domain(X)).
% 1.71/1.94 0 [] identity_map(codomain(X)).
% 1.71/1.94 0 [] defined(X,domain(X)).
% 1.71/1.94 0 [] defined(codomain(X),X).
% 1.71/1.94 0 [] product(X,domain(X),X).
% 1.71/1.94 0 [] product(codomain(X),X,X).
% 1.71/1.94 0 [] -defined(X,Y)| -identity_map(X)|product(X,Y,Y).
% 1.71/1.94 0 [] -defined(X,Y)| -identity_map(Y)|product(X,Y,X).
% 1.71/1.94 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.71/1.94 0 [] domain(a)=codomain(b).
% 1.71/1.94 0 [] -defined(a,b).
% 1.71/1.94 end_of_list.
% 1.71/1.94
% 1.71/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.71/1.94
% 1.71/1.94 This is a Horn set with equality. The strategy will be
% 1.71/1.94 Knuth-Bendix and hyper_res, with positive clauses in
% 1.71/1.94 sos and nonpositive clauses in usable.
% 1.71/1.94
% 1.71/1.94 dependent: set(knuth_bendix).
% 1.71/1.94 dependent: set(anl_eq).
% 1.71/1.94 dependent: set(para_from).
% 1.71/1.94 dependent: set(para_into).
% 1.71/1.94 dependent: clear(para_from_right).
% 1.71/1.94 dependent: clear(para_into_right).
% 1.71/1.94 dependent: set(para_from_vars).
% 1.71/1.94 dependent: set(eq_units_both_ways).
% 1.71/1.94 dependent: set(dynamic_demod_all).
% 1.71/1.94 dependent: set(dynamic_demod).
% 1.71/1.94 dependent: set(order_eq).
% 1.71/1.94 dependent: set(back_demod).
% 1.71/1.94 dependent: set(lrpo).
% 1.71/1.94 dependent: set(hyper_res).
% 1.71/1.94 dependent: clear(order_hyper).
% 1.71/1.94
% 1.71/1.94 ------------> process usable:
% 1.71/1.94 ** KEPT (pick-wt=9): 1 [] -defined(A,B)|product(A,B,compose(A,B)).
% 1.71/1.94 ** KEPT (pick-wt=7): 2 [] -product(A,B,C)|defined(A,B).
% 1.71/1.94 ** KEPT (pick-wt=10): 3 [] -product(A,B,C)| -defined(C,D)|defined(B,D).
% 1.71/1.94 ** KEPT (pick-wt=14): 4 [] -product(A,B,C)| -product(B,D,E)| -defined(C,D)|defined(A,E).
% 1.71/1.94 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(C,D,E)| -product(B,D,F)|product(A,F,E).
% 1.71/1.94 ** KEPT (pick-wt=10): 6 [] -product(A,B,C)| -defined(D,C)|defined(D,A).
% 1.71/1.94 ** KEPT (pick-wt=14): 7 [] -product(A,B,C)| -product(D,A,E)| -defined(D,C)|defined(E,B).
% 1.71/1.94 ** KEPT (pick-wt=16): 8 [] -product(A,B,C)| -product(D,C,E)| -product(D,A,F)|product(F,B,E).
% 1.71/1.94 ** KEPT (pick-wt=11): 9 [] -defined(A,B)| -defined(B,C)| -identity_map(B)|defined(A,C).
% 1.71/1.94 ** KEPT (pick-wt=9): 10 [] -defined(A,B)| -identity_map(A)|product(A,B,B).
% 1.71/1.94 ** KEPT (pick-wt=9): 11 [] -defined(A,B)| -identity_map(B)|product(A,B,A).
% 1.71/1.94 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.71/1.94 ** KEPT (pick-wt=3): 13 [] -defined(a,b).
% 1.71/1.94
% 1.71/1.94 ------------> process sos:
% 1.71/1.94 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.71/1.94 ** KEPT (pick-wt=3): 15 [] identity_map(domain(A)).
% 1.71/1.94 ** KEPT (pick-wt=3): 16 [] identity_map(codomain(A)).
% 1.71/1.94 ** KEPT (pick-wt=4): 17 [] defined(A,domain(A)).
% 1.71/1.94 ** KEPT (pick-wt=4): 18 [] defined(codomain(A),A).
% 1.71/1.94 ** KEPT (pick-wt=5): 19 [] product(A,domain(A),A).
% 1.71/1.94 ** KEPT (pick-wt=5): 20 [] product(codomain(A),A,A).
% 1.71/1.94 ** KEPT (pick-wt=5): 21 [] domain(a)=codomain(b).
% 1.71/1.94 ---> New Demodulator: 22 [new_demod,21] domain(a)=codomain(b).
% 1.71/1.94 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.71/1.94 >>>> Starting back demodulation with 22.
% 1.71/1.94
% 1.71/1.94 ======= end of input processing =======
% 1.71/1.94
% 1.71/1.94 =========== start of search ===========
% 1.71/1.94
% 1.71/1.94 -------- PROOF --------
% 1.71/1.94
% 1.71/1.94 ----> UNIT CONFLICT at 0.00 sec ----> 49 [binary,48.1,13.1] $F.
% 1.71/1.94
% 1.71/1.94 Length of proof is 2. Level of proof is 2.
% 1.71/1.94
% 1.71/1.94 ---------------- PROOF ----------------
% 1.71/1.94 % SZS status Unsatisfiable
% 1.71/1.94 % SZS output start Refutation
% See solution above
% 1.71/1.94 ------------ end of proof -------------
% 1.71/1.94
% 1.71/1.94
% 1.71/1.94 Search stopped by max_proofs option.
% 1.71/1.94
% 1.71/1.94
% 1.71/1.94 Search stopped by max_proofs option.
% 1.71/1.94
% 1.71/1.94 ============ end of search ============
% 1.71/1.94
% 1.71/1.94 -------------- statistics -------------
% 1.71/1.94 clauses given 9
% 1.71/1.94 clauses generated 58
% 1.71/1.94 clauses kept 47
% 1.71/1.94 clauses forward subsumed 33
% 1.71/1.94 clauses back subsumed 0
% 1.71/1.94 Kbytes malloced 976
% 1.71/1.94
% 1.71/1.94 ----------- times (seconds) -----------
% 1.71/1.94 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.71/1.94
% 1.71/1.94 That finishes the proof of the theorem.
% 1.71/1.94
% 1.71/1.94 Process 3686 finished Wed Jul 27 02:22:23 2022
% 1.71/1.94 Otter interrupted
% 1.71/1.94 PROOF FOUND
%------------------------------------------------------------------------------