TSTP Solution File: CAT002-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 12:47:44 EDT 2022
% Result : Unsatisfiable 2.00s 2.16s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 16 unt; 0 nHn; 22 RR)
% Number of literals : 33 ( 5 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ defined(A,B)
| product(A,B,compose(A,B)) ),
file('CAT002-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| defined(A,B) ),
file('CAT002-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ defined(C,D)
| defined(B,D) ),
file('CAT002-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ product(A,B,C)
| ~ product(C,D,E)
| ~ product(B,D,F)
| product(A,F,E) ),
file('CAT002-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(a,A,B)
| ~ product(a,C,B)
| A = C ),
file('CAT002-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(b,A,B)
| ~ product(b,C,B)
| A = C ),
file('CAT002-1.p',unknown),
[] ).
cnf(15,axiom,
h != g,
file('CAT002-1.p',unknown),
[] ).
cnf(23,axiom,
product(a,b,c),
file('CAT002-1.p',unknown),
[] ).
cnf(24,axiom,
product(c,h,d),
file('CAT002-1.p',unknown),
[] ).
cnf(25,axiom,
product(c,g,d),
file('CAT002-1.p',unknown),
[] ).
cnf(78,plain,
defined(c,h),
inference(hyper,[status(thm)],[24,2]),
[iquote('hyper,24,2')] ).
cnf(89,plain,
defined(b,h),
inference(hyper,[status(thm)],[78,3,23]),
[iquote('hyper,78,3,23')] ).
cnf(112,plain,
product(b,h,compose(b,h)),
inference(hyper,[status(thm)],[89,1]),
[iquote('hyper,89,1')] ).
cnf(120,plain,
defined(c,g),
inference(hyper,[status(thm)],[25,2]),
[iquote('hyper,25,2')] ).
cnf(132,plain,
defined(b,g),
inference(hyper,[status(thm)],[120,3,23]),
[iquote('hyper,120,3,23')] ).
cnf(143,plain,
product(b,g,compose(b,g)),
inference(hyper,[status(thm)],[132,1]),
[iquote('hyper,132,1')] ).
cnf(1325,plain,
product(a,compose(b,h),d),
inference(hyper,[status(thm)],[112,5,23,24]),
[iquote('hyper,112,5,23,24')] ).
cnf(1376,plain,
product(a,compose(b,g),d),
inference(hyper,[status(thm)],[143,5,23,25]),
[iquote('hyper,143,5,23,25')] ).
cnf(1711,plain,
compose(b,h) = compose(b,g),
inference(hyper,[status(thm)],[1376,13,1325]),
[iquote('hyper,1376,13,1325')] ).
cnf(1768,plain,
product(b,h,compose(b,g)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[112]),1711]),
[iquote('back_demod,112,demod,1711')] ).
cnf(1886,plain,
h = g,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1768,14,143])]),
[iquote('hyper,1768,14,143,flip.1')] ).
cnf(1888,plain,
$false,
inference(binary,[status(thm)],[1886,15]),
[iquote('binary,1886.1,15.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : CAT002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 01:54:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.73/1.93 ----- Otter 3.3f, August 2004 -----
% 1.73/1.93 The process was started by sandbox on n003.cluster.edu,
% 1.73/1.93 Wed Jul 27 01:54:41 2022
% 1.73/1.93 The command was "./otter". The process ID is 19257.
% 1.73/1.93
% 1.73/1.93 set(prolog_style_variables).
% 1.73/1.93 set(auto).
% 1.73/1.93 dependent: set(auto1).
% 1.73/1.93 dependent: set(process_input).
% 1.73/1.93 dependent: clear(print_kept).
% 1.73/1.93 dependent: clear(print_new_demod).
% 1.73/1.93 dependent: clear(print_back_demod).
% 1.73/1.93 dependent: clear(print_back_sub).
% 1.73/1.93 dependent: set(control_memory).
% 1.73/1.93 dependent: assign(max_mem, 12000).
% 1.73/1.93 dependent: assign(pick_given_ratio, 4).
% 1.73/1.93 dependent: assign(stats_level, 1).
% 1.73/1.93 dependent: assign(max_seconds, 10800).
% 1.73/1.93 clear(print_given).
% 1.73/1.93
% 1.73/1.93 list(usable).
% 1.73/1.93 0 [] A=A.
% 1.73/1.93 0 [] -defined(X,Y)|product(X,Y,compose(X,Y)).
% 1.73/1.93 0 [] -product(X,Y,Z)|defined(X,Y).
% 1.73/1.93 0 [] -product(X,Y,Xy)| -defined(Xy,Z)|defined(Y,Z).
% 1.73/1.93 0 [] -product(X,Y,Xy)| -product(Y,Z,Yz)| -defined(Xy,Z)|defined(X,Yz).
% 1.73/1.93 0 [] -product(X,Y,Xy)| -product(Xy,Z,Xyz)| -product(Y,Z,Yz)|product(X,Yz,Xyz).
% 1.73/1.93 0 [] -product(Y,Z,Yz)| -defined(X,Yz)|defined(X,Y).
% 1.73/1.93 0 [] -product(Y,Z,Yz)| -product(X,Y,Xy)| -defined(X,Yz)|defined(Xy,Z).
% 1.73/1.93 0 [] -product(Y,Z,Yz)| -product(X,Yz,Xyz)| -product(X,Y,Xy)|product(Xy,Z,Xyz).
% 1.73/1.93 0 [] -defined(X,Y)| -defined(Y,Z)| -identity_map(Y)|defined(X,Z).
% 1.73/1.93 0 [] identity_map(domain(X)).
% 1.73/1.93 0 [] identity_map(codomain(X)).
% 1.73/1.93 0 [] defined(X,domain(X)).
% 1.73/1.93 0 [] defined(codomain(X),X).
% 1.73/1.93 0 [] product(X,domain(X),X).
% 1.73/1.93 0 [] product(codomain(X),X,X).
% 1.73/1.93 0 [] -defined(X,Y)| -identity_map(X)|product(X,Y,Y).
% 1.73/1.93 0 [] -defined(X,Y)| -identity_map(Y)|product(X,Y,X).
% 1.73/1.93 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.73/1.93 0 [] -product(a,X,W)| -product(a,Y,W)|X=Y.
% 1.73/1.93 0 [] -product(b,X,W)| -product(b,Y,W)|X=Y.
% 1.73/1.93 0 [] product(a,b,c).
% 1.73/1.93 0 [] product(c,h,d).
% 1.73/1.93 0 [] product(c,g,d).
% 1.73/1.93 0 [] h!=g.
% 1.73/1.93 end_of_list.
% 1.73/1.93
% 1.73/1.93 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.73/1.93
% 1.73/1.93 This is a Horn set with equality. The strategy will be
% 1.73/1.93 Knuth-Bendix and hyper_res, with positive clauses in
% 1.73/1.93 sos and nonpositive clauses in usable.
% 1.73/1.93
% 1.73/1.93 dependent: set(knuth_bendix).
% 1.73/1.93 dependent: set(anl_eq).
% 1.73/1.93 dependent: set(para_from).
% 1.73/1.93 dependent: set(para_into).
% 1.73/1.93 dependent: clear(para_from_right).
% 1.73/1.93 dependent: clear(para_into_right).
% 1.73/1.93 dependent: set(para_from_vars).
% 1.73/1.93 dependent: set(eq_units_both_ways).
% 1.73/1.93 dependent: set(dynamic_demod_all).
% 1.73/1.93 dependent: set(dynamic_demod).
% 1.73/1.93 dependent: set(order_eq).
% 1.73/1.93 dependent: set(back_demod).
% 1.73/1.93 dependent: set(lrpo).
% 1.73/1.93 dependent: set(hyper_res).
% 1.73/1.93 dependent: clear(order_hyper).
% 1.73/1.93
% 1.73/1.93 ------------> process usable:
% 1.73/1.93 ** KEPT (pick-wt=9): 1 [] -defined(A,B)|product(A,B,compose(A,B)).
% 1.73/1.93 ** KEPT (pick-wt=7): 2 [] -product(A,B,C)|defined(A,B).
% 1.73/1.93 ** KEPT (pick-wt=10): 3 [] -product(A,B,C)| -defined(C,D)|defined(B,D).
% 1.73/1.93 ** KEPT (pick-wt=14): 4 [] -product(A,B,C)| -product(B,D,E)| -defined(C,D)|defined(A,E).
% 1.73/1.93 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(C,D,E)| -product(B,D,F)|product(A,F,E).
% 1.73/1.93 ** KEPT (pick-wt=10): 6 [] -product(A,B,C)| -defined(D,C)|defined(D,A).
% 1.73/1.93 ** KEPT (pick-wt=14): 7 [] -product(A,B,C)| -product(D,A,E)| -defined(D,C)|defined(E,B).
% 1.73/1.93 ** KEPT (pick-wt=16): 8 [] -product(A,B,C)| -product(D,C,E)| -product(D,A,F)|product(F,B,E).
% 1.73/1.93 ** KEPT (pick-wt=11): 9 [] -defined(A,B)| -defined(B,C)| -identity_map(B)|defined(A,C).
% 1.73/1.93 ** KEPT (pick-wt=9): 10 [] -defined(A,B)| -identity_map(A)|product(A,B,B).
% 1.73/1.93 ** KEPT (pick-wt=9): 11 [] -defined(A,B)| -identity_map(B)|product(A,B,A).
% 1.73/1.93 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.73/1.93 ** KEPT (pick-wt=11): 13 [] -product(a,A,B)| -product(a,C,B)|A=C.
% 1.73/1.93 ** KEPT (pick-wt=11): 14 [] -product(b,A,B)| -product(b,C,B)|A=C.
% 1.73/1.93 ** KEPT (pick-wt=3): 15 [] h!=g.
% 1.73/1.93
% 1.73/1.93 ------------> process sos:
% 1.73/1.93 ** KEPT (pick-wt=3): 16 [] A=A.
% 1.73/1.93 ** KEPT (pick-wt=3): 17 [] identity_map(domain(A)).
% 1.73/1.93 ** KEPT (pick-wt=3): 18 [] identity_map(codomain(A)).
% 1.73/1.93 ** KEPT (pick-wt=4): 19 [] defined(A,domain(A)).
% 1.73/1.93 ** KEPT (pick-wt=4): 20 [] defined(codomain(A),A).
% 1.73/1.93 ** KEPT (pick-wt=5): 21 [] product(A,domain(A),A).
% 1.73/1.93 ** KEPT (pick-wt=5): 22 [] product(codomain(A),A,A).
% 1.73/1.93 ** KEPT (pick-wt=4): 23 [] product(a,b,c).
% 1.73/1.93 ** KEPT (pick-wt=4): 24 [] product(c,h,d).
% 1.73/1.93 ** KEPT (pick-wt=4): 25 [] product(c,g,d).
% 1.73/1.93 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 2.00/2.16
% 2.00/2.16 ======= end of input processing =======
% 2.00/2.16
% 2.00/2.16 =========== start of search ===========
% 2.00/2.16
% 2.00/2.16 -------- PROOF --------
% 2.00/2.16
% 2.00/2.16 ----> UNIT CONFLICT at 0.23 sec ----> 1888 [binary,1886.1,15.1] $F.
% 2.00/2.16
% 2.00/2.16 Length of proof is 11. Level of proof is 7.
% 2.00/2.16
% 2.00/2.16 ---------------- PROOF ----------------
% 2.00/2.16 % SZS status Unsatisfiable
% 2.00/2.16 % SZS output start Refutation
% See solution above
% 2.00/2.16 ------------ end of proof -------------
% 2.00/2.16
% 2.00/2.16
% 2.00/2.16 Search stopped by max_proofs option.
% 2.00/2.16
% 2.00/2.16
% 2.00/2.16 Search stopped by max_proofs option.
% 2.00/2.16
% 2.00/2.16 ============ end of search ============
% 2.00/2.16
% 2.00/2.16 -------------- statistics -------------
% 2.00/2.16 clauses given 158
% 2.00/2.16 clauses generated 3637
% 2.00/2.16 clauses kept 1863
% 2.00/2.16 clauses forward subsumed 2310
% 2.00/2.16 clauses back subsumed 23
% 2.00/2.16 Kbytes malloced 2929
% 2.00/2.16
% 2.00/2.16 ----------- times (seconds) -----------
% 2.00/2.16 user CPU time 0.23 (0 hr, 0 min, 0 sec)
% 2.00/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.16 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.00/2.16
% 2.00/2.16 That finishes the proof of the theorem.
% 2.00/2.16
% 2.00/2.16 Process 19257 finished Wed Jul 27 01:54:43 2022
% 2.00/2.16 Otter interrupted
% 2.00/2.16 PROOF FOUND
%------------------------------------------------------------------------------