TSTP Solution File: GRP012-2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP012-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 12:55:51 EDT 2022
% Result : Unsatisfiable 1.92s 2.08s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of clauses : 19 ( 16 unt; 0 nHn; 11 RR)
% Number of literals : 27 ( 6 equ; 9 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('GRP012-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP012-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('GRP012-2.p',unknown),
[] ).
cnf(4,axiom,
inverse(c) != d,
file('GRP012-2.p',unknown),
[] ).
cnf(6,axiom,
product(identity,A,A),
file('GRP012-2.p',unknown),
[] ).
cnf(7,axiom,
product(A,identity,A),
file('GRP012-2.p',unknown),
[] ).
cnf(8,axiom,
product(inverse(A),A,identity),
file('GRP012-2.p',unknown),
[] ).
cnf(9,axiom,
product(A,inverse(A),identity),
file('GRP012-2.p',unknown),
[] ).
cnf(10,axiom,
product(A,B,multiply(A,B)),
file('GRP012-2.p',unknown),
[] ).
cnf(11,axiom,
product(a,b,c),
file('GRP012-2.p',unknown),
[] ).
cnf(12,axiom,
product(inverse(b),inverse(a),d),
file('GRP012-2.p',unknown),
[] ).
cnf(22,plain,
product(inverse(a),c,b),
inference(hyper,[status(thm)],[8,2,11,6]),
[iquote('hyper,8,2,11,6')] ).
cnf(171,plain,
multiply(inverse(A),A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[10,1,8])]),
[iquote('hyper,10,1,8,flip.1')] ).
cnf(173,plain,
multiply(A,identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[10,1,7])]),
[iquote('hyper,10,1,7,flip.1')] ).
cnf(175,plain,
multiply(identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[10,1,6])]),
[iquote('hyper,10,1,6,flip.1')] ).
cnf(183,plain,
product(d,c,identity),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[12,3,22,10]),171]),
[iquote('hyper,12,3,22,10,demod,171')] ).
cnf(212,plain,
product(identity,inverse(c),d),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[183,3,9,10]),173]),
[iquote('hyper,183,3,9,10,demod,173')] ).
cnf(360,plain,
inverse(c) = d,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[212,1,10]),175]),
[iquote('hyper,212,1,10,demod,175')] ).
cnf(362,plain,
$false,
inference(binary,[status(thm)],[360,4]),
[iquote('binary,360.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : GRP012-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 05:26:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.92/2.08 ----- Otter 3.3f, August 2004 -----
% 1.92/2.08 The process was started by sandbox2 on n011.cluster.edu,
% 1.92/2.08 Wed Jul 27 05:26:40 2022
% 1.92/2.08 The command was "./otter". The process ID is 31769.
% 1.92/2.08
% 1.92/2.08 set(prolog_style_variables).
% 1.92/2.08 set(auto).
% 1.92/2.08 dependent: set(auto1).
% 1.92/2.08 dependent: set(process_input).
% 1.92/2.08 dependent: clear(print_kept).
% 1.92/2.08 dependent: clear(print_new_demod).
% 1.92/2.08 dependent: clear(print_back_demod).
% 1.92/2.08 dependent: clear(print_back_sub).
% 1.92/2.08 dependent: set(control_memory).
% 1.92/2.08 dependent: assign(max_mem, 12000).
% 1.92/2.08 dependent: assign(pick_given_ratio, 4).
% 1.92/2.08 dependent: assign(stats_level, 1).
% 1.92/2.08 dependent: assign(max_seconds, 10800).
% 1.92/2.08 clear(print_given).
% 1.92/2.08
% 1.92/2.08 list(usable).
% 1.92/2.08 0 [] A=A.
% 1.92/2.08 0 [] product(identity,X,X).
% 1.92/2.08 0 [] product(X,identity,X).
% 1.92/2.08 0 [] product(inverse(X),X,identity).
% 1.92/2.08 0 [] product(X,inverse(X),identity).
% 1.92/2.08 0 [] product(X,Y,multiply(X,Y)).
% 1.92/2.08 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.92/2.08 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.92/2.08 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.92/2.08 0 [] product(a,b,c).
% 1.92/2.08 0 [] product(inverse(b),inverse(a),d).
% 1.92/2.08 0 [] inverse(c)!=d.
% 1.92/2.08 end_of_list.
% 1.92/2.08
% 1.92/2.08 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.92/2.08
% 1.92/2.08 This is a Horn set with equality. The strategy will be
% 1.92/2.08 Knuth-Bendix and hyper_res, with positive clauses in
% 1.92/2.08 sos and nonpositive clauses in usable.
% 1.92/2.08
% 1.92/2.08 dependent: set(knuth_bendix).
% 1.92/2.08 dependent: set(anl_eq).
% 1.92/2.08 dependent: set(para_from).
% 1.92/2.08 dependent: set(para_into).
% 1.92/2.08 dependent: clear(para_from_right).
% 1.92/2.08 dependent: clear(para_into_right).
% 1.92/2.08 dependent: set(para_from_vars).
% 1.92/2.08 dependent: set(eq_units_both_ways).
% 1.92/2.08 dependent: set(dynamic_demod_all).
% 1.92/2.08 dependent: set(dynamic_demod).
% 1.92/2.08 dependent: set(order_eq).
% 1.92/2.08 dependent: set(back_demod).
% 1.92/2.08 dependent: set(lrpo).
% 1.92/2.08 dependent: set(hyper_res).
% 1.92/2.08 dependent: clear(order_hyper).
% 1.92/2.08
% 1.92/2.08 ------------> process usable:
% 1.92/2.08 ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.92/2.08 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.92/2.08 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.92/2.08 ** KEPT (pick-wt=4): 4 [] inverse(c)!=d.
% 1.92/2.08
% 1.92/2.08 ------------> process sos:
% 1.92/2.08 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.92/2.08 ** KEPT (pick-wt=4): 6 [] product(identity,A,A).
% 1.92/2.08 ** KEPT (pick-wt=4): 7 [] product(A,identity,A).
% 1.92/2.08 ** KEPT (pick-wt=5): 8 [] product(inverse(A),A,identity).
% 1.92/2.08 ** KEPT (pick-wt=5): 9 [] product(A,inverse(A),identity).
% 1.92/2.08 ** KEPT (pick-wt=6): 10 [] product(A,B,multiply(A,B)).
% 1.92/2.08 ** KEPT (pick-wt=4): 11 [] product(a,b,c).
% 1.92/2.08 ** KEPT (pick-wt=6): 12 [] product(inverse(b),inverse(a),d).
% 1.92/2.08 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.92/2.08
% 1.92/2.08 ======= end of input processing =======
% 1.92/2.08
% 1.92/2.08 =========== start of search ===========
% 1.92/2.08
% 1.92/2.08 -------- PROOF --------
% 1.92/2.08
% 1.92/2.08 ----> UNIT CONFLICT at 0.01 sec ----> 362 [binary,360.1,4.1] $F.
% 1.92/2.08
% 1.92/2.08 Length of proof is 7. Level of proof is 4.
% 1.92/2.08
% 1.92/2.08 ---------------- PROOF ----------------
% 1.92/2.08 % SZS status Unsatisfiable
% 1.92/2.08 % SZS output start Refutation
% See solution above
% 1.92/2.08 ------------ end of proof -------------
% 1.92/2.08
% 1.92/2.08
% 1.92/2.08 Search stopped by max_proofs option.
% 1.92/2.08
% 1.92/2.08
% 1.92/2.08 Search stopped by max_proofs option.
% 1.92/2.08
% 1.92/2.08 ============ end of search ============
% 1.92/2.08
% 1.92/2.08 -------------- statistics -------------
% 1.92/2.08 clauses given 23
% 1.92/2.08 clauses generated 844
% 1.92/2.09 clauses kept 342
% 1.92/2.09 clauses forward subsumed 714
% 1.92/2.09 clauses back subsumed 7
% 1.92/2.09 Kbytes malloced 976
% 1.92/2.09
% 1.92/2.09 ----------- times (seconds) -----------
% 1.92/2.09 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.92/2.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.09 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.92/2.09
% 1.92/2.09 That finishes the proof of the theorem.
% 1.92/2.09
% 1.92/2.09 Process 31769 finished Wed Jul 27 05:26:42 2022
% 1.92/2.09 Otter interrupted
% 1.92/2.09 PROOF FOUND
%------------------------------------------------------------------------------