TSTP Solution File: GRP008-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 12:55:50 EDT 2022
% Result : Unsatisfiable 2.07s 2.23s
% Output : Refutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of clauses : 18 ( 12 unt; 2 nHn; 9 RR)
% Number of literals : 31 ( 4 equ; 11 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 : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('GRP008-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP008-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('GRP008-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ product(j(A),A,h(A))
| ~ product(A,j(A),h(A))
| q(A) ),
file('GRP008-1.p',unknown),
[] ).
cnf(6,axiom,
~ q(identity),
file('GRP008-1.p',unknown),
[] ).
cnf(15,axiom,
product(identity,A,A),
file('GRP008-1.p',unknown),
[] ).
cnf(16,axiom,
product(A,identity,A),
file('GRP008-1.p',unknown),
[] ).
cnf(17,axiom,
product(inverse(A),A,identity),
file('GRP008-1.p',unknown),
[] ).
cnf(18,axiom,
product(A,inverse(A),identity),
file('GRP008-1.p',unknown),
[] ).
cnf(19,axiom,
product(A,B,multiply(A,B)),
file('GRP008-1.p',unknown),
[] ).
cnf(20,axiom,
( product(j(A),A,h(A))
| product(A,j(A),h(A))
| q(A) ),
file('GRP008-1.p',unknown),
[] ).
cnf(87,plain,
product(inverse(A),multiply(A,B),B),
inference(hyper,[status(thm)],[19,2,17,15]),
[iquote('hyper,19,2,17,15')] ).
cnf(100,plain,
multiply(A,identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[19,1,16])]),
[iquote('hyper,19,1,16,flip.1')] ).
cnf(102,plain,
multiply(identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[19,1,15])]),
[iquote('hyper,19,1,15,flip.1')] ).
cnf(122,plain,
( product(j(identity),identity,h(identity))
| product(identity,j(identity),h(identity)) ),
inference(hyper,[status(thm)],[20,6]),
[iquote('hyper,20,6')] ).
cnf(872,plain,
product(identity,j(identity),h(identity)),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[122,3,18,87]),100])]),
[iquote('hyper,122,3,18,87,demod,100,factor_simp')] ).
cnf(909,plain,
j(identity) = h(identity),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[872,1,19]),102]),
[iquote('hyper,872,1,19,demod,102')] ).
cnf(911,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[909,5]),909]),16,15,6]),
[iquote('para_from,908.1.1,5.2.2,demod,909,unit_del,16,15,6')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : GRP008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 05:19:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.07/2.23 ----- Otter 3.3f, August 2004 -----
% 2.07/2.23 The process was started by sandbox on n025.cluster.edu,
% 2.07/2.23 Wed Jul 27 05:19:00 2022
% 2.07/2.23 The command was "./otter". The process ID is 18154.
% 2.07/2.23
% 2.07/2.23 set(prolog_style_variables).
% 2.07/2.23 set(auto).
% 2.07/2.23 dependent: set(auto1).
% 2.07/2.23 dependent: set(process_input).
% 2.07/2.23 dependent: clear(print_kept).
% 2.07/2.23 dependent: clear(print_new_demod).
% 2.07/2.23 dependent: clear(print_back_demod).
% 2.07/2.23 dependent: clear(print_back_sub).
% 2.07/2.23 dependent: set(control_memory).
% 2.07/2.23 dependent: assign(max_mem, 12000).
% 2.07/2.23 dependent: assign(pick_given_ratio, 4).
% 2.07/2.23 dependent: assign(stats_level, 1).
% 2.07/2.23 dependent: assign(max_seconds, 10800).
% 2.07/2.23 clear(print_given).
% 2.07/2.23
% 2.07/2.23 list(usable).
% 2.07/2.23 0 [] A=A.
% 2.07/2.23 0 [] product(identity,X,X).
% 2.07/2.23 0 [] product(X,identity,X).
% 2.07/2.23 0 [] product(inverse(X),X,identity).
% 2.07/2.23 0 [] product(X,inverse(X),identity).
% 2.07/2.23 0 [] product(X,Y,multiply(X,Y)).
% 2.07/2.23 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 2.07/2.23 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 2.07/2.23 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 2.07/2.23 0 [] -q(A)| -product(A,B,C)|product(B,A,C).
% 2.07/2.23 0 [] product(j(A),A,h(A))|product(A,j(A),h(A))|q(A).
% 2.07/2.23 0 [] -product(j(A),A,h(A))| -product(A,j(A),h(A))|q(A).
% 2.07/2.23 0 [] -q(identity).
% 2.07/2.23 end_of_list.
% 2.07/2.23
% 2.07/2.23 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.07/2.23
% 2.07/2.23 This ia a non-Horn set with equality. The strategy will be
% 2.07/2.23 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.07/2.23 deletion, with positive clauses in sos and nonpositive
% 2.07/2.23 clauses in usable.
% 2.07/2.23
% 2.07/2.23 dependent: set(knuth_bendix).
% 2.07/2.23 dependent: set(anl_eq).
% 2.07/2.23 dependent: set(para_from).
% 2.07/2.23 dependent: set(para_into).
% 2.07/2.23 dependent: clear(para_from_right).
% 2.07/2.23 dependent: clear(para_into_right).
% 2.07/2.23 dependent: set(para_from_vars).
% 2.07/2.23 dependent: set(eq_units_both_ways).
% 2.07/2.23 dependent: set(dynamic_demod_all).
% 2.07/2.23 dependent: set(dynamic_demod).
% 2.07/2.23 dependent: set(order_eq).
% 2.07/2.23 dependent: set(back_demod).
% 2.07/2.23 dependent: set(lrpo).
% 2.07/2.23 dependent: set(hyper_res).
% 2.07/2.23 dependent: set(unit_deletion).
% 2.07/2.23 dependent: set(factor).
% 2.07/2.23
% 2.07/2.23 ------------> process usable:
% 2.07/2.23 ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 2.07/2.23 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 2.07/2.23 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 2.07/2.23 ** KEPT (pick-wt=10): 4 [] -q(A)| -product(A,B,C)|product(B,A,C).
% 2.07/2.23 ** KEPT (pick-wt=14): 5 [] -product(j(A),A,h(A))| -product(A,j(A),h(A))|q(A).
% 2.07/2.23 ** KEPT (pick-wt=2): 6 [] -q(identity).
% 2.07/2.23
% 2.07/2.23 ------------> process sos:
% 2.07/2.23 ** KEPT (pick-wt=3): 14 [] A=A.
% 2.07/2.23 ** KEPT (pick-wt=4): 15 [] product(identity,A,A).
% 2.07/2.23 ** KEPT (pick-wt=4): 16 [] product(A,identity,A).
% 2.07/2.23 ** KEPT (pick-wt=5): 17 [] product(inverse(A),A,identity).
% 2.07/2.23 ** KEPT (pick-wt=5): 18 [] product(A,inverse(A),identity).
% 2.07/2.23 ** KEPT (pick-wt=6): 19 [] product(A,B,multiply(A,B)).
% 2.07/2.23 ** KEPT (pick-wt=14): 20 [] product(j(A),A,h(A))|product(A,j(A),h(A))|q(A).
% 2.07/2.23 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 2.07/2.23 14 back subsumes 7.
% 2.07/2.23
% 2.07/2.23 ======= end of input processing =======
% 2.07/2.23
% 2.07/2.23 =========== start of search ===========
% 2.07/2.23
% 2.07/2.23 -------- PROOF --------
% 2.07/2.23
% 2.07/2.23 -----> EMPTY CLAUSE at 0.12 sec ----> 911 [para_from,908.1.1,5.2.2,demod,909,unit_del,16,15,6] $F.
% 2.07/2.23
% 2.07/2.23 Length of proof is 6. Level of proof is 3.
% 2.07/2.23
% 2.07/2.23 ---------------- PROOF ----------------
% 2.07/2.23 % SZS status Unsatisfiable
% 2.07/2.23 % SZS output start Refutation
% See solution above
% 2.07/2.23 ------------ end of proof -------------
% 2.07/2.23
% 2.07/2.23
% 2.07/2.23 Search stopped by max_proofs option.
% 2.07/2.23
% 2.07/2.23
% 2.07/2.23 Search stopped by max_proofs option.
% 2.07/2.23
% 2.07/2.23 ============ end of search ============
% 2.07/2.23
% 2.07/2.23 -------------- statistics -------------
% 2.07/2.23 clauses given 49
% 2.07/2.23 clauses generated 7890
% 2.07/2.23 clauses kept 892
% 2.07/2.23 clauses forward subsumed 7617
% 2.07/2.23 clauses back subsumed 49
% 2.07/2.23 Kbytes malloced 2929
% 2.07/2.23
% 2.07/2.23 ----------- times (seconds) -----------
% 2.07/2.23 user CPU time 0.12 (0 hr, 0 min, 0 sec)
% 2.07/2.23 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.07/2.23 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.07/2.23
% 2.07/2.23 That finishes the proof of the theorem.
% 2.07/2.23
% 2.07/2.23 Process 18154 finished Wed Jul 27 05:19:02 2022
% 2.07/2.23 Otter interrupted
% 2.07/2.23 PROOF FOUND
%------------------------------------------------------------------------------