TSTP Solution File: GRP012-3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP012-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 1.64s 1.89s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 14 unt; 0 nHn; 5 RR)
% Number of literals : 25 ( 5 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('GRP012-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP012-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('GRP012-3.p',unknown),
[] ).
cnf(4,axiom,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('GRP012-3.p',unknown),
[] ).
cnf(6,axiom,
product(identity,A,A),
file('GRP012-3.p',unknown),
[] ).
cnf(7,axiom,
product(A,identity,A),
file('GRP012-3.p',unknown),
[] ).
cnf(8,axiom,
product(inverse(A),A,identity),
file('GRP012-3.p',unknown),
[] ).
cnf(9,axiom,
product(A,inverse(A),identity),
file('GRP012-3.p',unknown),
[] ).
cnf(10,axiom,
product(A,B,multiply(A,B)),
file('GRP012-3.p',unknown),
[] ).
cnf(47,plain,
product(multiply(A,B),inverse(B),A),
inference(hyper,[status(thm)],[10,3,9,7]),
[iquote('hyper,10,3,9,7')] ).
cnf(70,plain,
product(A,multiply(inverse(A),B),B),
inference(hyper,[status(thm)],[10,2,9,6]),
[iquote('hyper,10,2,9,6')] ).
cnf(86,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(88,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(123,plain,
product(inverse(multiply(A,B)),A,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[47,2,8,10]),88]),
[iquote('hyper,47,2,8,10,demod,88')] ).
cnf(230,plain,
product(inverse(A),inverse(B),inverse(multiply(B,A))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[123,3,70,7]),86]),
[iquote('hyper,123,3,70,7,demod,86')] ).
cnf(617,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[230,1,10])]),
[iquote('hyper,230,1,10,flip.1')] ).
cnf(619,plain,
$false,
inference(binary,[status(thm)],[617,4]),
[iquote('binary,617.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP012-3 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n010.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 05:12:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.64/1.89 ----- Otter 3.3f, August 2004 -----
% 1.64/1.89 The process was started by sandbox on n010.cluster.edu,
% 1.64/1.89 Wed Jul 27 05:12:40 2022
% 1.64/1.89 The command was "./otter". The process ID is 8025.
% 1.64/1.89
% 1.64/1.89 set(prolog_style_variables).
% 1.64/1.89 set(auto).
% 1.64/1.89 dependent: set(auto1).
% 1.64/1.89 dependent: set(process_input).
% 1.64/1.89 dependent: clear(print_kept).
% 1.64/1.89 dependent: clear(print_new_demod).
% 1.64/1.89 dependent: clear(print_back_demod).
% 1.64/1.89 dependent: clear(print_back_sub).
% 1.64/1.89 dependent: set(control_memory).
% 1.64/1.89 dependent: assign(max_mem, 12000).
% 1.64/1.89 dependent: assign(pick_given_ratio, 4).
% 1.64/1.89 dependent: assign(stats_level, 1).
% 1.64/1.89 dependent: assign(max_seconds, 10800).
% 1.64/1.89 clear(print_given).
% 1.64/1.89
% 1.64/1.89 list(usable).
% 1.64/1.89 0 [] A=A.
% 1.64/1.89 0 [] product(identity,X,X).
% 1.64/1.89 0 [] product(X,identity,X).
% 1.64/1.89 0 [] product(inverse(X),X,identity).
% 1.64/1.89 0 [] product(X,inverse(X),identity).
% 1.64/1.89 0 [] product(X,Y,multiply(X,Y)).
% 1.64/1.89 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.64/1.89 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.64/1.89 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.64/1.89 0 [] inverse(multiply(a,b))!=multiply(inverse(b),inverse(a)).
% 1.64/1.89 end_of_list.
% 1.64/1.89
% 1.64/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.64/1.89
% 1.64/1.89 This is a Horn set with equality. The strategy will be
% 1.64/1.89 Knuth-Bendix and hyper_res, with positive clauses in
% 1.64/1.89 sos and nonpositive clauses in usable.
% 1.64/1.89
% 1.64/1.89 dependent: set(knuth_bendix).
% 1.64/1.89 dependent: set(anl_eq).
% 1.64/1.89 dependent: set(para_from).
% 1.64/1.89 dependent: set(para_into).
% 1.64/1.89 dependent: clear(para_from_right).
% 1.64/1.89 dependent: clear(para_into_right).
% 1.64/1.89 dependent: set(para_from_vars).
% 1.64/1.89 dependent: set(eq_units_both_ways).
% 1.64/1.89 dependent: set(dynamic_demod_all).
% 1.64/1.89 dependent: set(dynamic_demod).
% 1.64/1.89 dependent: set(order_eq).
% 1.64/1.89 dependent: set(back_demod).
% 1.64/1.89 dependent: set(lrpo).
% 1.64/1.89 dependent: set(hyper_res).
% 1.64/1.89 dependent: clear(order_hyper).
% 1.64/1.89
% 1.64/1.89 ------------> process usable:
% 1.64/1.89 ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.64/1.89 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.64/1.89 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.64/1.89 ** KEPT (pick-wt=10): 4 [] inverse(multiply(a,b))!=multiply(inverse(b),inverse(a)).
% 1.64/1.89
% 1.64/1.89 ------------> process sos:
% 1.64/1.89 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.64/1.89 ** KEPT (pick-wt=4): 6 [] product(identity,A,A).
% 1.64/1.89 ** KEPT (pick-wt=4): 7 [] product(A,identity,A).
% 1.64/1.89 ** KEPT (pick-wt=5): 8 [] product(inverse(A),A,identity).
% 1.64/1.89 ** KEPT (pick-wt=5): 9 [] product(A,inverse(A),identity).
% 1.64/1.89 ** KEPT (pick-wt=6): 10 [] product(A,B,multiply(A,B)).
% 1.64/1.89 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.64/1.89
% 1.64/1.89 ======= end of input processing =======
% 1.64/1.89
% 1.64/1.89 =========== start of search ===========
% 1.64/1.89
% 1.64/1.89 -------- PROOF --------
% 1.64/1.89
% 1.64/1.89 ----> UNIT CONFLICT at 0.04 sec ----> 619 [binary,617.1,4.1] $F.
% 1.64/1.89
% 1.64/1.89 Length of proof is 7. Level of proof is 4.
% 1.64/1.89
% 1.64/1.89 ---------------- PROOF ----------------
% 1.64/1.89 % SZS status Unsatisfiable
% 1.64/1.89 % SZS output start Refutation
% See solution above
% 1.64/1.89 ------------ end of proof -------------
% 1.64/1.89
% 1.64/1.89
% 1.64/1.89 Search stopped by max_proofs option.
% 1.64/1.89
% 1.64/1.89
% 1.64/1.89 Search stopped by max_proofs option.
% 1.64/1.89
% 1.64/1.89 ============ end of search ============
% 1.64/1.89
% 1.64/1.89 -------------- statistics -------------
% 1.64/1.89 clauses given 32
% 1.64/1.89 clauses generated 3574
% 1.64/1.89 clauses kept 603
% 1.64/1.89 clauses forward subsumed 3260
% 1.64/1.89 clauses back subsumed 24
% 1.64/1.89 Kbytes malloced 1953
% 1.64/1.89
% 1.64/1.89 ----------- times (seconds) -----------
% 1.64/1.89 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.64/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.64/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.64/1.89
% 1.64/1.89 That finishes the proof of the theorem.
% 1.64/1.89
% 1.64/1.89 Process 8025 finished Wed Jul 27 05:12:41 2022
% 1.64/1.90 Otter interrupted
% 1.64/1.90 PROOF FOUND
%------------------------------------------------------------------------------