TSTP Solution File: GRP031-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP031-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 12:55:55 EDT 2022
% Result : Unsatisfiable 1.67s 1.88s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 6 unt; 0 nHn; 4 RR)
% Number of literals : 14 ( 0 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 17 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP031-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('GRP031-1.p',unknown),
[] ).
cnf(4,axiom,
~ product(a,A,identity),
file('GRP031-1.p',unknown),
[] ).
cnf(7,axiom,
product(identity,A,A),
file('GRP031-1.p',unknown),
[] ).
cnf(8,axiom,
product(inverse(A),A,identity),
file('GRP031-1.p',unknown),
[] ).
cnf(10,plain,
product(inverse(inverse(A)),identity,A),
inference(hyper,[status(thm)],[8,2,8,7]),
[iquote('hyper,8,2,8,7')] ).
cnf(58,plain,
product(A,inverse(A),identity),
inference(hyper,[status(thm)],[10,3,7,8]),
[iquote('hyper,10,3,7,8')] ).
cnf(59,plain,
$false,
inference(binary,[status(thm)],[58,4]),
[iquote('binary,58.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP031-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 05:27:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.88 ----- Otter 3.3f, August 2004 -----
% 1.67/1.88 The process was started by sandbox on n019.cluster.edu,
% 1.67/1.88 Wed Jul 27 05:27:22 2022
% 1.67/1.88 The command was "./otter". The process ID is 19324.
% 1.67/1.88
% 1.67/1.88 set(prolog_style_variables).
% 1.67/1.88 set(auto).
% 1.67/1.88 dependent: set(auto1).
% 1.67/1.88 dependent: set(process_input).
% 1.67/1.88 dependent: clear(print_kept).
% 1.67/1.88 dependent: clear(print_new_demod).
% 1.67/1.88 dependent: clear(print_back_demod).
% 1.67/1.88 dependent: clear(print_back_sub).
% 1.67/1.88 dependent: set(control_memory).
% 1.67/1.88 dependent: assign(max_mem, 12000).
% 1.67/1.88 dependent: assign(pick_given_ratio, 4).
% 1.67/1.88 dependent: assign(stats_level, 1).
% 1.67/1.88 dependent: assign(max_seconds, 10800).
% 1.67/1.88 clear(print_given).
% 1.67/1.88
% 1.67/1.88 list(usable).
% 1.67/1.88 0 [] A=A.
% 1.67/1.88 0 [] product(X,Y,multiply(X,Y)).
% 1.67/1.88 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.67/1.88 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.67/1.88 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.67/1.88 0 [] product(identity,A,A).
% 1.67/1.88 0 [] product(inverse(A),A,identity).
% 1.67/1.88 0 [] -product(a,A,identity).
% 1.67/1.88 end_of_list.
% 1.67/1.88
% 1.67/1.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.67/1.88
% 1.67/1.88 This is a Horn set with equality. The strategy will be
% 1.67/1.88 Knuth-Bendix and hyper_res, with positive clauses in
% 1.67/1.88 sos and nonpositive clauses in usable.
% 1.67/1.88
% 1.67/1.88 dependent: set(knuth_bendix).
% 1.67/1.88 dependent: set(anl_eq).
% 1.67/1.88 dependent: set(para_from).
% 1.67/1.88 dependent: set(para_into).
% 1.67/1.88 dependent: clear(para_from_right).
% 1.67/1.88 dependent: clear(para_into_right).
% 1.67/1.88 dependent: set(para_from_vars).
% 1.67/1.88 dependent: set(eq_units_both_ways).
% 1.67/1.88 dependent: set(dynamic_demod_all).
% 1.67/1.88 dependent: set(dynamic_demod).
% 1.67/1.88 dependent: set(order_eq).
% 1.67/1.88 dependent: set(back_demod).
% 1.67/1.88 dependent: set(lrpo).
% 1.67/1.88 dependent: set(hyper_res).
% 1.67/1.88 dependent: clear(order_hyper).
% 1.67/1.88
% 1.67/1.88 ------------> process usable:
% 1.67/1.88 ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.67/1.88 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.67/1.88 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.67/1.88 ** KEPT (pick-wt=4): 4 [] -product(a,A,identity).
% 1.67/1.88
% 1.67/1.88 ------------> process sos:
% 1.67/1.88 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.67/1.88 ** KEPT (pick-wt=6): 6 [] product(A,B,multiply(A,B)).
% 1.67/1.88 ** KEPT (pick-wt=4): 7 [] product(identity,A,A).
% 1.67/1.88 ** KEPT (pick-wt=5): 8 [] product(inverse(A),A,identity).
% 1.67/1.88 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.67/1.88
% 1.67/1.88 ======= end of input processing =======
% 1.67/1.88
% 1.67/1.88 =========== start of search ===========
% 1.67/1.88
% 1.67/1.88 -------- PROOF --------
% 1.67/1.88
% 1.67/1.88 ----> UNIT CONFLICT at 0.00 sec ----> 59 [binary,58.1,4.1] $F.
% 1.67/1.88
% 1.67/1.88 Length of proof is 2. Level of proof is 2.
% 1.67/1.88
% 1.67/1.88 ---------------- PROOF ----------------
% 1.67/1.88 % SZS status Unsatisfiable
% 1.67/1.88 % SZS output start Refutation
% See solution above
% 1.67/1.88 ------------ end of proof -------------
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88 ============ end of search ============
% 1.67/1.88
% 1.67/1.88 -------------- statistics -------------
% 1.67/1.88 clauses given 9
% 1.67/1.88 clauses generated 163
% 1.67/1.88 clauses kept 55
% 1.67/1.88 clauses forward subsumed 135
% 1.67/1.88 clauses back subsumed 0
% 1.67/1.88 Kbytes malloced 976
% 1.67/1.88
% 1.67/1.88 ----------- times (seconds) -----------
% 1.67/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.88 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.88
% 1.67/1.88 That finishes the proof of the theorem.
% 1.67/1.88
% 1.67/1.88 Process 19324 finished Wed Jul 27 05:27:23 2022
% 1.67/1.88 Otter interrupted
% 1.67/1.88 PROOF FOUND
%------------------------------------------------------------------------------