TSTP Solution File: GRP031-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP031-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 1.90s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 8 unt; 0 nHn; 4 RR)
% Number of literals : 16 ( 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP031-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('GRP031-2.p',unknown),
[] ).
cnf(4,axiom,
~ product(A,a,identity),
file('GRP031-2.p',unknown),
[] ).
cnf(5,axiom,
product(A,B,multiply(A,B)),
file('GRP031-2.p',unknown),
[] ).
cnf(6,axiom,
product(A,inverse(A),identity),
file('GRP031-2.p',unknown),
[] ).
cnf(7,axiom,
product(A,identity,A),
file('GRP031-2.p',unknown),
[] ).
cnf(11,plain,
product(multiply(A,identity),identity,A),
inference(hyper,[status(thm)],[7,3,5,7]),
[iquote('hyper,7,3,5,7')] ).
cnf(23,plain,
product(identity,inverse(inverse(A)),A),
inference(hyper,[status(thm)],[6,3,6,7]),
[iquote('hyper,6,3,6,7')] ).
cnf(811,plain,
product(multiply(inverse(A),identity),A,identity),
inference(hyper,[status(thm)],[23,2,11,6]),
[iquote('hyper,23,2,11,6')] ).
cnf(812,plain,
$false,
inference(binary,[status(thm)],[811,4]),
[iquote('binary,811.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP031-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n024.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 05:35:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.90 ----- Otter 3.3f, August 2004 -----
% 1.67/1.90 The process was started by sandbox on n024.cluster.edu,
% 1.67/1.90 Wed Jul 27 05:35:40 2022
% 1.67/1.90 The command was "./otter". The process ID is 12988.
% 1.67/1.90
% 1.67/1.90 set(prolog_style_variables).
% 1.67/1.90 set(auto).
% 1.67/1.90 dependent: set(auto1).
% 1.67/1.90 dependent: set(process_input).
% 1.67/1.90 dependent: clear(print_kept).
% 1.67/1.90 dependent: clear(print_new_demod).
% 1.67/1.90 dependent: clear(print_back_demod).
% 1.67/1.90 dependent: clear(print_back_sub).
% 1.67/1.90 dependent: set(control_memory).
% 1.67/1.90 dependent: assign(max_mem, 12000).
% 1.67/1.90 dependent: assign(pick_given_ratio, 4).
% 1.67/1.90 dependent: assign(stats_level, 1).
% 1.67/1.90 dependent: assign(max_seconds, 10800).
% 1.67/1.90 clear(print_given).
% 1.67/1.90
% 1.67/1.90 list(usable).
% 1.67/1.90 0 [] product(X,Y,multiply(X,Y)).
% 1.67/1.90 0 [] -product(X,Y,Z)| -product(X,Y,W)|e_qualish(Z,W).
% 1.67/1.90 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.67/1.90 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.67/1.90 0 [] product(A,inverse(A),identity).
% 1.67/1.90 0 [] product(A,identity,A).
% 1.67/1.90 0 [] -product(A,a,identity).
% 1.67/1.90 end_of_list.
% 1.67/1.90
% 1.67/1.90 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.67/1.90
% 1.67/1.90 This is a Horn set without equality. The strategy will
% 1.67/1.90 be hyperresolution, with satellites in sos and nuclei
% 1.67/1.90 in usable.
% 1.67/1.90
% 1.67/1.90 dependent: set(hyper_res).
% 1.67/1.90 dependent: clear(order_hyper).
% 1.67/1.90
% 1.67/1.90 ------------> process usable:
% 1.67/1.90 ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.67/1.90 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.67/1.90 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.67/1.90 ** KEPT (pick-wt=4): 4 [] -product(A,a,identity).
% 1.67/1.90
% 1.67/1.90 ------------> process sos:
% 1.67/1.90 ** KEPT (pick-wt=6): 5 [] product(A,B,multiply(A,B)).
% 1.67/1.90 ** KEPT (pick-wt=5): 6 [] product(A,inverse(A),identity).
% 1.67/1.90 ** KEPT (pick-wt=4): 7 [] product(A,identity,A).
% 1.67/1.90
% 1.67/1.90 ======= end of input processing =======
% 1.67/1.90
% 1.67/1.90 =========== start of search ===========
% 1.67/1.90
% 1.67/1.90 -------- PROOF --------
% 1.67/1.90
% 1.67/1.90 ----> UNIT CONFLICT at 0.02 sec ----> 812 [binary,811.1,4.1] $F.
% 1.67/1.90
% 1.67/1.90 Length of proof is 3. Level of proof is 2.
% 1.67/1.90
% 1.67/1.90 ---------------- PROOF ----------------
% 1.67/1.90 % SZS status Unsatisfiable
% 1.67/1.90 % SZS output start Refutation
% See solution above
% 1.67/1.90 ------------ end of proof -------------
% 1.67/1.90
% 1.67/1.90
% 1.67/1.90 Search stopped by max_proofs option.
% 1.67/1.90
% 1.67/1.90
% 1.67/1.90 Search stopped by max_proofs option.
% 1.67/1.90
% 1.67/1.90 ============ end of search ============
% 1.67/1.90
% 1.67/1.90 -------------- statistics -------------
% 1.67/1.90 clauses given 17
% 1.67/1.90 clauses generated 1536
% 1.67/1.90 clauses kept 811
% 1.67/1.90 clauses forward subsumed 732
% 1.67/1.90 clauses back subsumed 16
% 1.67/1.90 Kbytes malloced 1953
% 1.67/1.90
% 1.67/1.90 ----------- times (seconds) -----------
% 1.67/1.90 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.67/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.90
% 1.67/1.90 That finishes the proof of the theorem.
% 1.67/1.90
% 1.67/1.90 Process 12988 finished Wed Jul 27 05:35:41 2022
% 1.67/1.90 Otter interrupted
% 1.67/1.90 PROOF FOUND
%------------------------------------------------------------------------------