TSTP Solution File: GRP037-3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 12:55:56 EDT 2022
% Result : Unsatisfiable 1.70s 1.94s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 17 ( 4 equ; 5 neg)
% Maximal clause size : 3 ( 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; 3 con; 0-1 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( ~ subgroup_member(A)
| product(A,another_identity,A) ),
file('GRP037-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ subgroup_member(A)
| product(A,another_inverse(A),another_identity) ),
file('GRP037-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| D = B ),
file('GRP037-3.p',unknown),
[] ).
cnf(12,axiom,
inverse(a) != another_inverse(a),
file('GRP037-3.p',unknown),
[] ).
cnf(15,axiom,
product(A,identity,A),
file('GRP037-3.p',unknown),
[] ).
cnf(17,axiom,
product(A,inverse(A),identity),
file('GRP037-3.p',unknown),
[] ).
cnf(19,axiom,
subgroup_member(a),
file('GRP037-3.p',unknown),
[] ).
cnf(23,plain,
product(a,another_inverse(a),another_identity),
inference(hyper,[status(thm)],[19,7]),
[iquote('hyper,19,7')] ).
cnf(24,plain,
product(a,another_identity,a),
inference(hyper,[status(thm)],[19,6]),
[iquote('hyper,19,6')] ).
cnf(65,plain,
identity = another_identity,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[24,10,15])]),
[iquote('hyper,24,10,15,flip.1')] ).
cnf(72,plain,
product(A,inverse(A),another_identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),65]),
[iquote('back_demod,17,demod,65')] ).
cnf(455,plain,
inverse(a) = another_inverse(a),
inference(hyper,[status(thm)],[72,10,23]),
[iquote('hyper,72,10,23')] ).
cnf(457,plain,
$false,
inference(binary,[status(thm)],[455,12]),
[iquote('binary,455.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.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 05:30:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.94 ----- Otter 3.3f, August 2004 -----
% 1.70/1.94 The process was started by sandbox on n004.cluster.edu,
% 1.70/1.94 Wed Jul 27 05:30:51 2022
% 1.70/1.94 The command was "./otter". The process ID is 12511.
% 1.70/1.94
% 1.70/1.94 set(prolog_style_variables).
% 1.70/1.94 set(auto).
% 1.70/1.94 dependent: set(auto1).
% 1.70/1.94 dependent: set(process_input).
% 1.70/1.94 dependent: clear(print_kept).
% 1.70/1.94 dependent: clear(print_new_demod).
% 1.70/1.94 dependent: clear(print_back_demod).
% 1.70/1.94 dependent: clear(print_back_sub).
% 1.70/1.94 dependent: set(control_memory).
% 1.70/1.94 dependent: assign(max_mem, 12000).
% 1.70/1.94 dependent: assign(pick_given_ratio, 4).
% 1.70/1.94 dependent: assign(stats_level, 1).
% 1.70/1.94 dependent: assign(max_seconds, 10800).
% 1.70/1.94 clear(print_given).
% 1.70/1.94
% 1.70/1.94 list(usable).
% 1.70/1.94 0 [] A=A.
% 1.70/1.94 0 [] product(identity,X,X).
% 1.70/1.94 0 [] product(X,identity,X).
% 1.70/1.94 0 [] product(inverse(X),X,identity).
% 1.70/1.94 0 [] product(X,inverse(X),identity).
% 1.70/1.94 0 [] product(X,Y,multiply(X,Y)).
% 1.70/1.94 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.70/1.94 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.70/1.94 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.70/1.94 0 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.70/1.94 0 [] -subgroup_member(A)|product(another_identity,A,A).
% 1.70/1.94 0 [] -subgroup_member(A)|product(A,another_identity,A).
% 1.70/1.94 0 [] -subgroup_member(A)|product(A,another_inverse(A),another_identity).
% 1.70/1.94 0 [] -subgroup_member(A)|product(another_inverse(A),A,another_identity).
% 1.70/1.94 0 [] -subgroup_member(A)|subgroup_member(another_inverse(A)).
% 1.70/1.94 0 [] -product(A,B,C)| -product(A,D,C)|D=B.
% 1.70/1.94 0 [] -product(A,B,C)| -product(D,B,C)|D=A.
% 1.70/1.94 0 [] subgroup_member(a).
% 1.70/1.94 0 [] subgroup_member(another_identity).
% 1.70/1.94 0 [] inverse(a)!=another_inverse(a).
% 1.70/1.94 end_of_list.
% 1.70/1.94
% 1.70/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.70/1.94
% 1.70/1.94 This is a Horn set with equality. The strategy will be
% 1.70/1.94 Knuth-Bendix and hyper_res, with positive clauses in
% 1.70/1.94 sos and nonpositive clauses in usable.
% 1.70/1.94
% 1.70/1.94 dependent: set(knuth_bendix).
% 1.70/1.94 dependent: set(anl_eq).
% 1.70/1.94 dependent: set(para_from).
% 1.70/1.94 dependent: set(para_into).
% 1.70/1.94 dependent: clear(para_from_right).
% 1.70/1.94 dependent: clear(para_into_right).
% 1.70/1.94 dependent: set(para_from_vars).
% 1.70/1.94 dependent: set(eq_units_both_ways).
% 1.70/1.94 dependent: set(dynamic_demod_all).
% 1.70/1.94 dependent: set(dynamic_demod).
% 1.70/1.94 dependent: set(order_eq).
% 1.70/1.94 dependent: set(back_demod).
% 1.70/1.94 dependent: set(lrpo).
% 1.70/1.94 dependent: set(hyper_res).
% 1.70/1.94 dependent: clear(order_hyper).
% 1.70/1.94
% 1.70/1.94 ------------> process usable:
% 1.70/1.94 ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.70/1.94 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.70/1.94 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.70/1.94 ** KEPT (pick-wt=11): 4 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.70/1.94 ** KEPT (pick-wt=6): 5 [] -subgroup_member(A)|product(another_identity,A,A).
% 1.70/1.94 ** KEPT (pick-wt=6): 6 [] -subgroup_member(A)|product(A,another_identity,A).
% 1.70/1.94 ** KEPT (pick-wt=7): 7 [] -subgroup_member(A)|product(A,another_inverse(A),another_identity).
% 1.70/1.94 ** KEPT (pick-wt=7): 8 [] -subgroup_member(A)|product(another_inverse(A),A,another_identity).
% 1.70/1.94 ** KEPT (pick-wt=5): 9 [] -subgroup_member(A)|subgroup_member(another_inverse(A)).
% 1.70/1.94 ** KEPT (pick-wt=11): 10 [] -product(A,B,C)| -product(A,D,C)|D=B.
% 1.70/1.94 ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(D,B,C)|D=A.
% 1.70/1.94 ** KEPT (pick-wt=5): 12 [] inverse(a)!=another_inverse(a).
% 1.70/1.94
% 1.70/1.94 ------------> process sos:
% 1.70/1.94 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.70/1.94 ** KEPT (pick-wt=4): 14 [] product(identity,A,A).
% 1.70/1.94 ** KEPT (pick-wt=4): 15 [] product(A,identity,A).
% 1.70/1.94 ** KEPT (pick-wt=5): 16 [] product(inverse(A),A,identity).
% 1.70/1.94 ** KEPT (pick-wt=5): 17 [] product(A,inverse(A),identity).
% 1.70/1.94 ** KEPT (pick-wt=6): 18 [] product(A,B,multiply(A,B)).
% 1.70/1.94 ** KEPT (pick-wt=2): 19 [] subgroup_member(a).
% 1.70/1.94 ** KEPT (pick-wt=2): 20 [] subgroup_member(another_identity).
% 1.70/1.94 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.70/1.94
% 1.70/1.94 ======= end of input processing =======
% 1.70/1.94
% 1.70/1.94 =========== start of search ===========
% 1.70/1.94
% 1.70/1.94 -------- PROOF --------
% 1.70/1.94
% 1.70/1.94 ----> UNIT CONFLICT at 0.02 sec ----> 457 [binary,455.1,12.1] $F.
% 1.70/1.94
% 1.70/1.94 Length of proof is 5. Level of proof is 4.
% 1.70/1.94
% 1.70/1.94 ---------------- PROOF ----------------
% 1.70/1.94 % SZS status Unsatisfiable
% 1.70/1.94 % SZS output start Refutation
% See solution above
% 1.70/1.94 ------------ end of proof -------------
% 1.70/1.94
% 1.70/1.94
% 1.70/1.94 Search stopped by max_proofs option.
% 1.70/1.94
% 1.70/1.94
% 1.70/1.94 Search stopped by max_proofs option.
% 1.70/1.94
% 1.70/1.94 ============ end of search ============
% 1.70/1.94
% 1.70/1.94 -------------- statistics -------------
% 1.70/1.94 clauses given 28
% 1.70/1.94 clauses generated 744
% 1.70/1.94 clauses kept 448
% 1.70/1.94 clauses forward subsumed 442
% 1.70/1.94 clauses back subsumed 10
% 1.70/1.94 Kbytes malloced 1953
% 1.70/1.94
% 1.70/1.94 ----------- times (seconds) -----------
% 1.70/1.94 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.70/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.70/1.94
% 1.70/1.94 That finishes the proof of the theorem.
% 1.70/1.94
% 1.70/1.94 Process 12511 finished Wed Jul 27 05:30:52 2022
% 1.70/1.94 Otter interrupted
% 1.70/1.94 PROOF FOUND
%------------------------------------------------------------------------------