TSTP Solution File: GRP186-3 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP186-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:56:41 EDT 2022
% Result : Unsatisfiable 2.01s 2.19s
% Output : Refutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 5 RR)
% Number of literals : 13 ( 12 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)),
file('GRP186-3.p',unknown),
[] ).
cnf(2,plain,
multiply(a,least_upper_bound(inverse(a),b)) != least_upper_bound(multiply(a,b),identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(5,axiom,
multiply(identity,A) = A,
file('GRP186-3.p',unknown),
[] ).
cnf(6,axiom,
multiply(inverse(A),A) = identity,
file('GRP186-3.p',unknown),
[] ).
cnf(8,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP186-3.p',unknown),
[] ).
cnf(11,axiom,
least_upper_bound(A,B) = least_upper_bound(B,A),
file('GRP186-3.p',unknown),
[] ).
cnf(27,axiom,
multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)),
file('GRP186-3.p',unknown),
[] ).
cnf(34,plain,
least_upper_bound(multiply(a,inverse(a)),multiply(a,b)) != least_upper_bound(multiply(a,b),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),27]),
[iquote('back_demod,2,demod,27')] ).
cnf(35,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,6]),5])]),
[iquote('para_into,8.1.1.1,6.1.1,demod,5,flip.1')] ).
cnf(105,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[35,35]),
[iquote('para_into,35.1.1.2,35.1.1')] ).
cnf(195,plain,
multiply(A,inverse(A)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[105,6])]),
[iquote('para_into,105.1.1,6.1.1,flip.1')] ).
cnf(196,plain,
least_upper_bound(multiply(a,b),identity) != least_upper_bound(identity,multiply(a,b)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[34]),195])]),
[iquote('back_demod,34,demod,195,flip.1')] ).
cnf(197,plain,
$false,
inference(binary,[status(thm)],[196,11]),
[iquote('binary,196.1,11.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP186-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 05:10:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.01/2.19 ----- Otter 3.3f, August 2004 -----
% 2.01/2.19 The process was started by sandbox2 on n026.cluster.edu,
% 2.01/2.19 Wed Jul 27 05:10:39 2022
% 2.01/2.19 The command was "./otter". The process ID is 12708.
% 2.01/2.19
% 2.01/2.19 set(prolog_style_variables).
% 2.01/2.19 set(auto).
% 2.01/2.19 dependent: set(auto1).
% 2.01/2.19 dependent: set(process_input).
% 2.01/2.19 dependent: clear(print_kept).
% 2.01/2.19 dependent: clear(print_new_demod).
% 2.01/2.19 dependent: clear(print_back_demod).
% 2.01/2.19 dependent: clear(print_back_sub).
% 2.01/2.19 dependent: set(control_memory).
% 2.01/2.19 dependent: assign(max_mem, 12000).
% 2.01/2.19 dependent: assign(pick_given_ratio, 4).
% 2.01/2.19 dependent: assign(stats_level, 1).
% 2.01/2.19 dependent: assign(max_seconds, 10800).
% 2.01/2.19 clear(print_given).
% 2.01/2.19
% 2.01/2.19 list(usable).
% 2.01/2.19 0 [] A=A.
% 2.01/2.19 0 [] multiply(identity,X)=X.
% 2.01/2.19 0 [] multiply(inverse(X),X)=identity.
% 2.01/2.19 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 2.01/2.19 0 [] greatest_lower_bound(X,Y)=greatest_lower_bound(Y,X).
% 2.01/2.19 0 [] least_upper_bound(X,Y)=least_upper_bound(Y,X).
% 2.01/2.19 0 [] greatest_lower_bound(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(greatest_lower_bound(X,Y),Z).
% 2.01/2.19 0 [] least_upper_bound(X,least_upper_bound(Y,Z))=least_upper_bound(least_upper_bound(X,Y),Z).
% 2.01/2.19 0 [] least_upper_bound(X,X)=X.
% 2.01/2.19 0 [] greatest_lower_bound(X,X)=X.
% 2.01/2.19 0 [] least_upper_bound(X,greatest_lower_bound(X,Y))=X.
% 2.01/2.19 0 [] greatest_lower_bound(X,least_upper_bound(X,Y))=X.
% 2.01/2.19 0 [] multiply(X,least_upper_bound(Y,Z))=least_upper_bound(multiply(X,Y),multiply(X,Z)).
% 2.01/2.19 0 [] multiply(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(multiply(X,Y),multiply(X,Z)).
% 2.01/2.19 0 [] multiply(least_upper_bound(Y,Z),X)=least_upper_bound(multiply(Y,X),multiply(Z,X)).
% 2.01/2.19 0 [] multiply(greatest_lower_bound(Y,Z),X)=greatest_lower_bound(multiply(Y,X),multiply(Z,X)).
% 2.01/2.19 0 [] least_upper_bound(multiply(a,b),identity)!=multiply(a,least_upper_bound(inverse(a),b)).
% 2.01/2.19 end_of_list.
% 2.01/2.19
% 2.01/2.19 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.01/2.19
% 2.01/2.19 All clauses are units, and equality is present; the
% 2.01/2.19 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.01/2.19
% 2.01/2.19 dependent: set(knuth_bendix).
% 2.01/2.19 dependent: set(anl_eq).
% 2.01/2.19 dependent: set(para_from).
% 2.01/2.19 dependent: set(para_into).
% 2.01/2.19 dependent: clear(para_from_right).
% 2.01/2.19 dependent: clear(para_into_right).
% 2.01/2.19 dependent: set(para_from_vars).
% 2.01/2.19 dependent: set(eq_units_both_ways).
% 2.01/2.19 dependent: set(dynamic_demod_all).
% 2.01/2.19 dependent: set(dynamic_demod).
% 2.01/2.19 dependent: set(order_eq).
% 2.01/2.19 dependent: set(back_demod).
% 2.01/2.19 dependent: set(lrpo).
% 2.01/2.19
% 2.01/2.19 ------------> process usable:
% 2.01/2.19 ** KEPT (pick-wt=12): 2 [copy,1,flip.1] multiply(a,least_upper_bound(inverse(a),b))!=least_upper_bound(multiply(a,b),identity).
% 2.01/2.19
% 2.01/2.19 ------------> process sos:
% 2.01/2.19 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.01/2.19 ** KEPT (pick-wt=5): 4 [] multiply(identity,A)=A.
% 2.01/2.19 ---> New Demodulator: 5 [new_demod,4] multiply(identity,A)=A.
% 2.01/2.19 ** KEPT (pick-wt=6): 6 [] multiply(inverse(A),A)=identity.
% 2.01/2.19 ---> New Demodulator: 7 [new_demod,6] multiply(inverse(A),A)=identity.
% 2.01/2.19 ** KEPT (pick-wt=11): 8 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 2.01/2.19 ---> New Demodulator: 9 [new_demod,8] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 2.01/2.19 ** KEPT (pick-wt=7): 10 [] greatest_lower_bound(A,B)=greatest_lower_bound(B,A).
% 2.01/2.19 ** KEPT (pick-wt=7): 11 [] least_upper_bound(A,B)=least_upper_bound(B,A).
% 2.01/2.19 ** KEPT (pick-wt=11): 13 [copy,12,flip.1] greatest_lower_bound(greatest_lower_bound(A,B),C)=greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 2.01/2.19 ---> New Demodulator: 14 [new_demod,13] greatest_lower_bound(greatest_lower_bound(A,B),C)=greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 2.01/2.19 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] least_upper_bound(least_upper_bound(A,B),C)=least_upper_bound(A,least_upper_bound(B,C)).
% 2.01/2.19 ---> New Demodulator: 17 [new_demod,16] least_upper_bound(least_upper_bound(A,B),C)=least_upper_bound(A,least_upper_bound(B,C)).
% 2.01/2.19 ** KEPT (pick-wt=5): 18 [] least_upper_bound(A,A)=A.
% 2.01/2.19 ---> New Demodulator: 19 [new_demod,18] least_upper_bound(A,A)=A.
% 2.01/2.19 ** KEPT (pick-wt=5): 20 [] greatest_lower_bound(A,A)=A.
% 2.01/2.19 ---> New Demodulator: 21 [new_demod,20] greatest_lower_bound(A,A)=A.
% 2.01/2.19 ** KEPT (pick-wt=7): 22 [] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 2.01/2.19 ---> New Demodulator: 23 [new_demod,22] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 2.01/2.19 ** KEPT (pick-wt=7): 24 [] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 2.01/2.19 ---> New Demodulator: 25 [new_demod,24] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 2.01/2.19 ** KEPT (pick-wt=13): 26 [] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 2.01/2.19 ---> New Demodulator: 27 [new_demod,26] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 2.01/2.19 ** KEPT (pick-wt=13): 28 [] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 2.01/2.19 ---> New Demodulator: 29 [new_demod,28] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 2.01/2.19 ** KEPT (pick-wt=13): 30 [] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 2.01/2.19 ---> New Demodulator: 31 [new_demod,30] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 2.01/2.19 ** KEPT (pick-wt=13): 32 [] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 2.01/2.19 ---> New Demodulator: 33 [new_demod,32] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 2.01/2.19 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.01/2.19 >>>> Starting back demodulation with 5.
% 2.01/2.19 >>>> Starting back demodulation with 7.
% 2.01/2.19 >>>> Starting back demodulation with 9.
% 2.01/2.19 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] greatest_lower_bound(A,B)=greatest_lower_bound(B,A).
% 2.01/2.19 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] least_upper_bound(A,B)=least_upper_bound(B,A).
% 2.01/2.19 >>>> Starting back demodulation with 14.
% 2.01/2.19 >>>> Starting back demodulation with 17.
% 2.01/2.19 >>>> Starting back demodulation with 19.
% 2.01/2.19 >>>> Starting back demodulation with 21.
% 2.01/2.19 >>>> Starting back demodulation with 23.
% 2.01/2.19 >>>> Starting back demodulation with 25.
% 2.01/2.19 >>>> Starting back demodulation with 27.
% 2.01/2.19 >> back demodulating 2 with 27.
% 2.01/2.19 >>>> Starting back demodulation with 29.
% 2.01/2.19 >>>> Starting back demodulation with 31.
% 2.01/2.19 >>>> Starting back demodulation with 33.
% 2.01/2.19
% 2.01/2.19 ======= end of input processing =======
% 2.01/2.19
% 2.01/2.19 =========== start of search ===========
% 2.01/2.19
% 2.01/2.19 -------- PROOF --------
% 2.01/2.19
% 2.01/2.19 ----> UNIT CONFLICT at 0.01 sec ----> 197 [binary,196.1,11.1] $F.
% 2.01/2.19
% 2.01/2.19 Length of proof is 6. Level of proof is 4.
% 2.01/2.19
% 2.01/2.19 ---------------- PROOF ----------------
% 2.01/2.19 % SZS status Unsatisfiable
% 2.01/2.19 % SZS output start Refutation
% See solution above
% 2.01/2.19 ------------ end of proof -------------
% 2.01/2.19
% 2.01/2.19
% 2.01/2.19 Search stopped by max_proofs option.
% 2.01/2.19
% 2.01/2.19
% 2.01/2.19 Search stopped by max_proofs option.
% 2.01/2.19
% 2.01/2.19 ============ end of search ============
% 2.01/2.19
% 2.01/2.19 -------------- statistics -------------
% 2.01/2.19 clauses given 33
% 2.01/2.19 clauses generated 466
% 2.01/2.19 clauses kept 105
% 2.01/2.19 clauses forward subsumed 400
% 2.01/2.19 clauses back subsumed 0
% 2.01/2.19 Kbytes malloced 1953
% 2.01/2.19
% 2.01/2.19 ----------- times (seconds) -----------
% 2.01/2.19 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.01/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.01/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.01/2.19
% 2.01/2.19 That finishes the proof of the theorem.
% 2.01/2.19
% 2.01/2.19 Process 12708 finished Wed Jul 27 05:10:41 2022
% 2.01/2.19 Otter interrupted
% 2.01/2.19 PROOF FOUND
%------------------------------------------------------------------------------