TSTP Solution File: GRP167-5 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP167-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 12:56:36 EDT 2022
% Result : Unsatisfiable 1.81s 2.01s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 6 RR)
% Number of literals : 27 ( 26 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
a != multiply(positive_part(a),negative_part(a)),
file('GRP167-5.p',unknown),
[] ).
cnf(2,plain,
multiply(positive_part(a),negative_part(a)) != a,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(5,axiom,
multiply(identity,A) = A,
file('GRP167-5.p',unknown),
[] ).
cnf(6,axiom,
multiply(inverse(A),A) = identity,
file('GRP167-5.p',unknown),
[] ).
cnf(9,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP167-5.p',unknown),
[] ).
cnf(10,axiom,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
file('GRP167-5.p',unknown),
[] ).
cnf(29,axiom,
multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)),
file('GRP167-5.p',unknown),
[] ).
cnf(31,axiom,
multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)),
file('GRP167-5.p',unknown),
[] ).
cnf(33,axiom,
multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)),
file('GRP167-5.p',unknown),
[] ).
cnf(34,axiom,
inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)),
file('GRP167-5.p',unknown),
[] ).
cnf(37,axiom,
positive_part(A) = least_upper_bound(A,identity),
file('GRP167-5.p',unknown),
[] ).
cnf(39,axiom,
negative_part(A) = greatest_lower_bound(A,identity),
file('GRP167-5.p',unknown),
[] ).
cnf(45,plain,
greatest_lower_bound(least_upper_bound(multiply(a,a),a),least_upper_bound(multiply(a,identity),identity)) != a,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),37,39,29,31,5,31,5]),
[iquote('back_demod,2,demod,37,39,29,31,5,31,5')] ).
cnf(46,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)],[9,6]),5])]),
[iquote('para_into,8.1.1.1,6.1.1,demod,5,flip.1')] ).
cnf(89,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[46,46]),
[iquote('para_into,46.1.1.2,46.1.1')] ).
cnf(93,plain,
multiply(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[46,6]),89]),
[iquote('para_into,46.1.1.2,6.1.1,demod,89')] ).
cnf(96,plain,
greatest_lower_bound(least_upper_bound(multiply(a,a),a),least_upper_bound(a,identity)) != a,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[45]),93]),
[iquote('back_demod,45,demod,93')] ).
cnf(124,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[89,93]),93]),
[iquote('para_into,88.1.1,92.1.1,demod,93')] ).
cnf(126,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[89,46])]),
[iquote('para_into,88.1.1,46.1.1,flip.1')] ).
cnf(127,plain,
multiply(A,inverse(A)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[89,6])]),
[iquote('para_into,88.1.1,6.1.1,flip.1')] ).
cnf(131,plain,
multiply(A,multiply(B,inverse(multiply(A,B)))) = identity,
inference(para_into,[status(thm),theory(equality)],[127,9]),
[iquote('para_into,127.1.1,8.1.1')] ).
cnf(177,plain,
greatest_lower_bound(least_upper_bound(A,multiply(B,multiply(inverse(C),A))),least_upper_bound(multiply(C,multiply(inverse(B),A)),A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[34,126]),33,29,31,126,31,126]),
[iquote('para_from,34.1.1,125.1.1.2.1,demod,33,29,31,126,31,126')] ).
cnf(203,plain,
multiply(A,inverse(multiply(B,A))) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[131,46]),93])]),
[iquote('para_from,131.1.1,46.1.1.2,demod,93,flip.1')] ).
cnf(220,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[203,46])]),
[iquote('para_from,203.1.1,46.1.1.2,flip.1')] ).
cnf(500,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(multiply(a,a),a)) != a,
inference(para_into,[status(thm),theory(equality)],[96,10]),
[iquote('para_into,96.1.1,10.1.1')] ).
cnf(1297,plain,
greatest_lower_bound(least_upper_bound(A,identity),least_upper_bound(multiply(A,A),A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[177,6]),220,124,220,124,9,126]),
[iquote('para_into,177.1.1.1.2,6.1.1,demod,220,124,220,124,9,126')] ).
cnf(1299,plain,
$false,
inference(binary,[status(thm)],[1297,500]),
[iquote('binary,1297.1,500.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP167-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 05:30:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.90 ----- Otter 3.3f, August 2004 -----
% 1.72/1.90 The process was started by sandbox on n004.cluster.edu,
% 1.72/1.90 Wed Jul 27 05:30:36 2022
% 1.72/1.90 The command was "./otter". The process ID is 11624.
% 1.72/1.90
% 1.72/1.90 set(prolog_style_variables).
% 1.72/1.90 set(auto).
% 1.72/1.90 dependent: set(auto1).
% 1.72/1.90 dependent: set(process_input).
% 1.72/1.90 dependent: clear(print_kept).
% 1.72/1.90 dependent: clear(print_new_demod).
% 1.72/1.90 dependent: clear(print_back_demod).
% 1.72/1.90 dependent: clear(print_back_sub).
% 1.72/1.90 dependent: set(control_memory).
% 1.72/1.90 dependent: assign(max_mem, 12000).
% 1.72/1.90 dependent: assign(pick_given_ratio, 4).
% 1.72/1.90 dependent: assign(stats_level, 1).
% 1.72/1.90 dependent: assign(max_seconds, 10800).
% 1.72/1.90 clear(print_given).
% 1.72/1.90
% 1.72/1.90 list(usable).
% 1.72/1.90 0 [] A=A.
% 1.72/1.90 0 [] multiply(identity,X)=X.
% 1.72/1.90 0 [] multiply(inverse(X),X)=identity.
% 1.72/1.90 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.72/1.90 0 [] greatest_lower_bound(X,Y)=greatest_lower_bound(Y,X).
% 1.72/1.90 0 [] least_upper_bound(X,Y)=least_upper_bound(Y,X).
% 1.72/1.90 0 [] greatest_lower_bound(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(greatest_lower_bound(X,Y),Z).
% 1.72/1.90 0 [] least_upper_bound(X,least_upper_bound(Y,Z))=least_upper_bound(least_upper_bound(X,Y),Z).
% 1.72/1.90 0 [] least_upper_bound(X,X)=X.
% 1.72/1.90 0 [] greatest_lower_bound(X,X)=X.
% 1.72/1.90 0 [] least_upper_bound(X,greatest_lower_bound(X,Y))=X.
% 1.72/1.90 0 [] greatest_lower_bound(X,least_upper_bound(X,Y))=X.
% 1.72/1.90 0 [] multiply(X,least_upper_bound(Y,Z))=least_upper_bound(multiply(X,Y),multiply(X,Z)).
% 1.72/1.90 0 [] multiply(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(multiply(X,Y),multiply(X,Z)).
% 1.72/1.90 0 [] multiply(least_upper_bound(Y,Z),X)=least_upper_bound(multiply(Y,X),multiply(Z,X)).
% 1.72/1.90 0 [] multiply(greatest_lower_bound(Y,Z),X)=greatest_lower_bound(multiply(Y,X),multiply(Z,X)).
% 1.72/1.90 0 [] inverse(least_upper_bound(A,B))=greatest_lower_bound(inverse(A),inverse(B)).
% 1.72/1.90 0 [] positive_part(X)=least_upper_bound(X,identity).
% 1.72/1.90 0 [] negative_part(X)=greatest_lower_bound(X,identity).
% 1.72/1.90 0 [] least_upper_bound(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)).
% 1.72/1.90 0 [] greatest_lower_bound(X,least_upper_bound(Y,Z))=least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z)).
% 1.72/1.90 0 [] a!=multiply(positive_part(a),negative_part(a)).
% 1.72/1.90 end_of_list.
% 1.72/1.90
% 1.72/1.90 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.72/1.90
% 1.72/1.90 All clauses are units, and equality is present; the
% 1.72/1.90 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.72/1.90
% 1.72/1.90 dependent: set(knuth_bendix).
% 1.72/1.90 dependent: set(anl_eq).
% 1.72/1.90 dependent: set(para_from).
% 1.72/1.90 dependent: set(para_into).
% 1.72/1.90 dependent: clear(para_from_right).
% 1.72/1.90 dependent: clear(para_into_right).
% 1.72/1.90 dependent: set(para_from_vars).
% 1.72/1.90 dependent: set(eq_units_both_ways).
% 1.72/1.90 dependent: set(dynamic_demod_all).
% 1.72/1.90 dependent: set(dynamic_demod).
% 1.72/1.90 dependent: set(order_eq).
% 1.72/1.90 dependent: set(back_demod).
% 1.72/1.90 dependent: set(lrpo).
% 1.72/1.90
% 1.72/1.90 ------------> process usable:
% 1.72/1.90 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(positive_part(a),negative_part(a))!=a.
% 1.72/1.90
% 1.72/1.90 ------------> process sos:
% 1.72/1.90 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.72/1.90 ** KEPT (pick-wt=5): 4 [] multiply(identity,A)=A.
% 1.72/1.90 ---> New Demodulator: 5 [new_demod,4] multiply(identity,A)=A.
% 1.72/1.90 ** KEPT (pick-wt=6): 6 [] multiply(inverse(A),A)=identity.
% 1.72/1.90 ---> New Demodulator: 7 [new_demod,6] multiply(inverse(A),A)=identity.
% 1.72/1.90 ** KEPT (pick-wt=11): 8 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.72/1.90 ---> New Demodulator: 9 [new_demod,8] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.72/1.90 ** KEPT (pick-wt=7): 10 [] greatest_lower_bound(A,B)=greatest_lower_bound(B,A).
% 1.72/1.90 ** KEPT (pick-wt=7): 11 [] least_upper_bound(A,B)=least_upper_bound(B,A).
% 1.72/1.90 ** 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)).
% 1.72/1.90 ---> New Demodulator: 14 [new_demod,13] greatest_lower_bound(greatest_lower_bound(A,B),C)=greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 1.72/1.90 ** 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)).
% 1.72/1.90 ---> New Demodulator: 17 [new_demod,16] least_upper_bound(least_upper_bound(A,B),C)=least_upper_bound(A,least_upper_bound(B,C)).
% 1.72/1.90 ** KEPT (pick-wt=5): 18 [] least_upper_bound(A,A)=A.
% 1.72/1.90 ---> New Demodulator: 19 [new_demod,18] least_upper_bound(A,A)=A.
% 1.81/2.01 ** KEPT (pick-wt=5): 20 [] greatest_lower_bound(A,A)=A.
% 1.81/2.01 ---> New Demodulator: 21 [new_demod,20] greatest_lower_bound(A,A)=A.
% 1.81/2.01 ** KEPT (pick-wt=7): 22 [] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 1.81/2.01 ---> New Demodulator: 23 [new_demod,22] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 1.81/2.01 ** KEPT (pick-wt=7): 24 [] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 1.81/2.01 ---> New Demodulator: 25 [new_demod,24] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 1.81/2.01 ** KEPT (pick-wt=13): 26 [] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 1.81/2.01 ---> New Demodulator: 27 [new_demod,26] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 1.81/2.01 ** KEPT (pick-wt=13): 28 [] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 1.81/2.01 ---> New Demodulator: 29 [new_demod,28] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 1.81/2.01 ** KEPT (pick-wt=13): 30 [] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 1.81/2.01 ---> New Demodulator: 31 [new_demod,30] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 1.81/2.01 ** KEPT (pick-wt=13): 32 [] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 1.81/2.01 ---> New Demodulator: 33 [new_demod,32] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 1.81/2.01 ** KEPT (pick-wt=10): 34 [] inverse(least_upper_bound(A,B))=greatest_lower_bound(inverse(A),inverse(B)).
% 1.81/2.01 ---> New Demodulator: 35 [new_demod,34] inverse(least_upper_bound(A,B))=greatest_lower_bound(inverse(A),inverse(B)).
% 1.81/2.01 ** KEPT (pick-wt=6): 36 [] positive_part(A)=least_upper_bound(A,identity).
% 1.81/2.01 ---> New Demodulator: 37 [new_demod,36] positive_part(A)=least_upper_bound(A,identity).
% 1.81/2.01 ** KEPT (pick-wt=6): 38 [] negative_part(A)=greatest_lower_bound(A,identity).
% 1.81/2.01 ---> New Demodulator: 39 [new_demod,38] negative_part(A)=greatest_lower_bound(A,identity).
% 1.81/2.01 ** KEPT (pick-wt=13): 40 [] least_upper_bound(A,greatest_lower_bound(B,C))=greatest_lower_bound(least_upper_bound(A,B),least_upper_bound(A,C)).
% 1.81/2.01 ---> New Demodulator: 41 [new_demod,40] least_upper_bound(A,greatest_lower_bound(B,C))=greatest_lower_bound(least_upper_bound(A,B),least_upper_bound(A,C)).
% 1.81/2.01 ** KEPT (pick-wt=17): 43 [copy,42,demod,41,flip.1] greatest_lower_bound(least_upper_bound(greatest_lower_bound(A,B),A),least_upper_bound(greatest_lower_bound(A,B),C))=greatest_lower_bound(A,least_upper_bound(B,C)).
% 1.81/2.01 ---> New Demodulator: 44 [new_demod,43] greatest_lower_bound(least_upper_bound(greatest_lower_bound(A,B),A),least_upper_bound(greatest_lower_bound(A,B),C))=greatest_lower_bound(A,least_upper_bound(B,C)).
% 1.81/2.01 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.81/2.01 >>>> Starting back demodulation with 5.
% 1.81/2.01 >>>> Starting back demodulation with 7.
% 1.81/2.01 >>>> Starting back demodulation with 9.
% 1.81/2.01 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] greatest_lower_bound(A,B)=greatest_lower_bound(B,A).
% 1.81/2.01 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] least_upper_bound(A,B)=least_upper_bound(B,A).
% 1.81/2.01 >>>> Starting back demodulation with 14.
% 1.81/2.01 >>>> Starting back demodulation with 17.
% 1.81/2.01 >>>> Starting back demodulation with 19.
% 1.81/2.01 >>>> Starting back demodulation with 21.
% 1.81/2.01 >>>> Starting back demodulation with 23.
% 1.81/2.01 >>>> Starting back demodulation with 25.
% 1.81/2.01 >>>> Starting back demodulation with 27.
% 1.81/2.01 >>>> Starting back demodulation with 29.
% 1.81/2.01 >>>> Starting back demodulation with 31.
% 1.81/2.01 >>>> Starting back demodulation with 33.
% 1.81/2.01 >>>> Starting back demodulation with 35.
% 1.81/2.01 >>>> Starting back demodulation with 37.
% 1.81/2.01 >> back demodulating 2 with 37.
% 1.81/2.01 >>>> Starting back demodulation with 39.
% 1.81/2.01 >>>> Starting back demodulation with 41.
% 1.81/2.01 >> back demodulating 22 with 41.
% 1.81/2.01 >>>> Starting back demodulation with 44.
% 1.81/2.01
% 1.81/2.01 ======= end of input processing =======
% 1.81/2.01
% 1.81/2.01 =========== start of search ===========
% 1.81/2.01
% 1.81/2.01
% 1.81/2.01 Resetting weight limit to 13.
% 1.81/2.01
% 1.81/2.01
% 1.81/2.01 Resetting weight limit to 13.
% 1.81/2.01
% 1.81/2.01 sos_size=466
% 1.81/2.01
% 1.81/2.01 -------- PROOF --------
% 1.81/2.01
% 1.81/2.01 ----> UNIT CONFLICT at 0.10 sec ----> 1299 [binary,1297.1,500.1] $F.
% 1.81/2.01
% 1.81/2.01 Length of proof is 15. Level of proof is 7.
% 1.81/2.01
% 1.81/2.01 ---------------- PROOF ----------------
% 1.81/2.01 % SZS status Unsatisfiable
% 1.81/2.01 % SZS output start Refutation
% See solution above
% 1.81/2.01 ------------ end of proof -------------
% 1.81/2.01
% 1.81/2.01
% 1.81/2.01 Search stopped by max_proofs option.
% 1.81/2.01
% 1.81/2.01
% 1.81/2.01 Search stopped by max_proofs option.
% 1.81/2.01
% 1.81/2.01 ============ end of search ============
% 1.81/2.01
% 1.81/2.01 -------------- statistics -------------
% 1.81/2.01 clauses given 126
% 1.81/2.01 clauses generated 8513
% 1.81/2.01 clauses kept 753
% 1.81/2.01 clauses forward subsumed 6974
% 1.81/2.01 clauses back subsumed 7
% 1.81/2.01 Kbytes malloced 5859
% 1.81/2.01
% 1.81/2.01 ----------- times (seconds) -----------
% 1.81/2.01 user CPU time 0.10 (0 hr, 0 min, 0 sec)
% 1.81/2.01 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.01 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.81/2.01
% 1.81/2.01 That finishes the proof of the theorem.
% 1.81/2.01
% 1.81/2.01 Process 11624 finished Wed Jul 27 05:30:37 2022
% 1.81/2.01 Otter interrupted
% 1.81/2.01 PROOF FOUND
%------------------------------------------------------------------------------