TSTP Solution File: GRP148-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP148-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 12:56:33 EDT 2022
% Result : Unsatisfiable 1.98s 2.17s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 10 RR)
% Number of literals : 31 ( 30 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
greatest_lower_bound(least_upper_bound(a,b),c) != least_upper_bound(a,b),
file('GRP148-1.p',unknown),
[] ).
cnf(4,axiom,
multiply(identity,A) = A,
file('GRP148-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(inverse(A),A) = identity,
file('GRP148-1.p',unknown),
[] ).
cnf(8,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP148-1.p',unknown),
[] ).
cnf(10,axiom,
least_upper_bound(A,B) = least_upper_bound(B,A),
file('GRP148-1.p',unknown),
[] ).
cnf(14,axiom,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C),
file('GRP148-1.p',unknown),
[] ).
cnf(15,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[14])]),
[iquote('copy,14,flip.1')] ).
cnf(23,axiom,
greatest_lower_bound(A,least_upper_bound(A,B)) = A,
file('GRP148-1.p',unknown),
[] ).
cnf(25,axiom,
multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)),
file('GRP148-1.p',unknown),
[] ).
cnf(29,axiom,
multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)),
file('GRP148-1.p',unknown),
[] ).
cnf(33,axiom,
least_upper_bound(a,c) = c,
file('GRP148-1.p',unknown),
[] ).
cnf(35,axiom,
least_upper_bound(b,c) = c,
file('GRP148-1.p',unknown),
[] ).
cnf(38,plain,
least_upper_bound(c,b) = c,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,35])]),
[iquote('para_into,10.1.1,35.1.1,flip.1')] ).
cnf(40,plain,
least_upper_bound(c,a) = c,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,33])]),
[iquote('para_into,10.1.1,33.1.1,flip.1')] ).
cnf(43,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]),4])]),
[iquote('para_into,7.1.1.1,5.1.1,demod,4,flip.1')] ).
cnf(53,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(para_into,[status(thm),theory(equality)],[23,10]),
[iquote('para_into,23.1.1.2,10.1.1')] ).
cnf(90,plain,
least_upper_bound(c,least_upper_bound(a,A)) = least_upper_bound(c,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,40])]),
[iquote('para_into,15.1.1.1,40.1.1,flip.1')] ).
cnf(135,plain,
least_upper_bound(multiply(A,c),multiply(A,b)) = multiply(A,c),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,38])]),
[iquote('para_into,25.1.1.2,38.1.1,flip.1')] ).
cnf(141,plain,
least_upper_bound(multiply(inverse(least_upper_bound(A,B)),A),multiply(inverse(least_upper_bound(A,B)),B)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,6])]),
[iquote('para_into,25.1.1,5.1.1,flip.1')] ).
cnf(148,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[43,43]),
[iquote('para_into,43.1.1.2,43.1.1')] ).
cnf(152,plain,
multiply(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[43,6]),148]),
[iquote('para_into,43.1.1.2,5.1.1,demod,148')] ).
cnf(522,plain,
greatest_lower_bound(least_upper_bound(a,A),least_upper_bound(c,A)) = least_upper_bound(a,A),
inference(para_from,[status(thm),theory(equality)],[90,53]),
[iquote('para_from,90.1.1,53.1.1.2')] ).
cnf(681,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[148,152]),152]),
[iquote('para_into,147.1.1,151.1.1,demod,152')] ).
cnf(685,plain,
multiply(A,inverse(A)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[148,6])]),
[iquote('para_into,147.1.1,5.1.1,flip.1')] ).
cnf(1213,plain,
least_upper_bound(identity,multiply(inverse(c),b)) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[135,6]),6]),
[iquote('para_into,135.1.1.1,5.1.1,demod,6')] ).
cnf(1227,plain,
least_upper_bound(A,multiply(inverse(c),multiply(b,A))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1213,29]),4,4,8])]),
[iquote('para_from,1213.1.1,29.1.1.1,demod,4,4,8,flip.1')] ).
cnf(1290,plain,
least_upper_bound(inverse(b),inverse(c)) = inverse(b),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1227,685]),152]),
[iquote('para_into,1227.1.1.2.2,684.1.1,demod,152')] ).
cnf(1303,plain,
least_upper_bound(identity,multiply(b,inverse(c))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1290,141]),1290,681,685,681]),
[iquote('para_from,1289.1.1,141.1.1.2.1.1,demod,1290,681,685,681')] ).
cnf(1329,plain,
least_upper_bound(A,multiply(b,multiply(inverse(c),A))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1303,29]),4,4,8])]),
[iquote('para_from,1303.1.1,29.1.1.1,demod,4,4,8,flip.1')] ).
cnf(1703,plain,
greatest_lower_bound(least_upper_bound(a,b),c) = least_upper_bound(a,b),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[522,1329]),6,152,6,152]),
[iquote('para_into,522.1.1.2,1329.1.1,demod,6,152,6,152')] ).
cnf(1705,plain,
$false,
inference(binary,[status(thm)],[1703,1]),
[iquote('binary,1703.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP148-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 05:01:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.71/1.92 ----- Otter 3.3f, August 2004 -----
% 1.71/1.92 The process was started by sandbox on n024.cluster.edu,
% 1.71/1.92 Wed Jul 27 05:01:25 2022
% 1.71/1.92 The command was "./otter". The process ID is 10529.
% 1.71/1.92
% 1.71/1.92 set(prolog_style_variables).
% 1.71/1.92 set(auto).
% 1.71/1.92 dependent: set(auto1).
% 1.71/1.92 dependent: set(process_input).
% 1.71/1.92 dependent: clear(print_kept).
% 1.71/1.92 dependent: clear(print_new_demod).
% 1.71/1.92 dependent: clear(print_back_demod).
% 1.71/1.92 dependent: clear(print_back_sub).
% 1.71/1.92 dependent: set(control_memory).
% 1.71/1.92 dependent: assign(max_mem, 12000).
% 1.71/1.92 dependent: assign(pick_given_ratio, 4).
% 1.71/1.92 dependent: assign(stats_level, 1).
% 1.71/1.92 dependent: assign(max_seconds, 10800).
% 1.71/1.92 clear(print_given).
% 1.71/1.92
% 1.71/1.92 list(usable).
% 1.71/1.92 0 [] A=A.
% 1.71/1.92 0 [] multiply(identity,X)=X.
% 1.71/1.92 0 [] multiply(inverse(X),X)=identity.
% 1.71/1.92 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.71/1.92 0 [] greatest_lower_bound(X,Y)=greatest_lower_bound(Y,X).
% 1.71/1.92 0 [] least_upper_bound(X,Y)=least_upper_bound(Y,X).
% 1.71/1.92 0 [] greatest_lower_bound(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(greatest_lower_bound(X,Y),Z).
% 1.71/1.92 0 [] least_upper_bound(X,least_upper_bound(Y,Z))=least_upper_bound(least_upper_bound(X,Y),Z).
% 1.71/1.92 0 [] least_upper_bound(X,X)=X.
% 1.71/1.92 0 [] greatest_lower_bound(X,X)=X.
% 1.71/1.92 0 [] least_upper_bound(X,greatest_lower_bound(X,Y))=X.
% 1.71/1.92 0 [] greatest_lower_bound(X,least_upper_bound(X,Y))=X.
% 1.71/1.92 0 [] multiply(X,least_upper_bound(Y,Z))=least_upper_bound(multiply(X,Y),multiply(X,Z)).
% 1.71/1.92 0 [] multiply(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(multiply(X,Y),multiply(X,Z)).
% 1.71/1.92 0 [] multiply(least_upper_bound(Y,Z),X)=least_upper_bound(multiply(Y,X),multiply(Z,X)).
% 1.71/1.92 0 [] multiply(greatest_lower_bound(Y,Z),X)=greatest_lower_bound(multiply(Y,X),multiply(Z,X)).
% 1.71/1.92 0 [] least_upper_bound(a,c)=c.
% 1.71/1.92 0 [] least_upper_bound(b,c)=c.
% 1.71/1.92 0 [] greatest_lower_bound(least_upper_bound(a,b),c)!=least_upper_bound(a,b).
% 1.71/1.92 end_of_list.
% 1.71/1.92
% 1.71/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.71/1.92
% 1.71/1.92 All clauses are units, and equality is present; the
% 1.71/1.92 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.71/1.92
% 1.71/1.92 dependent: set(knuth_bendix).
% 1.71/1.92 dependent: set(anl_eq).
% 1.71/1.92 dependent: set(para_from).
% 1.71/1.92 dependent: set(para_into).
% 1.71/1.92 dependent: clear(para_from_right).
% 1.71/1.92 dependent: clear(para_into_right).
% 1.71/1.92 dependent: set(para_from_vars).
% 1.71/1.92 dependent: set(eq_units_both_ways).
% 1.71/1.92 dependent: set(dynamic_demod_all).
% 1.71/1.92 dependent: set(dynamic_demod).
% 1.71/1.92 dependent: set(order_eq).
% 1.71/1.92 dependent: set(back_demod).
% 1.71/1.92 dependent: set(lrpo).
% 1.71/1.92
% 1.71/1.92 ------------> process usable:
% 1.71/1.92 ** KEPT (pick-wt=9): 1 [] greatest_lower_bound(least_upper_bound(a,b),c)!=least_upper_bound(a,b).
% 1.71/1.92
% 1.71/1.92 ------------> process sos:
% 1.71/1.92 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.71/1.92 ** KEPT (pick-wt=5): 3 [] multiply(identity,A)=A.
% 1.71/1.92 ---> New Demodulator: 4 [new_demod,3] multiply(identity,A)=A.
% 1.71/1.92 ** KEPT (pick-wt=6): 5 [] multiply(inverse(A),A)=identity.
% 1.71/1.92 ---> New Demodulator: 6 [new_demod,5] multiply(inverse(A),A)=identity.
% 1.71/1.92 ** KEPT (pick-wt=11): 7 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.71/1.92 ---> New Demodulator: 8 [new_demod,7] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.71/1.92 ** KEPT (pick-wt=7): 9 [] greatest_lower_bound(A,B)=greatest_lower_bound(B,A).
% 1.71/1.92 ** KEPT (pick-wt=7): 10 [] least_upper_bound(A,B)=least_upper_bound(B,A).
% 1.71/1.92 ** KEPT (pick-wt=11): 12 [copy,11,flip.1] greatest_lower_bound(greatest_lower_bound(A,B),C)=greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 1.71/1.92 ---> New Demodulator: 13 [new_demod,12] greatest_lower_bound(greatest_lower_bound(A,B),C)=greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 1.71/1.92 ** KEPT (pick-wt=11): 15 [copy,14,flip.1] least_upper_bound(least_upper_bound(A,B),C)=least_upper_bound(A,least_upper_bound(B,C)).
% 1.71/1.92 ---> New Demodulator: 16 [new_demod,15] least_upper_bound(least_upper_bound(A,B),C)=least_upper_bound(A,least_upper_bound(B,C)).
% 1.71/1.92 ** KEPT (pick-wt=5): 17 [] least_upper_bound(A,A)=A.
% 1.71/1.92 ---> New Demodulator: 18 [new_demod,17] least_upper_bound(A,A)=A.
% 1.71/1.92 ** KEPT (pick-wt=5): 19 [] greatest_lower_bound(A,A)=A.
% 1.71/1.92 ---> New Demodulator: 20 [new_demod,19] greatest_lower_bound(A,A)=A.
% 1.71/1.92 ** KEPT (pick-wt=7): 21 [] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 1.71/1.92 ---> New Demodulator: 22 [new_demod,21] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 1.98/2.17 ** KEPT (pick-wt=7): 23 [] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 1.98/2.17 ---> New Demodulator: 24 [new_demod,23] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 1.98/2.17 ** KEPT (pick-wt=13): 25 [] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 1.98/2.17 ---> New Demodulator: 26 [new_demod,25] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 1.98/2.17 ** KEPT (pick-wt=13): 27 [] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 1.98/2.17 ---> New Demodulator: 28 [new_demod,27] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 1.98/2.17 ** KEPT (pick-wt=13): 29 [] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 1.98/2.17 ---> New Demodulator: 30 [new_demod,29] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 1.98/2.17 ** KEPT (pick-wt=13): 31 [] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 1.98/2.17 ---> New Demodulator: 32 [new_demod,31] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 1.98/2.17 ** KEPT (pick-wt=5): 33 [] least_upper_bound(a,c)=c.
% 1.98/2.17 ---> New Demodulator: 34 [new_demod,33] least_upper_bound(a,c)=c.
% 1.98/2.17 ** KEPT (pick-wt=5): 35 [] least_upper_bound(b,c)=c.
% 1.98/2.17 ---> New Demodulator: 36 [new_demod,35] least_upper_bound(b,c)=c.
% 1.98/2.17 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.98/2.17 >>>> Starting back demodulation with 4.
% 1.98/2.17 >>>> Starting back demodulation with 6.
% 1.98/2.17 >>>> Starting back demodulation with 8.
% 1.98/2.17 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] greatest_lower_bound(A,B)=greatest_lower_bound(B,A).
% 1.98/2.17 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] least_upper_bound(A,B)=least_upper_bound(B,A).
% 1.98/2.17 >>>> Starting back demodulation with 13.
% 1.98/2.17 >>>> Starting back demodulation with 16.
% 1.98/2.17 >>>> Starting back demodulation with 18.
% 1.98/2.17 >>>> Starting back demodulation with 20.
% 1.98/2.17 >>>> Starting back demodulation with 22.
% 1.98/2.17 >>>> Starting back demodulation with 24.
% 1.98/2.17 >>>> Starting back demodulation with 26.
% 1.98/2.17 >>>> Starting back demodulation with 28.
% 1.98/2.17 >>>> Starting back demodulation with 30.
% 1.98/2.17 >>>> Starting back demodulation with 32.
% 1.98/2.17 >>>> Starting back demodulation with 34.
% 1.98/2.17 >>>> Starting back demodulation with 36.
% 1.98/2.17
% 1.98/2.17 ======= end of input processing =======
% 1.98/2.17
% 1.98/2.17 =========== start of search ===========
% 1.98/2.17
% 1.98/2.17
% 1.98/2.17 Resetting weight limit to 11.
% 1.98/2.17
% 1.98/2.17
% 1.98/2.17 Resetting weight limit to 11.
% 1.98/2.17
% 1.98/2.17 sos_size=478
% 1.98/2.17
% 1.98/2.17
% 1.98/2.17 Resetting weight limit to 10.
% 1.98/2.17
% 1.98/2.17
% 1.98/2.17 Resetting weight limit to 10.
% 1.98/2.17
% 1.98/2.17 sos_size=512
% 1.98/2.17
% 1.98/2.17 -------- PROOF --------
% 1.98/2.17
% 1.98/2.17 ----> UNIT CONFLICT at 0.25 sec ----> 1705 [binary,1703.1,1.1] $F.
% 1.98/2.17
% 1.98/2.17 Length of proof is 19. Level of proof is 8.
% 1.98/2.17
% 1.98/2.17 ---------------- PROOF ----------------
% 1.98/2.17 % SZS status Unsatisfiable
% 1.98/2.17 % SZS output start Refutation
% See solution above
% 1.98/2.17 ------------ end of proof -------------
% 1.98/2.17
% 1.98/2.17
% 1.98/2.17 Search stopped by max_proofs option.
% 1.98/2.17
% 1.98/2.17
% 1.98/2.17 Search stopped by max_proofs option.
% 1.98/2.17
% 1.98/2.17 ============ end of search ============
% 1.98/2.17
% 1.98/2.17 -------------- statistics -------------
% 1.98/2.17 clauses given 478
% 1.98/2.17 clauses generated 43616
% 1.98/2.17 clauses kept 881
% 1.98/2.17 clauses forward subsumed 29696
% 1.98/2.17 clauses back subsumed 2
% 1.98/2.17 Kbytes malloced 7812
% 1.98/2.17
% 1.98/2.17 ----------- times (seconds) -----------
% 1.98/2.17 user CPU time 0.25 (0 hr, 0 min, 0 sec)
% 1.98/2.17 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.98/2.17 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.17
% 1.98/2.17 That finishes the proof of the theorem.
% 1.98/2.17
% 1.98/2.17 Process 10529 finished Wed Jul 27 05:01:27 2022
% 1.98/2.17 Otter interrupted
% 1.98/2.17 PROOF FOUND
%------------------------------------------------------------------------------