TSTP Solution File: GRP137-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP137-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 12:56:31 EDT 2022
% Result : Unsatisfiable 1.73s 1.92s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 6 RR)
% Number of literals : 6 ( 5 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
a != b,
file('GRP137-1.p',unknown),
[] ).
cnf(2,plain,
b != a,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(35,axiom,
greatest_lower_bound(a,b) = a,
file('GRP137-1.p',unknown),
[] ).
cnf(36,axiom,
greatest_lower_bound(a,b) = b,
file('GRP137-1.p',unknown),
[] ).
cnf(37,plain,
b = a,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[36]),35])]),
[iquote('copy,36,demod,35,flip.1')] ).
cnf(39,plain,
$false,
inference(binary,[status(thm)],[37,2]),
[iquote('binary,37.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP137-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n029.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 05:23:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.73/1.92 ----- Otter 3.3f, August 2004 -----
% 1.73/1.92 The process was started by sandbox2 on n029.cluster.edu,
% 1.73/1.92 Wed Jul 27 05:23:14 2022
% 1.73/1.92 The command was "./otter". The process ID is 15039.
% 1.73/1.92
% 1.73/1.92 set(prolog_style_variables).
% 1.73/1.92 set(auto).
% 1.73/1.92 dependent: set(auto1).
% 1.73/1.92 dependent: set(process_input).
% 1.73/1.92 dependent: clear(print_kept).
% 1.73/1.92 dependent: clear(print_new_demod).
% 1.73/1.92 dependent: clear(print_back_demod).
% 1.73/1.92 dependent: clear(print_back_sub).
% 1.73/1.92 dependent: set(control_memory).
% 1.73/1.92 dependent: assign(max_mem, 12000).
% 1.73/1.92 dependent: assign(pick_given_ratio, 4).
% 1.73/1.92 dependent: assign(stats_level, 1).
% 1.73/1.92 dependent: assign(max_seconds, 10800).
% 1.73/1.92 clear(print_given).
% 1.73/1.92
% 1.73/1.92 list(usable).
% 1.73/1.92 0 [] A=A.
% 1.73/1.92 0 [] multiply(identity,X)=X.
% 1.73/1.92 0 [] multiply(inverse(X),X)=identity.
% 1.73/1.92 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.73/1.92 0 [] greatest_lower_bound(X,Y)=greatest_lower_bound(Y,X).
% 1.73/1.92 0 [] least_upper_bound(X,Y)=least_upper_bound(Y,X).
% 1.73/1.92 0 [] greatest_lower_bound(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(greatest_lower_bound(X,Y),Z).
% 1.73/1.92 0 [] least_upper_bound(X,least_upper_bound(Y,Z))=least_upper_bound(least_upper_bound(X,Y),Z).
% 1.73/1.92 0 [] least_upper_bound(X,X)=X.
% 1.73/1.92 0 [] greatest_lower_bound(X,X)=X.
% 1.73/1.92 0 [] least_upper_bound(X,greatest_lower_bound(X,Y))=X.
% 1.73/1.92 0 [] greatest_lower_bound(X,least_upper_bound(X,Y))=X.
% 1.73/1.92 0 [] multiply(X,least_upper_bound(Y,Z))=least_upper_bound(multiply(X,Y),multiply(X,Z)).
% 1.73/1.92 0 [] multiply(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(multiply(X,Y),multiply(X,Z)).
% 1.73/1.92 0 [] multiply(least_upper_bound(Y,Z),X)=least_upper_bound(multiply(Y,X),multiply(Z,X)).
% 1.73/1.92 0 [] multiply(greatest_lower_bound(Y,Z),X)=greatest_lower_bound(multiply(Y,X),multiply(Z,X)).
% 1.73/1.92 0 [] greatest_lower_bound(a,b)=a.
% 1.73/1.92 0 [] greatest_lower_bound(a,b)=b.
% 1.73/1.92 0 [] a!=b.
% 1.73/1.92 end_of_list.
% 1.73/1.92
% 1.73/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.73/1.92
% 1.73/1.92 All clauses are units, and equality is present; the
% 1.73/1.92 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.73/1.92
% 1.73/1.92 dependent: set(knuth_bendix).
% 1.73/1.92 dependent: set(anl_eq).
% 1.73/1.92 dependent: set(para_from).
% 1.73/1.92 dependent: set(para_into).
% 1.73/1.92 dependent: clear(para_from_right).
% 1.73/1.92 dependent: clear(para_into_right).
% 1.73/1.92 dependent: set(para_from_vars).
% 1.73/1.92 dependent: set(eq_units_both_ways).
% 1.73/1.92 dependent: set(dynamic_demod_all).
% 1.73/1.92 dependent: set(dynamic_demod).
% 1.73/1.92 dependent: set(order_eq).
% 1.73/1.92 dependent: set(back_demod).
% 1.73/1.92 dependent: set(lrpo).
% 1.73/1.92
% 1.73/1.92 ------------> process usable:
% 1.73/1.92 ** KEPT (pick-wt=3): 2 [copy,1,flip.1] b!=a.
% 1.73/1.92
% 1.73/1.92 ------------> process sos:
% 1.73/1.92 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.73/1.92 ** KEPT (pick-wt=5): 4 [] multiply(identity,A)=A.
% 1.73/1.92 ---> New Demodulator: 5 [new_demod,4] multiply(identity,A)=A.
% 1.73/1.92 ** KEPT (pick-wt=6): 6 [] multiply(inverse(A),A)=identity.
% 1.73/1.92 ---> New Demodulator: 7 [new_demod,6] multiply(inverse(A),A)=identity.
% 1.73/1.92 ** KEPT (pick-wt=11): 8 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.73/1.92 ---> New Demodulator: 9 [new_demod,8] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.73/1.92 ** KEPT (pick-wt=7): 10 [] greatest_lower_bound(A,B)=greatest_lower_bound(B,A).
% 1.73/1.92 ** KEPT (pick-wt=7): 11 [] least_upper_bound(A,B)=least_upper_bound(B,A).
% 1.73/1.92 ** 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)).
% 1.73/1.92 ---> New Demodulator: 14 [new_demod,13] greatest_lower_bound(greatest_lower_bound(A,B),C)=greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 1.73/1.92 ** 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)).
% 1.73/1.92 ---> New Demodulator: 17 [new_demod,16] least_upper_bound(least_upper_bound(A,B),C)=least_upper_bound(A,least_upper_bound(B,C)).
% 1.73/1.92 ** KEPT (pick-wt=5): 18 [] least_upper_bound(A,A)=A.
% 1.73/1.92 ---> New Demodulator: 19 [new_demod,18] least_upper_bound(A,A)=A.
% 1.73/1.92 ** KEPT (pick-wt=5): 20 [] greatest_lower_bound(A,A)=A.
% 1.73/1.92 ---> New Demodulator: 21 [new_demod,20] greatest_lower_bound(A,A)=A.
% 1.73/1.92 ** KEPT (pick-wt=7): 22 [] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 1.73/1.92 ---> New Demodulator: 23 [new_demod,22] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 1.73/1.92 ** KEPT (pick-wt=7): 24 [] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 1.73/1.92 ---> New Demodulator: 25 [new_
% 1.73/1.92 -------- PROOF --------
% 1.73/1.92 demod,24] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 1.73/1.92 ** KEPT (pick-wt=13): 26 [] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 1.73/1.92 ---> New Demodulator: 27 [new_demod,26] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 1.73/1.92 ** KEPT (pick-wt=13): 28 [] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 1.73/1.92 ---> New Demodulator: 29 [new_demod,28] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 1.73/1.92 ** KEPT (pick-wt=13): 30 [] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 1.73/1.92 ---> New Demodulator: 31 [new_demod,30] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 1.73/1.92 ** KEPT (pick-wt=13): 32 [] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 1.73/1.92 ---> New Demodulator: 33 [new_demod,32] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 1.73/1.92 ** KEPT (pick-wt=5): 34 [] greatest_lower_bound(a,b)=a.
% 1.73/1.92 ---> New Demodulator: 35 [new_demod,34] greatest_lower_bound(a,b)=a.
% 1.73/1.92 ** KEPT (pick-wt=3): 37 [copy,36,demod,35,flip.1] b=a.
% 1.73/1.92 ---> New Demodulator: 38 [new_demod,37] b=a.
% 1.73/1.92
% 1.73/1.92 ----> UNIT CONFLICT at 0.00 sec ----> 39 [binary,37.1,2.1] $F.
% 1.73/1.92
% 1.73/1.92 Length of proof is 2. Level of proof is 1.
% 1.73/1.92
% 1.73/1.92 ---------------- PROOF ----------------
% 1.73/1.92 % SZS status Unsatisfiable
% 1.73/1.92 % SZS output start Refutation
% See solution above
% 1.73/1.92 ------------ end of proof -------------
% 1.73/1.92
% 1.73/1.92
% 1.73/1.92 Search stopped by max_proofs option.
% 1.73/1.92
% 1.73/1.92
% 1.73/1.92 Search stopped by max_proofs option.
% 1.73/1.92
% 1.73/1.92 ============ end of search ============
% 1.73/1.92
% 1.73/1.92 -------------- statistics -------------
% 1.73/1.92 clauses given 0
% 1.73/1.92 clauses generated 0
% 1.73/1.92 clauses kept 19
% 1.73/1.92 clauses forward subsumed 0
% 1.73/1.92 clauses back subsumed 0
% 1.73/1.92 Kbytes malloced 976
% 1.73/1.93
% 1.73/1.93 ----------- times (seconds) -----------
% 1.73/1.93 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.93 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.73/1.93
% 1.73/1.93 That finishes the proof of the theorem.
% 1.73/1.93
% 1.73/1.93 Process 15039 finished Wed Jul 27 05:23:16 2022
% 1.73/1.93 Otter interrupted
% 1.73/1.93 PROOF FOUND
%------------------------------------------------------------------------------