%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP166-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 1.70s 1.95s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 4 RR)
% Number of literals : 13 ( 12 equ; 1 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 : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
greatest_lower_bound(a,multiply(a,b)) != a,
file('GRP166-2.p',unknown),
[] ).
cnf(4,axiom,
multiply(identity,A) = A,
file('GRP166-2.p',unknown),
[] ).
cnf(5,axiom,
multiply(inverse(A),A) = identity,
file('GRP166-2.p',unknown),
[] ).
cnf(7,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP166-2.p',unknown),
[] ).
cnf(9,axiom,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
file('GRP166-2.p',unknown),
[] ).
cnf(27,axiom,
multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)),
file('GRP166-2.p',unknown),
[] ).
cnf(35,axiom,
greatest_lower_bound(b,identity) = identity,
file('GRP166-2.p',unknown),
[] ).
cnf(37,plain,
greatest_lower_bound(identity,b) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,35])]),
[iquote('para_into,9.1.1,35.1.1,flip.1')] ).
cnf(42,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)],[7,5]),4])]),
[iquote('para_into,7.1.1.1,5.1.1,demod,4,flip.1')] ).
cnf(149,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[42,42]),
[iquote('para_into,42.1.1.2,42.1.1')] ).
cnf(153,plain,
multiply(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[42,5]),149]),
[iquote('para_into,42.1.1.2,5.1.1,demod,149')] ).
cnf(168,plain,
greatest_lower_bound(A,multiply(A,b)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,37]),153,153])]),
[iquote('para_into,27.1.1.2,37.1.1,demod,153,153,flip.1')] ).
cnf(170,plain,
$false,
inference(binary,[status(thm)],[168,1]),
[iquote('binary,168.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP166-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n022.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 05:14:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.70/1.95 ----- Otter 3.3f, August 2004 -----
% 1.70/1.95 The process was started by sandbox2 on n022.cluster.edu,
% 1.70/1.95 Wed Jul 27 05:14:50 2022
% 1.70/1.95 The command was "./otter". The process ID is 9678.
% 1.70/1.95
% 1.70/1.95 set(prolog_style_variables).
% 1.70/1.95 set(auto).
% 1.70/1.95 dependent: set(auto1).
% 1.70/1.95 dependent: set(process_input).
% 1.70/1.95 dependent: clear(print_kept).
% 1.70/1.95 dependent: clear(print_new_demod).
% 1.70/1.95 dependent: clear(print_back_demod).
% 1.70/1.95 dependent: clear(print_back_sub).
% 1.70/1.95 dependent: set(control_memory).
% 1.70/1.95 dependent: assign(max_mem, 12000).
% 1.70/1.95 dependent: assign(pick_given_ratio, 4).
% 1.70/1.95 dependent: assign(stats_level, 1).
% 1.70/1.95 dependent: assign(max_seconds, 10800).
% 1.70/1.95 clear(print_given).
% 1.70/1.95
% 1.70/1.95 list(usable).
% 1.70/1.95 0 [] A=A.
% 1.70/1.95 0 [] multiply(identity,X)=X.
% 1.70/1.95 0 [] multiply(inverse(X),X)=identity.
% 1.70/1.95 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.70/1.95 0 [] greatest_lower_bound(X,Y)=greatest_lower_bound(Y,X).
% 1.70/1.95 0 [] least_upper_bound(X,Y)=least_upper_bound(Y,X).
% 1.70/1.95 0 [] greatest_lower_bound(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(greatest_lower_bound(X,Y),Z).
% 1.70/1.95 0 [] least_upper_bound(X,least_upper_bound(Y,Z))=least_upper_bound(least_upper_bound(X,Y),Z).
% 1.70/1.95 0 [] least_upper_bound(X,X)=X.
% 1.70/1.95 0 [] greatest_lower_bound(X,X)=X.
% 1.70/1.95 0 [] least_upper_bound(X,greatest_lower_bound(X,Y))=X.
% 1.70/1.95 0 [] greatest_lower_bound(X,least_upper_bound(X,Y))=X.
% 1.70/1.95 0 [] multiply(X,least_upper_bound(Y,Z))=least_upper_bound(multiply(X,Y),multiply(X,Z)).
% 1.70/1.95 0 [] multiply(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(multiply(X,Y),multiply(X,Z)).
% 1.70/1.95 0 [] multiply(least_upper_bound(Y,Z),X)=least_upper_bound(multiply(Y,X),multiply(Z,X)).
% 1.70/1.95 0 [] multiply(greatest_lower_bound(Y,Z),X)=greatest_lower_bound(multiply(Y,X),multiply(Z,X)).
% 1.70/1.95 0 [] greatest_lower_bound(a,identity)=identity.
% 1.70/1.95 0 [] greatest_lower_bound(b,identity)=identity.
% 1.70/1.95 0 [] greatest_lower_bound(a,multiply(a,b))!=a.
% 1.70/1.95 end_of_list.
% 1.70/1.95
% 1.70/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.70/1.95
% 1.70/1.95 All clauses are units, and equality is present; the
% 1.70/1.95 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.70/1.95
% 1.70/1.95 dependent: set(knuth_bendix).
% 1.70/1.95 dependent: set(anl_eq).
% 1.70/1.95 dependent: set(para_from).
% 1.70/1.95 dependent: set(para_into).
% 1.70/1.95 dependent: clear(para_from_right).
% 1.70/1.95 dependent: clear(para_into_right).
% 1.70/1.95 dependent: set(para_from_vars).
% 1.70/1.95 dependent: set(eq_units_both_ways).
% 1.70/1.95 dependent: set(dynamic_demod_all).
% 1.70/1.95 dependent: set(dynamic_demod).
% 1.70/1.95 dependent: set(order_eq).
% 1.70/1.95 dependent: set(back_demod).
% 1.70/1.95 dependent: set(lrpo).
% 1.70/1.95
% 1.70/1.95 ------------> process usable:
% 1.70/1.95 ** KEPT (pick-wt=7): 1 [] greatest_lower_bound(a,multiply(a,b))!=a.
% 1.70/1.95
% 1.70/1.95 ------------> process sos:
% 1.70/1.95 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.70/1.95 ** KEPT (pick-wt=5): 3 [] multiply(identity,A)=A.
% 1.70/1.95 ---> New Demodulator: 4 [new_demod,3] multiply(identity,A)=A.
% 1.70/1.95 ** KEPT (pick-wt=6): 5 [] multiply(inverse(A),A)=identity.
% 1.70/1.95 ---> New Demodulator: 6 [new_demod,5] multiply(inverse(A),A)=identity.
% 1.70/1.95 ** KEPT (pick-wt=11): 7 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.70/1.95 ---> New Demodulator: 8 [new_demod,7] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.70/1.95 ** KEPT (pick-wt=7): 9 [] greatest_lower_bound(A,B)=greatest_lower_bound(B,A).
% 1.70/1.95 ** KEPT (pick-wt=7): 10 [] least_upper_bound(A,B)=least_upper_bound(B,A).
% 1.70/1.95 ** 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)).
% 1.70/1.95 ---> New Demodulator: 13 [new_demod,12] greatest_lower_bound(greatest_lower_bound(A,B),C)=greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 1.70/1.95 ** 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)).
% 1.70/1.95 ---> New Demodulator: 16 [new_demod,15] least_upper_bound(least_upper_bound(A,B),C)=least_upper_bound(A,least_upper_bound(B,C)).
% 1.70/1.95 ** KEPT (pick-wt=5): 17 [] least_upper_bound(A,A)=A.
% 1.70/1.95 ---> New Demodulator: 18 [new_demod,17] least_upper_bound(A,A)=A.
% 1.70/1.95 ** KEPT (pick-wt=5): 19 [] greatest_lower_bound(A,A)=A.
% 1.70/1.95 ---> New Demodulator: 20 [new_demod,19] greatest_lower_bound(A,A)=A.
% 1.70/1.95 ** KEPT (pick-wt=7): 21 [] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 1.70/1.95 ---> New Demodulator: 22 [new_demod,21] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 1.70/1.95 ** KEPT (pick-wt=7): 23 [] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 1.70/1.95 ---> New Demodulator: 24 [new_demod,23] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 1.70/1.95 ** KEPT (pick-wt=13): 25 [] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 1.70/1.95 ---> New Demodulator: 26 [new_demod,25] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 1.70/1.95 ** KEPT (pick-wt=13): 27 [] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 1.70/1.95 ---> New Demodulator: 28 [new_demod,27] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 1.70/1.95 ** KEPT (pick-wt=13): 29 [] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 1.70/1.95 ---> New Demodulator: 30 [new_demod,29] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 1.70/1.95 ** KEPT (pick-wt=13): 31 [] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 1.70/1.95 ---> New Demodulator: 32 [new_demod,31] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 1.70/1.95 ** KEPT (pick-wt=5): 33 [] greatest_lower_bound(a,identity)=identity.
% 1.70/1.95 ---> New Demodulator: 34 [new_demod,33] greatest_lower_bound(a,identity)=identity.
% 1.70/1.95 ** KEPT (pick-wt=5): 35 [] greatest_lower_bound(b,identity)=identity.
% 1.70/1.95 ---> New Demodulator: 36 [new_demod,35] greatest_lower_bound(b,identity)=identity.
% 1.70/1.95 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.70/1.95 >>>> Starting back demodulation with 4.
% 1.70/1.95 >>>> Starting back demodulation with 6.
% 1.70/1.95 >>>> Starting back demodulation with 8.
% 1.70/1.95 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] greatest_lower_bound(A,B)=greatest_lower_bound(B,A).
% 1.70/1.95 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] least_upper_bound(A,B)=least_upper_bound(B,A).
% 1.70/1.95 >>>> Starting back demodulation with 13.
% 1.70/1.95 >>>> Starting back demodulation with 16.
% 1.70/1.95 >>>> Starting back demodulation with 18.
% 1.70/1.95 >>>> Starting back demodulation with 20.
% 1.70/1.95 >>>> Starting back demodulation with 22.
% 1.70/1.95 >>>> Starting back demodulation with 24.
% 1.70/1.95 >>>> Starting back demodulation with 26.
% 1.70/1.95 >>>> Starting back demodulation with 28.
% 1.70/1.95 >>>> Starting back demodulation with 30.
% 1.70/1.95 >>>> Starting back demodulation with 32.
% 1.70/1.95 >>>> Starting back demodulation with 34.
% 1.70/1.95 >>>> Starting back demodulation with 36.
% 1.70/1.95
% 1.70/1.95 ======= end of input processing =======
% 1.70/1.95
% 1.70/1.95 =========== start of search ===========
% 1.70/1.95
% 1.70/1.95 -------- PROOF --------
% 1.70/1.95
% 1.70/1.95 ----> UNIT CONFLICT at 0.01 sec ----> 170 [binary,168.1,1.1] $F.
% 1.70/1.95
% 1.70/1.95 Length of proof is 5. Level of proof is 4.
% 1.70/1.95
% 1.70/1.95 ---------------- PROOF ----------------
% 1.70/1.95 % SZS status Unsatisfiable
% 1.70/1.95 % SZS output start Refutation
% See solution above
% 1.70/1.95 ------------ end of proof -------------
% 1.70/1.95
% 1.70/1.95
% 1.70/1.95 Search stopped by max_proofs option.
% 1.70/1.95
% 1.70/1.95
% 1.70/1.95 Search stopped by max_proofs option.
% 1.70/1.95
% 1.70/1.95 ============ end of search ============
% 1.70/1.95
% 1.70/1.95 -------------- statistics -------------
% 1.70/1.95 clauses given 31
% 1.70/1.95 clauses generated 272
% 1.70/1.95 clauses kept 89
% 1.70/1.95 clauses forward subsumed 218
% 1.70/1.95 clauses back subsumed 0
% 1.70/1.95 Kbytes malloced 1953
% 1.70/1.95
% 1.70/1.95 ----------- times (seconds) -----------
% 1.70/1.95 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.70/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.95 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.70/1.95
% 1.70/1.95 That finishes the proof of the theorem.
% 1.70/1.95
% 1.70/1.95 Process 9678 finished Wed Jul 27 05:14:52 2022
% 1.70/1.95 Otter interrupted
% 1.70/1.95 PROOF FOUND
%------------------------------------------------------------------------------