TSTP Solution File: GRP184-4 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 12:56:40 EDT 2022
% Result : Unsatisfiable 1.96s 2.14s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 8 RR)
% Number of literals : 29 ( 28 equ; 6 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('GRP184-4.p',unknown),
[] ).
cnf(2,plain,
multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,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('GRP184-4.p',unknown),
[] ).
cnf(7,axiom,
multiply(inverse(A),A) = identity,
file('GRP184-4.p',unknown),
[] ).
cnf(8,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP184-4.p',unknown),
[] ).
cnf(10,axiom,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
file('GRP184-4.p',unknown),
[] ).
cnf(11,axiom,
least_upper_bound(A,B) = least_upper_bound(B,A),
file('GRP184-4.p',unknown),
[] ).
cnf(15,axiom,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C),
file('GRP184-4.p',unknown),
[] ).
cnf(17,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)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(22,axiom,
least_upper_bound(A,greatest_lower_bound(A,B)) = A,
file('GRP184-4.p',unknown),
[] ).
cnf(24,axiom,
greatest_lower_bound(A,least_upper_bound(A,B)) = A,
file('GRP184-4.p',unknown),
[] ).
cnf(27,axiom,
multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)),
file('GRP184-4.p',unknown),
[] ).
cnf(31,axiom,
multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)),
file('GRP184-4.p',unknown),
[] ).
cnf(35,axiom,
inverse(identity) = identity,
file('GRP184-4.p',unknown),
[] ).
cnf(37,axiom,
inverse(inverse(A)) = A,
file('GRP184-4.p',unknown),
[] ).
cnf(41,axiom,
inverse(greatest_lower_bound(A,B)) = least_upper_bound(inverse(A),inverse(B)),
file('GRP184-4.p',unknown),
[] ).
cnf(44,plain,
least_upper_bound(identity,least_upper_bound(a,least_upper_bound(multiply(inverse(a),identity),identity))) != least_upper_bound(multiply(a,inverse(a)),least_upper_bound(inverse(a),least_upper_bound(multiply(a,identity),identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),41,35,27,31,7,5,31,5,17,41,35,27,31,5,31,5,17]),
[iquote('back_demod,2,demod,41,35,27,31,7,5,31,5,17,41,35,27,31,5,31,5,17')] ).
cnf(46,plain,
multiply(A,inverse(A)) = identity,
inference(para_from,[status(thm),theory(equality)],[37,7]),
[iquote('para_from,36.1.1,6.1.1.1')] ).
cnf(47,plain,
least_upper_bound(identity,least_upper_bound(a,least_upper_bound(multiply(inverse(a),identity),identity))) != least_upper_bound(identity,least_upper_bound(inverse(a),least_upper_bound(multiply(a,identity),identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),46]),
[iquote('back_demod,44,demod,46')] ).
cnf(48,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,46]),5])]),
[iquote('para_into,8.1.1.1,45.1.1,demod,5,flip.1')] ).
cnf(52,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(para_into,[status(thm),theory(equality)],[22,10]),
[iquote('para_into,22.1.1.2,10.1.1')] ).
cnf(60,plain,
least_upper_bound(A,least_upper_bound(B,A)) = least_upper_bound(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[52,24]),17]),
[iquote('para_into,52.1.1.2,24.1.1,demod,17')] ).
cnf(103,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(B,least_upper_bound(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,11]),17]),
[iquote('para_into,16.1.1.1,11.1.1,demod,17')] ).
cnf(119,plain,
multiply(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,46]),37]),
[iquote('para_into,48.1.1.2,45.1.1,demod,37')] ).
cnf(120,plain,
least_upper_bound(identity,least_upper_bound(inverse(a),least_upper_bound(a,identity))) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(inverse(a),identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),119,119])]),
[iquote('back_demod,47,demod,119,119,flip.1')] ).
cnf(122,plain,
least_upper_bound(A,least_upper_bound(B,least_upper_bound(C,A))) = least_upper_bound(A,least_upper_bound(B,C)),
inference(para_into,[status(thm),theory(equality)],[60,17]),
[iquote('para_into,60.1.1.2,16.1.1')] ).
cnf(123,plain,
least_upper_bound(identity,least_upper_bound(inverse(a),a)) != least_upper_bound(identity,least_upper_bound(a,inverse(a))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[120]),122,122]),
[iquote('back_demod,120,demod,122,122')] ).
cnf(535,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(A,least_upper_bound(C,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[103,11]),17]),
[iquote('para_into,103.1.1,11.1.1,demod,17')] ).
cnf(536,plain,
$false,
inference(binary,[status(thm)],[535,123]),
[iquote('binary,535.1,123.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n020.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 05:05:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.96/2.12 ----- Otter 3.3f, August 2004 -----
% 1.96/2.12 The process was started by sandbox2 on n020.cluster.edu,
% 1.96/2.12 Wed Jul 27 05:05:38 2022
% 1.96/2.12 The command was "./otter". The process ID is 27516.
% 1.96/2.12
% 1.96/2.12 set(prolog_style_variables).
% 1.96/2.12 set(auto).
% 1.96/2.12 dependent: set(auto1).
% 1.96/2.12 dependent: set(process_input).
% 1.96/2.12 dependent: clear(print_kept).
% 1.96/2.12 dependent: clear(print_new_demod).
% 1.96/2.12 dependent: clear(print_back_demod).
% 1.96/2.12 dependent: clear(print_back_sub).
% 1.96/2.12 dependent: set(control_memory).
% 1.96/2.12 dependent: assign(max_mem, 12000).
% 1.96/2.12 dependent: assign(pick_given_ratio, 4).
% 1.96/2.12 dependent: assign(stats_level, 1).
% 1.96/2.12 dependent: assign(max_seconds, 10800).
% 1.96/2.12 clear(print_given).
% 1.96/2.12
% 1.96/2.12 list(usable).
% 1.96/2.12 0 [] A=A.
% 1.96/2.12 0 [] multiply(identity,X)=X.
% 1.96/2.12 0 [] multiply(inverse(X),X)=identity.
% 1.96/2.12 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.96/2.12 0 [] greatest_lower_bound(X,Y)=greatest_lower_bound(Y,X).
% 1.96/2.12 0 [] least_upper_bound(X,Y)=least_upper_bound(Y,X).
% 1.96/2.12 0 [] greatest_lower_bound(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(greatest_lower_bound(X,Y),Z).
% 1.96/2.12 0 [] least_upper_bound(X,least_upper_bound(Y,Z))=least_upper_bound(least_upper_bound(X,Y),Z).
% 1.96/2.12 0 [] least_upper_bound(X,X)=X.
% 1.96/2.12 0 [] greatest_lower_bound(X,X)=X.
% 1.96/2.12 0 [] least_upper_bound(X,greatest_lower_bound(X,Y))=X.
% 1.96/2.12 0 [] greatest_lower_bound(X,least_upper_bound(X,Y))=X.
% 1.96/2.12 0 [] multiply(X,least_upper_bound(Y,Z))=least_upper_bound(multiply(X,Y),multiply(X,Z)).
% 1.96/2.12 0 [] multiply(X,greatest_lower_bound(Y,Z))=greatest_lower_bound(multiply(X,Y),multiply(X,Z)).
% 1.96/2.12 0 [] multiply(least_upper_bound(Y,Z),X)=least_upper_bound(multiply(Y,X),multiply(Z,X)).
% 1.96/2.12 0 [] multiply(greatest_lower_bound(Y,Z),X)=greatest_lower_bound(multiply(Y,X),multiply(Z,X)).
% 1.96/2.12 0 [] inverse(identity)=identity.
% 1.96/2.12 0 [] inverse(inverse(X))=X.
% 1.96/2.12 0 [] inverse(multiply(X,Y))=multiply(inverse(Y),inverse(X)).
% 1.96/2.12 0 [] inverse(greatest_lower_bound(X,Y))=least_upper_bound(inverse(X),inverse(Y)).
% 1.96/2.12 0 [] inverse(least_upper_bound(X,Y))=greatest_lower_bound(inverse(X),inverse(Y)).
% 1.96/2.12 0 [] multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity)))!=multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)).
% 1.96/2.12 end_of_list.
% 1.96/2.12
% 1.96/2.12 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.96/2.12
% 1.96/2.12 All clauses are units, and equality is present; the
% 1.96/2.12 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.96/2.12
% 1.96/2.12 dependent: set(knuth_bendix).
% 1.96/2.12 dependent: set(anl_eq).
% 1.96/2.12 dependent: set(para_from).
% 1.96/2.12 dependent: set(para_into).
% 1.96/2.12 dependent: clear(para_from_right).
% 1.96/2.12 dependent: clear(para_into_right).
% 1.96/2.12 dependent: set(para_from_vars).
% 1.96/2.12 dependent: set(eq_units_both_ways).
% 1.96/2.12 dependent: set(dynamic_demod_all).
% 1.96/2.12 dependent: set(dynamic_demod).
% 1.96/2.12 dependent: set(order_eq).
% 1.96/2.12 dependent: set(back_demod).
% 1.96/2.12 dependent: set(lrpo).
% 1.96/2.12
% 1.96/2.12 ------------> process usable:
% 1.96/2.12 ** KEPT (pick-wt=17): 2 [copy,1,flip.1] multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity))!=multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))).
% 1.96/2.12
% 1.96/2.12 ------------> process sos:
% 1.96/2.12 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.96/2.12 ** KEPT (pick-wt=5): 4 [] multiply(identity,A)=A.
% 1.96/2.12 ---> New Demodulator: 5 [new_demod,4] multiply(identity,A)=A.
% 1.96/2.12 ** KEPT (pick-wt=6): 6 [] multiply(inverse(A),A)=identity.
% 1.96/2.12 ---> New Demodulator: 7 [new_demod,6] multiply(inverse(A),A)=identity.
% 1.96/2.12 ** KEPT (pick-wt=11): 8 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.96/2.12 ---> New Demodulator: 9 [new_demod,8] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.96/2.12 ** KEPT (pick-wt=7): 10 [] greatest_lower_bound(A,B)=greatest_lower_bound(B,A).
% 1.96/2.12 ** KEPT (pick-wt=7): 11 [] least_upper_bound(A,B)=least_upper_bound(B,A).
% 1.96/2.12 ** 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)).
% 1.96/2.12 ---> New Demodulator: 14 [new_demod,13] greatest_lower_bound(greatest_lower_bound(A,B),C)=greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 1.96/2.12 ** 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)).
% 1.96/2.12 ---> New Demodulator: 17 [new_demod,16] least_upper_bound(least_upper_bound(A,B),C)=least_upper_bound(A,least_upper_bound(B,C)).
% 1.96/2.14 ** KEPT (pick-wt=5): 18 [] least_upper_bound(A,A)=A.
% 1.96/2.14 ---> New Demodulator: 19 [new_demod,18] least_upper_bound(A,A)=A.
% 1.96/2.14 ** KEPT (pick-wt=5): 20 [] greatest_lower_bound(A,A)=A.
% 1.96/2.14 ---> New Demodulator: 21 [new_demod,20] greatest_lower_bound(A,A)=A.
% 1.96/2.14 ** KEPT (pick-wt=7): 22 [] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 1.96/2.14 ---> New Demodulator: 23 [new_demod,22] least_upper_bound(A,greatest_lower_bound(A,B))=A.
% 1.96/2.14 ** KEPT (pick-wt=7): 24 [] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 1.96/2.14 ---> New Demodulator: 25 [new_demod,24] greatest_lower_bound(A,least_upper_bound(A,B))=A.
% 1.96/2.14 ** KEPT (pick-wt=13): 26 [] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 1.96/2.14 ---> New Demodulator: 27 [new_demod,26] multiply(A,least_upper_bound(B,C))=least_upper_bound(multiply(A,B),multiply(A,C)).
% 1.96/2.14 ** KEPT (pick-wt=13): 28 [] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 1.96/2.14 ---> New Demodulator: 29 [new_demod,28] multiply(A,greatest_lower_bound(B,C))=greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 1.96/2.14 ** KEPT (pick-wt=13): 30 [] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 1.96/2.14 ---> New Demodulator: 31 [new_demod,30] multiply(least_upper_bound(A,B),C)=least_upper_bound(multiply(A,C),multiply(B,C)).
% 1.96/2.14 ** KEPT (pick-wt=13): 32 [] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 1.96/2.14 ---> New Demodulator: 33 [new_demod,32] multiply(greatest_lower_bound(A,B),C)=greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 1.96/2.14 ** KEPT (pick-wt=4): 34 [] inverse(identity)=identity.
% 1.96/2.14 ---> New Demodulator: 35 [new_demod,34] inverse(identity)=identity.
% 1.96/2.14 ** KEPT (pick-wt=5): 36 [] inverse(inverse(A))=A.
% 1.96/2.14 ---> New Demodulator: 37 [new_demod,36] inverse(inverse(A))=A.
% 1.96/2.14 ** KEPT (pick-wt=10): 38 [] inverse(multiply(A,B))=multiply(inverse(B),inverse(A)).
% 1.96/2.14 ---> New Demodulator: 39 [new_demod,38] inverse(multiply(A,B))=multiply(inverse(B),inverse(A)).
% 1.96/2.14 ** KEPT (pick-wt=10): 40 [] inverse(greatest_lower_bound(A,B))=least_upper_bound(inverse(A),inverse(B)).
% 1.96/2.14 ---> New Demodulator: 41 [new_demod,40] inverse(greatest_lower_bound(A,B))=least_upper_bound(inverse(A),inverse(B)).
% 1.96/2.14 ** KEPT (pick-wt=10): 42 [] inverse(least_upper_bound(A,B))=greatest_lower_bound(inverse(A),inverse(B)).
% 1.96/2.14 ---> New Demodulator: 43 [new_demod,42] inverse(least_upper_bound(A,B))=greatest_lower_bound(inverse(A),inverse(B)).
% 1.96/2.14 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.96/2.14 >>>> Starting back demodulation with 5.
% 1.96/2.14 >>>> Starting back demodulation with 7.
% 1.96/2.14 >>>> Starting back demodulation with 9.
% 1.96/2.14 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] greatest_lower_bound(A,B)=greatest_lower_bound(B,A).
% 1.96/2.14 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] least_upper_bound(A,B)=least_upper_bound(B,A).
% 1.96/2.14 >>>> Starting back demodulation with 14.
% 1.96/2.14 >>>> Starting back demodulation with 17.
% 1.96/2.14 >>>> Starting back demodulation with 19.
% 1.96/2.14 >>>> Starting back demodulation with 21.
% 1.96/2.14 >>>> Starting back demodulation with 23.
% 1.96/2.14 >>>> Starting back demodulation with 25.
% 1.96/2.14 >>>> Starting back demodulation with 27.
% 1.96/2.14 >> back demodulating 2 with 27.
% 1.96/2.14 >>>> Starting back demodulation with 29.
% 1.96/2.14 >>>> Starting back demodulation with 31.
% 1.96/2.14 >>>> Starting back demodulation with 33.
% 1.96/2.14 >>>> Starting back demodulation with 35.
% 1.96/2.14 >>>> Starting back demodulation with 37.
% 1.96/2.14 >>>> Starting back demodulation with 39.
% 1.96/2.14 >>>> Starting back demodulation with 41.
% 1.96/2.14 >>>> Starting back demodulation with 43.
% 1.96/2.14
% 1.96/2.14 ======= end of input processing =======
% 1.96/2.14
% 1.96/2.14 =========== start of search ===========
% 1.96/2.14
% 1.96/2.14 -------- PROOF --------
% 1.96/2.14
% 1.96/2.14 ----> UNIT CONFLICT at 0.02 sec ----> 536 [binary,535.1,123.1] $F.
% 1.96/2.14
% 1.96/2.14 Length of proof is 14. Level of proof is 5.
% 1.96/2.14
% 1.96/2.14 ---------------- PROOF ----------------
% 1.96/2.14 % SZS status Unsatisfiable
% 1.96/2.14 % SZS output start Refutation
% See solution above
% 1.96/2.14 ------------ end of proof -------------
% 1.96/2.14
% 1.96/2.14
% 1.96/2.14 Search stopped by max_proofs option.
% 1.96/2.14
% 1.96/2.14
% 1.96/2.14 Search stopped by max_proofs option.
% 1.96/2.14
% 1.96/2.14 ============ end of search ============
% 1.96/2.14
% 1.96/2.14 -------------- statistics -------------
% 1.96/2.14 clauses given 58
% 1.96/2.14 clauses generated 1792
% 1.96/2.14 clauses kept 288
% 1.96/2.14 clauses forward subsumed 1570
% 1.96/2.14 clauses back subsumed 2
% 1.96/2.14 Kbytes malloced 2929
% 1.96/2.14
% 1.96/2.14 ----------- times (seconds) -----------
% 1.96/2.14 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.96/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.96/2.14
% 1.96/2.14 That finishes the proof of the theorem.
% 1.96/2.14
% 1.96/2.14 Process 27516 finished Wed Jul 27 05:05:40 2022
% 1.96/2.14 Otter interrupted
% 1.96/2.14 PROOF FOUND
%------------------------------------------------------------------------------