TSTP Solution File: GRP067-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP067-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 12:55:59 EDT 2022
% Result : Unsatisfiable 2.23s 2.40s
% Output : Refutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of clauses : 30 ( 26 unt; 0 nHn; 5 RR)
% Number of literals : 38 ( 37 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('GRP067-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP067-1.p',unknown),
[] ).
cnf(3,axiom,
divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B,
file('GRP067-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(identity,B)),
file('GRP067-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = divide(identity,A),
file('GRP067-1.p',unknown),
[] ).
cnf(9,axiom,
identity = divide(A,A),
file('GRP067-1.p',unknown),
[] ).
cnf(11,plain,
divide(A,A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(12,plain,
( identity != identity
| divide(identity,divide(identity,a2)) != a2
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),8,6,11,6,6,6,6,6]),
[iquote('back_demod,1,demod,8,6,11,6,6,6,6,6')] ).
cnf(13,plain,
divide(divide(identity,divide(A,divide(B,divide(divide(identity,A),C)))),C) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),11]),
[iquote('back_demod,3,demod,11')] ).
cnf(15,plain,
divide(divide(identity,divide(identity,divide(A,divide(identity,B)))),B) = A,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.1.2.2.2.1,10.1.1')] ).
cnf(19,plain,
divide(divide(identity,divide(A,divide(B,identity))),divide(identity,A)) = B,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.1.2.2.2,10.1.1')] ).
cnf(25,plain,
divide(divide(identity,divide(identity,divide(A,identity))),identity) = A,
inference(para_into,[status(thm),theory(equality)],[15,11]),
[iquote('para_into,15.1.1.1.2.2.2,10.1.1')] ).
cnf(28,plain,
divide(divide(identity,divide(identity,A)),B) = divide(identity,divide(identity,divide(A,divide(identity,divide(identity,B))))),
inference(para_into,[status(thm),theory(equality)],[15,15]),
[iquote('para_into,15.1.1.1.2.2,15.1.1')] ).
cnf(30,plain,
divide(identity,divide(identity,divide(divide(A,identity),identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),28,11,11]),
[iquote('back_demod,25,demod,28,11,11')] ).
cnf(32,plain,
divide(identity,divide(identity,divide(divide(A,divide(identity,B)),divide(identity,divide(identity,B))))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),28]),
[iquote('back_demod,15,demod,28')] ).
cnf(39,plain,
divide(divide(identity,divide(A,B)),divide(identity,A)) = divide(identity,divide(C,divide(B,divide(divide(identity,C),identity)))),
inference(para_into,[status(thm),theory(equality)],[19,13]),
[iquote('para_into,19.1.1.1.2.2,13.1.1')] ).
cnf(45,plain,
divide(identity,divide(identity,divide(A,identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,11]),11]),
[iquote('para_into,19.1.1.1.2,10.1.1,demod,11')] ).
cnf(49,plain,
divide(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,11]),45]),
[iquote('para_into,19.1.1.2,10.1.1,demod,45')] ).
cnf(50,plain,
divide(identity,divide(A,divide(B,divide(identity,A)))) = divide(divide(identity,divide(C,B)),divide(identity,C)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[39])]),49]),
[iquote('copy,39,flip.1,demod,49')] ).
cnf(56,plain,
divide(identity,divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[30]),49,49]),
[iquote('back_demod,30,demod,49,49')] ).
cnf(63,plain,
divide(divide(identity,divide(A,B)),divide(identity,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),49]),
[iquote('back_demod,19,demod,49')] ).
cnf(64,plain,
divide(identity,divide(A,divide(B,divide(identity,A)))) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[50])]),63])]),
[iquote('copy,50,flip.1,demod,63,flip.1')] ).
cnf(68,plain,
divide(divide(A,divide(identity,B)),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[32]),56,56]),
[iquote('back_demod,32,demod,56,56')] ).
cnf(70,plain,
( identity != identity
| a2 != a2
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),56]),
[iquote('back_demod,12,demod,56')] ).
cnf(99,plain,
divide(divide(A,B),divide(identity,B)) = A,
inference(para_into,[status(thm),theory(equality)],[68,56]),
[iquote('para_into,68.1.1.1.2,55.1.1')] ).
cnf(108,plain,
divide(divide(identity,divide(A,B)),C) = divide(B,divide(identity,divide(divide(identity,A),C))),
inference(para_from,[status(thm),theory(equality)],[68,13]),
[iquote('para_from,68.1.1,13.1.1.1.2.2')] ).
cnf(115,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(para_into,[status(thm),theory(equality)],[64,99]),
[iquote('para_into,64.1.1.2.2,99.1.1')] ).
cnf(116,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[115])]),
[iquote('copy,115,flip.1')] ).
cnf(177,plain,
( identity != identity
| a2 != a2
| divide(a3,divide(identity,divide(b3,divide(identity,c3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[70,116]),108,56]),
[iquote('para_into,70.3.1.1,116.1.1,demod,108,56')] ).
cnf(2696,plain,
$false,
inference(hyper,[status(thm)],[177,2,2,2]),
[iquote('hyper,177,2,2,2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP067-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 05:27:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.23/2.40 ----- Otter 3.3f, August 2004 -----
% 2.23/2.40 The process was started by sandbox2 on n025.cluster.edu,
% 2.23/2.40 Wed Jul 27 05:27:45 2022
% 2.23/2.40 The command was "./otter". The process ID is 31494.
% 2.23/2.40
% 2.23/2.40 set(prolog_style_variables).
% 2.23/2.40 set(auto).
% 2.23/2.40 dependent: set(auto1).
% 2.23/2.40 dependent: set(process_input).
% 2.23/2.40 dependent: clear(print_kept).
% 2.23/2.40 dependent: clear(print_new_demod).
% 2.23/2.40 dependent: clear(print_back_demod).
% 2.23/2.40 dependent: clear(print_back_sub).
% 2.23/2.40 dependent: set(control_memory).
% 2.23/2.40 dependent: assign(max_mem, 12000).
% 2.23/2.40 dependent: assign(pick_given_ratio, 4).
% 2.23/2.40 dependent: assign(stats_level, 1).
% 2.23/2.40 dependent: assign(max_seconds, 10800).
% 2.23/2.40 clear(print_given).
% 2.23/2.40
% 2.23/2.40 list(usable).
% 2.23/2.40 0 [] A=A.
% 2.23/2.40 0 [] divide(divide(divide(X,X),divide(X,divide(Y,divide(divide(identity,X),Z)))),Z)=Y.
% 2.23/2.40 0 [] multiply(X,Y)=divide(X,divide(identity,Y)).
% 2.23/2.40 0 [] inverse(X)=divide(identity,X).
% 2.23/2.40 0 [] identity=divide(X,X).
% 2.23/2.40 0 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.23/2.40 end_of_list.
% 2.23/2.40
% 2.23/2.40 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.23/2.40
% 2.23/2.40 This is a Horn set with equality. The strategy will be
% 2.23/2.40 Knuth-Bendix and hyper_res, with positive clauses in
% 2.23/2.40 sos and nonpositive clauses in usable.
% 2.23/2.40
% 2.23/2.40 dependent: set(knuth_bendix).
% 2.23/2.40 dependent: set(anl_eq).
% 2.23/2.40 dependent: set(para_from).
% 2.23/2.40 dependent: set(para_into).
% 2.23/2.40 dependent: clear(para_from_right).
% 2.23/2.40 dependent: clear(para_into_right).
% 2.23/2.40 dependent: set(para_from_vars).
% 2.23/2.40 dependent: set(eq_units_both_ways).
% 2.23/2.40 dependent: set(dynamic_demod_all).
% 2.23/2.40 dependent: set(dynamic_demod).
% 2.23/2.40 dependent: set(order_eq).
% 2.23/2.40 dependent: set(back_demod).
% 2.23/2.40 dependent: set(lrpo).
% 2.23/2.40 dependent: set(hyper_res).
% 2.23/2.40 dependent: clear(order_hyper).
% 2.23/2.40
% 2.23/2.40 ------------> process usable:
% 2.23/2.40 ** KEPT (pick-wt=22): 1 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.23/2.40
% 2.23/2.40 ------------> process sos:
% 2.23/2.40 ** KEPT (pick-wt=3): 2 [] A=A.
% 2.23/2.40 ** KEPT (pick-wt=17): 3 [] divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C)=B.
% 2.23/2.40 ---> New Demodulator: 4 [new_demod,3] divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C)=B.
% 2.23/2.40 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=divide(A,divide(identity,B)).
% 2.23/2.40 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=divide(A,divide(identity,B)).
% 2.23/2.40 ** KEPT (pick-wt=6): 7 [] inverse(A)=divide(identity,A).
% 2.23/2.40 ---> New Demodulator: 8 [new_demod,7] inverse(A)=divide(identity,A).
% 2.23/2.40 ** KEPT (pick-wt=5): 10 [copy,9,flip.1] divide(A,A)=identity.
% 2.23/2.40 ---> New Demodulator: 11 [new_demod,10] divide(A,A)=identity.
% 2.23/2.40 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.23/2.40 >>>> Starting back demodulation with 4.
% 2.23/2.40 >>>> Starting back demodulation with 6.
% 2.23/2.40 >> back demodulating 1 with 6.
% 2.23/2.40 >>>> Starting back demodulation with 8.
% 2.23/2.40 >>>> Starting back demodulation with 11.
% 2.23/2.40 >> back demodulating 3 with 11.
% 2.23/2.40 >>>> Starting back demodulation with 14.
% 2.23/2.40
% 2.23/2.40 ======= end of input processing =======
% 2.23/2.40
% 2.23/2.40 =========== start of search ===========
% 2.23/2.40
% 2.23/2.40 -------- PROOF --------
% 2.23/2.40
% 2.23/2.40 -----> EMPTY CLAUSE at 0.28 sec ----> 2696 [hyper,177,2,2,2] $F.
% 2.23/2.40
% 2.23/2.40 Length of proof is 23. Level of proof is 11.
% 2.23/2.40
% 2.23/2.40 ---------------- PROOF ----------------
% 2.23/2.40 % SZS status Unsatisfiable
% 2.23/2.40 % SZS output start Refutation
% See solution above
% 2.23/2.40 ------------ end of proof -------------
% 2.23/2.40
% 2.23/2.40
% 2.23/2.40 Search stopped by max_proofs option.
% 2.23/2.40
% 2.23/2.40
% 2.23/2.40 Search stopped by max_proofs option.
% 2.23/2.40
% 2.23/2.40 ============ end of search ============
% 2.23/2.40
% 2.23/2.40 -------------- statistics -------------
% 2.23/2.40 clauses given 81
% 2.23/2.40 clauses generated 9655
% 2.23/2.40 clauses kept 2247
% 2.23/2.40 clauses forward subsumed 9693
% 2.23/2.40 clauses back subsumed 67
% 2.23/2.40 Kbytes malloced 3906
% 2.23/2.40
% 2.23/2.40 ----------- times (seconds) -----------
% 2.23/2.40 user CPU time 0.28 (0 hr, 0 min, 0 sec)
% 2.23/2.40 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.23/2.40 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.23/2.40
% 2.23/2.40 That finishes the proof of the theorem.
% 2.23/2.40
% 2.23/2.40 Process 31494 finished Wed Jul 27 05:27:47 2022
% 2.23/2.40 Otter interrupted
% 2.23/2.40 PROOF FOUND
%------------------------------------------------------------------------------