TSTP Solution File: GRP087-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP087-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 12:56:01 EDT 2022
% Result : Unsatisfiable 1.67s 1.83s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of clauses : 25 ( 21 unt; 0 nHn; 5 RR)
% Number of literals : 37 ( 36 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
file('GRP087-1.p',unknown),
[] ).
cnf(2,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])])]),
[iquote('copy,1,flip.1,flip.4')] ).
cnf(3,axiom,
A = A,
file('GRP087-1.p',unknown),
[] ).
cnf(4,axiom,
multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C,
file('GRP087-1.p',unknown),
[] ).
cnf(6,plain,
multiply(A,multiply(multiply(inverse(B),C),multiply(multiply(inverse(multiply(A,D)),B),D))) = C,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.2.1.1.1,4.1.1')] ).
cnf(8,plain,
multiply(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D),C) = multiply(A,multiply(D,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,4])]),
[iquote('para_into,4.1.1.2.1,4.1.1,flip.1')] ).
cnf(18,plain,
multiply(multiply(inverse(A),B),A) = B,
inference(para_into,[status(thm),theory(equality)],[6,4]),
[iquote('para_into,6.1.1.2,4.1.1')] ).
cnf(24,plain,
multiply(multiply(inverse(A),B),multiply(multiply(inverse(multiply(inverse(C),D)),A),D)) = multiply(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[18,6])]),
[iquote('para_into,18.1.1.1,6.1.1,flip.1')] ).
cnf(27,plain,
multiply(multiply(inverse(multiply(inverse(A),B)),C),B) = multiply(C,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[18,4])]),
[iquote('para_into,18.1.1.1,4.1.1,flip.1')] ).
cnf(30,plain,
multiply(multiply(inverse(A),B),multiply(A,C)) = multiply(B,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[24]),27]),
[iquote('back_demod,24,demod,27')] ).
cnf(34,plain,
multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[8]),27]),
[iquote('back_demod,8,demod,27')] ).
cnf(35,plain,
multiply(multiply(inverse(A),B),multiply(multiply(inverse(B),C),A)) = C,
inference(para_from,[status(thm),theory(equality)],[18,4]),
[iquote('para_from,18.1.1,4.1.1.2.1.1.1')] ).
cnf(38,plain,
multiply(A,B) = multiply(multiply(inverse(C),B),multiply(A,C)),
inference(para_into,[status(thm),theory(equality)],[34,18]),
[iquote('para_into,34.1.1.2,18.1.1')] ).
cnf(86,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[30,4]),27])]),
[iquote('para_into,30.1.1.1,4.1.1,demod,27,flip.1')] ).
cnf(93,plain,
multiply(A,multiply(inverse(A),multiply(B,C))) = multiply(B,C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[30,34]),86]),
[iquote('para_into,30.1.1,34.1.1,demod,86')] ).
cnf(121,plain,
multiply(A,B) = multiply(inverse(C),multiply(B,multiply(A,C))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[38]),86]),
[iquote('back_demod,38,demod,86')] ).
cnf(122,plain,
multiply(inverse(A),multiply(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[35]),86,86,93]),
[iquote('back_demod,35,demod,86,86,93')] ).
cnf(128,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| multiply(inverse(b2),multiply(b2,a2)) != a2
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),86,86]),
[iquote('back_demod,2,demod,86,86')] ).
cnf(136,plain,
multiply(A,multiply(inverse(B),B)) = A,
inference(para_into,[status(thm),theory(equality)],[122,34]),
[iquote('para_into,122.1.1,34.1.1')] ).
cnf(139,plain,
multiply(inverse(A),multiply(B,multiply(C,A))) = multiply(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[122,34])]),
[iquote('para_from,122.1.1,34.1.1.2,flip.1')] ).
cnf(140,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[121]),139]),
[iquote('back_demod,121,demod,139')] ).
cnf(145,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(para_from,[status(thm),theory(equality)],[140,122]),
[iquote('para_from,140.1.1,122.1.1.2')] ).
cnf(147,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| a2 != a2
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[128]),145]),
[iquote('back_demod,128,demod,145')] ).
cnf(188,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(para_into,[status(thm),theory(equality)],[145,136]),
[iquote('para_into,144.1.1.2,136.1.1')] ).
cnf(331,plain,
$false,
inference(hyper,[status(thm)],[147,188,3,3,140]),
[iquote('hyper,147,188,3,3,140')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP087-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 04:59:06 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.67/1.83 ----- Otter 3.3f, August 2004 -----
% 1.67/1.83 The process was started by sandbox2 on n004.cluster.edu,
% 1.67/1.83 Wed Jul 27 04:59:06 2022
% 1.67/1.83 The command was "./otter". The process ID is 12563.
% 1.67/1.83
% 1.67/1.83 set(prolog_style_variables).
% 1.67/1.83 set(auto).
% 1.67/1.83 dependent: set(auto1).
% 1.67/1.83 dependent: set(process_input).
% 1.67/1.83 dependent: clear(print_kept).
% 1.67/1.83 dependent: clear(print_new_demod).
% 1.67/1.83 dependent: clear(print_back_demod).
% 1.67/1.83 dependent: clear(print_back_sub).
% 1.67/1.83 dependent: set(control_memory).
% 1.67/1.83 dependent: assign(max_mem, 12000).
% 1.67/1.83 dependent: assign(pick_given_ratio, 4).
% 1.67/1.83 dependent: assign(stats_level, 1).
% 1.67/1.83 dependent: assign(max_seconds, 10800).
% 1.67/1.83 clear(print_given).
% 1.67/1.83
% 1.67/1.83 list(usable).
% 1.67/1.83 0 [] A=A.
% 1.67/1.83 0 [] multiply(X,multiply(multiply(inverse(multiply(X,Y)),Z),Y))=Z.
% 1.67/1.83 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1)|multiply(multiply(inverse(b2),b2),a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3))|multiply(a4,b4)!=multiply(b4,a4).
% 1.67/1.83 end_of_list.
% 1.67/1.83
% 1.67/1.83 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.67/1.83
% 1.67/1.83 This is a Horn set with equality. The strategy will be
% 1.67/1.83 Knuth-Bendix and hyper_res, with positive clauses in
% 1.67/1.83 sos and nonpositive clauses in usable.
% 1.67/1.83
% 1.67/1.83 dependent: set(knuth_bendix).
% 1.67/1.83 dependent: set(anl_eq).
% 1.67/1.83 dependent: set(para_from).
% 1.67/1.83 dependent: set(para_into).
% 1.67/1.83 dependent: clear(para_from_right).
% 1.67/1.83 dependent: clear(para_into_right).
% 1.67/1.83 dependent: set(para_from_vars).
% 1.67/1.83 dependent: set(eq_units_both_ways).
% 1.67/1.83 dependent: set(dynamic_demod_all).
% 1.67/1.83 dependent: set(dynamic_demod).
% 1.67/1.83 dependent: set(order_eq).
% 1.67/1.83 dependent: set(back_demod).
% 1.67/1.83 dependent: set(lrpo).
% 1.67/1.83 dependent: set(hyper_res).
% 1.67/1.83 dependent: clear(order_hyper).
% 1.67/1.83
% 1.67/1.83 ------------> process usable:
% 1.67/1.83 ** KEPT (pick-wt=35): 2 [copy,1,flip.1,flip.4] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1)|multiply(multiply(inverse(b2),b2),a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3))|multiply(b4,a4)!=multiply(a4,b4).
% 1.67/1.83
% 1.67/1.83 ------------> process sos:
% 1.67/1.83 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.67/1.83 ** KEPT (pick-wt=12): 4 [] multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B))=C.
% 1.67/1.83 ---> New Demodulator: 5 [new_demod,4] multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B))=C.
% 1.67/1.83 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.67/1.83 >>>> Starting back demodulation with 5.
% 1.67/1.83
% 1.67/1.83 ======= end of input processing =======
% 1.67/1.83
% 1.67/1.83 =========== start of search ===========
% 1.67/1.83
% 1.67/1.83 -------- PROOF --------
% 1.67/1.83
% 1.67/1.83 -----> EMPTY CLAUSE at 0.01 sec ----> 331 [hyper,147,188,3,3,140] $F.
% 1.67/1.83
% 1.67/1.83 Length of proof is 21. Level of proof is 11.
% 1.67/1.83
% 1.67/1.83 ---------------- PROOF ----------------
% 1.67/1.83 % SZS status Unsatisfiable
% 1.67/1.83 % SZS output start Refutation
% See solution above
% 1.67/1.83 ------------ end of proof -------------
% 1.67/1.83
% 1.67/1.83
% 1.67/1.83 Search stopped by max_proofs option.
% 1.67/1.83
% 1.67/1.83
% 1.67/1.83 Search stopped by max_proofs option.
% 1.67/1.83
% 1.67/1.83 ============ end of search ============
% 1.67/1.83
% 1.67/1.83 -------------- statistics -------------
% 1.67/1.83 clauses given 36
% 1.67/1.83 clauses generated 1378
% 1.67/1.83 clauses kept 242
% 1.67/1.83 clauses forward subsumed 1376
% 1.67/1.83 clauses back subsumed 2
% 1.67/1.83 Kbytes malloced 1953
% 1.67/1.83
% 1.67/1.83 ----------- times (seconds) -----------
% 1.67/1.83 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.67/1.83 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.83 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.83
% 1.67/1.83 That finishes the proof of the theorem.
% 1.67/1.83
% 1.67/1.83 Process 12563 finished Wed Jul 27 04:59:07 2022
% 1.67/1.83 Otter interrupted
% 1.67/1.83 PROOF FOUND
%------------------------------------------------------------------------------