TSTP Solution File: GRP086-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP086-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 1.63s 1.88s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of clauses : 27 ( 23 unt; 0 nHn; 5 RR)
% Number of literals : 39 ( 38 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 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 : 53 ( 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('GRP086-1.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('GRP086-1.p',unknown),
[] ).
cnf(4,axiom,
multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B,
file('GRP086-1.p',unknown),
[] ).
cnf(6,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(multiply(B,C),inverse(multiply(D,C))))))) = D,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.2.1,4.1.1')] ).
cnf(8,plain,
multiply(A,multiply(multiply(B,multiply(multiply(C,D),inverse(multiply(A,D)))),inverse(C))) = B,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.2.2.1,4.1.1')] ).
cnf(18,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(para_into,[status(thm),theory(equality)],[6,4]),
[iquote('para_into,6.1.1.2.2.1,4.1.1')] ).
cnf(22,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(para_from,[status(thm),theory(equality)],[18,6]),
[iquote('para_from,18.1.1,6.1.1.2.2.1')] ).
cnf(26,plain,
multiply(multiply(A,B),multiply(C,inverse(multiply(C,B)))) = A,
inference(para_from,[status(thm),theory(equality)],[22,6]),
[iquote('para_from,22.1.1,6.1.1.2.2.1')] ).
cnf(49,plain,
multiply(A,multiply(multiply(B,C),inverse(B))) = multiply(A,C),
inference(para_into,[status(thm),theory(equality)],[8,22]),
[iquote('para_into,8.1.1.2.1,22.1.1')] ).
cnf(64,plain,
multiply(multiply(A,multiply(B,inverse(multiply(B,C)))),C) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,26]),49]),
[iquote('para_into,26.1.1.2.2.1,26.1.1,demod,49')] ).
cnf(74,plain,
multiply(multiply(A,B),multiply(C,inverse(A))) = multiply(C,B),
inference(para_from,[status(thm),theory(equality)],[26,8]),
[iquote('para_from,26.1.1,8.1.1.2.1')] ).
cnf(124,plain,
multiply(A,multiply(B,inverse(multiply(B,inverse(C))))) = multiply(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[64,49])]),
[iquote('para_from,64.1.1,48.1.1.2,flip.1')] ).
cnf(125,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[64,22]),124]),
[iquote('para_from,64.1.1,22.1.1.2,demod,124')] ).
cnf(131,plain,
multiply(multiply(A,inverse(B)),B) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[125,22])]),
[iquote('para_into,125.1.1,22.1.1,flip.1')] ).
cnf(133,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[125,18])]),
[iquote('para_into,125.1.1,18.1.1,flip.1')] ).
cnf(148,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(para_from,[status(thm),theory(equality)],[125,22]),
[iquote('para_from,125.1.1,22.1.1.2')] ).
cnf(150,plain,
multiply(A,multiply(inverse(B),B)) = A,
inference(para_from,[status(thm),theory(equality)],[125,18]),
[iquote('para_from,125.1.1,18.1.1.2')] ).
cnf(157,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(para_from,[status(thm),theory(equality)],[125,2]),
[iquote('para_from,125.1.1,2.3.1')] ).
cnf(175,plain,
multiply(multiply(inverse(A),B),A) = B,
inference(para_into,[status(thm),theory(equality)],[131,125]),
[iquote('para_into,131.1.1.1,125.1.1')] ).
cnf(212,plain,
multiply(multiply(inverse(A),A),B) = B,
inference(para_into,[status(thm),theory(equality)],[133,125]),
[iquote('para_into,133.1.1.1,125.1.1')] ).
cnf(216,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| a2 != a2
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[157]),212]),
[iquote('back_demod,157,demod,212')] ).
cnf(223,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[148,18])]),
[iquote('para_into,148.1.1,18.1.1,flip.1')] ).
cnf(224,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(para_from,[status(thm),theory(equality)],[223,148]),
[iquote('para_from,222.1.1,148.1.1.2.1')] ).
cnf(244,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(para_into,[status(thm),theory(equality)],[175,150]),
[iquote('para_into,175.1.1.1,150.1.1')] ).
cnf(285,plain,
multiply(A,multiply(B,C)) = multiply(B,multiply(C,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[224,74]),223]),
[iquote('para_from,224.1.1,74.1.1.1,demod,223')] ).
cnf(449,plain,
$false,
inference(hyper,[status(thm)],[216,244,3,285,125]),
[iquote('hyper,216,244,3,285,125')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP086-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n010.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 05:17:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.63/1.88 ----- Otter 3.3f, August 2004 -----
% 1.63/1.88 The process was started by sandbox2 on n010.cluster.edu,
% 1.63/1.88 Wed Jul 27 05:17:40 2022
% 1.63/1.88 The command was "./otter". The process ID is 22337.
% 1.63/1.88
% 1.63/1.88 set(prolog_style_variables).
% 1.63/1.88 set(auto).
% 1.63/1.88 dependent: set(auto1).
% 1.63/1.88 dependent: set(process_input).
% 1.63/1.88 dependent: clear(print_kept).
% 1.63/1.88 dependent: clear(print_new_demod).
% 1.63/1.88 dependent: clear(print_back_demod).
% 1.63/1.88 dependent: clear(print_back_sub).
% 1.63/1.88 dependent: set(control_memory).
% 1.63/1.88 dependent: assign(max_mem, 12000).
% 1.63/1.88 dependent: assign(pick_given_ratio, 4).
% 1.63/1.88 dependent: assign(stats_level, 1).
% 1.63/1.88 dependent: assign(max_seconds, 10800).
% 1.63/1.88 clear(print_given).
% 1.63/1.88
% 1.63/1.88 list(usable).
% 1.63/1.88 0 [] A=A.
% 1.63/1.88 0 [] multiply(X,multiply(multiply(Y,Z),inverse(multiply(X,Z))))=Y.
% 1.63/1.88 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).
% 1.63/1.88 end_of_list.
% 1.63/1.88
% 1.63/1.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.63/1.88
% 1.63/1.88 This is a Horn set with equality. The strategy will be
% 1.63/1.88 Knuth-Bendix and hyper_res, with positive clauses in
% 1.63/1.88 sos and nonpositive clauses in usable.
% 1.63/1.88
% 1.63/1.88 dependent: set(knuth_bendix).
% 1.63/1.88 dependent: set(anl_eq).
% 1.63/1.88 dependent: set(para_from).
% 1.63/1.88 dependent: set(para_into).
% 1.63/1.88 dependent: clear(para_from_right).
% 1.63/1.88 dependent: clear(para_into_right).
% 1.63/1.88 dependent: set(para_from_vars).
% 1.63/1.88 dependent: set(eq_units_both_ways).
% 1.63/1.88 dependent: set(dynamic_demod_all).
% 1.63/1.88 dependent: set(dynamic_demod).
% 1.63/1.88 dependent: set(order_eq).
% 1.63/1.88 dependent: set(back_demod).
% 1.63/1.88 dependent: set(lrpo).
% 1.63/1.88 dependent: set(hyper_res).
% 1.63/1.88 dependent: clear(order_hyper).
% 1.63/1.88
% 1.63/1.88 ------------> process usable:
% 1.63/1.88 ** 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).
% 1.63/1.88
% 1.63/1.88 ------------> process sos:
% 1.63/1.88 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.63/1.88 ** KEPT (pick-wt=12): 4 [] multiply(A,multiply(multiply(B,C),inverse(multiply(A,C))))=B.
% 1.63/1.88 ---> New Demodulator: 5 [new_demod,4] multiply(A,multiply(multiply(B,C),inverse(multiply(A,C))))=B.
% 1.63/1.88 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.63/1.88 >>>> Starting back demodulation with 5.
% 1.63/1.88
% 1.63/1.88 ======= end of input processing =======
% 1.63/1.88
% 1.63/1.88 =========== start of search ===========
% 1.63/1.88
% 1.63/1.88 -------- PROOF --------
% 1.63/1.88
% 1.63/1.88 -----> EMPTY CLAUSE at 0.02 sec ----> 449 [hyper,216,244,3,285,125] $F.
% 1.63/1.88
% 1.63/1.88 Length of proof is 23. Level of proof is 11.
% 1.63/1.88
% 1.63/1.88 ---------------- PROOF ----------------
% 1.63/1.88 % SZS status Unsatisfiable
% 1.63/1.88 % SZS output start Refutation
% See solution above
% 1.63/1.88 ------------ end of proof -------------
% 1.63/1.88
% 1.63/1.88
% 1.63/1.88 Search stopped by max_proofs option.
% 1.63/1.88
% 1.63/1.88
% 1.63/1.88 Search stopped by max_proofs option.
% 1.63/1.88
% 1.63/1.88 ============ end of search ============
% 1.63/1.88
% 1.63/1.88 -------------- statistics -------------
% 1.63/1.88 clauses given 41
% 1.63/1.88 clauses generated 1069
% 1.63/1.88 clauses kept 273
% 1.63/1.88 clauses forward subsumed 1100
% 1.63/1.88 clauses back subsumed 5
% 1.63/1.88 Kbytes malloced 1953
% 1.63/1.88
% 1.63/1.88 ----------- times (seconds) -----------
% 1.63/1.88 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.63/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.63/1.88 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.63/1.88
% 1.63/1.88 That finishes the proof of the theorem.
% 1.63/1.88
% 1.63/1.88 Process 22337 finished Wed Jul 27 05:17:41 2022
% 1.63/1.88 Otter interrupted
% 1.63/1.88 PROOF FOUND
%------------------------------------------------------------------------------