TSTP Solution File: GRP448-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP448-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 12:57:02 EDT 2022
% Result : Unsatisfiable 1.79s 1.98s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 6 RR)
% Number of literals : 28 ( 27 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP448-1.p',unknown),
[] ).
cnf(2,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C))) = B,
file('GRP448-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP448-1.p',unknown),
[] ).
cnf(7,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP448-1.p',unknown),
[] ).
cnf(8,plain,
divide(A,divide(divide(B,B),C)) = multiply(A,C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(9,plain,
divide(divide(A,A),B) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(11,plain,
multiply(divide(divide(A,A),b1),b1) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[7,2]),
[iquote('para_from,7.1.1,2.1.1.1')] ).
cnf(13,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.1,9.1.1')] ).
cnf(14,plain,
inverse(A) = divide(inverse(divide(B,B)),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(16,plain,
divide(inverse(inverse(divide(A,A))),B) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[13,9]),
[iquote('para_into,13.1.1.1.1,9.1.1')] ).
cnf(21,plain,
divide(inverse(divide(A,A)),B) = divide(inverse(divide(C,C)),B),
inference(para_into,[status(thm),theory(equality)],[14,14]),
[iquote('para_into,14.1.1,14.1.1')] ).
cnf(31,plain,
divide(A,divide(divide(inverse(B),C),divide(divide(divide(B,B),A),C))) = B,
inference(para_into,[status(thm),theory(equality)],[4,9]),
[iquote('para_into,4.1.1.2.1.1,9.1.1')] ).
cnf(89,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[8,9]),
[iquote('para_into,8.1.1.2,9.1.1')] ).
cnf(156,plain,
inverse(inverse(A)) = multiply(divide(B,B),A),
inference(para_into,[status(thm),theory(equality)],[89,9]),
[iquote('para_into,89.1.1,9.1.1')] ).
cnf(160,plain,
multiply(divide(A,A),B) = inverse(inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[156])]),
[iquote('copy,156,flip.1')] ).
cnf(164,plain,
divide(multiply(inverse(A),A),B) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[89,9]),
[iquote('para_from,89.1.1,9.1.1.1')] ).
cnf(165,plain,
divide(A,multiply(divide(B,B),C)) = multiply(A,inverse(C)),
inference(para_from,[status(thm),theory(equality)],[89,8]),
[iquote('para_from,89.1.1,8.1.1.2')] ).
cnf(204,plain,
divide(divide(divide(A,A),b1),divide(divide(B,B),b1)) != multiply(inverse(a1),a1),
inference(para_into,[status(thm),theory(equality)],[11,6]),
[iquote('para_into,11.1.1,6.1.1')] ).
cnf(208,plain,
multiply(inverse(a1),a1) != divide(divide(divide(A,A),b1),divide(divide(B,B),b1)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[204])]),
[iquote('copy,204,flip.1')] ).
cnf(220,plain,
divide(inverse(inverse(inverse(multiply(inverse(A),A)))),B) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[164,16]),
[iquote('para_from,164.1.1,16.1.1.1.1.1')] ).
cnf(392,plain,
divide(divide(A,A),multiply(divide(inverse(A),B),B)) = A,
inference(para_into,[status(thm),theory(equality)],[31,8]),
[iquote('para_into,31.1.1.2,8.1.1')] ).
cnf(402,plain,
multiply(divide(A,A),inverse(inverse(A))) = A,
inference(para_into,[status(thm),theory(equality)],[392,165]),
[iquote('para_into,392.1.1,165.1.1')] ).
cnf(407,plain,
inverse(multiply(divide(inverse(A),B),B)) = A,
inference(para_into,[status(thm),theory(equality)],[392,9]),
[iquote('para_into,392.1.1,9.1.1')] ).
cnf(429,plain,
inverse(inverse(inverse(inverse(A)))) = A,
inference(para_into,[status(thm),theory(equality)],[402,160]),
[iquote('para_into,402.1.1,160.1.1')] ).
cnf(526,plain,
divide(A,A) = divide(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[407,21]),407]),
[iquote('para_into,406.1.1.1.1,21.1.1,demod,407')] ).
cnf(543,plain,
multiply(inverse(A),A) = divide(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[526,220]),429]),
[iquote('para_into,526.1.1,220.1.1,demod,429')] ).
cnf(544,plain,
$false,
inference(binary,[status(thm)],[543,208]),
[iquote('binary,543.1,208.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP448-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 05:07:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.79/1.98 ----- Otter 3.3f, August 2004 -----
% 1.79/1.98 The process was started by sandbox on n018.cluster.edu,
% 1.79/1.98 Wed Jul 27 05:07:31 2022
% 1.79/1.98 The command was "./otter". The process ID is 25178.
% 1.79/1.98
% 1.79/1.98 set(prolog_style_variables).
% 1.79/1.98 set(auto).
% 1.79/1.98 dependent: set(auto1).
% 1.79/1.98 dependent: set(process_input).
% 1.79/1.98 dependent: clear(print_kept).
% 1.79/1.98 dependent: clear(print_new_demod).
% 1.79/1.98 dependent: clear(print_back_demod).
% 1.79/1.98 dependent: clear(print_back_sub).
% 1.79/1.98 dependent: set(control_memory).
% 1.79/1.98 dependent: assign(max_mem, 12000).
% 1.79/1.98 dependent: assign(pick_given_ratio, 4).
% 1.79/1.98 dependent: assign(stats_level, 1).
% 1.79/1.98 dependent: assign(max_seconds, 10800).
% 1.79/1.98 clear(print_given).
% 1.79/1.98
% 1.79/1.98 list(usable).
% 1.79/1.98 0 [] A=A.
% 1.79/1.98 0 [] divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C)))=B.
% 1.79/1.98 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.79/1.98 0 [] inverse(A)=divide(divide(B,B),A).
% 1.79/1.98 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.79/1.98 end_of_list.
% 1.79/1.98
% 1.79/1.98 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.79/1.98
% 1.79/1.98 All clauses are units, and equality is present; the
% 1.79/1.98 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.79/1.98
% 1.79/1.98 dependent: set(knuth_bendix).
% 1.79/1.98 dependent: set(anl_eq).
% 1.79/1.98 dependent: set(para_from).
% 1.79/1.98 dependent: set(para_into).
% 1.79/1.98 dependent: clear(para_from_right).
% 1.79/1.98 dependent: clear(para_into_right).
% 1.79/1.98 dependent: set(para_from_vars).
% 1.79/1.98 dependent: set(eq_units_both_ways).
% 1.79/1.98 dependent: set(dynamic_demod_all).
% 1.79/1.98 dependent: set(dynamic_demod).
% 1.79/1.98 dependent: set(order_eq).
% 1.79/1.98 dependent: set(back_demod).
% 1.79/1.98 dependent: set(lrpo).
% 1.79/1.98
% 1.79/1.98 ------------> process usable:
% 1.79/1.98 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.79/1.98
% 1.79/1.98 ------------> process sos:
% 1.79/1.98 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.79/1.98 ** KEPT (pick-wt=19): 4 [] divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C)))=B.
% 1.79/1.98 ---> New Demodulator: 5 [new_demod,4] divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C)))=B.
% 1.79/1.98 ** KEPT (pick-wt=11): 6 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.79/1.98 ** KEPT (pick-wt=8): 7 [] inverse(A)=divide(divide(B,B),A).
% 1.79/1.98 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.79/1.98 >>>> Starting back demodulation with 5.
% 1.79/1.98 ** KEPT (pick-wt=11): 8 [copy,6,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.79/1.98 ** KEPT (pick-wt=8): 9 [copy,7,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.79/1.98 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.79/1.98 Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.79/1.98
% 1.79/1.98 ======= end of input processing =======
% 1.79/1.98
% 1.79/1.98 =========== start of search ===========
% 1.79/1.98
% 1.79/1.98
% 1.79/1.98 Resetting weight limit to 12.
% 1.79/1.98
% 1.79/1.98
% 1.79/1.98 Resetting weight limit to 12.
% 1.79/1.98
% 1.79/1.98 sos_size=311
% 1.79/1.98
% 1.79/1.98
% 1.79/1.98 Resetting weight limit to 10.
% 1.79/1.98
% 1.79/1.98
% 1.79/1.98 Resetting weight limit to 10.
% 1.79/1.98
% 1.79/1.98 sos_size=314
% 1.79/1.98
% 1.79/1.98 -------- PROOF --------
% 1.79/1.98
% 1.79/1.98 ----> UNIT CONFLICT at 0.09 sec ----> 544 [binary,543.1,208.1] $F.
% 1.79/1.98
% 1.79/1.98 Length of proof is 23. Level of proof is 6.
% 1.79/1.98
% 1.79/1.98 ---------------- PROOF ----------------
% 1.79/1.98 % SZS status Unsatisfiable
% 1.79/1.98 % SZS output start Refutation
% See solution above
% 1.79/1.98 ------------ end of proof -------------
% 1.79/1.98
% 1.79/1.98
% 1.79/1.98 Search stopped by max_proofs option.
% 1.79/1.98
% 1.79/1.98
% 1.79/1.98 Search stopped by max_proofs option.
% 1.79/1.98
% 1.79/1.98 ============ end of search ============
% 1.79/1.98
% 1.79/1.98 -------------- statistics -------------
% 1.79/1.98 clauses given 105
% 1.79/1.98 clauses generated 8362
% 1.79/1.98 clauses kept 444
% 1.79/1.98 clauses forward subsumed 768
% 1.79/1.98 clauses back subsumed 0
% 1.79/1.98 Kbytes malloced 5859
% 1.79/1.98
% 1.79/1.98 ----------- times (seconds) -----------
% 1.79/1.98 user CPU time 0.09 (0 hr, 0 min, 0 sec)
% 1.79/1.98 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.79/1.98 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.79/1.98
% 1.79/1.98 That finishes the proof of the theorem.
% 1.79/1.98
% 1.79/1.98 Process 25178 finished Wed Jul 27 05:07:32 2022
% 1.79/1.98 Otter interrupted
% 1.79/1.98 PROOF FOUND
%------------------------------------------------------------------------------