TSTP Solution File: GRP528-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP528-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 12:57:11 EDT 2022
% Result : Unsatisfiable 1.57s 1.77s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 3 RR)
% Number of literals : 25 ( 24 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP528-1.p',unknown),
[] ).
cnf(2,plain,
multiply(b,a) != multiply(a,b),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
divide(A,divide(divide(A,B),divide(C,B))) = C,
file('GRP528-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP528-1.p',unknown),
[] ).
cnf(7,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP528-1.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,
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(34,plain,
divide(A,inverse(divide(B,A))) = B,
inference(para_into,[status(thm),theory(equality)],[4,9]),
[iquote('para_into,4.1.1.2,9.1.1')] ).
cnf(44,plain,
divide(inverse(divide(A,B)),inverse(A)) = B,
inference(para_into,[status(thm),theory(equality)],[34,34]),
[iquote('para_into,34.1.1.2.1,34.1.1')] ).
cnf(48,plain,
divide(divide(divide(A,B),divide(C,B)),inverse(C)) = A,
inference(para_into,[status(thm),theory(equality)],[34,4]),
[iquote('para_into,34.1.1.2.1,4.1.1')] ).
cnf(56,plain,
inverse(inverse(divide(A,divide(B,B)))) = A,
inference(para_into,[status(thm),theory(equality)],[34,9]),
[iquote('para_into,34.1.1,9.1.1')] ).
cnf(67,plain,
inverse(divide(A,B)) = divide(inverse(A),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[44,34])]),
[iquote('para_into,44.1.1.1.1,34.1.1,flip.1')] ).
cnf(82,plain,
inverse(inverse(A)) = A,
inference(para_into,[status(thm),theory(equality)],[44,11]),
[iquote('para_into,44.1.1,11.1.1')] ).
cnf(89,plain,
divide(A,divide(B,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[56]),67,67,67,82,67,82,82]),
[iquote('back_demod,56,demod,67,67,67,82,67,82,82')] ).
cnf(106,plain,
divide(divide(A,A),inverse(B)) = B,
inference(para_into,[status(thm),theory(equality)],[82,7]),
[iquote('para_into,81.1.1,7.1.1')] ).
cnf(107,plain,
divide(A,divide(A,B)) = B,
inference(para_from,[status(thm),theory(equality)],[89,4]),
[iquote('para_from,89.1.1,4.1.1.2')] ).
cnf(113,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[107,4])]),
[iquote('para_into,107.1.1.2,4.1.1,flip.1')] ).
cnf(116,plain,
divide(divide(A,B),inverse(B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[48]),113]),
[iquote('back_demod,48,demod,113')] ).
cnf(130,plain,
multiply(A,divide(divide(B,B),C)) = divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,107])]),
[iquote('para_into,8.1.1.2,107.1.1,flip.1')] ).
cnf(147,plain,
divide(multiply(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[8,116]),67,67,106]),
[iquote('para_from,8.1.1,116.1.1.1,demod,67,67,106')] ).
cnf(156,plain,
multiply(divide(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[147,8]),130]),
[iquote('para_into,147.1.1,8.1.1,demod,130')] ).
cnf(158,plain,
divide(multiply(A,B),A) = B,
inference(para_from,[status(thm),theory(equality)],[147,107]),
[iquote('para_from,147.1.1,107.1.1.2')] ).
cnf(168,plain,
multiply(A,B) = multiply(B,A),
inference(para_from,[status(thm),theory(equality)],[158,156]),
[iquote('para_from,158.1.1,156.1.1.1')] ).
cnf(169,plain,
$false,
inference(binary,[status(thm)],[168,2]),
[iquote('binary,168.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP528-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:21:51 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.57/1.77 ----- Otter 3.3f, August 2004 -----
% 1.57/1.77 The process was started by sandbox2 on n009.cluster.edu,
% 1.57/1.77 Wed Jul 27 05:21:51 2022
% 1.57/1.77 The command was "./otter". The process ID is 21254.
% 1.57/1.77
% 1.57/1.77 set(prolog_style_variables).
% 1.57/1.77 set(auto).
% 1.57/1.77 dependent: set(auto1).
% 1.57/1.77 dependent: set(process_input).
% 1.57/1.77 dependent: clear(print_kept).
% 1.57/1.77 dependent: clear(print_new_demod).
% 1.57/1.77 dependent: clear(print_back_demod).
% 1.57/1.77 dependent: clear(print_back_sub).
% 1.57/1.77 dependent: set(control_memory).
% 1.57/1.77 dependent: assign(max_mem, 12000).
% 1.57/1.77 dependent: assign(pick_given_ratio, 4).
% 1.57/1.77 dependent: assign(stats_level, 1).
% 1.57/1.77 dependent: assign(max_seconds, 10800).
% 1.57/1.77 clear(print_given).
% 1.57/1.77
% 1.57/1.77 list(usable).
% 1.57/1.77 0 [] A=A.
% 1.57/1.77 0 [] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.57/1.77 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.57/1.77 0 [] inverse(A)=divide(divide(B,B),A).
% 1.57/1.77 0 [] multiply(a,b)!=multiply(b,a).
% 1.57/1.77 end_of_list.
% 1.57/1.77
% 1.57/1.77 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.57/1.77
% 1.57/1.77 All clauses are units, and equality is present; the
% 1.57/1.77 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.57/1.77
% 1.57/1.77 dependent: set(knuth_bendix).
% 1.57/1.77 dependent: set(anl_eq).
% 1.57/1.77 dependent: set(para_from).
% 1.57/1.77 dependent: set(para_into).
% 1.57/1.77 dependent: clear(para_from_right).
% 1.57/1.77 dependent: clear(para_into_right).
% 1.57/1.77 dependent: set(para_from_vars).
% 1.57/1.77 dependent: set(eq_units_both_ways).
% 1.57/1.77 dependent: set(dynamic_demod_all).
% 1.57/1.77 dependent: set(dynamic_demod).
% 1.57/1.77 dependent: set(order_eq).
% 1.57/1.77 dependent: set(back_demod).
% 1.57/1.77 dependent: set(lrpo).
% 1.57/1.77
% 1.57/1.77 ------------> process usable:
% 1.57/1.77 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.57/1.77
% 1.57/1.77 ------------> process sos:
% 1.57/1.77 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.57/1.77 ** KEPT (pick-wt=11): 4 [] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.57/1.77 ---> New Demodulator: 5 [new_demod,4] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.57/1.77 ** KEPT (pick-wt=11): 6 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.57/1.77 ** KEPT (pick-wt=8): 7 [] inverse(A)=divide(divide(B,B),A).
% 1.57/1.77 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.57/1.77 >>>> Starting back demodulation with 5.
% 1.57/1.77 ** KEPT (pick-wt=11): 8 [copy,6,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.57/1.77 ** KEPT (pick-wt=8): 9 [copy,7,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.57/1.77 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.57/1.77 Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.57/1.77
% 1.57/1.77 ======= end of input processing =======
% 1.57/1.77
% 1.57/1.77 =========== start of search ===========
% 1.57/1.77
% 1.57/1.77 -------- PROOF --------
% 1.57/1.77
% 1.57/1.77 ----> UNIT CONFLICT at 0.00 sec ----> 169 [binary,168.1,2.1] $F.
% 1.57/1.77
% 1.57/1.77 Length of proof is 20. Level of proof is 11.
% 1.57/1.77
% 1.57/1.77 ---------------- PROOF ----------------
% 1.57/1.77 % SZS status Unsatisfiable
% 1.57/1.77 % SZS output start Refutation
% See solution above
% 1.57/1.77 ------------ end of proof -------------
% 1.57/1.77
% 1.57/1.77
% 1.57/1.77 Search stopped by max_proofs option.
% 1.57/1.77
% 1.57/1.77
% 1.57/1.77 Search stopped by max_proofs option.
% 1.57/1.77
% 1.57/1.77 ============ end of search ============
% 1.57/1.77
% 1.57/1.77 -------------- statistics -------------
% 1.57/1.77 clauses given 22
% 1.57/1.77 clauses generated 252
% 1.57/1.77 clauses kept 111
% 1.57/1.77 clauses forward subsumed 255
% 1.57/1.77 clauses back subsumed 2
% 1.57/1.77 Kbytes malloced 1953
% 1.57/1.77
% 1.57/1.77 ----------- times (seconds) -----------
% 1.57/1.77 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.57/1.77 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.57/1.77 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.57/1.77
% 1.57/1.77 That finishes the proof of the theorem.
% 1.57/1.77
% 1.57/1.77 Process 21254 finished Wed Jul 27 05:21:52 2022
% 1.57/1.77 Otter interrupted
% 1.57/1.77 PROOF FOUND
%------------------------------------------------------------------------------