TSTP Solution File: GRP538-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP538-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 12:57:12 EDT 2022
% Result : Unsatisfiable 1.82s 2.04s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 3 RR)
% Number of literals : 12 ( 11 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP538-1.p',unknown),
[] ).
cnf(3,axiom,
divide(divide(A,B),divide(divide(A,C),B)) = C,
file('GRP538-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP538-1.p',unknown),
[] ).
cnf(6,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP538-1.p',unknown),
[] ).
cnf(7,axiom,
identity = divide(A,A),
file('GRP538-1.p',unknown),
[] ).
cnf(9,plain,
divide(A,A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(11,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),9])]),
[iquote('copy,5,flip.1,demod,9,flip.1')] ).
cnf(13,plain,
inverse(A) = divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),9])]),
[iquote('copy,6,flip.1,demod,9,flip.1')] ).
cnf(14,plain,
divide(identity,divide(identity,a2)) != a2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),13,11,9,11]),
[iquote('back_demod,1,demod,13,11,9,11')] ).
cnf(15,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(para_into,[status(thm),theory(equality)],[3,9]),
[iquote('para_into,3.1.1.1,8.1.1')] ).
cnf(29,plain,
divide(identity,divide(identity,A)) = A,
inference(para_into,[status(thm),theory(equality)],[15,9]),
[iquote('para_into,15.1.1.2.1,8.1.1')] ).
cnf(31,plain,
$false,
inference(binary,[status(thm)],[29,14]),
[iquote('binary,29.1,14.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP538-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n020.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 05:10:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.82/2.04 ----- Otter 3.3f, August 2004 -----
% 1.82/2.04 The process was started by sandbox on n020.cluster.edu,
% 1.82/2.04 Wed Jul 27 05:10:53 2022
% 1.82/2.04 The command was "./otter". The process ID is 30677.
% 1.82/2.04
% 1.82/2.04 set(prolog_style_variables).
% 1.82/2.04 set(auto).
% 1.82/2.04 dependent: set(auto1).
% 1.82/2.04 dependent: set(process_input).
% 1.82/2.04 dependent: clear(print_kept).
% 1.82/2.04 dependent: clear(print_new_demod).
% 1.82/2.04 dependent: clear(print_back_demod).
% 1.82/2.04 dependent: clear(print_back_sub).
% 1.82/2.04 dependent: set(control_memory).
% 1.82/2.04 dependent: assign(max_mem, 12000).
% 1.82/2.04 dependent: assign(pick_given_ratio, 4).
% 1.82/2.04 dependent: assign(stats_level, 1).
% 1.82/2.04 dependent: assign(max_seconds, 10800).
% 1.82/2.04 clear(print_given).
% 1.82/2.04
% 1.82/2.04 list(usable).
% 1.82/2.04 0 [] A=A.
% 1.82/2.04 0 [] divide(divide(A,B),divide(divide(A,C),B))=C.
% 1.82/2.04 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.82/2.04 0 [] inverse(A)=divide(divide(B,B),A).
% 1.82/2.04 0 [] identity=divide(A,A).
% 1.82/2.04 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.82/2.04 end_of_list.
% 1.82/2.04
% 1.82/2.04 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.82/2.04
% 1.82/2.04 All clauses are units, and equality is present; the
% 1.82/2.04 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.82/2.04
% 1.82/2.04 dependent: set(knuth_bendix).
% 1.82/2.04 dependent: set(anl_eq).
% 1.82/2.04 dependent: set(para_from).
% 1.82/2.04 dependent: set(para_into).
% 1.82/2.04 dependent: clear(para_from_right).
% 1.82/2.04 dependent: clear(para_into_right).
% 1.82/2.04 dependent: set(para_from_vars).
% 1.82/2.04 dependent: set(eq_units_both_ways).
% 1.82/2.04 dependent: set(dynamic_demod_all).
% 1.82/2.04 dependent: set(dynamic_demod).
% 1.82/2.04 dependent: set(order_eq).
% 1.82/2.04 dependent: set(back_demod).
% 1.82/2.04 dependent: set(lrpo).
% 1.82/2.04
% 1.82/2.04 ------------> process usable:
% 1.82/2.04 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.82/2.04
% 1.82/2.04 ------------> process sos:
% 1.82/2.04 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.82/2.04 ** KEPT (pick-wt=11): 3 [] divide(divide(A,B),divide(divide(A,C),B))=C.
% 1.82/2.04 ---> New Demodulator: 4 [new_demod,3] divide(divide(A,B),divide(divide(A,C),B))=C.
% 1.82/2.04 ** KEPT (pick-wt=11): 5 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.82/2.04 ** KEPT (pick-wt=8): 6 [] inverse(A)=divide(divide(B,B),A).
% 1.82/2.04 ** KEPT (pick-wt=5): 8 [copy,7,flip.1] divide(A,A)=identity.
% 1.82/2.04 ---> New Demodulator: 9 [new_demod,8] divide(A,A)=identity.
% 1.82/2.04 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.82/2.04 >>>> Starting back demodulation with 4.
% 1.82/2.04 ** KEPT (pick-wt=9): 10 [copy,5,flip.1,demod,9,flip.1] multiply(A,B)=divide(A,divide(identity,B)).
% 1.82/2.04 ---> New Demodulator: 11 [new_demod,10] multiply(A,B)=divide(A,divide(identity,B)).
% 1.82/2.04 ** KEPT (pick-wt=6): 12 [copy,6,flip.1,demod,9,flip.1] inverse(A)=divide(identity,A).
% 1.82/2.04 ---> New Demodulator: 13 [new_demod,12] inverse(A)=divide(identity,A).
% 1.82/2.04 >>>> Starting back demodulation with 9.
% 1.82/2.04 >> back demodulating 6 with 9.
% 1.82/2.04 >> back demodulating 5 with 9.
% 1.82/2.04 >>>> Starting back demodulation with 11.
% 1.82/2.04 >> back demodulating 1 with 11.
% 1.82/2.04 >>>> Starting back demodulation with 13.
% 1.82/2.04
% 1.82/2.04 ======= end of input processing =======
% 1.82/2.04
% 1.82/2.04 =========== start of search ===========
% 1.82/2.04
% 1.82/2.04 -------- PROOF --------
% 1.82/2.04
% 1.82/2.04 ----> UNIT CONFLICT at 0.00 sec ----> 31 [binary,29.1,14.1] $F.
% 1.82/2.04
% 1.82/2.04 Length of proof is 6. Level of proof is 3.
% 1.82/2.04
% 1.82/2.04 ---------------- PROOF ----------------
% 1.82/2.04 % SZS status Unsatisfiable
% 1.82/2.04 % SZS output start Refutation
% See solution above
% 1.82/2.04 ------------ end of proof -------------
% 1.82/2.04
% 1.82/2.04
% 1.82/2.04 Search stopped by max_proofs option.
% 1.82/2.04
% 1.82/2.04
% 1.82/2.04 Search stopped by max_proofs option.
% 1.82/2.04
% 1.82/2.04 ============ end of search ============
% 1.82/2.04
% 1.82/2.04 -------------- statistics -------------
% 1.82/2.04 clauses given 7
% 1.82/2.04 clauses generated 19
% 1.82/2.04 clauses kept 18
% 1.82/2.04 clauses forward subsumed 15
% 1.82/2.04 clauses back subsumed 0
% 1.82/2.04 Kbytes malloced 976
% 1.82/2.04
% 1.82/2.04 ----------- times (seconds) -----------
% 1.82/2.04 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.04 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.04 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/2.04
% 1.82/2.04 That finishes the proof of the theorem.
% 1.82/2.04
% 1.82/2.04 Process 30677 finished Wed Jul 27 05:10:55 2022
% 1.82/2.04 Otter interrupted
% 1.82/2.04 PROOF FOUND
%------------------------------------------------------------------------------