TSTP Solution File: HEN010-5 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN010-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 12:58:00 EDT 2022
% Result : Unsatisfiable 2.61s 2.82s
% Output : Refutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 20 unt; 0 nHn; 9 RR)
% Number of literals : 35 ( 34 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( divide(A,B) != zero
| divide(B,A) != zero
| A = B ),
file('HEN010-5.p',unknown),
[] ).
cnf(2,axiom,
( divide(A,B) != zero
| divide(B,C) != zero
| divide(A,C) = zero ),
file('HEN010-5.p',unknown),
[] ).
cnf(3,axiom,
( divide(divide(A,B),C) != zero
| divide(divide(A,C),B) = zero ),
file('HEN010-5.p',unknown),
[] ).
cnf(4,axiom,
( divide(A,B) != zero
| divide(divide(A,C),divide(B,C)) = zero ),
file('HEN010-5.p',unknown),
[] ).
cnf(5,axiom,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('HEN010-5.p',unknown),
[] ).
cnf(6,plain,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(7,axiom,
A = A,
file('HEN010-5.p',unknown),
[] ).
cnf(8,axiom,
divide(divide(A,B),A) = zero,
file('HEN010-5.p',unknown),
[] ).
cnf(10,axiom,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = zero,
file('HEN010-5.p',unknown),
[] ).
cnf(12,axiom,
divide(zero,A) = zero,
file('HEN010-5.p',unknown),
[] ).
cnf(14,axiom,
divide(A,identity) = zero,
file('HEN010-5.p',unknown),
[] ).
cnf(20,plain,
divide(divide(A,B),divide(identity,B)) = zero,
inference(hyper,[status(thm)],[14,4]),
[iquote('hyper,14,4')] ).
cnf(27,plain,
divide(divide(A,A),B) = zero,
inference(hyper,[status(thm)],[8,3]),
[iquote('hyper,8,3')] ).
cnf(37,plain,
divide(A,A) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[27,1,12])]),
[iquote('hyper,27,1,12,flip.1')] ).
cnf(47,plain,
divide(divide(divide(A,B),divide(C,B)),divide(A,C)) = zero,
inference(hyper,[status(thm)],[10,2,8]),
[iquote('hyper,10,2,8')] ).
cnf(76,plain,
divide(divide(A,divide(A,B)),B) = zero,
inference(hyper,[status(thm)],[37,3]),
[iquote('hyper,37,3')] ).
cnf(95,plain,
divide(divide(divide(A,divide(identity,B)),divide(B,divide(identity,B))),zero) = zero,
inference(para_from,[status(thm),theory(equality)],[20,10]),
[iquote('para_from,20.1.1,10.1.1.2')] ).
cnf(142,plain,
divide(A,divide(A,zero)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[76,1,12])]),
[iquote('hyper,76,1,12,flip.1')] ).
cnf(154,plain,
( divide(A,divide(B,divide(B,A))) != zero
| zero != zero
| divide(B,divide(B,A)) = A ),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[76,1])]),
[iquote('para_from,76.1.1,1.2.1,flip.3')] ).
cnf(196,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[142,1,8]),
[iquote('hyper,142,1,8')] ).
cnf(218,plain,
divide(divide(A,divide(identity,B)),divide(B,divide(identity,B))) = zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[95]),196]),
[iquote('back_demod,95,demod,196')] ).
cnf(1582,plain,
divide(divide(A,B),divide(A,divide(C,divide(C,B)))) = zero,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[47,76]),196]),
[iquote('para_into,47.1.1.1.2,76.1.1,demod,196')] ).
cnf(3209,plain,
divide(A,divide(identity,A)) = divide(identity,divide(identity,A)),
inference(hyper,[status(thm)],[218,1,20]),
[iquote('hyper,218,1,20')] ).
cnf(3225,plain,
divide(identity,divide(identity,divide(identity,a))) != divide(identity,a),
inference(para_from,[status(thm),theory(equality)],[3209,6]),
[iquote('para_from,3209.1.1,6.1.1')] ).
cnf(3323,plain,
( divide(identity,a) != divide(identity,a)
| zero != zero ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[154,3225]),1582]),
[iquote('para_from,154.3.1,3225.1.1,demod,1582')] ).
cnf(3324,plain,
$false,
inference(hyper,[status(thm)],[3323,7,7]),
[iquote('hyper,3323,7,7')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : HEN010-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n016.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 09:19:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.61/2.82 ----- Otter 3.3f, August 2004 -----
% 2.61/2.82 The process was started by sandbox2 on n016.cluster.edu,
% 2.61/2.82 Wed Jul 27 09:19:52 2022
% 2.61/2.82 The command was "./otter". The process ID is 10298.
% 2.61/2.82
% 2.61/2.82 set(prolog_style_variables).
% 2.61/2.82 set(auto).
% 2.61/2.82 dependent: set(auto1).
% 2.61/2.82 dependent: set(process_input).
% 2.61/2.82 dependent: clear(print_kept).
% 2.61/2.82 dependent: clear(print_new_demod).
% 2.61/2.82 dependent: clear(print_back_demod).
% 2.61/2.82 dependent: clear(print_back_sub).
% 2.61/2.82 dependent: set(control_memory).
% 2.61/2.82 dependent: assign(max_mem, 12000).
% 2.61/2.82 dependent: assign(pick_given_ratio, 4).
% 2.61/2.82 dependent: assign(stats_level, 1).
% 2.61/2.82 dependent: assign(max_seconds, 10800).
% 2.61/2.82 clear(print_given).
% 2.61/2.82
% 2.61/2.82 list(usable).
% 2.61/2.82 0 [] A=A.
% 2.61/2.82 0 [] divide(divide(X,Y),X)=zero.
% 2.61/2.82 0 [] divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z))=zero.
% 2.61/2.82 0 [] divide(zero,X)=zero.
% 2.61/2.82 0 [] divide(X,Y)!=zero|divide(Y,X)!=zero|X=Y.
% 2.61/2.82 0 [] divide(X,identity)=zero.
% 2.61/2.82 0 [] divide(X,Y)!=zero|divide(Y,Z)!=zero|divide(X,Z)=zero.
% 2.61/2.82 0 [] divide(divide(X,Y),Z)!=zero|divide(divide(X,Z),Y)=zero.
% 2.61/2.82 0 [] divide(X,Y)!=zero|divide(divide(X,Z),divide(Y,Z))=zero.
% 2.61/2.82 0 [] divide(identity,a)!=divide(divide(identity,a),divide(identity,divide(identity,a))).
% 2.61/2.82 end_of_list.
% 2.61/2.82
% 2.61/2.82 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.61/2.82
% 2.61/2.82 This is a Horn set with equality. The strategy will be
% 2.61/2.82 Knuth-Bendix and hyper_res, with positive clauses in
% 2.61/2.82 sos and nonpositive clauses in usable.
% 2.61/2.82
% 2.61/2.82 dependent: set(knuth_bendix).
% 2.61/2.82 dependent: set(anl_eq).
% 2.61/2.82 dependent: set(para_from).
% 2.61/2.82 dependent: set(para_into).
% 2.61/2.82 dependent: clear(para_from_right).
% 2.61/2.82 dependent: clear(para_into_right).
% 2.61/2.82 dependent: set(para_from_vars).
% 2.61/2.82 dependent: set(eq_units_both_ways).
% 2.61/2.82 dependent: set(dynamic_demod_all).
% 2.61/2.82 dependent: set(dynamic_demod).
% 2.61/2.82 dependent: set(order_eq).
% 2.61/2.82 dependent: set(back_demod).
% 2.61/2.82 dependent: set(lrpo).
% 2.61/2.82 dependent: set(hyper_res).
% 2.61/2.82 dependent: clear(order_hyper).
% 2.61/2.82
% 2.61/2.82 ------------> process usable:
% 2.61/2.82 ** KEPT (pick-wt=13): 1 [] divide(A,B)!=zero|divide(B,A)!=zero|A=B.
% 2.61/2.82 ** KEPT (pick-wt=15): 2 [] divide(A,B)!=zero|divide(B,C)!=zero|divide(A,C)=zero.
% 2.61/2.82 ** KEPT (pick-wt=14): 3 [] divide(divide(A,B),C)!=zero|divide(divide(A,C),B)=zero.
% 2.61/2.82 ** KEPT (pick-wt=14): 4 [] divide(A,B)!=zero|divide(divide(A,C),divide(B,C))=zero.
% 2.61/2.82 ** KEPT (pick-wt=13): 6 [copy,5,flip.1] divide(divide(identity,a),divide(identity,divide(identity,a)))!=divide(identity,a).
% 2.61/2.82
% 2.61/2.82 ------------> process sos:
% 2.61/2.82 ** KEPT (pick-wt=3): 7 [] A=A.
% 2.61/2.82 ** KEPT (pick-wt=7): 8 [] divide(divide(A,B),A)=zero.
% 2.61/2.82 ---> New Demodulator: 9 [new_demod,8] divide(divide(A,B),A)=zero.
% 2.61/2.82 ** KEPT (pick-wt=15): 10 [] divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B))=zero.
% 2.61/2.82 ---> New Demodulator: 11 [new_demod,10] divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B))=zero.
% 2.61/2.82 ** KEPT (pick-wt=5): 12 [] divide(zero,A)=zero.
% 2.61/2.82 ---> New Demodulator: 13 [new_demod,12] divide(zero,A)=zero.
% 2.61/2.82 ** KEPT (pick-wt=5): 14 [] divide(A,identity)=zero.
% 2.61/2.82 ---> New Demodulator: 15 [new_demod,14] divide(A,identity)=zero.
% 2.61/2.82 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 2.61/2.82 >>>> Starting back demodulation with 9.
% 2.61/2.82 >>>> Starting back demodulation with 11.
% 2.61/2.82 >>>> Starting back demodulation with 13.
% 2.61/2.82 >>>> Starting back demodulation with 15.
% 2.61/2.82
% 2.61/2.82 ======= end of input processing =======
% 2.61/2.82
% 2.61/2.82 =========== start of search ===========
% 2.61/2.82
% 2.61/2.82
% 2.61/2.82 Resetting weight limit to 15.
% 2.61/2.82
% 2.61/2.82
% 2.61/2.82 Resetting weight limit to 15.
% 2.61/2.82
% 2.61/2.82 sos_size=2038
% 2.61/2.82
% 2.61/2.82
% 2.61/2.82 Resetting weight limit to 14.
% 2.61/2.82
% 2.61/2.82
% 2.61/2.82 Resetting weight limit to 14.
% 2.61/2.82
% 2.61/2.82 sos_size=2079
% 2.61/2.82
% 2.61/2.82 -------- PROOF --------
% 2.61/2.82
% 2.61/2.82 -----> EMPTY CLAUSE at 0.94 sec ----> 3324 [hyper,3323,7,7] $F.
% 2.61/2.82
% 2.61/2.82 Length of proof is 15. Level of proof is 9.
% 2.61/2.82
% 2.61/2.82 ---------------- PROOF ----------------
% 2.61/2.82 % SZS status Unsatisfiable
% 2.61/2.82 % SZS output start Refutation
% See solution above
% 2.61/2.82 ------------ end of proof -------------
% 2.61/2.82
% 2.61/2.82
% 2.61/2.82 Search stopped by max_proofs option.
% 2.61/2.82
% 2.61/2.82
% 2.61/2.82 Search stopped by max_proofs option.
% 2.61/2.82
% 2.61/2.82 ============ end of search ============
% 2.61/2.82
% 2.61/2.82 -------------- statistics -------------
% 2.61/2.82 clauses given 117
% 2.61/2.82 clauses generated 27287
% 2.61/2.82 clauses kept 2623
% 2.61/2.82 clauses forward subsumed 18447
% 2.61/2.82 clauses back subsumed 332
% 2.61/2.82 Kbytes malloced 4882
% 2.61/2.82
% 2.61/2.82 ----------- times (seconds) -----------
% 2.61/2.82 user CPU time 0.94 (0 hr, 0 min, 0 sec)
% 2.61/2.82 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.61/2.82 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.61/2.82
% 2.61/2.82 That finishes the proof of the theorem.
% 2.61/2.82
% 2.61/2.82 Process 10298 finished Wed Jul 27 09:19:55 2022
% 2.61/2.82 Otter interrupted
% 2.61/2.82 PROOF FOUND
%------------------------------------------------------------------------------