TSTP Solution File: HEN006-4 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN006-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 12:57:57 EDT 2022
% Result : Unsatisfiable 1.68s 1.94s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 15 ( 11 unt; 0 nHn; 12 RR)
% Number of literals : 21 ( 5 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| divide(A,B) = zero ),
file('HEN006-4.p',unknown),
[] ).
cnf(2,axiom,
( divide(A,B) != zero
| less_e_qual(A,B) ),
file('HEN006-4.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN006-4.p',unknown),
[] ).
cnf(4,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,C)
| less_e_qual(A,C) ),
file('HEN006-4.p',unknown),
[] ).
cnf(5,axiom,
~ less_e_qual(divide(a,d),b),
file('HEN006-4.p',unknown),
[] ).
cnf(7,axiom,
less_e_qual(divide(A,B),A),
file('HEN006-4.p',unknown),
[] ).
cnf(8,axiom,
less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
file('HEN006-4.p',unknown),
[] ).
cnf(9,axiom,
less_e_qual(zero,A),
file('HEN006-4.p',unknown),
[] ).
cnf(19,axiom,
less_e_qual(divide(a,b),d),
file('HEN006-4.p',unknown),
[] ).
cnf(53,plain,
divide(divide(a,b),d) = zero,
inference(hyper,[status(thm)],[19,1]),
[iquote('hyper,19,1')] ).
cnf(98,plain,
less_e_qual(divide(divide(a,d),divide(b,d)),zero),
inference(para_from,[status(thm),theory(equality)],[53,8]),
[iquote('para_from,53.1.1,8.1.2')] ).
cnf(208,plain,
divide(divide(a,d),divide(b,d)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[98,3,9])]),
[iquote('hyper,98,3,9,flip.1')] ).
cnf(629,plain,
less_e_qual(divide(a,d),divide(b,d)),
inference(hyper,[status(thm)],[208,2]),
[iquote('hyper,208,2')] ).
cnf(660,plain,
less_e_qual(divide(a,d),b),
inference(hyper,[status(thm)],[629,4,7]),
[iquote('hyper,629,4,7')] ).
cnf(661,plain,
$false,
inference(binary,[status(thm)],[660,5]),
[iquote('binary,660.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : HEN006-4 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 09:13:21 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.68/1.94 ----- Otter 3.3f, August 2004 -----
% 1.68/1.94 The process was started by sandbox on n027.cluster.edu,
% 1.68/1.94 Wed Jul 27 09:13:21 2022
% 1.68/1.94 The command was "./otter". The process ID is 17458.
% 1.68/1.94
% 1.68/1.94 set(prolog_style_variables).
% 1.68/1.94 set(auto).
% 1.68/1.94 dependent: set(auto1).
% 1.68/1.94 dependent: set(process_input).
% 1.68/1.94 dependent: clear(print_kept).
% 1.68/1.94 dependent: clear(print_new_demod).
% 1.68/1.94 dependent: clear(print_back_demod).
% 1.68/1.94 dependent: clear(print_back_sub).
% 1.68/1.94 dependent: set(control_memory).
% 1.68/1.94 dependent: assign(max_mem, 12000).
% 1.68/1.94 dependent: assign(pick_given_ratio, 4).
% 1.68/1.94 dependent: assign(stats_level, 1).
% 1.68/1.94 dependent: assign(max_seconds, 10800).
% 1.68/1.94 clear(print_given).
% 1.68/1.94
% 1.68/1.94 list(usable).
% 1.68/1.94 0 [] A=A.
% 1.68/1.94 0 [] -less_e_qual(X,Y)|divide(X,Y)=zero.
% 1.68/1.94 0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 1.68/1.94 0 [] less_e_qual(divide(X,Y),X).
% 1.68/1.94 0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 1.68/1.94 0 [] less_e_qual(zero,X).
% 1.68/1.94 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.68/1.94 0 [] less_e_qual(X,identity).
% 1.68/1.94 0 [] divide(X,identity)=zero.
% 1.68/1.94 0 [] divide(zero,X)=zero.
% 1.68/1.94 0 [] divide(X,X)=zero.
% 1.68/1.94 0 [] divide(a,zero)=a.
% 1.68/1.94 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,Z)|less_e_qual(X,Z).
% 1.68/1.94 0 [] less_e_qual(divide(a,b),d).
% 1.68/1.94 0 [] -less_e_qual(divide(a,d),b).
% 1.68/1.94 end_of_list.
% 1.68/1.94
% 1.68/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.68/1.94
% 1.68/1.94 This is a Horn set with equality. The strategy will be
% 1.68/1.94 Knuth-Bendix and hyper_res, with positive clauses in
% 1.68/1.94 sos and nonpositive clauses in usable.
% 1.68/1.94
% 1.68/1.94 dependent: set(knuth_bendix).
% 1.68/1.94 dependent: set(anl_eq).
% 1.68/1.94 dependent: set(para_from).
% 1.68/1.94 dependent: set(para_into).
% 1.68/1.94 dependent: clear(para_from_right).
% 1.68/1.94 dependent: clear(para_into_right).
% 1.68/1.94 dependent: set(para_from_vars).
% 1.68/1.94 dependent: set(eq_units_both_ways).
% 1.68/1.94 dependent: set(dynamic_demod_all).
% 1.68/1.94 dependent: set(dynamic_demod).
% 1.68/1.94 dependent: set(order_eq).
% 1.68/1.94 dependent: set(back_demod).
% 1.68/1.94 dependent: set(lrpo).
% 1.68/1.94 dependent: set(hyper_res).
% 1.68/1.94 dependent: clear(order_hyper).
% 1.68/1.94
% 1.68/1.94 ------------> process usable:
% 1.68/1.94 ** KEPT (pick-wt=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 1.68/1.94 ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 1.68/1.94 ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.68/1.94 ** KEPT (pick-wt=9): 4 [] -less_e_qual(A,B)| -less_e_qual(B,C)|less_e_qual(A,C).
% 1.68/1.94 ** KEPT (pick-wt=5): 5 [] -less_e_qual(divide(a,d),b).
% 1.68/1.94
% 1.68/1.94 ------------> process sos:
% 1.68/1.94 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.68/1.94 ** KEPT (pick-wt=5): 7 [] less_e_qual(divide(A,B),A).
% 1.68/1.94 ** KEPT (pick-wt=13): 8 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 1.68/1.94 ** KEPT (pick-wt=3): 9 [] less_e_qual(zero,A).
% 1.68/1.94 ** KEPT (pick-wt=3): 10 [] less_e_qual(A,identity).
% 1.68/1.94 ** KEPT (pick-wt=5): 11 [] divide(A,identity)=zero.
% 1.68/1.94 ---> New Demodulator: 12 [new_demod,11] divide(A,identity)=zero.
% 1.68/1.94 ** KEPT (pick-wt=5): 13 [] divide(zero,A)=zero.
% 1.68/1.94 ---> New Demodulator: 14 [new_demod,13] divide(zero,A)=zero.
% 1.68/1.94 ** KEPT (pick-wt=5): 15 [] divide(A,A)=zero.
% 1.68/1.94 ---> New Demodulator: 16 [new_demod,15] divide(A,A)=zero.
% 1.68/1.94 ** KEPT (pick-wt=5): 17 [] divide(a,zero)=a.
% 1.68/1.94 ---> New Demodulator: 18 [new_demod,17] divide(a,zero)=a.
% 1.68/1.94 ** KEPT (pick-wt=5): 19 [] less_e_qual(divide(a,b),d).
% 1.68/1.94 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.68/1.94 >>>> Starting back demodulation with 12.
% 1.68/1.94 >>>> Starting back demodulation with 14.
% 1.68/1.94 >>>> Starting back demodulation with 16.
% 1.68/1.94 >>>> Starting back demodulation with 18.
% 1.68/1.94
% 1.68/1.94 ======= end of input processing =======
% 1.68/1.94
% 1.68/1.94 =========== start of search ===========
% 1.68/1.94
% 1.68/1.94 -------- PROOF --------
% 1.68/1.94
% 1.68/1.94 ----> UNIT CONFLICT at 0.04 sec ----> 661 [binary,660.1,5.1] $F.
% 1.68/1.94
% 1.68/1.94 Length of proof is 5. Level of proof is 5.
% 1.68/1.94
% 1.68/1.94 ---------------- PROOF ----------------
% 1.68/1.94 % SZS status Unsatisfiable
% 1.68/1.94 % SZS output start Refutation
% See solution above
% 1.68/1.94 ------------ end of proof -------------
% 1.68/1.94
% 1.68/1.94
% 1.68/1.94 Search stopped by max_proofs option.
% 1.68/1.94
% 1.68/1.94
% 1.68/1.94 Search stopped by max_proofs option.
% 1.68/1.94
% 1.68/1.94 ============ end of search ============
% 1.68/1.94
% 1.68/1.94 -------------- statistics -------------
% 1.68/1.94 clauses given 60
% 1.68/1.94 clauses generated 1614
% 1.68/1.94 clauses kept 612
% 1.68/1.94 clauses forward subsumed 1019
% 1.68/1.94 clauses back subsumed 20
% 1.68/1.94 Kbytes malloced 1953
% 1.68/1.94
% 1.68/1.94 ----------- times (seconds) -----------
% 1.68/1.94 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.68/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.68/1.94
% 1.68/1.94 That finishes the proof of the theorem.
% 1.68/1.94
% 1.68/1.94 Process 17458 finished Wed Jul 27 09:13:23 2022
% 1.68/1.94 Otter interrupted
% 1.68/1.94 PROOF FOUND
%------------------------------------------------------------------------------