TSTP Solution File: HEN006-6 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN006-6 : TPTP v8.1.0. Released v1.0.0.
% 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 12:57:57 EDT 2022
% Result : Unsatisfiable 2.01s 2.24s
% Output : Refutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 24 unt; 0 nHn; 18 RR)
% Number of literals : 44 ( 16 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 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 : 36 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| divide(A,B) = zero ),
file('HEN006-6.p',unknown),
[] ).
cnf(2,axiom,
( divide(A,B) != zero
| less_e_qual(A,B) ),
file('HEN006-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN006-6.p',unknown),
[] ).
cnf(4,axiom,
~ less_e_qual(divide(a,d),b),
file('HEN006-6.p',unknown),
[] ).
cnf(6,axiom,
less_e_qual(divide(A,B),A),
file('HEN006-6.p',unknown),
[] ).
cnf(7,axiom,
less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
file('HEN006-6.p',unknown),
[] ).
cnf(8,axiom,
less_e_qual(zero,A),
file('HEN006-6.p',unknown),
[] ).
cnf(13,axiom,
divide(zero,A) = zero,
file('HEN006-6.p',unknown),
[] ).
cnf(14,axiom,
divide(A,A) = zero,
file('HEN006-6.p',unknown),
[] ).
cnf(16,axiom,
less_e_qual(divide(a,b),d),
file('HEN006-6.p',unknown),
[] ).
cnf(19,plain,
divide(divide(A,B),A) = zero,
inference(hyper,[status(thm)],[6,1]),
[iquote('hyper,6,1')] ).
cnf(31,plain,
( less_e_qual(divide(divide(A,B),divide(C,B)),zero)
| ~ less_e_qual(A,C) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,1]),13]),
[iquote('para_into,7.1.2.1,1.2.1,demod,13')] ).
cnf(35,plain,
less_e_qual(divide(divide(A,B),zero),divide(divide(A,zero),B)),
inference(para_from,[status(thm),theory(equality)],[13,7]),
[iquote('para_from,12.1.1,7.1.1.2')] ).
cnf(36,plain,
less_e_qual(A,A),
inference(hyper,[status(thm)],[14,2]),
[iquote('hyper,14,2')] ).
cnf(39,plain,
divide(divide(a,b),d) = zero,
inference(hyper,[status(thm)],[16,1]),
[iquote('hyper,16,1')] ).
cnf(54,plain,
less_e_qual(divide(divide(a,d),divide(b,d)),zero),
inference(para_from,[status(thm),theory(equality)],[39,7]),
[iquote('para_from,39.1.1,7.1.2')] ).
cnf(67,plain,
divide(divide(a,d),divide(b,d)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[54,3,8])]),
[iquote('hyper,54,3,8,flip.1')] ).
cnf(93,plain,
less_e_qual(divide(a,d),divide(b,d)),
inference(hyper,[status(thm)],[67,2]),
[iquote('hyper,67,2')] ).
cnf(281,plain,
less_e_qual(divide(divide(A,divide(A,zero)),zero),zero),
inference(para_into,[status(thm),theory(equality)],[35,14]),
[iquote('para_into,35.1.2,14.1.1')] ).
cnf(292,plain,
divide(divide(A,divide(A,zero)),zero) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[281,3,8])]),
[iquote('hyper,281,3,8,flip.1')] ).
cnf(527,plain,
less_e_qual(divide(A,divide(A,zero)),zero),
inference(hyper,[status(thm)],[292,2]),
[iquote('hyper,292,2')] ).
cnf(533,plain,
( divide(divide(A,zero),zero) = zero
| ~ less_e_qual(A,zero) ),
inference(para_into,[status(thm),theory(equality)],[292,1]),
[iquote('para_into,292.1.1.1.2,1.2.1')] ).
cnf(556,plain,
divide(A,divide(A,zero)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[527,3,8])]),
[iquote('hyper,527,3,8,flip.1')] ).
cnf(603,plain,
less_e_qual(A,divide(A,zero)),
inference(hyper,[status(thm)],[556,2]),
[iquote('hyper,556,2')] ).
cnf(637,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[603,3,6]),
[iquote('hyper,603,3,6')] ).
cnf(663,plain,
( A = zero
| ~ less_e_qual(A,zero) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[533]),637,637]),
[iquote('back_demod,533,demod,637,637')] ).
cnf(793,plain,
( zero = A
| ~ less_e_qual(A,zero) ),
inference(para_into,[status(thm),theory(equality)],[637,1]),
[iquote('para_into,636.1.1,1.2.1')] ).
cnf(862,plain,
( less_e_qual(divide(A,B),zero)
| ~ less_e_qual(A,divide(B,C)) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[31,19]),637]),
[iquote('para_into,31.1.1.2,19.1.1,demod,637')] ).
cnf(892,plain,
( A = zero
| ~ less_e_qual(A,B)
| ~ less_e_qual(B,zero) ),
inference(para_from,[status(thm),theory(equality)],[793,663]),
[iquote('para_from,793.1.1,663.2.2')] ).
cnf(2336,plain,
less_e_qual(divide(divide(a,d),b),zero),
inference(hyper,[status(thm)],[862,93]),
[iquote('hyper,862,93')] ).
cnf(2352,plain,
divide(divide(a,d),b) = zero,
inference(hyper,[status(thm)],[2336,892,36]),
[iquote('hyper,2336,892,36')] ).
cnf(2370,plain,
less_e_qual(divide(a,d),b),
inference(hyper,[status(thm)],[2352,2]),
[iquote('hyper,2352,2')] ).
cnf(2371,plain,
$false,
inference(binary,[status(thm)],[2370,4]),
[iquote('binary,2370.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN006-6 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:20:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.01/2.24 ----- Otter 3.3f, August 2004 -----
% 2.01/2.24 The process was started by sandbox on n016.cluster.edu,
% 2.01/2.24 Wed Jul 27 09:20:52 2022
% 2.01/2.24 The command was "./otter". The process ID is 15102.
% 2.01/2.24
% 2.01/2.24 set(prolog_style_variables).
% 2.01/2.24 set(auto).
% 2.01/2.24 dependent: set(auto1).
% 2.01/2.24 dependent: set(process_input).
% 2.01/2.24 dependent: clear(print_kept).
% 2.01/2.24 dependent: clear(print_new_demod).
% 2.01/2.24 dependent: clear(print_back_demod).
% 2.01/2.24 dependent: clear(print_back_sub).
% 2.01/2.24 dependent: set(control_memory).
% 2.01/2.24 dependent: assign(max_mem, 12000).
% 2.01/2.24 dependent: assign(pick_given_ratio, 4).
% 2.01/2.24 dependent: assign(stats_level, 1).
% 2.01/2.24 dependent: assign(max_seconds, 10800).
% 2.01/2.24 clear(print_given).
% 2.01/2.24
% 2.01/2.24 list(usable).
% 2.01/2.24 0 [] A=A.
% 2.01/2.24 0 [] -less_e_qual(X,Y)|divide(X,Y)=zero.
% 2.01/2.24 0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 2.01/2.24 0 [] less_e_qual(divide(X,Y),X).
% 2.01/2.24 0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 2.01/2.24 0 [] less_e_qual(zero,X).
% 2.01/2.24 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 2.01/2.24 0 [] less_e_qual(X,identity).
% 2.01/2.24 0 [] divide(X,identity)=zero.
% 2.01/2.24 0 [] divide(zero,X)=zero.
% 2.01/2.24 0 [] divide(X,X)=zero.
% 2.01/2.24 0 [] less_e_qual(divide(a,b),d).
% 2.01/2.24 0 [] -less_e_qual(divide(a,d),b).
% 2.01/2.24 end_of_list.
% 2.01/2.24
% 2.01/2.24 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.01/2.24
% 2.01/2.24 This is a Horn set with equality. The strategy will be
% 2.01/2.24 Knuth-Bendix and hyper_res, with positive clauses in
% 2.01/2.24 sos and nonpositive clauses in usable.
% 2.01/2.24
% 2.01/2.24 dependent: set(knuth_bendix).
% 2.01/2.24 dependent: set(anl_eq).
% 2.01/2.24 dependent: set(para_from).
% 2.01/2.24 dependent: set(para_into).
% 2.01/2.24 dependent: clear(para_from_right).
% 2.01/2.24 dependent: clear(para_into_right).
% 2.01/2.24 dependent: set(para_from_vars).
% 2.01/2.24 dependent: set(eq_units_both_ways).
% 2.01/2.24 dependent: set(dynamic_demod_all).
% 2.01/2.24 dependent: set(dynamic_demod).
% 2.01/2.24 dependent: set(order_eq).
% 2.01/2.24 dependent: set(back_demod).
% 2.01/2.24 dependent: set(lrpo).
% 2.01/2.24 dependent: set(hyper_res).
% 2.01/2.24 dependent: clear(order_hyper).
% 2.01/2.24
% 2.01/2.24 ------------> process usable:
% 2.01/2.24 ** KEPT (pick-wt=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 2.01/2.24 ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 2.01/2.24 ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 2.01/2.24 ** KEPT (pick-wt=5): 4 [] -less_e_qual(divide(a,d),b).
% 2.01/2.24
% 2.01/2.24 ------------> process sos:
% 2.01/2.24 ** KEPT (pick-wt=3): 5 [] A=A.
% 2.01/2.24 ** KEPT (pick-wt=5): 6 [] less_e_qual(divide(A,B),A).
% 2.01/2.24 ** KEPT (pick-wt=13): 7 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 2.01/2.24 ** KEPT (pick-wt=3): 8 [] less_e_qual(zero,A).
% 2.01/2.24 ** KEPT (pick-wt=3): 9 [] less_e_qual(A,identity).
% 2.01/2.24 ** KEPT (pick-wt=5): 10 [] divide(A,identity)=zero.
% 2.01/2.24 ---> New Demodulator: 11 [new_demod,10] divide(A,identity)=zero.
% 2.01/2.24 ** KEPT (pick-wt=5): 12 [] divide(zero,A)=zero.
% 2.01/2.24 ---> New Demodulator: 13 [new_demod,12] divide(zero,A)=zero.
% 2.01/2.24 ** KEPT (pick-wt=5): 14 [] divide(A,A)=zero.
% 2.01/2.24 ---> New Demodulator: 15 [new_demod,14] divide(A,A)=zero.
% 2.01/2.24 ** KEPT (pick-wt=5): 16 [] less_e_qual(divide(a,b),d).
% 2.01/2.24 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 2.01/2.24 >>>> Starting back demodulation with 11.
% 2.01/2.24 >>>> Starting back demodulation with 13.
% 2.01/2.24 >>>> Starting back demodulation with 15.
% 2.01/2.24
% 2.01/2.24 ======= end of input processing =======
% 2.01/2.24
% 2.01/2.24 =========== start of search ===========
% 2.01/2.24
% 2.01/2.24 -------- PROOF --------
% 2.01/2.24
% 2.01/2.24 ----> UNIT CONFLICT at 0.44 sec ----> 2371 [binary,2370.1,4.1] $F.
% 2.01/2.24
% 2.01/2.24 Length of proof is 22. Level of proof is 11.
% 2.01/2.24
% 2.01/2.24 ---------------- PROOF ----------------
% 2.01/2.24 % SZS status Unsatisfiable
% 2.01/2.24 % SZS output start Refutation
% See solution above
% 2.01/2.24 ------------ end of proof -------------
% 2.01/2.24
% 2.01/2.24
% 2.01/2.24 Search stopped by max_proofs option.
% 2.01/2.24
% 2.01/2.24
% 2.01/2.24 Search stopped by max_proofs option.
% 2.01/2.24
% 2.01/2.24 ============ end of search ============
% 2.01/2.24
% 2.01/2.24 -------------- statistics -------------
% 2.01/2.24 clauses given 162
% 2.01/2.24 clauses generated 7968
% 2.01/2.24 clauses kept 2292
% 2.01/2.24 clauses forward subsumed 5828
% 2.01/2.24 clauses back subsumed 480
% 2.01/2.24 Kbytes malloced 2929
% 2.01/2.24
% 2.01/2.24 ----------- times (seconds) -----------
% 2.01/2.24 user CPU time 0.44 (0 hr, 0 min, 0 sec)
% 2.01/2.24 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.01/2.24 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.01/2.24
% 2.01/2.24 That finishes the proof of the theorem.
% 2.01/2.24
% 2.01/2.24 Process 15102 finished Wed Jul 27 09:20:54 2022
% 2.01/2.24 Otter interrupted
% 2.01/2.24 PROOF FOUND
%------------------------------------------------------------------------------