TSTP Solution File: HEN006-3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 12:57:56 EDT 2022
% Result : Unsatisfiable 2.11s 2.29s
% Output : Refutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of clauses : 36 ( 27 unt; 0 nHn; 18 RR)
% Number of literals : 47 ( 17 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 : 42 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| divide(A,B) = zero ),
file('HEN006-3.p',unknown),
[] ).
cnf(2,axiom,
( divide(A,B) != zero
| less_e_qual(A,B) ),
file('HEN006-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN006-3.p',unknown),
[] ).
cnf(4,axiom,
~ less_e_qual(divide(a,d),b),
file('HEN006-3.p',unknown),
[] ).
cnf(6,axiom,
less_e_qual(divide(A,B),A),
file('HEN006-3.p',unknown),
[] ).
cnf(7,axiom,
less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
file('HEN006-3.p',unknown),
[] ).
cnf(8,axiom,
less_e_qual(zero,A),
file('HEN006-3.p',unknown),
[] ).
cnf(10,axiom,
less_e_qual(divide(a,b),d),
file('HEN006-3.p',unknown),
[] ).
cnf(12,plain,
divide(zero,A) = zero,
inference(hyper,[status(thm)],[8,1]),
[iquote('hyper,8,1')] ).
cnf(18,plain,
divide(divide(A,B),A) = zero,
inference(hyper,[status(thm)],[6,1]),
[iquote('hyper,6,1')] ).
cnf(20,plain,
divide(divide(a,b),d) = zero,
inference(hyper,[status(thm)],[10,1]),
[iquote('hyper,10,1')] ).
cnf(33,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]),12]),
[iquote('para_into,7.1.2.1,1.2.1,demod,12')] ).
cnf(37,plain,
less_e_qual(divide(divide(A,B),zero),divide(divide(A,zero),B)),
inference(para_from,[status(thm),theory(equality)],[12,7]),
[iquote('para_from,11.1.1,7.1.1.2')] ).
cnf(41,plain,
less_e_qual(divide(divide(A,A),divide(B,A)),zero),
inference(para_from,[status(thm),theory(equality)],[18,7]),
[iquote('para_from,17.1.1,7.1.2')] ).
cnf(48,plain,
less_e_qual(divide(divide(a,d),divide(b,d)),zero),
inference(para_from,[status(thm),theory(equality)],[20,7]),
[iquote('para_from,20.1.1,7.1.2')] ).
cnf(59,plain,
divide(divide(A,A),divide(B,A)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[41,3,8])]),
[iquote('hyper,41,3,8,flip.1')] ).
cnf(62,plain,
divide(divide(a,d),divide(b,d)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[48,3,8])]),
[iquote('hyper,48,3,8,flip.1')] ).
cnf(83,plain,
less_e_qual(divide(A,A),divide(B,A)),
inference(hyper,[status(thm)],[59,2]),
[iquote('hyper,59,2')] ).
cnf(100,plain,
divide(A,A) = zero,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[83,3,6]),18])]),
[iquote('hyper,83,3,6,demod,18,flip.1')] ).
cnf(102,plain,
less_e_qual(A,A),
inference(hyper,[status(thm)],[100,2]),
[iquote('hyper,100,2')] ).
cnf(105,plain,
less_e_qual(divide(a,d),divide(b,d)),
inference(hyper,[status(thm)],[62,2]),
[iquote('hyper,62,2')] ).
cnf(192,plain,
less_e_qual(divide(divide(A,divide(A,zero)),zero),zero),
inference(para_into,[status(thm),theory(equality)],[37,100]),
[iquote('para_into,37.1.2,100.1.1')] ).
cnf(250,plain,
divide(divide(A,divide(A,zero)),zero) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[192,3,8])]),
[iquote('hyper,192,3,8,flip.1')] ).
cnf(257,plain,
less_e_qual(divide(A,divide(A,zero)),zero),
inference(hyper,[status(thm)],[250,2]),
[iquote('hyper,250,2')] ).
cnf(263,plain,
( divide(divide(A,zero),zero) = zero
| ~ less_e_qual(A,zero) ),
inference(para_into,[status(thm),theory(equality)],[250,1]),
[iquote('para_into,250.1.1.1.2,1.2.1')] ).
cnf(275,plain,
divide(A,divide(A,zero)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[257,3,8])]),
[iquote('hyper,257,3,8,flip.1')] ).
cnf(328,plain,
less_e_qual(A,divide(A,zero)),
inference(hyper,[status(thm)],[275,2]),
[iquote('hyper,275,2')] ).
cnf(362,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[328,3,6]),
[iquote('hyper,328,3,6')] ).
cnf(384,plain,
( A = zero
| ~ less_e_qual(A,zero) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[263]),362,362]),
[iquote('back_demod,263,demod,362,362')] ).
cnf(449,plain,
( zero = A
| ~ less_e_qual(A,zero) ),
inference(para_into,[status(thm),theory(equality)],[362,1]),
[iquote('para_into,361.1.1,1.2.1')] ).
cnf(546,plain,
( A = zero
| ~ less_e_qual(A,B)
| ~ less_e_qual(B,zero) ),
inference(para_from,[status(thm),theory(equality)],[449,384]),
[iquote('para_from,449.1.1,384.2.2')] ).
cnf(670,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)],[33,18]),362]),
[iquote('para_into,33.1.1.2,17.1.1,demod,362')] ).
cnf(1961,plain,
less_e_qual(divide(divide(a,d),b),zero),
inference(hyper,[status(thm)],[670,105]),
[iquote('hyper,670,105')] ).
cnf(1977,plain,
divide(divide(a,d),b) = zero,
inference(hyper,[status(thm)],[1961,546,102]),
[iquote('hyper,1961,546,102')] ).
cnf(1983,plain,
less_e_qual(divide(a,d),b),
inference(hyper,[status(thm)],[1977,2]),
[iquote('hyper,1977,2')] ).
cnf(1984,plain,
$false,
inference(binary,[status(thm)],[1983,4]),
[iquote('binary,1983.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 08:51:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.11/2.29 ----- Otter 3.3f, August 2004 -----
% 2.11/2.29 The process was started by sandbox on n010.cluster.edu,
% 2.11/2.29 Wed Jul 27 08:51:10 2022
% 2.11/2.29 The command was "./otter". The process ID is 15158.
% 2.11/2.29
% 2.11/2.29 set(prolog_style_variables).
% 2.11/2.29 set(auto).
% 2.11/2.29 dependent: set(auto1).
% 2.11/2.29 dependent: set(process_input).
% 2.11/2.29 dependent: clear(print_kept).
% 2.11/2.29 dependent: clear(print_new_demod).
% 2.11/2.29 dependent: clear(print_back_demod).
% 2.11/2.29 dependent: clear(print_back_sub).
% 2.11/2.29 dependent: set(control_memory).
% 2.11/2.29 dependent: assign(max_mem, 12000).
% 2.11/2.29 dependent: assign(pick_given_ratio, 4).
% 2.11/2.29 dependent: assign(stats_level, 1).
% 2.11/2.29 dependent: assign(max_seconds, 10800).
% 2.11/2.29 clear(print_given).
% 2.11/2.29
% 2.11/2.29 list(usable).
% 2.11/2.29 0 [] A=A.
% 2.11/2.29 0 [] -less_e_qual(X,Y)|divide(X,Y)=zero.
% 2.11/2.29 0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 2.11/2.29 0 [] less_e_qual(divide(X,Y),X).
% 2.11/2.29 0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 2.11/2.29 0 [] less_e_qual(zero,X).
% 2.11/2.29 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 2.11/2.29 0 [] less_e_qual(X,identity).
% 2.11/2.29 0 [] less_e_qual(divide(a,b),d).
% 2.11/2.29 0 [] -less_e_qual(divide(a,d),b).
% 2.11/2.29 end_of_list.
% 2.11/2.29
% 2.11/2.29 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.11/2.29
% 2.11/2.29 This is a Horn set with equality. The strategy will be
% 2.11/2.29 Knuth-Bendix and hyper_res, with positive clauses in
% 2.11/2.29 sos and nonpositive clauses in usable.
% 2.11/2.29
% 2.11/2.29 dependent: set(knuth_bendix).
% 2.11/2.29 dependent: set(anl_eq).
% 2.11/2.29 dependent: set(para_from).
% 2.11/2.29 dependent: set(para_into).
% 2.11/2.29 dependent: clear(para_from_right).
% 2.11/2.29 dependent: clear(para_into_right).
% 2.11/2.29 dependent: set(para_from_vars).
% 2.11/2.29 dependent: set(eq_units_both_ways).
% 2.11/2.29 dependent: set(dynamic_demod_all).
% 2.11/2.29 dependent: set(dynamic_demod).
% 2.11/2.29 dependent: set(order_eq).
% 2.11/2.29 dependent: set(back_demod).
% 2.11/2.29 dependent: set(lrpo).
% 2.11/2.29 dependent: set(hyper_res).
% 2.11/2.29 dependent: clear(order_hyper).
% 2.11/2.29
% 2.11/2.29 ------------> process usable:
% 2.11/2.29 ** KEPT (pick-wt=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 2.11/2.29 ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 2.11/2.29 ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 2.11/2.29 ** KEPT (pick-wt=5): 4 [] -less_e_qual(divide(a,d),b).
% 2.11/2.29
% 2.11/2.29 ------------> process sos:
% 2.11/2.29 ** KEPT (pick-wt=3): 5 [] A=A.
% 2.11/2.29 ** KEPT (pick-wt=5): 6 [] less_e_qual(divide(A,B),A).
% 2.11/2.29 ** KEPT (pick-wt=13): 7 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 2.11/2.29 ** KEPT (pick-wt=3): 8 [] less_e_qual(zero,A).
% 2.11/2.29 ** KEPT (pick-wt=3): 9 [] less_e_qual(A,identity).
% 2.11/2.29 ** KEPT (pick-wt=5): 10 [] less_e_qual(divide(a,b),d).
% 2.11/2.29 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 2.11/2.29
% 2.11/2.29 ======= end of input processing =======
% 2.11/2.29
% 2.11/2.29 =========== start of search ===========
% 2.11/2.29
% 2.11/2.29 -------- PROOF --------
% 2.11/2.29
% 2.11/2.29 ----> UNIT CONFLICT at 0.36 sec ----> 1984 [binary,1983.1,4.1] $F.
% 2.11/2.29
% 2.11/2.29 Length of proof is 27. Level of proof is 15.
% 2.11/2.29
% 2.11/2.29 ---------------- PROOF ----------------
% 2.11/2.29 % SZS status Unsatisfiable
% 2.11/2.29 % SZS output start Refutation
% See solution above
% 2.11/2.29 ------------ end of proof -------------
% 2.11/2.29
% 2.11/2.29
% 2.11/2.29 Search stopped by max_proofs option.
% 2.11/2.29
% 2.11/2.29
% 2.11/2.29 Search stopped by max_proofs option.
% 2.11/2.29
% 2.11/2.29 ============ end of search ============
% 2.11/2.29
% 2.11/2.29 -------------- statistics -------------
% 2.11/2.29 clauses given 140
% 2.11/2.29 clauses generated 6527
% 2.11/2.29 clauses kept 1911
% 2.11/2.29 clauses forward subsumed 4655
% 2.11/2.29 clauses back subsumed 350
% 2.11/2.29 Kbytes malloced 2929
% 2.11/2.29
% 2.11/2.29 ----------- times (seconds) -----------
% 2.11/2.29 user CPU time 0.36 (0 hr, 0 min, 0 sec)
% 2.11/2.29 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.11/2.29 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 2.11/2.29
% 2.11/2.29 That finishes the proof of the theorem.
% 2.11/2.29
% 2.11/2.29 Process 15158 finished Wed Jul 27 08:51:11 2022
% 2.11/2.29 Otter interrupted
% 2.11/2.29 PROOF FOUND
%------------------------------------------------------------------------------