TSTP Solution File: HEN006-7 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN006-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 1.81s 2.07s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 24 ( 19 unt; 0 nHn; 18 RR)
% Number of literals : 34 ( 3 equ; 11 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| quotient(A,B,zero) ),
file('HEN006-7.p',unknown),
[] ).
cnf(2,axiom,
( ~ quotient(A,B,zero)
| less_e_qual(A,B) ),
file('HEN006-7.p',unknown),
[] ).
cnf(3,axiom,
( ~ quotient(A,B,C)
| less_e_qual(C,A) ),
file('HEN006-7.p',unknown),
[] ).
cnf(4,axiom,
( ~ quotient(A,B,C)
| ~ quotient(B,D,E)
| ~ quotient(A,D,F)
| ~ quotient(F,E,G)
| ~ quotient(C,D,H)
| less_e_qual(G,H) ),
file('HEN006-7.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN006-7.p',unknown),
[] ).
cnf(7,axiom,
~ less_e_qual(xQz,y),
file('HEN006-7.p',unknown),
[] ).
cnf(9,axiom,
less_e_qual(zero,A),
file('HEN006-7.p',unknown),
[] ).
cnf(11,axiom,
quotient(A,B,divide(A,B)),
file('HEN006-7.p',unknown),
[] ).
cnf(13,axiom,
quotient(zero,A,zero),
file('HEN006-7.p',unknown),
[] ).
cnf(15,axiom,
quotient(A,zero,A),
file('HEN006-7.p',unknown),
[] ).
cnf(16,axiom,
quotient(x,y,xQy),
file('HEN006-7.p',unknown),
[] ).
cnf(17,axiom,
less_e_qual(xQy,z),
file('HEN006-7.p',unknown),
[] ).
cnf(18,axiom,
quotient(x,z,xQz),
file('HEN006-7.p',unknown),
[] ).
cnf(23,plain,
quotient(xQy,z,zero),
inference(hyper,[status(thm)],[17,1]),
[iquote('hyper,17,1')] ).
cnf(37,plain,
less_e_qual(divide(A,B),A),
inference(hyper,[status(thm)],[11,3]),
[iquote('hyper,11,3')] ).
cnf(105,plain,
less_e_qual(divide(xQz,divide(y,z)),zero),
inference(hyper,[status(thm)],[23,4,16,11,18,11]),
[iquote('hyper,23,4,16,11,18,11')] ).
cnf(142,plain,
quotient(divide(A,B),A,zero),
inference(hyper,[status(thm)],[37,1]),
[iquote('hyper,37,1')] ).
cnf(246,plain,
divide(xQz,divide(y,z)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[105,5,9])]),
[iquote('hyper,105,5,9,flip.1')] ).
cnf(381,plain,
quotient(xQz,divide(y,z),zero),
inference(para_from,[status(thm),theory(equality)],[246,11]),
[iquote('para_from,246.1.1,11.1.3')] ).
cnf(385,plain,
less_e_qual(divide(xQz,y),zero),
inference(hyper,[status(thm)],[381,4,142,11,15,13]),
[iquote('hyper,381,4,142,11,15,13')] ).
cnf(400,plain,
divide(xQz,y) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[385,5,9])]),
[iquote('hyper,385,5,9,flip.1')] ).
cnf(416,plain,
quotient(xQz,y,zero),
inference(para_from,[status(thm),theory(equality)],[400,11]),
[iquote('para_from,400.1.1,11.1.3')] ).
cnf(422,plain,
less_e_qual(xQz,y),
inference(hyper,[status(thm)],[416,2]),
[iquote('hyper,416,2')] ).
cnf(423,plain,
$false,
inference(binary,[status(thm)],[422,7]),
[iquote('binary,422.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : HEN006-7 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 09:06:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.81/2.07 ----- Otter 3.3f, August 2004 -----
% 1.81/2.07 The process was started by sandbox2 on n025.cluster.edu,
% 1.81/2.07 Wed Jul 27 09:06:30 2022
% 1.81/2.07 The command was "./otter". The process ID is 17229.
% 1.81/2.07
% 1.81/2.07 set(prolog_style_variables).
% 1.81/2.07 set(auto).
% 1.81/2.07 dependent: set(auto1).
% 1.81/2.07 dependent: set(process_input).
% 1.81/2.07 dependent: clear(print_kept).
% 1.81/2.07 dependent: clear(print_new_demod).
% 1.81/2.07 dependent: clear(print_back_demod).
% 1.81/2.07 dependent: clear(print_back_sub).
% 1.81/2.07 dependent: set(control_memory).
% 1.81/2.07 dependent: assign(max_mem, 12000).
% 1.81/2.07 dependent: assign(pick_given_ratio, 4).
% 1.81/2.07 dependent: assign(stats_level, 1).
% 1.81/2.07 dependent: assign(max_seconds, 10800).
% 1.81/2.07 clear(print_given).
% 1.81/2.07
% 1.81/2.07 list(usable).
% 1.81/2.07 0 [] A=A.
% 1.81/2.07 0 [] -less_e_qual(X,Y)|quotient(X,Y,zero).
% 1.81/2.07 0 [] -quotient(X,Y,zero)|less_e_qual(X,Y).
% 1.81/2.07 0 [] -quotient(X,Y,Z)|less_e_qual(Z,X).
% 1.81/2.07 0 [] -quotient(X,Y,V1)| -quotient(Y,Z,V2)| -quotient(X,Z,V3)| -quotient(V3,V2,V4)| -quotient(V1,Z,V5)|less_e_qual(V4,V5).
% 1.81/2.07 0 [] less_e_qual(zero,X).
% 1.81/2.07 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.81/2.07 0 [] less_e_qual(X,identity).
% 1.81/2.07 0 [] quotient(X,Y,divide(X,Y)).
% 1.81/2.07 0 [] -quotient(X,Y,Z)| -quotient(X,Y,W)|Z=W.
% 1.81/2.07 0 [] quotient(X,identity,zero).
% 1.81/2.07 0 [] quotient(zero,X,zero).
% 1.81/2.07 0 [] quotient(X,X,zero).
% 1.81/2.07 0 [] quotient(X,zero,X).
% 1.81/2.07 0 [] quotient(x,y,xQy).
% 1.81/2.07 0 [] less_e_qual(xQy,z).
% 1.81/2.07 0 [] quotient(x,z,xQz).
% 1.81/2.07 0 [] -less_e_qual(xQz,y).
% 1.81/2.07 end_of_list.
% 1.81/2.07
% 1.81/2.07 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 1.81/2.07
% 1.81/2.07 This is a Horn set with equality. The strategy will be
% 1.81/2.07 Knuth-Bendix and hyper_res, with positive clauses in
% 1.81/2.07 sos and nonpositive clauses in usable.
% 1.81/2.07
% 1.81/2.07 dependent: set(knuth_bendix).
% 1.81/2.07 dependent: set(anl_eq).
% 1.81/2.07 dependent: set(para_from).
% 1.81/2.07 dependent: set(para_into).
% 1.81/2.07 dependent: clear(para_from_right).
% 1.81/2.07 dependent: clear(para_into_right).
% 1.81/2.07 dependent: set(para_from_vars).
% 1.81/2.07 dependent: set(eq_units_both_ways).
% 1.81/2.07 dependent: set(dynamic_demod_all).
% 1.81/2.07 dependent: set(dynamic_demod).
% 1.81/2.07 dependent: set(order_eq).
% 1.81/2.07 dependent: set(back_demod).
% 1.81/2.07 dependent: set(lrpo).
% 1.81/2.07 dependent: set(hyper_res).
% 1.81/2.07 dependent: clear(order_hyper).
% 1.81/2.07
% 1.81/2.07 ------------> process usable:
% 1.81/2.07 ** KEPT (pick-wt=7): 1 [] -less_e_qual(A,B)|quotient(A,B,zero).
% 1.81/2.07 ** KEPT (pick-wt=7): 2 [] -quotient(A,B,zero)|less_e_qual(A,B).
% 1.81/2.07 ** KEPT (pick-wt=7): 3 [] -quotient(A,B,C)|less_e_qual(C,A).
% 1.81/2.07 ** KEPT (pick-wt=23): 4 [] -quotient(A,B,C)| -quotient(B,D,E)| -quotient(A,D,F)| -quotient(F,E,G)| -quotient(C,D,H)|less_e_qual(G,H).
% 1.81/2.07 ** KEPT (pick-wt=9): 5 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.81/2.07 ** KEPT (pick-wt=11): 6 [] -quotient(A,B,C)| -quotient(A,B,D)|C=D.
% 1.81/2.07 ** KEPT (pick-wt=3): 7 [] -less_e_qual(xQz,y).
% 1.81/2.07
% 1.81/2.07 ------------> process sos:
% 1.81/2.07 ** KEPT (pick-wt=3): 8 [] A=A.
% 1.81/2.07 ** KEPT (pick-wt=3): 9 [] less_e_qual(zero,A).
% 1.81/2.07 ** KEPT (pick-wt=3): 10 [] less_e_qual(A,identity).
% 1.81/2.07 ** KEPT (pick-wt=6): 11 [] quotient(A,B,divide(A,B)).
% 1.81/2.07 ** KEPT (pick-wt=4): 12 [] quotient(A,identity,zero).
% 1.81/2.07 ** KEPT (pick-wt=4): 13 [] quotient(zero,A,zero).
% 1.81/2.07 ** KEPT (pick-wt=4): 14 [] quotient(A,A,zero).
% 1.81/2.07 ** KEPT (pick-wt=4): 15 [] quotient(A,zero,A).
% 1.81/2.07 ** KEPT (pick-wt=4): 16 [] quotient(x,y,xQy).
% 1.81/2.07 ** KEPT (pick-wt=3): 17 [] less_e_qual(xQy,z).
% 1.81/2.07 ** KEPT (pick-wt=4): 18 [] quotient(x,z,xQz).
% 1.81/2.07 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 1.81/2.07
% 1.81/2.07 ======= end of input processing =======
% 1.81/2.07
% 1.81/2.07 =========== start of search ===========
% 1.81/2.07
% 1.81/2.07 -------- PROOF --------
% 1.81/2.07
% 1.81/2.07 ----> UNIT CONFLICT at 0.04 sec ----> 423 [binary,422.1,7.1] $F.
% 1.81/2.07
% 1.81/2.07 Length of proof is 10. Level of proof is 8.
% 1.81/2.07
% 1.81/2.07 ---------------- PROOF ----------------
% 1.81/2.07 % SZS status Unsatisfiable
% 1.81/2.07 % SZS output start Refutation
% See solution above
% 1.81/2.07 ------------ end of proof -------------
% 1.81/2.07
% 1.81/2.07
% 1.81/2.07 Search stopped by max_proofs option.
% 1.81/2.07
% 1.81/2.07
% 1.81/2.07 Search stopped by max_proofs option.
% 1.81/2.07
% 1.81/2.07 ============ end of search ============
% 1.81/2.07
% 1.81/2.07 -------------- statistics -------------
% 1.81/2.07 clauses given 68
% 1.81/2.07 clauses generated 5871
% 1.81/2.07 clauses kept 401
% 1.81/2.07 clauses forward subsumed 5508
% 1.81/2.07 clauses back subsumed 17
% 1.81/2.07 Kbytes malloced 1953
% 1.81/2.07
% 1.81/2.07 ----------- times (seconds) -----------
% 1.81/2.07 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.81/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.07 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.81/2.07
% 1.81/2.07 That finishes the proof of the theorem.
% 1.81/2.07
% 1.81/2.07 Process 17229 finished Wed Jul 27 09:06:32 2022
% 1.81/2.07 Otter interrupted
% 1.81/2.07 PROOF FOUND
%------------------------------------------------------------------------------