TSTP Solution File: HEN006-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN006-1 : 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 12:57:56 EDT 2022
% Result : Unsatisfiable 1.65s 1.91s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 26 ( 21 unt; 0 nHn; 21 RR)
% Number of literals : 36 ( 4 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 : 25 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| quotient(A,B,zero) ),
file('HEN006-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ quotient(A,B,zero)
| less_e_qual(A,B) ),
file('HEN006-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ quotient(A,B,C)
| less_e_qual(C,A) ),
file('HEN006-1.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('HEN006-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN006-1.p',unknown),
[] ).
cnf(7,axiom,
~ less_e_qual(xQz,y),
file('HEN006-1.p',unknown),
[] ).
cnf(9,axiom,
less_e_qual(zero,A),
file('HEN006-1.p',unknown),
[] ).
cnf(11,axiom,
quotient(A,B,divide(A,B)),
file('HEN006-1.p',unknown),
[] ).
cnf(12,axiom,
quotient(x,y,xQy),
file('HEN006-1.p',unknown),
[] ).
cnf(13,axiom,
less_e_qual(xQy,z),
file('HEN006-1.p',unknown),
[] ).
cnf(14,axiom,
quotient(x,z,xQz),
file('HEN006-1.p',unknown),
[] ).
cnf(15,plain,
quotient(zero,A,zero),
inference(hyper,[status(thm)],[9,1]),
[iquote('hyper,9,1')] ).
cnf(21,plain,
quotient(xQy,z,zero),
inference(hyper,[status(thm)],[13,1]),
[iquote('hyper,13,1')] ).
cnf(41,plain,
less_e_qual(divide(A,B),A),
inference(hyper,[status(thm)],[11,3]),
[iquote('hyper,11,3')] ).
cnf(92,plain,
less_e_qual(divide(xQz,divide(y,z)),zero),
inference(hyper,[status(thm)],[21,4,12,11,14,11]),
[iquote('hyper,21,4,12,11,14,11')] ).
cnf(135,plain,
quotient(divide(A,B),A,zero),
inference(hyper,[status(thm)],[41,1]),
[iquote('hyper,41,1')] ).
cnf(191,plain,
divide(xQz,divide(y,z)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[92,5,9])]),
[iquote('hyper,92,5,9,flip.1')] ).
cnf(291,plain,
quotient(xQz,divide(y,z),zero),
inference(para_from,[status(thm),theory(equality)],[191,11]),
[iquote('para_from,191.1.1,11.1.3')] ).
cnf(299,plain,
less_e_qual(divide(divide(xQz,y),zero),zero),
inference(hyper,[status(thm)],[291,4,135,11,11,15]),
[iquote('hyper,291,4,135,11,11,15')] ).
cnf(399,plain,
divide(divide(xQz,y),zero) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[299,5,9])]),
[iquote('hyper,299,5,9,flip.1')] ).
cnf(439,plain,
quotient(divide(xQz,y),zero,zero),
inference(para_from,[status(thm),theory(equality)],[399,11]),
[iquote('para_from,399.1.1,11.1.3')] ).
cnf(444,plain,
less_e_qual(divide(xQz,y),zero),
inference(hyper,[status(thm)],[439,2]),
[iquote('hyper,439,2')] ).
cnf(462,plain,
divide(xQz,y) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[444,5,9])]),
[iquote('hyper,444,5,9,flip.1')] ).
cnf(469,plain,
quotient(xQz,y,zero),
inference(para_from,[status(thm),theory(equality)],[462,11]),
[iquote('para_from,462.1.1,11.1.3')] ).
cnf(474,plain,
less_e_qual(xQz,y),
inference(hyper,[status(thm)],[469,2]),
[iquote('hyper,469,2')] ).
cnf(475,plain,
$false,
inference(binary,[status(thm)],[474,7]),
[iquote('binary,474.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : HEN006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n016.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 09:20:07 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.65/1.91 ----- Otter 3.3f, August 2004 -----
% 1.65/1.91 The process was started by sandbox2 on n016.cluster.edu,
% 1.65/1.91 Wed Jul 27 09:20:07 2022
% 1.65/1.91 The command was "./otter". The process ID is 11199.
% 1.65/1.91
% 1.65/1.91 set(prolog_style_variables).
% 1.65/1.91 set(auto).
% 1.65/1.91 dependent: set(auto1).
% 1.65/1.91 dependent: set(process_input).
% 1.65/1.91 dependent: clear(print_kept).
% 1.65/1.91 dependent: clear(print_new_demod).
% 1.65/1.91 dependent: clear(print_back_demod).
% 1.65/1.91 dependent: clear(print_back_sub).
% 1.65/1.91 dependent: set(control_memory).
% 1.65/1.91 dependent: assign(max_mem, 12000).
% 1.65/1.91 dependent: assign(pick_given_ratio, 4).
% 1.65/1.91 dependent: assign(stats_level, 1).
% 1.65/1.91 dependent: assign(max_seconds, 10800).
% 1.65/1.91 clear(print_given).
% 1.65/1.91
% 1.65/1.91 list(usable).
% 1.65/1.91 0 [] A=A.
% 1.65/1.91 0 [] -less_e_qual(X,Y)|quotient(X,Y,zero).
% 1.65/1.91 0 [] -quotient(X,Y,zero)|less_e_qual(X,Y).
% 1.65/1.91 0 [] -quotient(X,Y,Z)|less_e_qual(Z,X).
% 1.65/1.91 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).
% 1.65/1.91 0 [] less_e_qual(zero,X).
% 1.65/1.91 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.65/1.91 0 [] less_e_qual(X,identity).
% 1.65/1.91 0 [] quotient(X,Y,divide(X,Y)).
% 1.65/1.91 0 [] -quotient(X,Y,Z)| -quotient(X,Y,W)|Z=W.
% 1.65/1.91 0 [] quotient(x,y,xQy).
% 1.65/1.91 0 [] less_e_qual(xQy,z).
% 1.65/1.91 0 [] quotient(x,z,xQz).
% 1.65/1.91 0 [] -less_e_qual(xQz,y).
% 1.65/1.91 end_of_list.
% 1.65/1.91
% 1.65/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 1.65/1.91
% 1.65/1.91 This is a Horn set with equality. The strategy will be
% 1.65/1.91 Knuth-Bendix and hyper_res, with positive clauses in
% 1.65/1.91 sos and nonpositive clauses in usable.
% 1.65/1.91
% 1.65/1.91 dependent: set(knuth_bendix).
% 1.65/1.91 dependent: set(anl_eq).
% 1.65/1.91 dependent: set(para_from).
% 1.65/1.91 dependent: set(para_into).
% 1.65/1.91 dependent: clear(para_from_right).
% 1.65/1.91 dependent: clear(para_into_right).
% 1.65/1.91 dependent: set(para_from_vars).
% 1.65/1.91 dependent: set(eq_units_both_ways).
% 1.65/1.91 dependent: set(dynamic_demod_all).
% 1.65/1.91 dependent: set(dynamic_demod).
% 1.65/1.91 dependent: set(order_eq).
% 1.65/1.91 dependent: set(back_demod).
% 1.65/1.91 dependent: set(lrpo).
% 1.65/1.91 dependent: set(hyper_res).
% 1.65/1.91 dependent: clear(order_hyper).
% 1.65/1.91
% 1.65/1.91 ------------> process usable:
% 1.65/1.91 ** KEPT (pick-wt=7): 1 [] -less_e_qual(A,B)|quotient(A,B,zero).
% 1.65/1.91 ** KEPT (pick-wt=7): 2 [] -quotient(A,B,zero)|less_e_qual(A,B).
% 1.65/1.91 ** KEPT (pick-wt=7): 3 [] -quotient(A,B,C)|less_e_qual(C,A).
% 1.65/1.91 ** 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).
% 1.65/1.91 ** KEPT (pick-wt=9): 5 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.65/1.91 ** KEPT (pick-wt=11): 6 [] -quotient(A,B,C)| -quotient(A,B,D)|C=D.
% 1.65/1.91 ** KEPT (pick-wt=3): 7 [] -less_e_qual(xQz,y).
% 1.65/1.91
% 1.65/1.91 ------------> process sos:
% 1.65/1.91 ** KEPT (pick-wt=3): 8 [] A=A.
% 1.65/1.91 ** KEPT (pick-wt=3): 9 [] less_e_qual(zero,A).
% 1.65/1.91 ** KEPT (pick-wt=3): 10 [] less_e_qual(A,identity).
% 1.65/1.91 ** KEPT (pick-wt=6): 11 [] quotient(A,B,divide(A,B)).
% 1.65/1.91 ** KEPT (pick-wt=4): 12 [] quotient(x,y,xQy).
% 1.65/1.91 ** KEPT (pick-wt=3): 13 [] less_e_qual(xQy,z).
% 1.65/1.91 ** KEPT (pick-wt=4): 14 [] quotient(x,z,xQz).
% 1.65/1.91 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 1.65/1.91
% 1.65/1.91 ======= end of input processing =======
% 1.65/1.91
% 1.65/1.91 =========== start of search ===========
% 1.65/1.91
% 1.65/1.91 -------- PROOF --------
% 1.65/1.91
% 1.65/1.91 ----> UNIT CONFLICT at 0.04 sec ----> 475 [binary,474.1,7.1] $F.
% 1.65/1.91
% 1.65/1.91 Length of proof is 14. Level of proof is 11.
% 1.65/1.91
% 1.65/1.91 ---------------- PROOF ----------------
% 1.65/1.91 % SZS status Unsatisfiable
% 1.65/1.91 % SZS output start Refutation
% See solution above
% 1.65/1.91 ------------ end of proof -------------
% 1.65/1.91
% 1.65/1.91
% 1.65/1.91 Search stopped by max_proofs option.
% 1.65/1.91
% 1.65/1.91
% 1.65/1.91 Search stopped by max_proofs option.
% 1.65/1.91
% 1.65/1.91 ============ end of search ============
% 1.65/1.91
% 1.65/1.91 -------------- statistics -------------
% 1.65/1.91 clauses given 69
% 1.65/1.91 clauses generated 3467
% 1.65/1.91 clauses kept 456
% 1.65/1.91 clauses forward subsumed 3092
% 1.65/1.91 clauses back subsumed 26
% 1.65/1.91 Kbytes malloced 1953
% 1.65/1.91
% 1.65/1.91 ----------- times (seconds) -----------
% 1.65/1.91 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.65/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.91 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.65/1.91
% 1.65/1.91 That finishes the proof of the theorem.
% 1.65/1.91
% 1.65/1.91 Process 11199 finished Wed Jul 27 09:20:09 2022
% 1.65/1.91 Otter interrupted
% 1.65/1.91 PROOF FOUND
%------------------------------------------------------------------------------