TSTP Solution File: HEN008-4 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN008-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:57:58 EDT 2022
% Result : Unsatisfiable 1.74s 1.94s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 20 ( 16 unt; 0 nHn; 8 RR)
% Number of literals : 25 ( 8 equ; 6 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 : 27 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| divide(A,B) = zero ),
file('HEN008-4.p',unknown),
[] ).
cnf(2,axiom,
( divide(A,B) != zero
| less_e_qual(A,B) ),
file('HEN008-4.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN008-4.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(divide(A,B),C)
| less_e_qual(divide(A,C),B) ),
file('HEN008-4.p',unknown),
[] ).
cnf(7,axiom,
~ less_e_qual(divide(a,c),divide(b,c)),
file('HEN008-4.p',unknown),
[] ).
cnf(9,axiom,
less_e_qual(divide(A,B),A),
file('HEN008-4.p',unknown),
[] ).
cnf(10,axiom,
less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
file('HEN008-4.p',unknown),
[] ).
cnf(11,axiom,
less_e_qual(zero,A),
file('HEN008-4.p',unknown),
[] ).
cnf(16,axiom,
divide(zero,A) = zero,
file('HEN008-4.p',unknown),
[] ).
cnf(17,axiom,
divide(A,A) = zero,
file('HEN008-4.p',unknown),
[] ).
cnf(21,axiom,
less_e_qual(a,b),
file('HEN008-4.p',unknown),
[] ).
cnf(26,plain,
divide(a,b) = zero,
inference(hyper,[status(thm)],[21,1]),
[iquote('hyper,21,1')] ).
cnf(37,plain,
less_e_qual(divide(divide(A,B),divide(divide(A,C),B)),divide(C,B)),
inference(hyper,[status(thm)],[10,5]),
[iquote('hyper,10,5')] ).
cnf(56,plain,
less_e_qual(A,A),
inference(hyper,[status(thm)],[17,2]),
[iquote('hyper,17,2')] ).
cnf(60,plain,
less_e_qual(divide(A,divide(A,B)),B),
inference(hyper,[status(thm)],[56,5]),
[iquote('hyper,56,5')] ).
cnf(144,plain,
divide(A,divide(A,zero)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[60,3,11])]),
[iquote('hyper,60,3,11,flip.1')] ).
cnf(179,plain,
less_e_qual(A,divide(A,zero)),
inference(hyper,[status(thm)],[144,2]),
[iquote('hyper,144,2')] ).
cnf(200,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[179,3,9]),
[iquote('hyper,179,3,9')] ).
cnf(401,plain,
less_e_qual(divide(a,A),divide(b,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[37,26]),16,200]),
[iquote('para_into,37.1.1.2.1,26.1.1,demod,16,200')] ).
cnf(402,plain,
$false,
inference(binary,[status(thm)],[401,7]),
[iquote('binary,401.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : HEN008-4 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 08:58:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.74/1.94 ----- Otter 3.3f, August 2004 -----
% 1.74/1.94 The process was started by sandbox on n022.cluster.edu,
% 1.74/1.94 Wed Jul 27 08:58:50 2022
% 1.74/1.94 The command was "./otter". The process ID is 13749.
% 1.74/1.94
% 1.74/1.94 set(prolog_style_variables).
% 1.74/1.94 set(auto).
% 1.74/1.94 dependent: set(auto1).
% 1.74/1.94 dependent: set(process_input).
% 1.74/1.94 dependent: clear(print_kept).
% 1.74/1.94 dependent: clear(print_new_demod).
% 1.74/1.94 dependent: clear(print_back_demod).
% 1.74/1.94 dependent: clear(print_back_sub).
% 1.74/1.94 dependent: set(control_memory).
% 1.74/1.94 dependent: assign(max_mem, 12000).
% 1.74/1.94 dependent: assign(pick_given_ratio, 4).
% 1.74/1.94 dependent: assign(stats_level, 1).
% 1.74/1.94 dependent: assign(max_seconds, 10800).
% 1.74/1.94 clear(print_given).
% 1.74/1.94
% 1.74/1.94 list(usable).
% 1.74/1.94 0 [] A=A.
% 1.74/1.94 0 [] -less_e_qual(X,Y)|divide(X,Y)=zero.
% 1.74/1.94 0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 1.74/1.94 0 [] less_e_qual(divide(X,Y),X).
% 1.74/1.94 0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 1.74/1.94 0 [] less_e_qual(zero,X).
% 1.74/1.94 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.74/1.94 0 [] less_e_qual(X,identity).
% 1.74/1.94 0 [] divide(X,identity)=zero.
% 1.74/1.94 0 [] divide(zero,X)=zero.
% 1.74/1.94 0 [] divide(X,X)=zero.
% 1.74/1.94 0 [] divide(a,zero)=a.
% 1.74/1.94 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,Z)|less_e_qual(X,Z).
% 1.74/1.94 0 [] -less_e_qual(divide(X,Y),Z)|less_e_qual(divide(X,Z),Y).
% 1.74/1.94 0 [] -less_e_qual(X,Y)|less_e_qual(divide(Z,Y),divide(Z,X)).
% 1.74/1.94 0 [] less_e_qual(a,b).
% 1.74/1.94 0 [] -less_e_qual(divide(a,c),divide(b,c)).
% 1.74/1.94 end_of_list.
% 1.74/1.94
% 1.74/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.74/1.94
% 1.74/1.94 This is a Horn set with equality. The strategy will be
% 1.74/1.94 Knuth-Bendix and hyper_res, with positive clauses in
% 1.74/1.94 sos and nonpositive clauses in usable.
% 1.74/1.94
% 1.74/1.94 dependent: set(knuth_bendix).
% 1.74/1.94 dependent: set(anl_eq).
% 1.74/1.94 dependent: set(para_from).
% 1.74/1.94 dependent: set(para_into).
% 1.74/1.94 dependent: clear(para_from_right).
% 1.74/1.94 dependent: clear(para_into_right).
% 1.74/1.94 dependent: set(para_from_vars).
% 1.74/1.94 dependent: set(eq_units_both_ways).
% 1.74/1.94 dependent: set(dynamic_demod_all).
% 1.74/1.94 dependent: set(dynamic_demod).
% 1.74/1.94 dependent: set(order_eq).
% 1.74/1.94 dependent: set(back_demod).
% 1.74/1.94 dependent: set(lrpo).
% 1.74/1.94 dependent: set(hyper_res).
% 1.74/1.94 dependent: clear(order_hyper).
% 1.74/1.94
% 1.74/1.94 ------------> process usable:
% 1.74/1.94 ** KEPT (pick-wt=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 1.74/1.94 ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 1.74/1.94 ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.74/1.94 ** KEPT (pick-wt=9): 4 [] -less_e_qual(A,B)| -less_e_qual(B,C)|less_e_qual(A,C).
% 1.74/1.94 ** KEPT (pick-wt=10): 5 [] -less_e_qual(divide(A,B),C)|less_e_qual(divide(A,C),B).
% 1.74/1.94 ** KEPT (pick-wt=10): 6 [] -less_e_qual(A,B)|less_e_qual(divide(C,B),divide(C,A)).
% 1.74/1.94 ** KEPT (pick-wt=7): 7 [] -less_e_qual(divide(a,c),divide(b,c)).
% 1.74/1.94
% 1.74/1.94 ------------> process sos:
% 1.74/1.94 ** KEPT (pick-wt=3): 8 [] A=A.
% 1.74/1.94 ** KEPT (pick-wt=5): 9 [] less_e_qual(divide(A,B),A).
% 1.74/1.94 ** KEPT (pick-wt=13): 10 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 1.74/1.94 ** KEPT (pick-wt=3): 11 [] less_e_qual(zero,A).
% 1.74/1.94 ** KEPT (pick-wt=3): 12 [] less_e_qual(A,identity).
% 1.74/1.94 ** KEPT (pick-wt=5): 13 [] divide(A,identity)=zero.
% 1.74/1.94 ---> New Demodulator: 14 [new_demod,13] divide(A,identity)=zero.
% 1.74/1.94 ** KEPT (pick-wt=5): 15 [] divide(zero,A)=zero.
% 1.74/1.94 ---> New Demodulator: 16 [new_demod,15] divide(zero,A)=zero.
% 1.74/1.94 ** KEPT (pick-wt=5): 17 [] divide(A,A)=zero.
% 1.74/1.94 ---> New Demodulator: 18 [new_demod,17] divide(A,A)=zero.
% 1.74/1.94 ** KEPT (pick-wt=5): 19 [] divide(a,zero)=a.
% 1.74/1.94 ---> New Demodulator: 20 [new_demod,19] divide(a,zero)=a.
% 1.74/1.94 ** KEPT (pick-wt=3): 21 [] less_e_qual(a,b).
% 1.74/1.94 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 1.74/1.94 >>>> Starting back demodulation with 14.
% 1.74/1.94 >>>> Starting back demodulation with 16.
% 1.74/1.94 >>>> Starting back demodulation with 18.
% 1.74/1.94 >>>> Starting back demodulation with 20.
% 1.74/1.94
% 1.74/1.94 ======= end of input processing =======
% 1.74/1.94
% 1.74/1.94 =========== start of search ===========
% 1.74/1.94
% 1.74/1.94 -------- PROOF --------
% 1.74/1.94
% 1.74/1.94 ----> UNIT CONFLICT at 0.01 sec ----> 402 [binary,401.1,7.1] $F.
% 1.74/1.94
% 1.74/1.94 Length of proof is 8. Level of proof is 6.
% 1.74/1.94
% 1.74/1.94 ---------------- PROOF ----------------
% 1.74/1.94 % SZS status Unsatisfiable
% 1.74/1.94 % SZS output start Refutation
% See solution above
% 1.74/1.94 ------------ end of proof -------------
% 1.74/1.94
% 1.74/1.94
% 1.74/1.94 Search stopped by max_proofs option.
% 1.74/1.94
% 1.74/1.94
% 1.74/1.94 Search stopped by max_proofs option.
% 1.74/1.94
% 1.74/1.94 ============ end of search ============
% 1.74/1.94
% 1.74/1.94 -------------- statistics -------------
% 1.74/1.94 clauses given 51
% 1.74/1.94 clauses generated 1259
% 1.74/1.94 clauses kept 380
% 1.74/1.94 clauses forward subsumed 930
% 1.74/1.94 clauses back subsumed 54
% 1.74/1.94 Kbytes malloced 1953
% 1.74/1.94
% 1.74/1.94 ----------- times (seconds) -----------
% 1.74/1.94 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.74/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.74/1.94
% 1.74/1.94 That finishes the proof of the theorem.
% 1.74/1.94
% 1.74/1.94 Process 13749 finished Wed Jul 27 08:58:52 2022
% 1.74/1.94 Otter interrupted
% 1.74/1.94 PROOF FOUND
%------------------------------------------------------------------------------