TSTP Solution File: COL066-2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL066-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 12:48:10 EDT 2022
% Result : Unsatisfiable 1.68s 1.91s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 7 unt; 0 nHn; 4 RR)
% Number of literals : 7 ( 6 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('COL066-2.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('COL066-2.p',unknown),
[] ).
cnf(6,axiom,
apply(apply(apply(q,A),B),C) = apply(B,apply(A,C)),
file('COL066-2.p',unknown),
[] ).
cnf(7,axiom,
apply(apply(w,A),B) = apply(apply(A,B),B),
file('COL066-2.p',unknown),
[] ).
cnf(8,plain,
apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),6]),
[iquote('back_demod,1,demod,6')] ).
cnf(64,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,7]),6,6,6,6,6]),
[iquote('para_into,8.1.1.1.1.1,7.1.1,demod,6,6,6,6,6')] ).
cnf(65,plain,
$false,
inference(binary,[status(thm)],[64,2]),
[iquote('binary,64.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : COL066-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 02:20:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.91 ----- Otter 3.3f, August 2004 -----
% 1.68/1.91 The process was started by sandbox2 on n012.cluster.edu,
% 1.68/1.91 Wed Jul 27 02:20:20 2022
% 1.68/1.91 The command was "./otter". The process ID is 4438.
% 1.68/1.91
% 1.68/1.91 set(prolog_style_variables).
% 1.68/1.91 set(auto).
% 1.68/1.91 dependent: set(auto1).
% 1.68/1.91 dependent: set(process_input).
% 1.68/1.91 dependent: clear(print_kept).
% 1.68/1.91 dependent: clear(print_new_demod).
% 1.68/1.91 dependent: clear(print_back_demod).
% 1.68/1.91 dependent: clear(print_back_sub).
% 1.68/1.91 dependent: set(control_memory).
% 1.68/1.91 dependent: assign(max_mem, 12000).
% 1.68/1.91 dependent: assign(pick_given_ratio, 4).
% 1.68/1.91 dependent: assign(stats_level, 1).
% 1.68/1.91 dependent: assign(max_seconds, 10800).
% 1.68/1.91 clear(print_given).
% 1.68/1.91
% 1.68/1.91 list(usable).
% 1.68/1.91 0 [] A=A.
% 1.68/1.91 0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.68/1.91 0 [] apply(apply(apply(q,X),Y),Z)=apply(Y,apply(X,Z)).
% 1.68/1.91 0 [] apply(apply(w,X),Y)=apply(apply(X,Y),Y).
% 1.68/1.91 0 [] apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z)!=apply(apply(x,y),apply(apply(x,y),z)).
% 1.68/1.91 end_of_list.
% 1.68/1.91
% 1.68/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.68/1.91
% 1.68/1.91 All clauses are units, and equality is present; the
% 1.68/1.91 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.68/1.91
% 1.68/1.91 dependent: set(knuth_bendix).
% 1.68/1.91 dependent: set(anl_eq).
% 1.68/1.91 dependent: set(para_from).
% 1.68/1.91 dependent: set(para_into).
% 1.68/1.91 dependent: clear(para_from_right).
% 1.68/1.91 dependent: clear(para_into_right).
% 1.68/1.91 dependent: set(para_from_vars).
% 1.68/1.91 dependent: set(eq_units_both_ways).
% 1.68/1.91 dependent: set(dynamic_demod_all).
% 1.68/1.91 dependent: set(dynamic_demod).
% 1.68/1.91 dependent: set(order_eq).
% 1.68/1.91 dependent: set(back_demod).
% 1.68/1.91 dependent: set(lrpo).
% 1.68/1.91
% 1.68/1.91 ------------> process usable:
% 1.68/1.91 ** KEPT (pick-wt=29): 1 [] apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z)!=apply(apply(x,y),apply(apply(x,y),z)).
% 1.68/1.91
% 1.68/1.91 ------------> process sos:
% 1.68/1.91 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.68/1.91 ** KEPT (pick-wt=13): 3 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.68/1.91 ---> New Demodulator: 4 [new_demod,3] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.68/1.91 ** KEPT (pick-wt=13): 5 [] apply(apply(apply(q,A),B),C)=apply(B,apply(A,C)).
% 1.68/1.91 ---> New Demodulator: 6 [new_demod,5] apply(apply(apply(q,A),B),C)=apply(B,apply(A,C)).
% 1.68/1.91 ** KEPT (pick-wt=11): 7 [] apply(apply(w,A),B)=apply(apply(A,B),B).
% 1.68/1.91 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.68/1.91 >>>> Starting back demodulation with 4.
% 1.68/1.91 >>>> Starting back demodulation with 6.
% 1.68/1.91 >> back demodulating 1 with 6.
% 1.68/1.91 ** KEPT (pick-wt=11): 9 [copy,7,flip.1] apply(apply(A,B),B)=apply(apply(w,A),B).
% 1.68/1.91 Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] apply(apply(w,A),B)=apply(apply(A,B),B).
% 1.68/1.91
% 1.68/1.91 ======= end of input processing =======
% 1.68/1.91
% 1.68/1.91 =========== start of search ===========
% 1.68/1.91
% 1.68/1.91 -------- PROOF --------
% 1.68/1.91
% 1.68/1.91 ----> UNIT CONFLICT at 0.00 sec ----> 65 [binary,64.1,2.1] $F.
% 1.68/1.91
% 1.68/1.91 Length of proof is 2. Level of proof is 2.
% 1.68/1.91
% 1.68/1.91 ---------------- PROOF ----------------
% 1.68/1.91 % SZS status Unsatisfiable
% 1.68/1.91 % SZS output start Refutation
% See solution above
% 1.68/1.91 ------------ end of proof -------------
% 1.68/1.91
% 1.68/1.91
% 1.68/1.91 Search stopped by max_proofs option.
% 1.68/1.91
% 1.68/1.91
% 1.68/1.91 Search stopped by max_proofs option.
% 1.68/1.91
% 1.68/1.91 ============ end of search ============
% 1.68/1.91
% 1.68/1.91 -------------- statistics -------------
% 1.68/1.91 clauses given 11
% 1.68/1.91 clauses generated 74
% 1.68/1.91 clauses kept 48
% 1.68/1.91 clauses forward subsumed 61
% 1.68/1.91 clauses back subsumed 0
% 1.68/1.91 Kbytes malloced 976
% 1.68/1.91
% 1.68/1.91 ----------- times (seconds) -----------
% 1.68/1.91 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.91 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.68/1.91
% 1.68/1.91 That finishes the proof of the theorem.
% 1.68/1.91
% 1.68/1.91 Process 4438 finished Wed Jul 27 02:20:22 2022
% 1.68/1.91 Otter interrupted
% 1.68/1.91 PROOF FOUND
%------------------------------------------------------------------------------