TSTP Solution File: COL002-4 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL002-4 : TPTP v8.1.0. Bugfixed v3.1.0.
% 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 12:47:56 EDT 2022
% Result : Unsatisfiable 1.56s 1.81s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 4 RR)
% Number of literals : 11 ( 10 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
file('COL002-4.p',unknown),
[] ).
cnf(2,plain,
apply(fixed_pt,weak_fixed_point(fixed_pt)) != weak_fixed_point(fixed_pt),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)),
file('COL002-4.p',unknown),
[] ).
cnf(5,axiom,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
file('COL002-4.p',unknown),
[] ).
cnf(8,axiom,
apply(i,A) = A,
file('COL002-4.p',unknown),
[] ).
cnf(11,axiom,
weak_fixed_point(A) = apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)),
file('COL002-4.p',unknown),
[] ).
cnf(12,plain,
apply(apply(A,B),apply(C,B)) = apply(apply(apply(s,A),C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(14,plain,
apply(fixed_pt,apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))) != apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),11,11]),
[iquote('back_demod,2,demod,11,11')] ).
cnf(173,plain,
apply(apply(A,B),B) = apply(apply(apply(s,A),i),B),
inference(para_into,[status(thm),theory(equality)],[12,8]),
[iquote('para_into,12.1.1.2,8.1.1')] ).
cnf(420,plain,
apply(A,apply(B,B)) = apply(apply(apply(s,apply(b,A)),i),B),
inference(para_into,[status(thm),theory(equality)],[173,5]),
[iquote('para_into,173.1.1,5.1.1')] ).
cnf(421,plain,
$false,
inference(binary,[status(thm)],[420,14]),
[iquote('binary,420.1,14.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : COL002-4 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Jul 27 02:44:22 EDT 2022
% 0.11/0.32 % CPUTime :
% 1.56/1.81 ----- Otter 3.3f, August 2004 -----
% 1.56/1.81 The process was started by sandbox2 on n016.cluster.edu,
% 1.56/1.81 Wed Jul 27 02:44:22 2022
% 1.56/1.81 The command was "./otter". The process ID is 28380.
% 1.56/1.81
% 1.56/1.81 set(prolog_style_variables).
% 1.56/1.81 set(auto).
% 1.56/1.81 dependent: set(auto1).
% 1.56/1.81 dependent: set(process_input).
% 1.56/1.81 dependent: clear(print_kept).
% 1.56/1.81 dependent: clear(print_new_demod).
% 1.56/1.81 dependent: clear(print_back_demod).
% 1.56/1.81 dependent: clear(print_back_sub).
% 1.56/1.81 dependent: set(control_memory).
% 1.56/1.81 dependent: assign(max_mem, 12000).
% 1.56/1.81 dependent: assign(pick_given_ratio, 4).
% 1.56/1.81 dependent: assign(stats_level, 1).
% 1.56/1.81 dependent: assign(max_seconds, 10800).
% 1.56/1.81 clear(print_given).
% 1.56/1.81
% 1.56/1.81 list(usable).
% 1.56/1.81 0 [] A=A.
% 1.56/1.81 0 [] apply(apply(apply(s,X),Y),Z)=apply(apply(X,Z),apply(Y,Z)).
% 1.56/1.81 0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.56/1.81 0 [] apply(apply(apply(c,X),Y),Z)=apply(apply(X,Z),Y).
% 1.56/1.81 0 [] apply(i,X)=X.
% 1.56/1.81 0 [] weak_fixed_point(X)=apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)).
% 1.56/1.81 0 [] weak_fixed_point(fixed_pt)!=apply(fixed_pt,weak_fixed_point(fixed_pt)).
% 1.56/1.81 end_of_list.
% 1.56/1.81
% 1.56/1.81 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.56/1.81
% 1.56/1.81 All clauses are units, and equality is present; the
% 1.56/1.81 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.56/1.81
% 1.56/1.81 dependent: set(knuth_bendix).
% 1.56/1.81 dependent: set(anl_eq).
% 1.56/1.81 dependent: set(para_from).
% 1.56/1.81 dependent: set(para_into).
% 1.56/1.81 dependent: clear(para_from_right).
% 1.56/1.81 dependent: clear(para_into_right).
% 1.56/1.81 dependent: set(para_from_vars).
% 1.56/1.81 dependent: set(eq_units_both_ways).
% 1.56/1.81 dependent: set(dynamic_demod_all).
% 1.56/1.81 dependent: set(dynamic_demod).
% 1.56/1.81 dependent: set(order_eq).
% 1.56/1.81 dependent: set(back_demod).
% 1.56/1.81 dependent: set(lrpo).
% 1.56/1.81
% 1.56/1.81 ------------> process usable:
% 1.56/1.81 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] apply(fixed_pt,weak_fixed_point(fixed_pt))!=weak_fixed_point(fixed_pt).
% 1.56/1.81
% 1.56/1.81 ------------> process sos:
% 1.56/1.81 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.56/1.81 ** KEPT (pick-wt=15): 4 [] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.56/1.81 ** KEPT (pick-wt=13): 5 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.56/1.81 ---> New Demodulator: 6 [new_demod,5] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.56/1.81 ** KEPT (pick-wt=13): 7 [] apply(apply(apply(c,A),B),C)=apply(apply(A,C),B).
% 1.56/1.81 ** KEPT (pick-wt=5): 8 [] apply(i,A)=A.
% 1.56/1.81 ---> New Demodulator: 9 [new_demod,8] apply(i,A)=A.
% 1.56/1.81 ** KEPT (pick-wt=18): 10 [] weak_fixed_point(A)=apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)).
% 1.56/1.81 ---> New Demodulator: 11 [new_demod,10] weak_fixed_point(A)=apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i)).
% 1.56/1.81 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.56/1.81 ** KEPT (pick-wt=15): 12 [copy,4,flip.1] apply(apply(A,B),apply(C,B))=apply(apply(apply(s,A),C),B).
% 1.56/1.81 >>>> Starting back demodulation with 6.
% 1.56/1.81 ** KEPT (pick-wt=13): 13 [copy,7,flip.1] apply(apply(A,B),C)=apply(apply(apply(c,A),C),B).
% 1.56/1.81 >>>> Starting back demodulation with 9.
% 1.56/1.81 >>>> Starting back demodulation with 11.
% 1.56/1.81 >> back demodulating 2 with 11.
% 1.56/1.81 Following clause subsumed by 4 during input processing: 0 [copy,12,flip.1] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.56/1.81 Following clause subsumed by 7 during input processing: 0 [copy,13,flip.1] apply(apply(apply(c,A),B),C)=apply(apply(A,C),B).
% 1.56/1.81
% 1.56/1.81 ======= end of input processing =======
% 1.56/1.81
% 1.56/1.81 =========== start of search ===========
% 1.56/1.81
% 1.56/1.81 -------- PROOF --------
% 1.56/1.81
% 1.56/1.81 ----> UNIT CONFLICT at 0.01 sec ----> 421 [binary,420.1,14.1] $F.
% 1.56/1.81
% 1.56/1.81 Length of proof is 5. Level of proof is 3.
% 1.56/1.81
% 1.56/1.81 ---------------- PROOF ----------------
% 1.56/1.81 % SZS status Unsatisfiable
% 1.56/1.81 % SZS output start Refutation
% See solution above
% 1.56/1.81 ------------ end of proof -------------
% 1.56/1.81
% 1.56/1.81
% 1.56/1.81 Search stopped by max_proofs option.
% 1.56/1.81
% 1.56/1.81
% 1.56/1.81 Search stopped by max_proofs option.
% 1.56/1.81
% 1.56/1.81 ============ end of search ============
% 1.56/1.81
% 1.56/1.81 -------------- statistics -------------
% 1.56/1.81 clauses given 23
% 1.56/1.81 clauses generated 370
% 1.56/1.81 clauses kept 330
% 1.56/1.81 clauses forward subsumed 271
% 1.56/1.81 clauses back subsumed 0
% 1.56/1.81 Kbytes malloced 1953
% 1.56/1.81
% 1.56/1.81 ----------- times (seconds) -----------
% 1.56/1.81 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.56/1.81 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.56/1.81 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.56/1.81
% 1.56/1.81 That finishes the proof of the theorem.
% 1.56/1.81
% 1.56/1.81 Process 28380 finished Wed Jul 27 02:44:23 2022
% 1.56/1.81 Otter interrupted
% 1.56/1.81 PROOF FOUND
%------------------------------------------------------------------------------