TSTP Solution File: COL008-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL008-1 : 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 12:47:59 EDT 2022
% Result : Unsatisfiable 1.54s 1.76s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 3 RR)
% Number of literals : 8 ( 7 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
A != apply(combinator,A),
file('COL008-1.p',unknown),
[] ).
cnf(2,plain,
apply(combinator,A) != A,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
file('COL008-1.p',unknown),
[] ).
cnf(6,axiom,
apply(m,A) = apply(A,A),
file('COL008-1.p',unknown),
[] ).
cnf(7,plain,
apply(A,A) = apply(m,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(13,plain,
apply(m,apply(apply(b,A),B)) = apply(A,apply(B,apply(apply(b,A),B))),
inference(para_into,[status(thm),theory(equality)],[4,7]),
[iquote('para_into,4.1.1,7.1.1')] ).
cnf(14,plain,
apply(A,apply(B,apply(apply(b,A),B))) = apply(m,apply(apply(b,A),B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(15,plain,
$false,
inference(binary,[status(thm)],[14,2]),
[iquote('binary,14.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n016.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 02:45:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.54/1.76 ----- Otter 3.3f, August 2004 -----
% 1.54/1.76 The process was started by sandbox on n016.cluster.edu,
% 1.54/1.76 Wed Jul 27 02:45:22 2022
% 1.54/1.76 The command was "./otter". The process ID is 2928.
% 1.54/1.76
% 1.54/1.76 set(prolog_style_variables).
% 1.54/1.76 set(auto).
% 1.54/1.76 dependent: set(auto1).
% 1.54/1.76 dependent: set(process_input).
% 1.54/1.76 dependent: clear(print_kept).
% 1.54/1.76 dependent: clear(print_new_demod).
% 1.54/1.76 dependent: clear(print_back_demod).
% 1.54/1.76 dependent: clear(print_back_sub).
% 1.54/1.76 dependent: set(control_memory).
% 1.54/1.76 dependent: assign(max_mem, 12000).
% 1.54/1.76 dependent: assign(pick_given_ratio, 4).
% 1.54/1.76 dependent: assign(stats_level, 1).
% 1.54/1.76 dependent: assign(max_seconds, 10800).
% 1.54/1.76 clear(print_given).
% 1.54/1.76
% 1.54/1.76 list(usable).
% 1.54/1.76 0 [] A=A.
% 1.54/1.76 0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.54/1.76 0 [] apply(m,X)=apply(X,X).
% 1.54/1.76 0 [] Y!=apply(combinator,Y).
% 1.54/1.76 end_of_list.
% 1.54/1.76
% 1.54/1.76 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.54/1.76
% 1.54/1.76 All clauses are units, and equality is present; the
% 1.54/1.76 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.54/1.76
% 1.54/1.76 dependent: set(knuth_bendix).
% 1.54/1.76 dependent: set(anl_eq).
% 1.54/1.76 dependent: set(para_from).
% 1.54/1.76 dependent: set(para_into).
% 1.54/1.76 dependent: clear(para_from_right).
% 1.54/1.76 dependent: clear(para_into_right).
% 1.54/1.76 dependent: set(para_from_vars).
% 1.54/1.76 dependent: set(eq_units_both_ways).
% 1.54/1.76 dependent: set(dynamic_demod_all).
% 1.54/1.76 dependent: set(dynamic_demod).
% 1.54/1.76 dependent: set(order_eq).
% 1.54/1.76 dependent: set(back_demod).
% 1.54/1.76 dependent: set(lrpo).
% 1.54/1.76
% 1.54/1.76 ------------> process usable:
% 1.54/1.76 ** KEPT (pick-wt=5): 2 [copy,1,flip.1] apply(combinator,A)!=A.
% 1.54/1.76
% 1.54/1.76 ------------> process sos:
% 1.54/1.76 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.54/1.76 ** KEPT (pick-wt=13): 4 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.54/1.76 ---> New Demodulator: 5 [new_demod,4] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.54/1.76 ** KEPT (pick-wt=7): 6 [] apply(m,A)=apply(A,A).
% 1.54/1.76 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.54/1.76 >>>> Starting back demodulation with 5.
% 1.54/1.76 ** KEPT (pick-wt=7): 7 [copy,6,flip.1] apply(A,A)=apply(m,A).
% 1.54/1.76 Following clause subsumed by 6 during input processing: 0 [copy,7,flip.1] apply(m,A)=apply(A,A).
% 1.54/1.76
% 1.54/1.76 ======= end of input processing =======
% 1.54/1.76
% 1.54/1.76 =========== start of search ===========
% 1.54/1.76
% 1.54/1.76 -------- PROOF --------
% 1.54/1.76
% 1.54/1.76 ----> UNIT CONFLICT at 0.00 sec ----> 15 [binary,14.1,2.1] $F.
% 1.54/1.76
% 1.54/1.76 Length of proof is 4. Level of proof is 3.
% 1.54/1.76
% 1.54/1.76 ---------------- PROOF ----------------
% 1.54/1.76 % SZS status Unsatisfiable
% 1.54/1.76 % SZS output start Refutation
% See solution above
% 1.54/1.76 ------------ end of proof -------------
% 1.54/1.76
% 1.54/1.76
% 1.54/1.76 Search stopped by max_proofs option.
% 1.54/1.76
% 1.54/1.76
% 1.54/1.76 Search stopped by max_proofs option.
% 1.54/1.76
% 1.54/1.76 ============ end of search ============
% 1.54/1.76
% 1.54/1.76 -------------- statistics -------------
% 1.54/1.76 clauses given 5
% 1.54/1.76 clauses generated 12
% 1.54/1.76 clauses kept 10
% 1.54/1.76 clauses forward subsumed 10
% 1.54/1.76 clauses back subsumed 0
% 1.54/1.76 Kbytes malloced 976
% 1.54/1.76
% 1.54/1.76 ----------- times (seconds) -----------
% 1.54/1.76 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.54/1.76 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.54/1.76 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.54/1.76
% 1.54/1.76 That finishes the proof of the theorem.
% 1.54/1.76
% 1.54/1.76 Process 2928 finished Wed Jul 27 02:45:23 2022
% 1.54/1.76 Otter interrupted
% 1.54/1.76 PROOF FOUND
%------------------------------------------------------------------------------