%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL031-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 12:48:02 EDT 2022
% Result : Unsatisfiable 1.68s 1.89s
% Output : Refutation 1.68s
% 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 : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
apply(A,f(A)) != apply(f(A),apply(A,f(A))),
file('COL031-1.p',unknown),
[] ).
cnf(2,plain,
apply(f(A),apply(A,f(A))) != apply(A,f(A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
apply(apply(l,A),B) = apply(A,apply(B,B)),
file('COL031-1.p',unknown),
[] ).
cnf(5,axiom,
apply(apply(o,A),B) = apply(B,apply(A,B)),
file('COL031-1.p',unknown),
[] ).
cnf(6,plain,
apply(A,apply(B,B)) = apply(apply(l,A),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(20,plain,
apply(apply(apply(l,o),A),B) = apply(B,apply(apply(A,A),B)),
inference(para_from,[status(thm),theory(equality)],[6,5]),
[iquote('para_from,6.1.1,5.1.1.1')] ).
cnf(22,plain,
apply(A,apply(apply(B,B),A)) = apply(apply(apply(l,o),B),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
[iquote('copy,20,flip.1')] ).
cnf(23,plain,
$false,
inference(binary,[status(thm)],[22,2]),
[iquote('binary,22.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL031-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n009.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 02:21:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.68/1.89 ----- Otter 3.3f, August 2004 -----
% 1.68/1.89 The process was started by sandbox on n009.cluster.edu,
% 1.68/1.89 Wed Jul 27 02:21:36 2022
% 1.68/1.89 The command was "./otter". The process ID is 25651.
% 1.68/1.89
% 1.68/1.89 set(prolog_style_variables).
% 1.68/1.89 set(auto).
% 1.68/1.89 dependent: set(auto1).
% 1.68/1.89 dependent: set(process_input).
% 1.68/1.89 dependent: clear(print_kept).
% 1.68/1.89 dependent: clear(print_new_demod).
% 1.68/1.89 dependent: clear(print_back_demod).
% 1.68/1.89 dependent: clear(print_back_sub).
% 1.68/1.89 dependent: set(control_memory).
% 1.68/1.89 dependent: assign(max_mem, 12000).
% 1.68/1.89 dependent: assign(pick_given_ratio, 4).
% 1.68/1.89 dependent: assign(stats_level, 1).
% 1.68/1.89 dependent: assign(max_seconds, 10800).
% 1.68/1.89 clear(print_given).
% 1.68/1.89
% 1.68/1.89 list(usable).
% 1.68/1.89 0 [] A=A.
% 1.68/1.89 0 [] apply(apply(l,X),Y)=apply(X,apply(Y,Y)).
% 1.68/1.89 0 [] apply(apply(o,X),Y)=apply(Y,apply(X,Y)).
% 1.68/1.89 0 [] apply(Y,f(Y))!=apply(f(Y),apply(Y,f(Y))).
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.68/1.89
% 1.68/1.89 All clauses are units, and equality is present; the
% 1.68/1.89 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.68/1.89
% 1.68/1.89 dependent: set(knuth_bendix).
% 1.68/1.89 dependent: set(anl_eq).
% 1.68/1.89 dependent: set(para_from).
% 1.68/1.89 dependent: set(para_into).
% 1.68/1.89 dependent: clear(para_from_right).
% 1.68/1.89 dependent: clear(para_into_right).
% 1.68/1.89 dependent: set(para_from_vars).
% 1.68/1.89 dependent: set(eq_units_both_ways).
% 1.68/1.89 dependent: set(dynamic_demod_all).
% 1.68/1.89 dependent: set(dynamic_demod).
% 1.68/1.89 dependent: set(order_eq).
% 1.68/1.89 dependent: set(back_demod).
% 1.68/1.89 dependent: set(lrpo).
% 1.68/1.89
% 1.68/1.89 ------------> process usable:
% 1.68/1.89 ** KEPT (pick-wt=12): 2 [copy,1,flip.1] apply(f(A),apply(A,f(A)))!=apply(A,f(A)).
% 1.68/1.89
% 1.68/1.89 ------------> process sos:
% 1.68/1.89 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.68/1.89 ** KEPT (pick-wt=11): 4 [] apply(apply(l,A),B)=apply(A,apply(B,B)).
% 1.68/1.89 ** KEPT (pick-wt=11): 5 [] apply(apply(o,A),B)=apply(B,apply(A,B)).
% 1.68/1.89 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.68/1.89 ** KEPT (pick-wt=11): 6 [copy,4,flip.1] apply(A,apply(B,B))=apply(apply(l,A),B).
% 1.68/1.89 ** KEPT (pick-wt=11): 7 [copy,5,flip.1] apply(A,apply(B,A))=apply(apply(o,B),A).
% 1.68/1.89 Following clause subsumed by 4 during input processing: 0 [copy,6,flip.1] apply(apply(l,A),B)=apply(A,apply(B,B)).
% 1.68/1.89 Following clause subsumed by 5 during input processing: 0 [copy,7,flip.1] apply(apply(o,A),B)=apply(B,apply(A,B)).
% 1.68/1.89
% 1.68/1.89 ======= end of input processing =======
% 1.68/1.89
% 1.68/1.89 =========== start of search ===========
% 1.68/1.89
% 1.68/1.89 -------- PROOF --------
% 1.68/1.89
% 1.68/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 23 [binary,22.1,2.1] $F.
% 1.68/1.89
% 1.68/1.89 Length of proof is 4. Level of proof is 3.
% 1.68/1.89
% 1.68/1.89 ---------------- PROOF ----------------
% 1.68/1.89 % SZS status Unsatisfiable
% 1.68/1.89 % SZS output start Refutation
% See solution above
% 1.68/1.89 ------------ end of proof -------------
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89 ============ end of search ============
% 1.68/1.89
% 1.68/1.89 -------------- statistics -------------
% 1.68/1.89 clauses given 4
% 1.68/1.89 clauses generated 18
% 1.68/1.89 clauses kept 21
% 1.68/1.89 clauses forward subsumed 17
% 1.68/1.89 clauses back subsumed 0
% 1.68/1.89 Kbytes malloced 976
% 1.68/1.89
% 1.68/1.89 ----------- times (seconds) -----------
% 1.68/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.68/1.89
% 1.68/1.89 That finishes the proof of the theorem.
% 1.68/1.89
% 1.68/1.89 Process 25651 finished Wed Jul 27 02:21:37 2022
% 1.68/1.89 Otter interrupted
% 1.68/1.89 PROOF FOUND
%------------------------------------------------------------------------------