TSTP Solution File: COL075-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL075-2 : TPTP v8.1.0. Released v1.2.0.
% 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 12:48:11 EDT 2022
% Result : Unsatisfiable 1.74s 1.96s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 4 RR)
% Number of literals : 10 ( 9 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
apply(apply(A,b(A)),c(A)) != apply(b(A),b(A)),
file('COL075-2.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('COL075-2.p',unknown),
[] ).
cnf(4,axiom,
apply(apply(k,A),B) = A,
file('COL075-2.p',unknown),
[] ).
cnf(5,axiom,
apply(apply(apply(abstraction,A),B),C) = apply(apply(A,apply(k,C)),apply(B,C)),
file('COL075-2.p',unknown),
[] ).
cnf(6,plain,
apply(apply(A,apply(k,B)),apply(C,B)) = apply(apply(apply(abstraction,A),C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(12,plain,
apply(apply(apply(A,apply(k,b(apply(apply(abstraction,A),B)))),apply(B,b(apply(apply(abstraction,A),B)))),c(apply(apply(abstraction,A),B))) != apply(b(apply(apply(abstraction,A),B)),b(apply(apply(abstraction,A),B))),
inference(para_from,[status(thm),theory(equality)],[5,1]),
[iquote('para_from,5.1.1,1.1.1.1')] ).
cnf(19,plain,
apply(apply(A,apply(k,B)),C) = apply(apply(apply(abstraction,A),apply(k,C)),B),
inference(para_into,[status(thm),theory(equality)],[6,4]),
[iquote('para_into,6.1.1.2,3.1.1')] ).
cnf(27,plain,
apply(apply(apply(abstraction,A),apply(k,B)),C) = apply(apply(A,apply(k,C)),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.1')] ).
cnf(213,plain,
apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,27]),4]),
[iquote('para_into,12.1.1,27.1.1,demod,4')] ).
cnf(214,plain,
$false,
inference(binary,[status(thm)],[213,2]),
[iquote('binary,213.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL075-2 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 02:20:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.74/1.96 ----- Otter 3.3f, August 2004 -----
% 1.74/1.96 The process was started by sandbox on n009.cluster.edu,
% 1.74/1.96 Wed Jul 27 02:20:51 2022
% 1.74/1.96 The command was "./otter". The process ID is 23027.
% 1.74/1.96
% 1.74/1.96 set(prolog_style_variables).
% 1.74/1.96 set(auto).
% 1.74/1.96 dependent: set(auto1).
% 1.74/1.96 dependent: set(process_input).
% 1.74/1.96 dependent: clear(print_kept).
% 1.74/1.96 dependent: clear(print_new_demod).
% 1.74/1.96 dependent: clear(print_back_demod).
% 1.74/1.96 dependent: clear(print_back_sub).
% 1.74/1.96 dependent: set(control_memory).
% 1.74/1.96 dependent: assign(max_mem, 12000).
% 1.74/1.96 dependent: assign(pick_given_ratio, 4).
% 1.74/1.96 dependent: assign(stats_level, 1).
% 1.74/1.96 dependent: assign(max_seconds, 10800).
% 1.74/1.96 clear(print_given).
% 1.74/1.96
% 1.74/1.96 list(usable).
% 1.74/1.96 0 [] A=A.
% 1.74/1.96 0 [] apply(apply(k,X),Y)=X.
% 1.74/1.96 0 [] apply(apply(apply(abstraction,X),Y),Z)=apply(apply(X,apply(k,Z)),apply(Y,Z)).
% 1.74/1.96 0 [] apply(apply(Y,b(Y)),c(Y))!=apply(b(Y),b(Y)).
% 1.74/1.96 end_of_list.
% 1.74/1.96
% 1.74/1.96 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.74/1.96
% 1.74/1.96 All clauses are units, and equality is present; the
% 1.74/1.96 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.74/1.96
% 1.74/1.96 dependent: set(knuth_bendix).
% 1.74/1.96 dependent: set(anl_eq).
% 1.74/1.96 dependent: set(para_from).
% 1.74/1.96 dependent: set(para_into).
% 1.74/1.96 dependent: clear(para_from_right).
% 1.74/1.96 dependent: clear(para_into_right).
% 1.74/1.96 dependent: set(para_from_vars).
% 1.74/1.96 dependent: set(eq_units_both_ways).
% 1.74/1.96 dependent: set(dynamic_demod_all).
% 1.74/1.96 dependent: set(dynamic_demod).
% 1.74/1.96 dependent: set(order_eq).
% 1.74/1.96 dependent: set(back_demod).
% 1.74/1.96 dependent: set(lrpo).
% 1.74/1.96
% 1.74/1.96 ------------> process usable:
% 1.74/1.96 ** KEPT (pick-wt=13): 1 [] apply(apply(A,b(A)),c(A))!=apply(b(A),b(A)).
% 1.74/1.96
% 1.74/1.96 ------------> process sos:
% 1.74/1.96 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.74/1.96 ** KEPT (pick-wt=7): 3 [] apply(apply(k,A),B)=A.
% 1.74/1.96 ---> New Demodulator: 4 [new_demod,3] apply(apply(k,A),B)=A.
% 1.74/1.96 ** KEPT (pick-wt=17): 5 [] apply(apply(apply(abstraction,A),B),C)=apply(apply(A,apply(k,C)),apply(B,C)).
% 1.74/1.96 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.74/1.96 >>>> Starting back demodulation with 4.
% 1.74/1.96 ** KEPT (pick-wt=17): 6 [copy,5,flip.1] apply(apply(A,apply(k,B)),apply(C,B))=apply(apply(apply(abstraction,A),C),B).
% 1.74/1.96 Following clause subsumed by 5 during input processing: 0 [copy,6,flip.1] apply(apply(apply(abstraction,A),B),C)=apply(apply(A,apply(k,C)),apply(B,C)).
% 1.74/1.96
% 1.74/1.96 ======= end of input processing =======
% 1.74/1.96
% 1.74/1.96 =========== start of search ===========
% 1.74/1.96
% 1.74/1.96 -------- PROOF --------
% 1.74/1.96
% 1.74/1.96 ----> UNIT CONFLICT at 0.02 sec ----> 214 [binary,213.1,2.1] $F.
% 1.74/1.96
% 1.74/1.96 Length of proof is 5. Level of proof is 4.
% 1.74/1.96
% 1.74/1.96 ---------------- PROOF ----------------
% 1.74/1.96 % SZS status Unsatisfiable
% 1.74/1.96 % SZS output start Refutation
% See solution above
% 1.74/1.96 ------------ end of proof -------------
% 1.74/1.96
% 1.74/1.96
% 1.74/1.96 Search stopped by max_proofs option.
% 1.74/1.96
% 1.74/1.96
% 1.74/1.96 Search stopped by max_proofs option.
% 1.74/1.96
% 1.74/1.96 ============ end of search ============
% 1.74/1.96
% 1.74/1.96 -------------- statistics -------------
% 1.74/1.96 clauses given 21
% 1.74/1.96 clauses generated 299
% 1.74/1.96 clauses kept 191
% 1.74/1.96 clauses forward subsumed 173
% 1.74/1.96 clauses back subsumed 0
% 1.74/1.96 Kbytes malloced 4882
% 1.74/1.96
% 1.74/1.96 ----------- times (seconds) -----------
% 1.74/1.96 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.74/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.96 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.96
% 1.74/1.96 That finishes the proof of the theorem.
% 1.74/1.96
% 1.74/1.96 Process 23027 finished Wed Jul 27 02:20:52 2022
% 1.74/1.96 Otter interrupted
% 1.74/1.96 PROOF FOUND
%------------------------------------------------------------------------------