TSTP Solution File: COL019-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL019-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:48:00 EDT 2022
% Result : Unsatisfiable 1.71s 1.90s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 3 RR)
% Number of literals : 11 ( 10 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
A != apply(combinator,A),
file('COL019-1.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(s,A),B),C) = apply(apply(A,C),apply(B,C)),
file('COL019-1.p',unknown),
[] ).
cnf(5,axiom,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
file('COL019-1.p',unknown),
[] ).
cnf(7,axiom,
apply(apply(t,A),B) = apply(B,A),
file('COL019-1.p',unknown),
[] ).
cnf(8,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(9,plain,
apply(A,B) = apply(apply(t,B),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(10,plain,
apply(apply(t,A),apply(t,B)) = apply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,7])]),
[iquote('para_into,9.1.1,7.1.1,flip.1')] ).
cnf(52,plain,
apply(A,A) = apply(apply(apply(s,t),t),A),
inference(para_into,[status(thm),theory(equality)],[8,10]),
[iquote('para_into,8.1.1,10.1.1')] ).
cnf(81,plain,
apply(A,apply(B,apply(apply(b,A),B))) = apply(apply(apply(s,t),t),apply(apply(b,A),B)),
inference(para_into,[status(thm),theory(equality)],[52,5]),
[iquote('para_into,52.1.1,5.1.1')] ).
cnf(82,plain,
$false,
inference(binary,[status(thm)],[81,2]),
[iquote('binary,81.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL019-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 02:26:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.71/1.90 ----- Otter 3.3f, August 2004 -----
% 1.71/1.90 The process was started by sandbox2 on n022.cluster.edu,
% 1.71/1.90 Wed Jul 27 02:26:05 2022
% 1.71/1.90 The command was "./otter". The process ID is 12164.
% 1.71/1.90
% 1.71/1.90 set(prolog_style_variables).
% 1.71/1.90 set(auto).
% 1.71/1.90 dependent: set(auto1).
% 1.71/1.90 dependent: set(process_input).
% 1.71/1.90 dependent: clear(print_kept).
% 1.71/1.90 dependent: clear(print_new_demod).
% 1.71/1.90 dependent: clear(print_back_demod).
% 1.71/1.90 dependent: clear(print_back_sub).
% 1.71/1.90 dependent: set(control_memory).
% 1.71/1.90 dependent: assign(max_mem, 12000).
% 1.71/1.90 dependent: assign(pick_given_ratio, 4).
% 1.71/1.90 dependent: assign(stats_level, 1).
% 1.71/1.90 dependent: assign(max_seconds, 10800).
% 1.71/1.90 clear(print_given).
% 1.71/1.90
% 1.71/1.90 list(usable).
% 1.71/1.90 0 [] A=A.
% 1.71/1.90 0 [] apply(apply(apply(s,X),Y),Z)=apply(apply(X,Z),apply(Y,Z)).
% 1.71/1.90 0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.71/1.90 0 [] apply(apply(t,X),Y)=apply(Y,X).
% 1.71/1.90 0 [] Y!=apply(combinator,Y).
% 1.71/1.90 end_of_list.
% 1.71/1.90
% 1.71/1.90 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.71/1.90
% 1.71/1.90 All clauses are units, and equality is present; the
% 1.71/1.90 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.71/1.90
% 1.71/1.90 dependent: set(knuth_bendix).
% 1.71/1.90 dependent: set(anl_eq).
% 1.71/1.90 dependent: set(para_from).
% 1.71/1.90 dependent: set(para_into).
% 1.71/1.90 dependent: clear(para_from_right).
% 1.71/1.90 dependent: clear(para_into_right).
% 1.71/1.90 dependent: set(para_from_vars).
% 1.71/1.90 dependent: set(eq_units_both_ways).
% 1.71/1.90 dependent: set(dynamic_demod_all).
% 1.71/1.90 dependent: set(dynamic_demod).
% 1.71/1.90 dependent: set(order_eq).
% 1.71/1.90 dependent: set(back_demod).
% 1.71/1.90 dependent: set(lrpo).
% 1.71/1.90
% 1.71/1.90 ------------> process usable:
% 1.71/1.90 ** KEPT (pick-wt=5): 2 [copy,1,flip.1] apply(combinator,A)!=A.
% 1.71/1.90
% 1.71/1.90 ------------> process sos:
% 1.71/1.90 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.71/1.90 ** KEPT (pick-wt=15): 4 [] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.71/1.90 ** KEPT (pick-wt=13): 5 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.71/1.90 ---> New Demodulator: 6 [new_demod,5] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.71/1.90 ** KEPT (pick-wt=9): 7 [] apply(apply(t,A),B)=apply(B,A).
% 1.71/1.90 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.71/1.90 ** KEPT (pick-wt=15): 8 [copy,4,flip.1] apply(apply(A,B),apply(C,B))=apply(apply(apply(s,A),C),B).
% 1.71/1.90 >>>> Starting back demodulation with 6.
% 1.71/1.90 ** KEPT (pick-wt=9): 9 [copy,7,flip.1] apply(A,B)=apply(apply(t,B),A).
% 1.71/1.90 Following clause subsumed by 4 during input processing: 0 [copy,8,flip.1] apply(apply(apply(s,A),B),C)=apply(apply(A,C),apply(B,C)).
% 1.71/1.90 Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] apply(apply(t,A),B)=apply(B,A).
% 1.71/1.90
% 1.71/1.90 ======= end of input processing =======
% 1.71/1.90
% 1.71/1.90 =========== start of search ===========
% 1.71/1.90
% 1.71/1.90 -------- PROOF --------
% 1.71/1.90
% 1.71/1.90 ----> UNIT CONFLICT at 0.00 sec ----> 82 [binary,81.1,2.1] $F.
% 1.71/1.90
% 1.71/1.90 Length of proof is 6. Level of proof is 4.
% 1.71/1.90
% 1.71/1.90 ---------------- PROOF ----------------
% 1.71/1.90 % SZS status Unsatisfiable
% 1.71/1.90 % SZS output start Refutation
% See solution above
% 1.74/1.90 ------------ end of proof -------------
% 1.74/1.90
% 1.74/1.90
% 1.74/1.90 Search stopped by max_proofs option.
% 1.74/1.90
% 1.74/1.90
% 1.74/1.90 Search stopped by max_proofs option.
% 1.74/1.90
% 1.74/1.90 ============ end of search ============
% 1.74/1.90
% 1.74/1.90 -------------- statistics -------------
% 1.74/1.90 clauses given 12
% 1.74/1.90 clauses generated 83
% 1.74/1.90 clauses kept 71
% 1.74/1.90 clauses forward subsumed 79
% 1.74/1.90 clauses back subsumed 0
% 1.74/1.90 Kbytes malloced 976
% 1.74/1.90
% 1.74/1.90 ----------- times (seconds) -----------
% 1.74/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.90 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.74/1.90
% 1.74/1.90 That finishes the proof of the theorem.
% 1.74/1.90
% 1.74/1.90 Process 12164 finished Wed Jul 27 02:26:07 2022
% 1.74/1.90 Otter interrupted
% 1.74/1.90 PROOF FOUND
%------------------------------------------------------------------------------