TSTP Solution File: COL034-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL034-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 2.05s 2.18s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 5 RR)
% Number of literals : 13 ( 12 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
apply(A,f(A)) != apply(f(A),apply(A,f(A))),
file('COL034-1.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(5,axiom,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
file('COL034-1.p',unknown),
[] ).
cnf(6,axiom,
apply(m,A) = apply(A,A),
file('COL034-1.p',unknown),
[] ).
cnf(7,axiom,
apply(apply(t,A),B) = apply(B,A),
file('COL034-1.p',unknown),
[] ).
cnf(8,plain,
apply(A,A) = apply(m,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,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(33,plain,
apply(apply(apply(t,A),apply(b,B)),C) = apply(B,apply(A,C)),
inference(para_into,[status(thm),theory(equality)],[5,9]),
[iquote('para_into,4.1.1.1,9.1.1')] ).
cnf(40,plain,
apply(f(apply(apply(b,A),B)),apply(A,apply(B,f(apply(apply(b,A),B))))) != apply(A,apply(B,f(apply(apply(b,A),B)))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[5,2]),5]),
[iquote('para_from,4.1.1,2.1.1.2,demod,5')] ).
cnf(133,plain,
apply(m,apply(apply(t,A),apply(b,B))) = apply(B,apply(A,apply(apply(t,A),apply(b,B)))),
inference(para_into,[status(thm),theory(equality)],[33,8]),
[iquote('para_into,32.1.1,8.1.1')] ).
cnf(136,plain,
apply(A,apply(B,apply(apply(t,B),apply(b,A)))) = apply(m,apply(apply(t,B),apply(b,A))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[133])]),
[iquote('copy,133,flip.1')] ).
cnf(733,plain,
apply(f(apply(apply(b,A),apply(apply(t,B),apply(b,C)))),apply(A,apply(C,apply(B,f(apply(apply(b,A),apply(apply(t,B),apply(b,C)))))))) != apply(A,apply(C,apply(B,f(apply(apply(b,A),apply(apply(t,B),apply(b,C))))))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[40,33]),33]),
[iquote('para_into,40.1.1.2.2,32.1.1,demod,33')] ).
cnf(734,plain,
$false,
inference(binary,[status(thm)],[733,136]),
[iquote('binary,733.1,136.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL034-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 02:44:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.05/2.18 ----- Otter 3.3f, August 2004 -----
% 2.05/2.18 The process was started by sandbox on n023.cluster.edu,
% 2.05/2.18 Wed Jul 27 02:44:18 2022
% 2.05/2.18 The command was "./otter". The process ID is 31525.
% 2.05/2.18
% 2.05/2.18 set(prolog_style_variables).
% 2.05/2.18 set(auto).
% 2.05/2.18 dependent: set(auto1).
% 2.05/2.18 dependent: set(process_input).
% 2.05/2.18 dependent: clear(print_kept).
% 2.05/2.18 dependent: clear(print_new_demod).
% 2.05/2.18 dependent: clear(print_back_demod).
% 2.05/2.18 dependent: clear(print_back_sub).
% 2.05/2.18 dependent: set(control_memory).
% 2.05/2.18 dependent: assign(max_mem, 12000).
% 2.05/2.18 dependent: assign(pick_given_ratio, 4).
% 2.05/2.18 dependent: assign(stats_level, 1).
% 2.05/2.18 dependent: assign(max_seconds, 10800).
% 2.05/2.18 clear(print_given).
% 2.05/2.18
% 2.05/2.18 list(usable).
% 2.05/2.18 0 [] A=A.
% 2.05/2.18 0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 2.05/2.18 0 [] apply(m,X)=apply(X,X).
% 2.05/2.18 0 [] apply(apply(t,X),Y)=apply(Y,X).
% 2.05/2.18 0 [] apply(Y,f(Y))!=apply(f(Y),apply(Y,f(Y))).
% 2.05/2.18 end_of_list.
% 2.05/2.18
% 2.05/2.18 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.05/2.18
% 2.05/2.18 All clauses are units, and equality is present; the
% 2.05/2.18 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.05/2.18
% 2.05/2.18 dependent: set(knuth_bendix).
% 2.05/2.18 dependent: set(anl_eq).
% 2.05/2.18 dependent: set(para_from).
% 2.05/2.18 dependent: set(para_into).
% 2.05/2.18 dependent: clear(para_from_right).
% 2.05/2.18 dependent: clear(para_into_right).
% 2.05/2.18 dependent: set(para_from_vars).
% 2.05/2.18 dependent: set(eq_units_both_ways).
% 2.05/2.18 dependent: set(dynamic_demod_all).
% 2.05/2.18 dependent: set(dynamic_demod).
% 2.05/2.18 dependent: set(order_eq).
% 2.05/2.18 dependent: set(back_demod).
% 2.05/2.18 dependent: set(lrpo).
% 2.05/2.18
% 2.05/2.18 ------------> process usable:
% 2.05/2.18 ** KEPT (pick-wt=12): 2 [copy,1,flip.1] apply(f(A),apply(A,f(A)))!=apply(A,f(A)).
% 2.05/2.18
% 2.05/2.18 ------------> process sos:
% 2.05/2.18 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.05/2.18 ** KEPT (pick-wt=13): 4 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 2.05/2.18 ---> New Demodulator: 5 [new_demod,4] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 2.05/2.18 ** KEPT (pick-wt=7): 6 [] apply(m,A)=apply(A,A).
% 2.05/2.18 ** KEPT (pick-wt=9): 7 [] apply(apply(t,A),B)=apply(B,A).
% 2.05/2.18 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.05/2.18 >>>> Starting back demodulation with 5.
% 2.05/2.18 ** KEPT (pick-wt=7): 8 [copy,6,flip.1] apply(A,A)=apply(m,A).
% 2.05/2.18 ** KEPT (pick-wt=9): 9 [copy,7,flip.1] apply(A,B)=apply(apply(t,B),A).
% 2.05/2.18 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] apply(m,A)=apply(A,A).
% 2.05/2.18 Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] apply(apply(t,A),B)=apply(B,A).
% 2.05/2.18
% 2.05/2.18 ======= end of input processing =======
% 2.05/2.18
% 2.05/2.18 =========== start of search ===========
% 2.05/2.18
% 2.05/2.18 -------- PROOF --------
% 2.05/2.18
% 2.05/2.18 ----> UNIT CONFLICT at 0.02 sec ----> 734 [binary,733.1,136.1] $F.
% 2.05/2.18
% 2.05/2.18 Length of proof is 8. Level of proof is 4.
% 2.05/2.18
% 2.05/2.18 ---------------- PROOF ----------------
% 2.05/2.18 % SZS status Unsatisfiable
% 2.05/2.18 % SZS output start Refutation
% See solution above
% 2.05/2.18 ------------ end of proof -------------
% 2.05/2.18
% 2.05/2.18
% 2.05/2.18 Search stopped by max_proofs option.
% 2.05/2.18
% 2.05/2.18
% 2.05/2.18 Search stopped by max_proofs option.
% 2.05/2.18
% 2.05/2.18 ============ end of search ============
% 2.05/2.18
% 2.05/2.18 -------------- statistics -------------
% 2.05/2.18 clauses given 46
% 2.05/2.18 clauses generated 1017
% 2.05/2.18 clauses kept 586
% 2.05/2.18 clauses forward subsumed 833
% 2.05/2.18 clauses back subsumed 6
% 2.05/2.18 Kbytes malloced 3906
% 2.05/2.18
% 2.05/2.18 ----------- times (seconds) -----------
% 2.05/2.18 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 2.05/2.18 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.05/2.18 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.05/2.18
% 2.05/2.18 That finishes the proof of the theorem.
% 2.05/2.18
% 2.05/2.18 Process 31525 finished Wed Jul 27 02:44:20 2022
% 2.05/2.18 Otter interrupted
% 2.05/2.18 PROOF FOUND
%------------------------------------------------------------------------------