TSTP Solution File: COL042-8 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL042-8 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 12:48:03 EDT 2022
% Result : Unsatisfiable 1.81s 2.06s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 5 RR)
% Number of literals : 17 ( 16 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('COL042-8.p',unknown),
[] ).
cnf(2,plain,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) != apply(strong_fixed_point,fixed_pt),
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('COL042-8.p',unknown),
[] ).
cnf(6,axiom,
apply(apply(w1,A),B) = apply(apply(B,A),A),
file('COL042-8.p',unknown),
[] ).
cnf(7,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),
file('COL042-8.p',unknown),
[] ).
cnf(8,plain,
apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b) = strong_fixed_point,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(10,plain,
apply(apply(A,B),B) = apply(apply(w1,B),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(32,plain,
apply(apply(A,apply(B,C)),C) = apply(apply(w1,C),apply(apply(b,A),B)),
inference(para_from,[status(thm),theory(equality)],[5,10]),
[iquote('para_from,4.1.1,10.1.1.1')] ).
cnf(34,plain,
apply(apply(w1,A),apply(apply(b,B),C)) = apply(apply(B,apply(C,A)),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[32])]),
[iquote('copy,32,flip.1')] ).
cnf(96,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,A)))) = apply(strong_fixed_point,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[8,5]),5,5])]),
[iquote('para_from,8.1.1,4.1.1.1,demod,5,5,flip.1')] ).
cnf(367,plain,
apply(apply(A,apply(B,A)),apply(B,A)) = apply(apply(w1,A),apply(apply(b,w1),B)),
inference(para_into,[status(thm),theory(equality)],[32,6]),
[iquote('para_into,32.1.1,6.1.1')] ).
cnf(368,plain,
apply(A,apply(apply(B,C),C)) = apply(apply(w1,C),apply(apply(b,apply(b,A)),B)),
inference(para_into,[status(thm),theory(equality)],[32,5]),
[iquote('para_into,32.1.1,4.1.1')] ).
cnf(407,plain,
apply(apply(w1,A),apply(apply(b,apply(b,B)),C)) = apply(B,apply(apply(C,A),A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[368])]),
[iquote('copy,368,flip.1')] ).
cnf(672,plain,
apply(apply(w1,apply(apply(b,apply(b,A)),w1)),w1) = apply(strong_fixed_point,A),
inference(para_into,[status(thm),theory(equality)],[96,34]),
[iquote('para_into,95.1.1,34.1.1')] ).
cnf(700,plain,
apply(apply(w1,apply(apply(b,apply(b,A)),w1)),apply(apply(b,apply(b,A)),w1)) = apply(strong_fixed_point,A),
inference(para_into,[status(thm),theory(equality)],[672,6]),
[iquote('para_into,672.1.1,6.1.1')] ).
cnf(1536,plain,
apply(A,apply(strong_fixed_point,A)) = apply(strong_fixed_point,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[407,367]),96,700])]),
[iquote('para_into,407.1.1,367.1.1,demod,96,700,flip.1')] ).
cnf(1538,plain,
$false,
inference(binary,[status(thm)],[1536,2]),
[iquote('binary,1536.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COL042-8 : TPTP v8.1.0. Released v2.1.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 02:35:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.81/2.06 ----- Otter 3.3f, August 2004 -----
% 1.81/2.06 The process was started by sandbox on n027.cluster.edu,
% 1.81/2.06 Wed Jul 27 02:35:51 2022
% 1.81/2.06 The command was "./otter". The process ID is 1146.
% 1.81/2.06
% 1.81/2.06 set(prolog_style_variables).
% 1.81/2.06 set(auto).
% 1.81/2.06 dependent: set(auto1).
% 1.81/2.06 dependent: set(process_input).
% 1.81/2.06 dependent: clear(print_kept).
% 1.81/2.06 dependent: clear(print_new_demod).
% 1.81/2.06 dependent: clear(print_back_demod).
% 1.81/2.06 dependent: clear(print_back_sub).
% 1.81/2.06 dependent: set(control_memory).
% 1.81/2.06 dependent: assign(max_mem, 12000).
% 1.81/2.06 dependent: assign(pick_given_ratio, 4).
% 1.81/2.06 dependent: assign(stats_level, 1).
% 1.81/2.06 dependent: assign(max_seconds, 10800).
% 1.81/2.06 clear(print_given).
% 1.81/2.06
% 1.81/2.06 list(usable).
% 1.81/2.06 0 [] A=A.
% 1.81/2.06 0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.81/2.06 0 [] apply(apply(w1,X),Y)=apply(apply(Y,X),X).
% 1.81/2.06 0 [] strong_fixed_point=apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b).
% 1.81/2.06 0 [] apply(strong_fixed_point,fixed_pt)!=apply(fixed_pt,apply(strong_fixed_point,fixed_pt)).
% 1.81/2.06 end_of_list.
% 1.81/2.06
% 1.81/2.06 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.81/2.06
% 1.81/2.06 All clauses are units, and equality is present; the
% 1.81/2.06 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.81/2.06
% 1.81/2.06 dependent: set(knuth_bendix).
% 1.81/2.06 dependent: set(anl_eq).
% 1.81/2.06 dependent: set(para_from).
% 1.81/2.06 dependent: set(para_into).
% 1.81/2.06 dependent: clear(para_from_right).
% 1.81/2.06 dependent: clear(para_into_right).
% 1.81/2.06 dependent: set(para_from_vars).
% 1.81/2.06 dependent: set(eq_units_both_ways).
% 1.81/2.06 dependent: set(dynamic_demod_all).
% 1.81/2.06 dependent: set(dynamic_demod).
% 1.81/2.06 dependent: set(order_eq).
% 1.81/2.06 dependent: set(back_demod).
% 1.81/2.06 dependent: set(lrpo).
% 1.81/2.06
% 1.81/2.06 ------------> process usable:
% 1.81/2.06 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] apply(fixed_pt,apply(strong_fixed_point,fixed_pt))!=apply(strong_fixed_point,fixed_pt).
% 1.81/2.06
% 1.81/2.06 ------------> process sos:
% 1.81/2.06 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.81/2.06 ** KEPT (pick-wt=13): 4 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.81/2.06 ---> New Demodulator: 5 [new_demod,4] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.81/2.06 ** KEPT (pick-wt=11): 6 [] apply(apply(w1,A),B)=apply(apply(B,A),A).
% 1.81/2.06 ** KEPT (pick-wt=19): 8 [copy,7,flip.1] apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)=strong_fixed_point.
% 1.81/2.06 ---> New Demodulator: 9 [new_demod,8] apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)=strong_fixed_point.
% 1.81/2.06 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.81/2.06 >>>> Starting back demodulation with 5.
% 1.81/2.06 ** KEPT (pick-wt=11): 10 [copy,6,flip.1] apply(apply(A,B),B)=apply(apply(w1,B),A).
% 1.81/2.06 >>>> Starting back demodulation with 9.
% 1.81/2.06 Following clause subsumed by 6 during input processing: 0 [copy,10,flip.1] apply(apply(w1,A),B)=apply(apply(B,A),A).
% 1.81/2.06
% 1.81/2.06 ======= end of input processing =======
% 1.81/2.06
% 1.81/2.06 =========== start of search ===========
% 1.81/2.06
% 1.81/2.06
% 1.81/2.06 Resetting weight limit to 19.
% 1.81/2.06
% 1.81/2.06
% 1.81/2.06 Resetting weight limit to 19.
% 1.81/2.06
% 1.81/2.06 sos_size=883
% 1.81/2.06
% 1.81/2.06 -------- PROOF --------
% 1.81/2.06
% 1.81/2.06 ----> UNIT CONFLICT at 0.19 sec ----> 1538 [binary,1536.1,2.1] $F.
% 1.81/2.06
% 1.81/2.06 Length of proof is 12. Level of proof is 6.
% 1.81/2.06
% 1.81/2.06 ---------------- PROOF ----------------
% 1.81/2.06 % SZS status Unsatisfiable
% 1.81/2.06 % SZS output start Refutation
% See solution above
% 1.81/2.06 ------------ end of proof -------------
% 1.81/2.06
% 1.81/2.06
% 1.81/2.06 Search stopped by max_proofs option.
% 1.81/2.06
% 1.81/2.06
% 1.81/2.06 Search stopped by max_proofs option.
% 1.81/2.06
% 1.81/2.06 ============ end of search ============
% 1.81/2.06
% 1.81/2.06 -------------- statistics -------------
% 1.81/2.06 clauses given 130
% 1.81/2.06 clauses generated 8319
% 1.81/2.06 clauses kept 1105
% 1.81/2.06 clauses forward subsumed 1798
% 1.81/2.06 clauses back subsumed 12
% 1.81/2.06 Kbytes malloced 4882
% 1.81/2.06
% 1.81/2.06 ----------- times (seconds) -----------
% 1.81/2.06 user CPU time 0.19 (0 hr, 0 min, 0 sec)
% 1.81/2.06 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.06 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.81/2.06
% 1.81/2.06 That finishes the proof of the theorem.
% 1.81/2.06
% 1.81/2.06 Process 1146 finished Wed Jul 27 02:35:53 2022
% 1.81/2.06 Otter interrupted
% 1.81/2.06 PROOF FOUND
%------------------------------------------------------------------------------