%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL003-20 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 12:47:58 EDT 2022
% Result : Unsatisfiable 2.11s 2.34s
% Output : Refutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 5 RR)
% Number of literals : 21 ( 20 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('COL003-20.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('COL003-20.p',unknown),
[] ).
cnf(6,axiom,
apply(apply(w,A),B) = apply(apply(A,B),B),
file('COL003-20.p',unknown),
[] ).
cnf(7,axiom,
strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),
file('COL003-20.p',unknown),
[] ).
cnf(8,plain,
apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,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(w,A),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(11,plain,
apply(apply(apply(w,A),B),B) = apply(apply(w,apply(A,B)),B),
inference(para_into,[status(thm),theory(equality)],[10,10]),
[iquote('para_into,10.1.1.1,10.1.1')] ).
cnf(14,plain,
apply(apply(apply(A,B),B),B) = apply(apply(w,apply(w,A)),B),
inference(para_into,[status(thm),theory(equality)],[10,6]),
[iquote('para_into,10.1.1.1,6.1.1')] ).
cnf(15,plain,
apply(apply(A,A),A) = apply(apply(w,w),A),
inference(para_into,[status(thm),theory(equality)],[10,6]),
[iquote('para_into,10.1.1,6.1.1')] ).
cnf(31,plain,
apply(apply(A,apply(B,apply(apply(b,A),B))),apply(apply(b,A),B)) = apply(apply(w,w),apply(apply(b,A),B)),
inference(para_from,[status(thm),theory(equality)],[5,15]),
[iquote('para_from,4.1.1,15.1.1.1')] ).
cnf(33,plain,
apply(apply(A,apply(B,C)),C) = apply(apply(w,apply(apply(b,A),B)),C),
inference(para_from,[status(thm),theory(equality)],[5,10]),
[iquote('para_from,4.1.1,10.1.1.1')] ).
cnf(108,plain,
apply(apply(w,w),apply(apply(b,w),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(165,plain,
apply(apply(w,apply(w,A)),B) = apply(apply(w,apply(A,B)),B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,6]),14]),
[iquote('para_into,11.1.1.1,6.1.1,demod,14')] ).
cnf(170,plain,
apply(apply(w,apply(A,B)),B) = apply(apply(w,apply(w,A)),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[165])]),
[iquote('copy,165,flip.1')] ).
cnf(466,plain,
apply(apply(w,apply(apply(b,w),A)),B) = apply(apply(w,apply(w,A)),B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,170])]),
[iquote('para_into,33.1.1,170.1.1,flip.1')] ).
cnf(469,plain,
apply(A,apply(apply(B,C),C)) = apply(apply(w,apply(apply(b,apply(b,A)),B)),C),
inference(para_into,[status(thm),theory(equality)],[33,5]),
[iquote('para_into,33.1.1,4.1.1')] ).
cnf(627,plain,
apply(apply(w,apply(w,A)),apply(apply(b,w),A)) = apply(apply(w,w),apply(apply(b,w),A)),
inference(para_into,[status(thm),theory(equality)],[31,170]),
[iquote('para_into,31.1.1,170.1.1')] ).
cnf(1322,plain,
apply(apply(w,apply(apply(b,apply(b,A)),B)),C) = apply(A,apply(apply(w,B),C)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[469,10])]),
[iquote('para_into,469.1.1.2,10.1.1,flip.1')] ).
cnf(1361,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)],[1322,31]),108,466,627,108])]),
[iquote('para_into,1322.1.1,31.1.1,demod,108,466,627,108,flip.1')] ).
cnf(1363,plain,
$false,
inference(binary,[status(thm)],[1361,2]),
[iquote('binary,1361.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL003-20 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n008.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 02:25:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.80/2.00 ----- Otter 3.3f, August 2004 -----
% 1.80/2.00 The process was started by sandbox on n008.cluster.edu,
% 1.80/2.00 Wed Jul 27 02:25:08 2022
% 1.80/2.00 The command was "./otter". The process ID is 24004.
% 1.80/2.00
% 1.80/2.00 set(prolog_style_variables).
% 1.80/2.00 set(auto).
% 1.80/2.00 dependent: set(auto1).
% 1.80/2.00 dependent: set(process_input).
% 1.80/2.00 dependent: clear(print_kept).
% 1.80/2.00 dependent: clear(print_new_demod).
% 1.80/2.00 dependent: clear(print_back_demod).
% 1.80/2.00 dependent: clear(print_back_sub).
% 1.80/2.00 dependent: set(control_memory).
% 1.80/2.00 dependent: assign(max_mem, 12000).
% 1.80/2.00 dependent: assign(pick_given_ratio, 4).
% 1.80/2.00 dependent: assign(stats_level, 1).
% 1.80/2.00 dependent: assign(max_seconds, 10800).
% 1.80/2.00 clear(print_given).
% 1.80/2.00
% 1.80/2.00 list(usable).
% 1.80/2.00 0 [] A=A.
% 1.80/2.00 0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.80/2.00 0 [] apply(apply(w,X),Y)=apply(apply(X,Y),Y).
% 1.80/2.00 0 [] strong_fixed_point=apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))).
% 1.80/2.00 0 [] apply(strong_fixed_point,fixed_pt)!=apply(fixed_pt,apply(strong_fixed_point,fixed_pt)).
% 1.80/2.00 end_of_list.
% 1.80/2.00
% 1.80/2.00 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.80/2.00
% 1.80/2.00 All clauses are units, and equality is present; the
% 1.80/2.00 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.80/2.00
% 1.80/2.00 dependent: set(knuth_bendix).
% 1.80/2.00 dependent: set(anl_eq).
% 1.80/2.00 dependent: set(para_from).
% 1.80/2.00 dependent: set(para_into).
% 1.80/2.00 dependent: clear(para_from_right).
% 1.80/2.00 dependent: clear(para_into_right).
% 1.80/2.00 dependent: set(para_from_vars).
% 1.80/2.00 dependent: set(eq_units_both_ways).
% 1.80/2.00 dependent: set(dynamic_demod_all).
% 1.80/2.00 dependent: set(dynamic_demod).
% 1.80/2.00 dependent: set(order_eq).
% 1.80/2.00 dependent: set(back_demod).
% 1.80/2.00 dependent: set(lrpo).
% 1.80/2.00
% 1.80/2.00 ------------> process usable:
% 1.80/2.00 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] apply(fixed_pt,apply(strong_fixed_point,fixed_pt))!=apply(strong_fixed_point,fixed_pt).
% 1.80/2.00
% 1.80/2.00 ------------> process sos:
% 1.80/2.00 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.80/2.00 ** KEPT (pick-wt=13): 4 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.80/2.00 ---> New Demodulator: 5 [new_demod,4] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.80/2.00 ** KEPT (pick-wt=11): 6 [] apply(apply(w,A),B)=apply(apply(A,B),B).
% 1.80/2.00 ** KEPT (pick-wt=19): 8 [copy,7,flip.1] apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b)))=strong_fixed_point.
% 1.80/2.00 ---> New Demodulator: 9 [new_demod,8] apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b)))=strong_fixed_point.
% 1.80/2.00 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.80/2.00 >>>> Starting back demodulation with 5.
% 1.80/2.00 ** KEPT (pick-wt=11): 10 [copy,6,flip.1] apply(apply(A,B),B)=apply(apply(w,A),B).
% 1.80/2.00 >>>> Starting back demodulation with 9.
% 1.80/2.00 Following clause subsumed by 6 during input processing: 0 [copy,10,flip.1] apply(apply(w,A),B)=apply(apply(A,B),B).
% 1.80/2.00
% 1.80/2.00 ======= end of input processing =======
% 1.80/2.00
% 1.80/2.00 =========== start of search ===========
% 1.80/2.00 WARNING, demod_limit (given clause 46): 0 [back_demod,1069,1193,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,821,828,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26] 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% 1.80/2.02 WARNING, demod_limit stopped the demodulation of a clause.
% 1.80/2.02 This warning will not be repeated.
% 1.80/2.02
% 1.80/2.02
% 1.80/2.02
% 1.80/2.02 Resetting weight limit to 19.
% 1.80/2.02
% 1.80/2.02 ,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(w,b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))=apply(apply(w,apply(apply(w,b),apply(w,w))),apply(w,b)).
% 2.11/2.34
% 2.11/2.34 Resetting weight limit to 19.
% 2.11/2.34
% 2.11/2.34 sos_size=693
% 2.11/2.34
% 2.11/2.34 -------- PROOF --------
% 2.11/2.34
% 2.11/2.34 ----> UNIT CONFLICT at 0.44 sec ----> 1363 [binary,1361.1,2.1] $F.
% 2.11/2.34
% 2.11/2.34 Length of proof is 16. Level of proof is 6.
% 2.11/2.34
% 2.11/2.34 ---------------- PROOF ----------------
% 2.11/2.34 % SZS status Unsatisfiable
% 2.11/2.34 % SZS output start Refutation
% See solution above
% 2.11/2.34 ------------ end of proof -------------
% 2.11/2.34
% 2.11/2.34
% 2.11/2.34 Search stopped by max_proofs option.
% 2.11/2.34
% 2.11/2.34
% 2.11/2.34 Search stopped by max_proofs option.
% 2.11/2.34
% 2.11/2.34 ============ end of search ============
% 2.11/2.34
% 2.11/2.34 -------------- statistics -------------
% 2.11/2.34 clauses given 168
% 2.11/2.34 clauses generated 23527
% 2.11/2.34 clauses kept 952
% 2.11/2.34 clauses forward subsumed 2863
% 2.11/2.34 clauses back subsumed 62
% 2.11/2.34 Kbytes malloced 6835
% 2.11/2.34
% 2.11/2.34 ----------- times (seconds) -----------
% 2.11/2.34 user CPU time 0.44 (0 hr, 0 min, 0 sec)
% 2.11/2.34 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.11/2.34 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.11/2.34
% 2.11/2.34 That finishes the proof of the theorem.
% 2.11/2.34
% 2.11/2.34 Process 24004 finished Wed Jul 27 02:25:10 2022
% 2.11/2.34 Otter interrupted
% 2.11/2.34 PROOF FOUND
%------------------------------------------------------------------------------