TSTP Solution File: LDA007-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LDA007-2 : TPTP v8.1.0. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:05:48 EDT 2022
% Result : Unsatisfiable 1.73s 1.94s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 15 RR)
% Number of literals : 19 ( 18 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
f(t,tsk) != f(tt_ts,tk),
file('LDA007-2.p',unknown),
[] ).
cnf(6,plain,
f(tt_ts,tk) != f(t,tsk),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(8,axiom,
f(A,f(B,C)) = f(f(A,B),f(A,C)),
file('LDA007-2.p',unknown),
[] ).
cnf(9,plain,
f(f(A,B),f(A,C)) = f(A,f(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.1')] ).
cnf(19,axiom,
tt = f(t,t),
file('LDA007-2.p',unknown),
[] ).
cnf(20,plain,
f(t,t) = tt,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.1')] ).
cnf(25,axiom,
ts = f(t,s),
file('LDA007-2.p',unknown),
[] ).
cnf(27,plain,
f(t,s) = ts,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[25])]),
[iquote('copy,25,flip.1')] ).
cnf(28,axiom,
tt_ts = f(tt,ts),
file('LDA007-2.p',unknown),
[] ).
cnf(30,plain,
f(tt,ts) = tt_ts,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[28])]),
[iquote('copy,28,flip.1')] ).
cnf(37,axiom,
tk = f(t,k),
file('LDA007-2.p',unknown),
[] ).
cnf(38,plain,
f(t,k) = tk,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[37])]),
[iquote('copy,37,flip.1')] ).
cnf(43,axiom,
tsk = f(ts,k),
file('LDA007-2.p',unknown),
[] ).
cnf(45,plain,
f(ts,k) = tsk,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[43])]),
[iquote('copy,43,flip.1')] ).
cnf(57,plain,
f(tt,f(t,A)) = f(t,f(t,A)),
inference(para_into,[status(thm),theory(equality)],[9,20]),
[iquote('para_into,9.1.1.1,20.1.1')] ).
cnf(80,plain,
f(f(t,A),tk) = f(t,f(A,k)),
inference(para_from,[status(thm),theory(equality)],[38,9]),
[iquote('para_from,38.1.1,9.1.1.2')] ).
cnf(332,plain,
f(t,ts) = tt_ts,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[57,27]),30,27])]),
[iquote('para_into,57.1.1.2,26.1.1,demod,30,27,flip.1')] ).
cnf(1103,plain,
f(tt_ts,tk) = f(t,tsk),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[80,332]),45]),
[iquote('para_into,80.1.1.1,332.1.1,demod,45')] ).
cnf(1105,plain,
$false,
inference(binary,[status(thm)],[1103,6]),
[iquote('binary,1103.1,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LDA007-2 : TPTP v8.1.0. Bugfixed v2.6.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 02:06:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.90 ----- Otter 3.3f, August 2004 -----
% 1.68/1.90 The process was started by sandbox on n003.cluster.edu,
% 1.68/1.90 Wed Jul 27 02:06:11 2022
% 1.68/1.90 The command was "./otter". The process ID is 29827.
% 1.68/1.90
% 1.68/1.90 set(prolog_style_variables).
% 1.68/1.90 set(auto).
% 1.68/1.90 dependent: set(auto1).
% 1.68/1.90 dependent: set(process_input).
% 1.68/1.90 dependent: clear(print_kept).
% 1.68/1.90 dependent: clear(print_new_demod).
% 1.68/1.90 dependent: clear(print_back_demod).
% 1.68/1.90 dependent: clear(print_back_sub).
% 1.68/1.90 dependent: set(control_memory).
% 1.68/1.90 dependent: assign(max_mem, 12000).
% 1.68/1.90 dependent: assign(pick_given_ratio, 4).
% 1.68/1.90 dependent: assign(stats_level, 1).
% 1.68/1.90 dependent: assign(max_seconds, 10800).
% 1.68/1.90 clear(print_given).
% 1.68/1.90
% 1.68/1.90 list(usable).
% 1.68/1.90 0 [] A=A.
% 1.68/1.90 0 [] f(X,f(Y,Z))=f(f(X,Y),f(X,Z)).
% 1.68/1.90 0 [] a(X,a(Y,Z))=a(f(X,Y),a(X,Z)).
% 1.68/1.90 0 [] critical_point(f(U,V))=a(U,critical_point(V)).
% 1.68/1.90 0 [] -less(X,X).
% 1.68/1.90 0 [] -less(X,Y)|less(a(U,X),a(U,Y)).
% 1.68/1.90 0 [] X=a(U,X)|less(X,a(U,X)).
% 1.68/1.90 0 [] -less(X,critical_point(U))|a(U,X)=X.
% 1.68/1.90 0 [] less(X,critical_point(U))|less(X,a(U,X)).
% 1.68/1.90 0 [] a(U,X)!=X|a(f(V,U),X)=X.
% 1.68/1.90 0 [] tt=f(t,t).
% 1.68/1.90 0 [] st=f(s,t).
% 1.68/1.90 0 [] ts=f(t,s).
% 1.68/1.90 0 [] tt_ts=f(tt,ts).
% 1.68/1.90 0 [] k=critical_point(t).
% 1.68/1.90 0 [] sk=f(s,k).
% 1.68/1.90 0 [] tk=f(t,k).
% 1.68/1.90 0 [] stk=f(st,k).
% 1.68/1.90 0 [] tsk=f(ts,k).
% 1.68/1.90 0 [] ttk=f(tt,k).
% 1.68/1.90 0 [] f(t,tsk)!=f(tt_ts,tk).
% 1.68/1.90 end_of_list.
% 1.68/1.90
% 1.68/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.68/1.90
% 1.68/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.68/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.90 deletion, with positive clauses in sos and nonpositive
% 1.68/1.90 clauses in usable.
% 1.68/1.90
% 1.68/1.90 dependent: set(knuth_bendix).
% 1.68/1.90 dependent: set(anl_eq).
% 1.68/1.90 dependent: set(para_from).
% 1.68/1.90 dependent: set(para_into).
% 1.68/1.90 dependent: clear(para_from_right).
% 1.68/1.90 dependent: clear(para_into_right).
% 1.68/1.90 dependent: set(para_from_vars).
% 1.68/1.90 dependent: set(eq_units_both_ways).
% 1.68/1.90 dependent: set(dynamic_demod_all).
% 1.68/1.90 dependent: set(dynamic_demod).
% 1.68/1.90 dependent: set(order_eq).
% 1.68/1.90 dependent: set(back_demod).
% 1.68/1.90 dependent: set(lrpo).
% 1.68/1.90 dependent: set(hyper_res).
% 1.68/1.90 dependent: set(unit_deletion).
% 1.68/1.90 dependent: set(factor).
% 1.68/1.90
% 1.68/1.90 ------------> process usable:
% 1.68/1.90 ** KEPT (pick-wt=3): 1 [] -less(A,A).
% 1.68/1.90 ** KEPT (pick-wt=10): 2 [] -less(A,B)|less(a(C,A),a(C,B)).
% 1.68/1.90 ** KEPT (pick-wt=9): 3 [] -less(A,critical_point(B))|a(B,A)=A.
% 1.68/1.90 ** KEPT (pick-wt=12): 4 [] a(A,B)!=B|a(f(C,A),B)=B.
% 1.68/1.90 ** KEPT (pick-wt=7): 6 [copy,5,flip.1] f(tt_ts,tk)!=f(t,tsk).
% 1.68/1.90
% 1.68/1.90 ------------> process sos:
% 1.68/1.90 ** KEPT (pick-wt=3): 7 [] A=A.
% 1.68/1.90 ** KEPT (pick-wt=13): 9 [copy,8,flip.1] f(f(A,B),f(A,C))=f(A,f(B,C)).
% 1.68/1.90 ---> New Demodulator: 10 [new_demod,9] f(f(A,B),f(A,C))=f(A,f(B,C)).
% 1.68/1.90 ** KEPT (pick-wt=13): 12 [copy,11,flip.1] a(f(A,B),a(A,C))=a(A,a(B,C)).
% 1.68/1.90 ---> New Demodulator: 13 [new_demod,12] a(f(A,B),a(A,C))=a(A,a(B,C)).
% 1.68/1.90 ** KEPT (pick-wt=9): 14 [] critical_point(f(A,B))=a(A,critical_point(B)).
% 1.68/1.90 ---> New Demodulator: 15 [new_demod,14] critical_point(f(A,B))=a(A,critical_point(B)).
% 1.68/1.90 ** KEPT (pick-wt=10): 17 [copy,16,flip.1] a(A,B)=B|less(B,a(A,B)).
% 1.68/1.90 ** KEPT (pick-wt=9): 18 [] less(A,critical_point(B))|less(A,a(B,A)).
% 1.68/1.90 ** KEPT (pick-wt=5): 20 [copy,19,flip.1] f(t,t)=tt.
% 1.68/1.90 ---> New Demodulator: 21 [new_demod,20] f(t,t)=tt.
% 1.68/1.90 ** KEPT (pick-wt=5): 23 [copy,22,flip.1] f(s,t)=st.
% 1.68/1.90 ---> New Demodulator: 24 [new_demod,23] f(s,t)=st.
% 1.68/1.90 ** KEPT (pick-wt=5): 26 [copy,25,flip.1] f(t,s)=ts.
% 1.68/1.90 ---> New Demodulator: 27 [new_demod,26] f(t,s)=ts.
% 1.68/1.90 ** KEPT (pick-wt=5): 29 [copy,28,flip.1] f(tt,ts)=tt_ts.
% 1.68/1.90 ---> New Demodulator: 30 [new_demod,29] f(tt,ts)=tt_ts.
% 1.68/1.90 ** KEPT (pick-wt=4): 32 [copy,31,flip.1] critical_point(t)=k.
% 1.68/1.90 ---> New Demodulator: 33 [new_demod,32] critical_point(t)=k.
% 1.68/1.90 ** KEPT (pick-wt=5): 35 [copy,34,flip.1] f(s,k)=sk.
% 1.68/1.90 ---> New Demodulator: 36 [new_demod,35] f(s,k)=sk.
% 1.68/1.90 ** KEPT (pick-wt=5): 38 [copy,37,flip.1] f(t,k)=tk.
% 1.68/1.90 ---> New Demodulator: 39 [new_demod,38] f(t,k)=tk.
% 1.68/1.90 ** KEPT (pick-wt=5): 41 [copy,40,flip.1] f(st,k)=stk.
% 1.68/1.90 ---> New Demodulator: 42 [new_demod,41] f(st,k)=stk.
% 1.68/1.90 ** KEPT (pick-wt=5): 44 [copy,43,flip.1] f(ts,k)=tsk.
% 1.68/1.90 ---> New Demodulator: 45 [new_demod,44] f(ts,k)=tsk.
% 1.68/1.90 ** KEPT (pick-wt=5): 47 [copy,46,flip.1] f(tt,k)=ttk.
% 1.68/1.90 ---> New Demodulator: 48 [new_demod,47] f(tt,k)=ttk.
% 1.68/1.90 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.68/1.90 >>>> Starting back demodulation with 10.
% 1.73/1.94 >>>> Starting back demodulation with 13.
% 1.73/1.94 >>>> Starting back demodulation with 15.
% 1.73/1.94 >>>> Starting back demodulation with 21.
% 1.73/1.94 >>>> Starting back demodulation with 24.
% 1.73/1.94 >>>> Starting back demodulation with 27.
% 1.73/1.94 >>>> Starting back demodulation with 30.
% 1.73/1.94 >>>> Starting back demodulation with 33.
% 1.73/1.94 >>>> Starting back demodulation with 36.
% 1.73/1.94 >>>> Starting back demodulation with 39.
% 1.73/1.94 >>>> Starting back demodulation with 42.
% 1.73/1.94 >>>> Starting back demodulation with 45.
% 1.73/1.94 >>>> Starting back demodulation with 48.
% 1.73/1.94
% 1.73/1.94 ======= end of input processing =======
% 1.73/1.94
% 1.73/1.94 =========== start of search ===========
% 1.73/1.94
% 1.73/1.94 -------- PROOF --------
% 1.73/1.94
% 1.73/1.94 ----> UNIT CONFLICT at 0.04 sec ----> 1105 [binary,1103.1,6.1] $F.
% 1.73/1.94
% 1.73/1.94 Length of proof is 11. Level of proof is 4.
% 1.73/1.94
% 1.73/1.94 ---------------- PROOF ----------------
% 1.73/1.94 % SZS status Unsatisfiable
% 1.73/1.94 % SZS output start Refutation
% See solution above
% 1.73/1.94 ------------ end of proof -------------
% 1.73/1.94
% 1.73/1.94
% 1.73/1.94 Search stopped by max_proofs option.
% 1.73/1.94
% 1.73/1.94
% 1.73/1.94 Search stopped by max_proofs option.
% 1.73/1.94
% 1.73/1.94 ============ end of search ============
% 1.73/1.94
% 1.73/1.94 -------------- statistics -------------
% 1.73/1.94 clauses given 111
% 1.73/1.94 clauses generated 1571
% 1.73/1.94 clauses kept 778
% 1.73/1.94 clauses forward subsumed 800
% 1.73/1.94 clauses back subsumed 75
% 1.73/1.94 Kbytes malloced 3906
% 1.73/1.94
% 1.73/1.94 ----------- times (seconds) -----------
% 1.73/1.94 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.73/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.73/1.94
% 1.73/1.94 That finishes the proof of the theorem.
% 1.73/1.94
% 1.73/1.94 Process 29827 finished Wed Jul 27 02:06:13 2022
% 1.73/1.94 Otter interrupted
% 1.73/1.94 PROOF FOUND
%------------------------------------------------------------------------------