TSTP Solution File: CAT011-3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT011-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 12:47:48 EDT 2022
% Result : Unsatisfiable 2.44s 2.61s
% Output : Refutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 11 unt; 0 nHn; 15 RR)
% Number of literals : 26 ( 11 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ e_quivalent(A,B)
| A = B ),
file('CAT011-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ there_exists(A)
| A != B
| e_quivalent(A,B) ),
file('CAT011-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ there_exists(domain(A))
| there_exists(A) ),
file('CAT011-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ there_exists(compose(A,B))
| domain(A) = codomain(B) ),
file('CAT011-3.p',unknown),
[] ).
cnf(13,axiom,
domain(domain(a)) != domain(a),
file('CAT011-3.p',unknown),
[] ).
cnf(15,axiom,
A = A,
file('CAT011-3.p',unknown),
[] ).
cnf(20,axiom,
compose(A,domain(A)) = A,
file('CAT011-3.p',unknown),
[] ).
cnf(21,axiom,
compose(codomain(A),A) = A,
file('CAT011-3.p',unknown),
[] ).
cnf(26,axiom,
there_exists(domain(a)),
file('CAT011-3.p',unknown),
[] ).
cnf(27,plain,
there_exists(a),
inference(hyper,[status(thm)],[26,4]),
[iquote('hyper,26,4')] ).
cnf(28,plain,
e_quivalent(domain(a),domain(a)),
inference(hyper,[status(thm)],[26,3,15]),
[iquote('hyper,26,3,15')] ).
cnf(41,plain,
( e_quivalent(codomain(A),domain(a))
| ~ there_exists(compose(a,A)) ),
inference(para_into,[status(thm),theory(equality)],[28,7]),
[iquote('para_into,28.1.1,7.2.1')] ).
cnf(61,plain,
( A = B
| ~ e_quivalent(B,A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,2]),20]),
[iquote('para_into,19.1.1,2.2.1,demod,20')] ).
cnf(89,plain,
( ~ there_exists(A)
| domain(codomain(A)) = codomain(A) ),
inference(para_from,[status(thm),theory(equality)],[21,7]),
[iquote('para_from,21.1.1,7.1.1')] ).
cnf(1511,plain,
e_quivalent(codomain(domain(a)),domain(a)),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[41,20]),27]),
[iquote('para_into,41.2.1,19.1.1,unit_del,27')] ).
cnf(1516,plain,
codomain(domain(a)) = domain(a),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1511,61])]),
[iquote('hyper,1511,61,flip.1')] ).
cnf(2377,plain,
domain(domain(a)) = domain(a),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[89,26]),1516,1516]),
[iquote('hyper,89,26,demod,1516,1516')] ).
cnf(2379,plain,
$false,
inference(binary,[status(thm)],[2377,13]),
[iquote('binary,2377.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT011-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n020.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 01:56:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.97/2.15 ----- Otter 3.3f, August 2004 -----
% 1.97/2.15 The process was started by sandbox2 on n020.cluster.edu,
% 1.97/2.15 Wed Jul 27 01:56:38 2022
% 1.97/2.15 The command was "./otter". The process ID is 23816.
% 1.97/2.15
% 1.97/2.15 set(prolog_style_variables).
% 1.97/2.15 set(auto).
% 1.97/2.15 dependent: set(auto1).
% 1.97/2.15 dependent: set(process_input).
% 1.97/2.15 dependent: clear(print_kept).
% 1.97/2.15 dependent: clear(print_new_demod).
% 1.97/2.15 dependent: clear(print_back_demod).
% 1.97/2.15 dependent: clear(print_back_sub).
% 1.97/2.15 dependent: set(control_memory).
% 1.97/2.15 dependent: assign(max_mem, 12000).
% 1.97/2.15 dependent: assign(pick_given_ratio, 4).
% 1.97/2.15 dependent: assign(stats_level, 1).
% 1.97/2.15 dependent: assign(max_seconds, 10800).
% 1.97/2.15 clear(print_given).
% 1.97/2.15
% 1.97/2.15 list(usable).
% 1.97/2.15 0 [] A=A.
% 1.97/2.15 0 [] -e_quivalent(X,Y)|there_exists(X).
% 1.97/2.15 0 [] -e_quivalent(X,Y)|X=Y.
% 1.97/2.15 0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 1.97/2.15 0 [] -there_exists(domain(X))|there_exists(X).
% 1.97/2.15 0 [] -there_exists(codomain(X))|there_exists(X).
% 1.97/2.15 0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 1.97/2.15 0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 1.97/2.15 0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 1.97/2.15 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 1.97/2.15 0 [] compose(X,domain(X))=X.
% 1.97/2.15 0 [] compose(codomain(X),X)=X.
% 1.97/2.15 0 [] -e_quivalent(X,Y)|there_exists(Y).
% 1.97/2.15 0 [] -there_exists(X)| -there_exists(Y)|X!=Y|e_quivalent(X,Y).
% 1.97/2.15 0 [] -there_exists(compose(X,Y))|there_exists(codomain(X)).
% 1.97/2.15 0 [] there_exists(f1(X,Y))|X=Y.
% 1.97/2.15 0 [] X=f1(X,Y)|Y=f1(X,Y)|X=Y.
% 1.97/2.15 0 [] X!=f1(X,Y)|Y!=f1(X,Y)|X=Y.
% 1.97/2.15 0 [] there_exists(domain(a)).
% 1.97/2.15 0 [] domain(domain(a))!=domain(a).
% 1.97/2.15 end_of_list.
% 1.97/2.15
% 1.97/2.15 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.97/2.15
% 1.97/2.15 This ia a non-Horn set with equality. The strategy will be
% 1.97/2.15 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.97/2.15 deletion, with positive clauses in sos and nonpositive
% 1.97/2.15 clauses in usable.
% 1.97/2.15
% 1.97/2.15 dependent: set(knuth_bendix).
% 1.97/2.15 dependent: set(anl_eq).
% 1.97/2.15 dependent: set(para_from).
% 1.97/2.15 dependent: set(para_into).
% 1.97/2.15 dependent: clear(para_from_right).
% 1.97/2.15 dependent: clear(para_into_right).
% 1.97/2.15 dependent: set(para_from_vars).
% 1.97/2.15 dependent: set(eq_units_both_ways).
% 1.97/2.15 dependent: set(dynamic_demod_all).
% 1.97/2.15 dependent: set(dynamic_demod).
% 1.97/2.15 dependent: set(order_eq).
% 1.97/2.15 dependent: set(back_demod).
% 1.97/2.15 dependent: set(lrpo).
% 1.97/2.15 dependent: set(hyper_res).
% 1.97/2.15 dependent: set(unit_deletion).
% 1.97/2.15 dependent: set(factor).
% 1.97/2.15
% 1.97/2.15 ------------> process usable:
% 1.97/2.15 ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 1.97/2.15 ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 1.97/2.15 ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 1.97/2.15 ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 1.97/2.15 ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 1.97/2.15 ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 1.97/2.15 ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 1.97/2.15 ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 1.97/2.15 ** KEPT (pick-wt=5): 9 [] -e_quivalent(A,B)|there_exists(B).
% 1.97/2.15 Following clause subsumed by 3 during input processing: 0 [] -there_exists(A)| -there_exists(B)|A!=B|e_quivalent(A,B).
% 1.97/2.15 ** KEPT (pick-wt=7): 10 [] -there_exists(compose(A,B))|there_exists(codomain(A)).
% 1.97/2.15 ** KEPT (pick-wt=13): 12 [copy,11,flip.1,flip.2] f1(A,B)!=A|f1(A,B)!=B|A=B.
% 1.97/2.15 ** KEPT (pick-wt=6): 13 [] domain(domain(a))!=domain(a).
% 1.97/2.15
% 1.97/2.15 ------------> process sos:
% 1.97/2.15 ** KEPT (pick-wt=3): 15 [] A=A.
% 1.97/2.15 ** KEPT (pick-wt=11): 17 [copy,16,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.97/2.15 ---> New Demodulator: 18 [new_demod,17] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.97/2.15 ** KEPT (pick-wt=6): 19 [] compose(A,domain(A))=A.
% 1.97/2.15 ---> New Demodulator: 20 [new_demod,19] compose(A,domain(A))=A.
% 1.97/2.15 ** KEPT (pick-wt=6): 21 [] compose(codomain(A),A)=A.
% 1.97/2.15 ---> New Demodulator: 22 [new_demod,21] compose(codomain(A),A)=A.
% 1.97/2.15 ** KEPT (pick-wt=7): 23 [] there_exists(f1(A,B))|A=B.
% 1.97/2.15 ** KEPT (pick-wt=13): 25 [copy,24,flip.1,flip.2] f1(A,B)=A|f1(A,B)=B|A=B.
% 1.97/2.15 ** KEPT (pick-wt=3): 26 [] there_exists(domain(a)).
% 1.97/2.15 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 1.97/2.15 15 back subsumes 14.
% 1.97/2.15 >>>> Starting back demodulation with 18.
% 1.97/2.15 >>>> Starting back demodulation with 20.
% 2.44/2.61 >>>> Starting back demodulation with 22.
% 2.44/2.61
% 2.44/2.61 ======= end of input processing =======
% 2.44/2.61
% 2.44/2.61 =========== start of search ===========
% 2.44/2.61
% 2.44/2.61
% 2.44/2.61 Resetting weight limit to 8.
% 2.44/2.61
% 2.44/2.61
% 2.44/2.61 Resetting weight limit to 8.
% 2.44/2.61
% 2.44/2.61 sos_size=2030
% 2.44/2.61
% 2.44/2.61 -------- PROOF --------
% 2.44/2.61
% 2.44/2.61 ----> UNIT CONFLICT at 0.45 sec ----> 2379 [binary,2377.1,13.1] $F.
% 2.44/2.61
% 2.44/2.61 Length of proof is 8. Level of proof is 5.
% 2.44/2.61
% 2.44/2.61 ---------------- PROOF ----------------
% 2.44/2.61 % SZS status Unsatisfiable
% 2.44/2.61 % SZS output start Refutation
% See solution above
% 2.44/2.61 ------------ end of proof -------------
% 2.44/2.61
% 2.44/2.61
% 2.44/2.61 Search stopped by max_proofs option.
% 2.44/2.61
% 2.44/2.61
% 2.44/2.61 Search stopped by max_proofs option.
% 2.44/2.61
% 2.44/2.61 ============ end of search ============
% 2.44/2.61
% 2.44/2.61 -------------- statistics -------------
% 2.44/2.61 clauses given 154
% 2.44/2.61 clauses generated 7514
% 2.44/2.61 clauses kept 2360
% 2.44/2.61 clauses forward subsumed 2086
% 2.44/2.61 clauses back subsumed 4
% 2.44/2.61 Kbytes malloced 4882
% 2.44/2.61
% 2.44/2.61 ----------- times (seconds) -----------
% 2.44/2.61 user CPU time 0.45 (0 hr, 0 min, 0 sec)
% 2.44/2.61 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.44/2.61 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.44/2.61
% 2.44/2.61 That finishes the proof of the theorem.
% 2.44/2.61
% 2.44/2.61 Process 23816 finished Wed Jul 27 01:56:41 2022
% 2.44/2.61 Otter interrupted
% 2.44/2.61 PROOF FOUND
%------------------------------------------------------------------------------