TSTP Solution File: CAT006-3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 12:47:46 EDT 2022
% Result : Unsatisfiable 1.65s 1.81s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 11 unt; 0 nHn; 15 RR)
% Number of literals : 21 ( 6 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( ~ there_exists(codomain(A))
| there_exists(A) ),
file('CAT006-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ there_exists(compose(A,B))
| there_exists(domain(A)) ),
file('CAT006-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ there_exists(compose(A,B))
| domain(A) = codomain(B) ),
file('CAT006-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ there_exists(compose(A,B))
| there_exists(codomain(A)) ),
file('CAT006-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ there_exists(compose(d,A))
| compose(d,A) = A ),
file('CAT006-3.p',unknown),
[] ).
cnf(15,axiom,
codomain(a) != d,
file('CAT006-3.p',unknown),
[] ).
cnf(21,axiom,
compose(A,domain(A)) = A,
file('CAT006-3.p',unknown),
[] ).
cnf(28,axiom,
there_exists(compose(d,a)),
file('CAT006-3.p',unknown),
[] ).
cnf(31,plain,
there_exists(codomain(d)),
inference(hyper,[status(thm)],[28,10]),
[iquote('hyper,28,10')] ).
cnf(33,plain,
domain(d) = codomain(a),
inference(hyper,[status(thm)],[28,7]),
[iquote('hyper,28,7')] ).
cnf(34,plain,
there_exists(codomain(a)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[28,6]),33]),
[iquote('hyper,28,6,demod,33')] ).
cnf(38,plain,
there_exists(d),
inference(hyper,[status(thm)],[31,5]),
[iquote('hyper,31,5')] ).
cnf(79,plain,
~ there_exists(compose(d,codomain(a))),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[21,14]),33,33]),15]),
[iquote('para_into,21.1.1,14.2.1,demod,33,33,unit_del,15')] ).
cnf(83,plain,
compose(d,codomain(a)) = codomain(a),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[21,14]),33,33]),38]),
[iquote('para_from,21.1.1,14.1.1,demod,33,33,unit_del,38')] ).
cnf(89,plain,
~ there_exists(codomain(a)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[79]),83]),
[iquote('back_demod,79,demod,83')] ).
cnf(90,plain,
$false,
inference(binary,[status(thm)],[89,34]),
[iquote('binary,89.1,34.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 01:57:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.65/1.81 ----- Otter 3.3f, August 2004 -----
% 1.65/1.81 The process was started by sandbox2 on n019.cluster.edu,
% 1.65/1.81 Wed Jul 27 01:57:07 2022
% 1.65/1.81 The command was "./otter". The process ID is 28798.
% 1.65/1.81
% 1.65/1.81 set(prolog_style_variables).
% 1.65/1.81 set(auto).
% 1.65/1.81 dependent: set(auto1).
% 1.65/1.81 dependent: set(process_input).
% 1.65/1.81 dependent: clear(print_kept).
% 1.65/1.81 dependent: clear(print_new_demod).
% 1.65/1.81 dependent: clear(print_back_demod).
% 1.65/1.81 dependent: clear(print_back_sub).
% 1.65/1.81 dependent: set(control_memory).
% 1.65/1.81 dependent: assign(max_mem, 12000).
% 1.65/1.81 dependent: assign(pick_given_ratio, 4).
% 1.65/1.81 dependent: assign(stats_level, 1).
% 1.65/1.81 dependent: assign(max_seconds, 10800).
% 1.65/1.81 clear(print_given).
% 1.65/1.81
% 1.65/1.81 list(usable).
% 1.65/1.81 0 [] A=A.
% 1.65/1.81 0 [] -e_quivalent(X,Y)|there_exists(X).
% 1.65/1.81 0 [] -e_quivalent(X,Y)|X=Y.
% 1.65/1.81 0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 1.65/1.81 0 [] -there_exists(domain(X))|there_exists(X).
% 1.65/1.81 0 [] -there_exists(codomain(X))|there_exists(X).
% 1.65/1.81 0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 1.65/1.81 0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 1.65/1.81 0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 1.65/1.81 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 1.65/1.81 0 [] compose(X,domain(X))=X.
% 1.65/1.81 0 [] compose(codomain(X),X)=X.
% 1.65/1.81 0 [] -e_quivalent(X,Y)|there_exists(Y).
% 1.65/1.81 0 [] -there_exists(X)| -there_exists(Y)|X!=Y|e_quivalent(X,Y).
% 1.65/1.81 0 [] -there_exists(compose(X,Y))|there_exists(codomain(X)).
% 1.65/1.81 0 [] there_exists(f1(X,Y))|X=Y.
% 1.65/1.81 0 [] X=f1(X,Y)|Y=f1(X,Y)|X=Y.
% 1.65/1.81 0 [] X!=f1(X,Y)|Y!=f1(X,Y)|X=Y.
% 1.65/1.81 0 [] there_exists(compose(d,a)).
% 1.65/1.81 0 [] -there_exists(compose(X,d))|compose(X,d)=X.
% 1.65/1.81 0 [] -there_exists(compose(d,X))|compose(d,X)=X.
% 1.65/1.81 0 [] codomain(a)!=d.
% 1.65/1.81 end_of_list.
% 1.65/1.81
% 1.65/1.81 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.65/1.81
% 1.65/1.81 This ia a non-Horn set with equality. The strategy will be
% 1.65/1.81 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.65/1.81 deletion, with positive clauses in sos and nonpositive
% 1.65/1.81 clauses in usable.
% 1.65/1.81
% 1.65/1.81 dependent: set(knuth_bendix).
% 1.65/1.81 dependent: set(anl_eq).
% 1.65/1.81 dependent: set(para_from).
% 1.65/1.81 dependent: set(para_into).
% 1.65/1.81 dependent: clear(para_from_right).
% 1.65/1.81 dependent: clear(para_into_right).
% 1.65/1.81 dependent: set(para_from_vars).
% 1.65/1.81 dependent: set(eq_units_both_ways).
% 1.65/1.81 dependent: set(dynamic_demod_all).
% 1.65/1.81 dependent: set(dynamic_demod).
% 1.65/1.81 dependent: set(order_eq).
% 1.65/1.81 dependent: set(back_demod).
% 1.65/1.81 dependent: set(lrpo).
% 1.65/1.81 dependent: set(hyper_res).
% 1.65/1.81 dependent: set(unit_deletion).
% 1.65/1.81 dependent: set(factor).
% 1.65/1.81
% 1.65/1.81 ------------> process usable:
% 1.65/1.81 ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 1.65/1.81 ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 1.65/1.81 ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 1.65/1.81 ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 1.65/1.81 ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 1.65/1.81 ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 1.65/1.81 ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 1.65/1.81 ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 1.65/1.81 ** KEPT (pick-wt=5): 9 [] -e_quivalent(A,B)|there_exists(B).
% 1.65/1.81 Following clause subsumed by 3 during input processing: 0 [] -there_exists(A)| -there_exists(B)|A!=B|e_quivalent(A,B).
% 1.65/1.81 ** KEPT (pick-wt=7): 10 [] -there_exists(compose(A,B))|there_exists(codomain(A)).
% 1.65/1.81 ** KEPT (pick-wt=13): 12 [copy,11,flip.1,flip.2] f1(A,B)!=A|f1(A,B)!=B|A=B.
% 1.65/1.81 ** KEPT (pick-wt=9): 13 [] -there_exists(compose(A,d))|compose(A,d)=A.
% 1.65/1.81 ** KEPT (pick-wt=9): 14 [] -there_exists(compose(d,A))|compose(d,A)=A.
% 1.65/1.81 ** KEPT (pick-wt=4): 15 [] codomain(a)!=d.
% 1.65/1.81
% 1.65/1.81 ------------> process sos:
% 1.65/1.81 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.65/1.81 ** KEPT (pick-wt=11): 19 [copy,18,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.65/1.81 ---> New Demodulator: 20 [new_demod,19] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.65/1.81 ** KEPT (pick-wt=6): 21 [] compose(A,domain(A))=A.
% 1.65/1.81 ---> New Demodulator: 22 [new_demod,21] compose(A,domain(A))=A.
% 1.65/1.81 ** KEPT (pick-wt=6): 23 [] compose(codomain(A),A)=A.
% 1.65/1.81 ---> New Demodulator: 24 [new_demod,23] compose(codomain(A),A)=A.
% 1.65/1.81 ** KEPT (pick-wt=7): 25 [] there_exists(f1(A,B))|A=B.
% 1.65/1.81 ** KEPT (pick-wt=13): 27 [copy,26,flip.1,flip.2] f1(A,B)=A|f1(A,B)=B|A=B.
% 1.65/1.81 ** KEPT (pick-wt=4): 28 [] there_exists(compose(d,a)).
% 1.65/1.81 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.65/1.81 17 back subsumes 16.
% 1.65/1.81 >>>> Starting back demodulation with 20.
% 1.65/1.81 >>>> Starting back demodulation with 22.
% 1.65/1.81 >>>> Starting back demodulation with 24.
% 1.65/1.81
% 1.65/1.81 ======= end of input processing =======
% 1.65/1.81
% 1.65/1.81 =========== start of search ===========
% 1.65/1.81
% 1.65/1.81 -------- PROOF --------
% 1.65/1.81
% 1.65/1.81 ----> UNIT CONFLICT at 0.00 sec ----> 90 [binary,89.1,34.1] $F.
% 1.65/1.81
% 1.65/1.81 Length of proof is 7. Level of proof is 4.
% 1.65/1.81
% 1.65/1.81 ---------------- PROOF ----------------
% 1.65/1.81 % SZS status Unsatisfiable
% 1.65/1.81 % SZS output start Refutation
% See solution above
% 1.65/1.81 ------------ end of proof -------------
% 1.65/1.81
% 1.65/1.81
% 1.65/1.81 Search stopped by max_proofs option.
% 1.65/1.81
% 1.65/1.81
% 1.65/1.81 Search stopped by max_proofs option.
% 1.65/1.81
% 1.65/1.81 ============ end of search ============
% 1.65/1.81
% 1.65/1.81 -------------- statistics -------------
% 1.65/1.81 clauses given 11
% 1.65/1.81 clauses generated 106
% 1.65/1.81 clauses kept 77
% 1.65/1.81 clauses forward subsumed 52
% 1.65/1.81 clauses back subsumed 5
% 1.65/1.81 Kbytes malloced 976
% 1.65/1.81
% 1.65/1.81 ----------- times (seconds) -----------
% 1.65/1.81 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.81 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.81 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.65/1.81
% 1.65/1.81 That finishes the proof of the theorem.
% 1.65/1.81
% 1.65/1.81 Process 28798 finished Wed Jul 27 01:57:08 2022
% 1.65/1.81 Otter interrupted
% 1.65/1.81 PROOF FOUND
%------------------------------------------------------------------------------