TSTP Solution File: CAT006-4 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT006-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 1.59s 2.14s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 9 unt; 0 nHn; 14 RR)
% Number of literals : 21 ( 8 equ; 7 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 : 7 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( ~ there_exists(domain(A))
| there_exists(A) ),
file('CAT006-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ there_exists(compose(A,B))
| there_exists(domain(A)) ),
file('CAT006-4.p',unknown),
[] ).
cnf(7,axiom,
( ~ there_exists(compose(A,B))
| domain(A) = codomain(B) ),
file('CAT006-4.p',unknown),
[] ).
cnf(10,axiom,
( ~ there_exists(compose(d,A))
| compose(d,A) = A ),
file('CAT006-4.p',unknown),
[] ).
cnf(11,axiom,
codomain(a) != d,
file('CAT006-4.p',unknown),
[] ).
cnf(16,axiom,
compose(A,domain(A)) = A,
file('CAT006-4.p',unknown),
[] ).
cnf(20,axiom,
there_exists(compose(d,a)),
file('CAT006-4.p',unknown),
[] ).
cnf(24,plain,
domain(d) = codomain(a),
inference(hyper,[status(thm)],[20,7]),
[iquote('hyper,20,7')] ).
cnf(25,plain,
there_exists(codomain(a)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[20,6]),24]),
[iquote('hyper,20,6,demod,24')] ).
cnf(51,plain,
( ~ there_exists(codomain(a))
| there_exists(d) ),
inference(para_from,[status(thm),theory(equality)],[24,4]),
[iquote('para_from,23.1.1,4.1.1')] ).
cnf(57,plain,
compose(d,codomain(a)) = d,
inference(para_into,[status(thm),theory(equality)],[16,24]),
[iquote('para_into,16.1.1.2,23.1.1')] ).
cnf(62,plain,
( codomain(a) = d
| ~ there_exists(d) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,10]),24,24,57]),
[iquote('para_into,16.1.1,10.2.1,demod,24,24,57')] ).
cnf(68,plain,
there_exists(d),
inference(hyper,[status(thm)],[51,25]),
[iquote('hyper,51,25')] ).
cnf(135,plain,
codomain(a) = d,
inference(hyper,[status(thm)],[62,68]),
[iquote('hyper,62,68')] ).
cnf(137,plain,
$false,
inference(binary,[status(thm)],[135,11]),
[iquote('binary,135.1,11.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT006-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 01:50:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.59/2.14 ----- Otter 3.3f, August 2004 -----
% 1.59/2.14 The process was started by sandbox2 on n011.cluster.edu,
% 1.59/2.14 Wed Jul 27 01:50:55 2022
% 1.59/2.14 The command was "./otter". The process ID is 11018.
% 1.59/2.14
% 1.59/2.14 set(prolog_style_variables).
% 1.59/2.14 set(auto).
% 1.59/2.14 dependent: set(auto1).
% 1.59/2.14 dependent: set(process_input).
% 1.59/2.14 dependent: clear(print_kept).
% 1.59/2.14 dependent: clear(print_new_demod).
% 1.59/2.14 dependent: clear(print_back_demod).
% 1.59/2.14 dependent: clear(print_back_sub).
% 1.59/2.14 dependent: set(control_memory).
% 1.59/2.14 dependent: assign(max_mem, 12000).
% 1.59/2.14 dependent: assign(pick_given_ratio, 4).
% 1.59/2.14 dependent: assign(stats_level, 1).
% 1.59/2.14 dependent: assign(max_seconds, 10800).
% 1.59/2.14 clear(print_given).
% 1.59/2.14
% 1.59/2.14 list(usable).
% 1.59/2.14 0 [] A=A.
% 1.59/2.14 0 [] -e_quivalent(X,Y)|there_exists(X).
% 1.59/2.14 0 [] -e_quivalent(X,Y)|X=Y.
% 1.59/2.14 0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 1.59/2.14 0 [] -there_exists(domain(X))|there_exists(X).
% 1.59/2.14 0 [] -there_exists(codomain(X))|there_exists(X).
% 1.59/2.14 0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 1.59/2.14 0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 1.59/2.14 0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 1.59/2.14 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 1.59/2.14 0 [] compose(X,domain(X))=X.
% 1.59/2.14 0 [] compose(codomain(X),X)=X.
% 1.59/2.14 0 [] there_exists(compose(d,a)).
% 1.59/2.14 0 [] -there_exists(compose(X,d))|compose(X,d)=X.
% 1.59/2.14 0 [] -there_exists(compose(d,X))|compose(d,X)=X.
% 1.59/2.14 0 [] codomain(a)!=d.
% 1.59/2.14 end_of_list.
% 1.59/2.14
% 1.59/2.14 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.59/2.14
% 1.59/2.14 This is a Horn set with equality. The strategy will be
% 1.59/2.14 Knuth-Bendix and hyper_res, with positive clauses in
% 1.59/2.14 sos and nonpositive clauses in usable.
% 1.59/2.14
% 1.59/2.14 dependent: set(knuth_bendix).
% 1.59/2.14 dependent: set(anl_eq).
% 1.59/2.14 dependent: set(para_from).
% 1.59/2.14 dependent: set(para_into).
% 1.59/2.14 dependent: clear(para_from_right).
% 1.59/2.14 dependent: clear(para_into_right).
% 1.59/2.14 dependent: set(para_from_vars).
% 1.59/2.14 dependent: set(eq_units_both_ways).
% 1.59/2.14 dependent: set(dynamic_demod_all).
% 1.59/2.14 dependent: set(dynamic_demod).
% 1.59/2.14 dependent: set(order_eq).
% 1.59/2.14 dependent: set(back_demod).
% 1.59/2.14 dependent: set(lrpo).
% 1.59/2.14 dependent: set(hyper_res).
% 1.59/2.14 dependent: clear(order_hyper).
% 1.59/2.14
% 1.59/2.14 ------------> process usable:
% 1.59/2.14 ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 1.59/2.14 ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 1.59/2.14 ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 1.59/2.14 ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 1.59/2.14 ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 1.59/2.14 ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 1.59/2.14 ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 1.59/2.14 ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 1.59/2.14 ** KEPT (pick-wt=9): 9 [] -there_exists(compose(A,d))|compose(A,d)=A.
% 1.59/2.14 ** KEPT (pick-wt=9): 10 [] -there_exists(compose(d,A))|compose(d,A)=A.
% 1.59/2.14 ** KEPT (pick-wt=4): 11 [] codomain(a)!=d.
% 1.59/2.14
% 1.59/2.14 ------------> process sos:
% 1.59/2.14 ** KEPT (pick-wt=3): 12 [] A=A.
% 1.59/2.14 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.59/2.14 ---> New Demodulator: 15 [new_demod,14] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.59/2.14 ** KEPT (pick-wt=6): 16 [] compose(A,domain(A))=A.
% 1.59/2.14 ---> New Demodulator: 17 [new_demod,16] compose(A,domain(A))=A.
% 1.59/2.14 ** KEPT (pick-wt=6): 18 [] compose(codomain(A),A)=A.
% 1.59/2.14 ---> New Demodulator: 19 [new_demod,18] compose(codomain(A),A)=A.
% 1.59/2.14 ** KEPT (pick-wt=4): 20 [] there_exists(compose(d,a)).
% 1.59/2.14 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 1.59/2.14 >>>> Starting back demodulation with 15.
% 1.59/2.14 >>>> Starting back demodulation with 17.
% 1.59/2.14 >>>> Starting back demodulation with 19.
% 1.59/2.14
% 1.59/2.14 ======= end of input processing =======
% 1.59/2.14
% 1.59/2.14 =========== start of search ===========
% 1.59/2.14
% 1.59/2.14 -------- PROOF --------
% 1.59/2.14
% 1.59/2.14 ----> UNIT CONFLICT at 0.00 sec ----> 137 [binary,135.1,11.1] $F.
% 1.59/2.14
% 1.59/2.14 Length of proof is 7. Level of proof is 4.
% 1.59/2.14
% 1.59/2.14 ---------------- PROOF ----------------
% 1.59/2.14 % SZS status Unsatisfiable
% 1.59/2.14 % SZS output start Refutation
% See solution above
% 1.59/2.14 ------------ end of proof -------------
% 1.59/2.14
% 1.59/2.14
% 1.59/2.14 Search stopped by max_proofs option.
% 1.59/2.14
% 1.59/2.14
% 1.59/2.14 Search stopped by max_proofs option.
% 1.59/2.14
% 1.59/2.14 ============ end of search ============
% 1.59/2.14
% 1.59/2.14 -------------- statistics -------------
% 1.59/2.14 clauses given 28
% 1.59/2.14 clauses generated 170
% 1.59/2.14 clauses kept 123
% 1.59/2.14 clauses forward subsumed 61
% 1.59/2.14 clauses back subsumed 4
% 1.59/2.14 Kbytes malloced 976
% 1.59/2.14
% 1.59/2.14 ----------- times (seconds) -----------
% 1.59/2.14 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.59/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.59/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.59/2.14
% 1.59/2.14 That finishes the proof of the theorem.
% 1.59/2.14
% 1.59/2.14 Process 11018 finished Wed Jul 27 01:50:57 2022
% 1.59/2.14 Otter interrupted
% 1.59/2.14 PROOF FOUND
%------------------------------------------------------------------------------