TSTP Solution File: CAT009-4 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT009-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 12:47:47 EDT 2022
% Result : Unsatisfiable 2.15s 2.35s
% Output : Refutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 11 unt; 0 nHn; 14 RR)
% Number of literals : 23 ( 11 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 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 : 18 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( ~ there_exists(codomain(A))
| there_exists(A) ),
file('CAT009-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ there_exists(compose(A,B))
| there_exists(domain(A)) ),
file('CAT009-4.p',unknown),
[] ).
cnf(7,axiom,
( ~ there_exists(compose(A,B))
| domain(A) = codomain(B) ),
file('CAT009-4.p',unknown),
[] ).
cnf(9,axiom,
domain(compose(a,b)) != domain(b),
file('CAT009-4.p',unknown),
[] ).
cnf(11,axiom,
compose(A,compose(B,C)) = compose(compose(A,B),C),
file('CAT009-4.p',unknown),
[] ).
cnf(12,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(14,axiom,
compose(A,domain(A)) = A,
file('CAT009-4.p',unknown),
[] ).
cnf(18,axiom,
there_exists(compose(a,b)),
file('CAT009-4.p',unknown),
[] ).
cnf(20,plain,
domain(a) = codomain(b),
inference(hyper,[status(thm)],[18,7]),
[iquote('hyper,18,7')] ).
cnf(21,plain,
there_exists(codomain(b)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[18,6]),20]),
[iquote('hyper,18,6,demod,20')] ).
cnf(26,plain,
there_exists(b),
inference(hyper,[status(thm)],[21,5]),
[iquote('hyper,21,5')] ).
cnf(36,plain,
( ~ there_exists(compose(A,compose(B,C)))
| domain(compose(A,B)) = codomain(C) ),
inference(para_from,[status(thm),theory(equality)],[12,7]),
[iquote('para_from,12.1.1,7.1.1')] ).
cnf(58,plain,
( ~ there_exists(A)
| codomain(domain(A)) = domain(A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[14,7])]),
[iquote('para_from,14.1.1,7.1.1,flip.2')] ).
cnf(404,plain,
( ~ there_exists(compose(A,B))
| domain(compose(A,B)) = codomain(domain(B)) ),
inference(para_into,[status(thm),theory(equality)],[36,14]),
[iquote('para_into,36.1.1.2,14.1.1')] ).
cnf(1266,plain,
codomain(domain(b)) = domain(b),
inference(hyper,[status(thm)],[58,26]),
[iquote('hyper,58,26')] ).
cnf(1483,plain,
domain(compose(a,b)) = domain(b),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[404,18]),1266]),
[iquote('hyper,404,18,demod,1266')] ).
cnf(1485,plain,
$false,
inference(binary,[status(thm)],[1483,9]),
[iquote('binary,1483.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : CAT009-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 01:56:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.15/2.34 ----- Otter 3.3f, August 2004 -----
% 2.15/2.34 The process was started by sandbox on n009.cluster.edu,
% 2.15/2.34 Wed Jul 27 01:56:21 2022
% 2.15/2.34 The command was "./otter". The process ID is 30216.
% 2.15/2.34
% 2.15/2.34 set(prolog_style_variables).
% 2.15/2.34 set(auto).
% 2.15/2.34 dependent: set(auto1).
% 2.15/2.34 dependent: set(process_input).
% 2.15/2.34 dependent: clear(print_kept).
% 2.15/2.34 dependent: clear(print_new_demod).
% 2.15/2.34 dependent: clear(print_back_demod).
% 2.15/2.34 dependent: clear(print_back_sub).
% 2.15/2.34 dependent: set(control_memory).
% 2.15/2.34 dependent: assign(max_mem, 12000).
% 2.15/2.34 dependent: assign(pick_given_ratio, 4).
% 2.15/2.34 dependent: assign(stats_level, 1).
% 2.15/2.34 dependent: assign(max_seconds, 10800).
% 2.15/2.34 clear(print_given).
% 2.15/2.34
% 2.15/2.34 list(usable).
% 2.15/2.34 0 [] A=A.
% 2.15/2.34 0 [] -e_quivalent(X,Y)|there_exists(X).
% 2.15/2.34 0 [] -e_quivalent(X,Y)|X=Y.
% 2.15/2.34 0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 2.15/2.34 0 [] -there_exists(domain(X))|there_exists(X).
% 2.15/2.34 0 [] -there_exists(codomain(X))|there_exists(X).
% 2.15/2.34 0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 2.15/2.34 0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 2.15/2.34 0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 2.15/2.35 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 2.15/2.35 0 [] compose(X,domain(X))=X.
% 2.15/2.35 0 [] compose(codomain(X),X)=X.
% 2.15/2.35 0 [] there_exists(compose(a,b)).
% 2.15/2.35 0 [] domain(compose(a,b))!=domain(b).
% 2.15/2.35 end_of_list.
% 2.15/2.35
% 2.15/2.35 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.15/2.35
% 2.15/2.35 This is a Horn set with equality. The strategy will be
% 2.15/2.35 Knuth-Bendix and hyper_res, with positive clauses in
% 2.15/2.35 sos and nonpositive clauses in usable.
% 2.15/2.35
% 2.15/2.35 dependent: set(knuth_bendix).
% 2.15/2.35 dependent: set(anl_eq).
% 2.15/2.35 dependent: set(para_from).
% 2.15/2.35 dependent: set(para_into).
% 2.15/2.35 dependent: clear(para_from_right).
% 2.15/2.35 dependent: clear(para_into_right).
% 2.15/2.35 dependent: set(para_from_vars).
% 2.15/2.35 dependent: set(eq_units_both_ways).
% 2.15/2.35 dependent: set(dynamic_demod_all).
% 2.15/2.35 dependent: set(dynamic_demod).
% 2.15/2.35 dependent: set(order_eq).
% 2.15/2.35 dependent: set(back_demod).
% 2.15/2.35 dependent: set(lrpo).
% 2.15/2.35 dependent: set(hyper_res).
% 2.15/2.35 dependent: clear(order_hyper).
% 2.15/2.35
% 2.15/2.35 ------------> process usable:
% 2.15/2.35 ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 2.15/2.35 ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 2.15/2.35 ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 2.15/2.35 ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 2.15/2.35 ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 2.15/2.35 ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 2.15/2.35 ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 2.15/2.35 ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 2.15/2.35 ** KEPT (pick-wt=7): 9 [] domain(compose(a,b))!=domain(b).
% 2.15/2.35
% 2.15/2.35 ------------> process sos:
% 2.15/2.35 ** KEPT (pick-wt=3): 10 [] A=A.
% 2.15/2.35 ** KEPT (pick-wt=11): 12 [copy,11,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 2.15/2.35 ---> New Demodulator: 13 [new_demod,12] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 2.15/2.35 ** KEPT (pick-wt=6): 14 [] compose(A,domain(A))=A.
% 2.15/2.35 ---> New Demodulator: 15 [new_demod,14] compose(A,domain(A))=A.
% 2.15/2.35 ** KEPT (pick-wt=6): 16 [] compose(codomain(A),A)=A.
% 2.15/2.35 ---> New Demodulator: 17 [new_demod,16] compose(codomain(A),A)=A.
% 2.15/2.35 ** KEPT (pick-wt=4): 18 [] there_exists(compose(a,b)).
% 2.15/2.35 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 2.15/2.35 >>>> Starting back demodulation with 13.
% 2.15/2.35 >>>> Starting back demodulation with 15.
% 2.15/2.35 >>>> Starting back demodulation with 17.
% 2.15/2.35
% 2.15/2.35 ======= end of input processing =======
% 2.15/2.35
% 2.15/2.35 =========== start of search ===========
% 2.15/2.35
% 2.15/2.35
% 2.15/2.35 Resetting weight limit to 8.
% 2.15/2.35
% 2.15/2.35
% 2.15/2.35 Resetting weight limit to 8.
% 2.15/2.35
% 2.15/2.35 sos_size=1000
% 2.15/2.35
% 2.15/2.35 -------- PROOF --------
% 2.15/2.35
% 2.15/2.35 ----> UNIT CONFLICT at 0.33 sec ----> 1485 [binary,1483.1,9.1] $F.
% 2.15/2.35
% 2.15/2.35 Length of proof is 9. Level of proof is 5.
% 2.15/2.35
% 2.15/2.35 ---------------- PROOF ----------------
% 2.15/2.35 % SZS status Unsatisfiable
% 2.15/2.35 % SZS output start Refutation
% See solution above
% 2.15/2.35 ------------ end of proof -------------
% 2.15/2.35
% 2.15/2.35
% 2.15/2.35 Search stopped by max_proofs option.
% 2.15/2.35
% 2.15/2.35
% 2.15/2.35 Search stopped by max_proofs option.
% 2.15/2.35
% 2.15/2.35 ============ end of search ============
% 2.15/2.35
% 2.15/2.35 -------------- statistics -------------
% 2.15/2.35 clauses given 686
% 2.15/2.35 clauses generated 46304
% 2.15/2.35 clauses kept 1406
% 2.15/2.35 clauses forward subsumed 3839
% 2.15/2.35 clauses back subsumed 37
% 2.15/2.35 Kbytes malloced 4882
% 2.15/2.35
% 2.15/2.35 ----------- times (seconds) -----------
% 2.15/2.35 user CPU time 0.33 (0 hr, 0 min, 0 sec)
% 2.15/2.35 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.15/2.35 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.15/2.35
% 2.15/2.35 That finishes the proof of the theorem.
% 2.15/2.35
% 2.15/2.35 Process 30216 finished Wed Jul 27 01:56:23 2022
% 2.15/2.35 Otter interrupted
% 2.15/2.35 PROOF FOUND
%------------------------------------------------------------------------------