%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT016-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 12:47:49 EDT 2022
% Result : Unsatisfiable 1.67s 1.88s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 6 RR)
% Number of literals : 9 ( 1 equ; 3 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 : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 4 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( ~ there_exists(compose(A,B))
| there_exists(domain(A)) ),
file('CAT016-4.p',unknown),
[] ).
cnf(9,axiom,
~ there_exists(domain(a)),
file('CAT016-4.p',unknown),
[] ).
cnf(14,axiom,
compose(A,domain(A)) = A,
file('CAT016-4.p',unknown),
[] ).
cnf(18,axiom,
there_exists(a),
file('CAT016-4.p',unknown),
[] ).
cnf(27,plain,
( ~ there_exists(A)
| there_exists(domain(A)) ),
inference(para_from,[status(thm),theory(equality)],[14,6]),
[iquote('para_from,14.1.1,6.1.1')] ).
cnf(36,plain,
there_exists(domain(a)),
inference(hyper,[status(thm)],[27,18]),
[iquote('hyper,27,18')] ).
cnf(37,plain,
$false,
inference(binary,[status(thm)],[36,9]),
[iquote('binary,36.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT016-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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 01:46:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.88 ----- Otter 3.3f, August 2004 -----
% 1.67/1.88 The process was started by sandbox on n007.cluster.edu,
% 1.67/1.88 Wed Jul 27 01:46:16 2022
% 1.67/1.88 The command was "./otter". The process ID is 30976.
% 1.67/1.88
% 1.67/1.88 set(prolog_style_variables).
% 1.67/1.88 set(auto).
% 1.67/1.88 dependent: set(auto1).
% 1.67/1.88 dependent: set(process_input).
% 1.67/1.88 dependent: clear(print_kept).
% 1.67/1.88 dependent: clear(print_new_demod).
% 1.67/1.88 dependent: clear(print_back_demod).
% 1.67/1.88 dependent: clear(print_back_sub).
% 1.67/1.88 dependent: set(control_memory).
% 1.67/1.88 dependent: assign(max_mem, 12000).
% 1.67/1.88 dependent: assign(pick_given_ratio, 4).
% 1.67/1.88 dependent: assign(stats_level, 1).
% 1.67/1.88 dependent: assign(max_seconds, 10800).
% 1.67/1.88 clear(print_given).
% 1.67/1.88
% 1.67/1.88 list(usable).
% 1.67/1.88 0 [] A=A.
% 1.67/1.88 0 [] -e_quivalent(X,Y)|there_exists(X).
% 1.67/1.88 0 [] -e_quivalent(X,Y)|X=Y.
% 1.67/1.88 0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 1.67/1.88 0 [] -there_exists(domain(X))|there_exists(X).
% 1.67/1.88 0 [] -there_exists(codomain(X))|there_exists(X).
% 1.67/1.88 0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 1.67/1.88 0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 1.67/1.88 0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 1.67/1.88 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 1.67/1.88 0 [] compose(X,domain(X))=X.
% 1.67/1.88 0 [] compose(codomain(X),X)=X.
% 1.67/1.88 0 [] there_exists(a).
% 1.67/1.88 0 [] -there_exists(domain(a)).
% 1.67/1.88 end_of_list.
% 1.67/1.88
% 1.67/1.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.67/1.88
% 1.67/1.88 This is a Horn set with equality. The strategy will be
% 1.67/1.88 Knuth-Bendix and hyper_res, with positive clauses in
% 1.67/1.88 sos and nonpositive clauses in usable.
% 1.67/1.88
% 1.67/1.88 dependent: set(knuth_bendix).
% 1.67/1.88 dependent: set(anl_eq).
% 1.67/1.88 dependent: set(para_from).
% 1.67/1.88 dependent: set(para_into).
% 1.67/1.88 dependent: clear(para_from_right).
% 1.67/1.88 dependent: clear(para_into_right).
% 1.67/1.88 dependent: set(para_from_vars).
% 1.67/1.88 dependent: set(eq_units_both_ways).
% 1.67/1.88 dependent: set(dynamic_demod_all).
% 1.67/1.88 dependent: set(dynamic_demod).
% 1.67/1.88 dependent: set(order_eq).
% 1.67/1.88 dependent: set(back_demod).
% 1.67/1.88 dependent: set(lrpo).
% 1.67/1.88 dependent: set(hyper_res).
% 1.67/1.88 dependent: clear(order_hyper).
% 1.67/1.88
% 1.67/1.88 ------------> process usable:
% 1.67/1.88 ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 1.67/1.88 ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 1.67/1.88 ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 1.67/1.88 ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 1.67/1.88 ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 1.67/1.88 ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 1.67/1.88 ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 1.67/1.88 ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 1.67/1.88 ** KEPT (pick-wt=3): 9 [] -there_exists(domain(a)).
% 1.67/1.88
% 1.67/1.88 ------------> process sos:
% 1.67/1.88 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.67/1.88 ** KEPT (pick-wt=11): 12 [copy,11,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.67/1.88 ---> New Demodulator: 13 [new_demod,12] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.67/1.88 ** KEPT (pick-wt=6): 14 [] compose(A,domain(A))=A.
% 1.67/1.88 ---> New Demodulator: 15 [new_demod,14] compose(A,domain(A))=A.
% 1.67/1.88 ** KEPT (pick-wt=6): 16 [] compose(codomain(A),A)=A.
% 1.67/1.88 ---> New Demodulator: 17 [new_demod,16] compose(codomain(A),A)=A.
% 1.67/1.88 ** KEPT (pick-wt=2): 18 [] there_exists(a).
% 1.67/1.88 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.67/1.88 >>>> Starting back demodulation with 13.
% 1.67/1.88 >>>> Starting back demodulation with 15.
% 1.67/1.88 >>>> Starting back demodulation with 17.
% 1.67/1.88
% 1.67/1.88 ======= end of input processing =======
% 1.67/1.88
% 1.67/1.88 =========== start of search ===========
% 1.67/1.88
% 1.67/1.88 -------- PROOF --------
% 1.67/1.88
% 1.67/1.88 ----> UNIT CONFLICT at 0.00 sec ----> 37 [binary,36.1,9.1] $F.
% 1.67/1.88
% 1.67/1.88 Length of proof is 2. Level of proof is 2.
% 1.67/1.88
% 1.67/1.88 ---------------- PROOF ----------------
% 1.67/1.88 % SZS status Unsatisfiable
% 1.67/1.88 % SZS output start Refutation
% See solution above
% 1.67/1.88 ------------ end of proof -------------
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88 ============ end of search ============
% 1.67/1.88
% 1.67/1.88 -------------- statistics -------------
% 1.67/1.88 clauses given 7
% 1.67/1.88 clauses generated 29
% 1.67/1.88 clauses kept 30
% 1.67/1.88 clauses forward subsumed 13
% 1.67/1.88 clauses back subsumed 0
% 1.67/1.88 Kbytes malloced 976
% 1.67/1.88
% 1.67/1.88 ----------- times (seconds) -----------
% 1.67/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.88 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.88
% 1.67/1.88 That finishes the proof of the theorem.
% 1.67/1.88
% 1.67/1.88 Process 30976 finished Wed Jul 27 01:46:17 2022
% 1.67/1.88 Otter interrupted
% 1.67/1.88 PROOF FOUND
%------------------------------------------------------------------------------