%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT019-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:47:50 EDT 2022
% Result : Unsatisfiable 1.82s 2.08s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 11 unt; 5 nHn; 16 RR)
% Number of literals : 41 ( 22 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 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 : 17 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(13,axiom,
( ~ there_exists(A)
| a != A
| b = A ),
file('CAT019-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ there_exists(A)
| a = A
| b != A ),
file('CAT019-3.p',unknown),
[] ).
cnf(15,axiom,
a != b,
file('CAT019-3.p',unknown),
[] ).
cnf(16,plain,
b != a,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(18,axiom,
A = A,
file('CAT019-3.p',unknown),
[] ).
cnf(25,axiom,
compose(codomain(A),A) = A,
file('CAT019-3.p',unknown),
[] ).
cnf(26,axiom,
( there_exists(f1(A,B))
| A = B ),
file('CAT019-3.p',unknown),
[] ).
cnf(27,axiom,
( A = f1(A,B)
| B = f1(A,B)
| A = B ),
file('CAT019-3.p',unknown),
[] ).
cnf(28,plain,
( f1(A,B) = A
| f1(A,B) = B
| A = B ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[27])])]),
[iquote('copy,27,flip.1,flip.2')] ).
cnf(100,plain,
( A = B
| there_exists(f1(B,A)) ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[26,25]),25]),
[iquote('para_from,26.2.1,24.1.1,demod,25')] ).
cnf(102,plain,
( A != a
| there_exists(f1(b,A)) ),
inference(para_from,[status(thm),theory(equality)],[26,16]),
[iquote('para_from,26.2.1,16.1.1')] ).
cnf(271,plain,
there_exists(f1(b,a)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[102,25]),25]),
[iquote('hyper,102,24,demod,25')] ).
cnf(276,plain,
( A != a
| there_exists(f1(B,A))
| ~ there_exists(B)
| a != B ),
inference(para_into,[status(thm),theory(equality)],[102,13]),
[iquote('para_into,102.2.1.1,13.3.1')] ).
cnf(283,plain,
( there_exists(f1(a,a))
| ~ there_exists(a) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[276]),18]),
[iquote('factor,276.1.4,unit_del,18')] ).
cnf(310,plain,
( there_exists(a)
| f1(b,a) = b ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[271,28]),16]),
[iquote('para_into,271.1.1,28.2.1,unit_del,16')] ).
cnf(419,plain,
( there_exists(f1(A,a))
| ~ there_exists(a) ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[283,100])]),
[iquote('para_into,283.1.1.1,100.1.1,factor_simp')] ).
cnf(626,plain,
( there_exists(f1(A,a))
| ~ there_exists(A) ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[419,100])]),
[iquote('para_into,419.2.1,100.1.1,factor_simp')] ).
cnf(665,plain,
there_exists(f1(f1(b,a),a)),
inference(hyper,[status(thm)],[626,271]),
[iquote('hyper,626,271')] ).
cnf(701,plain,
there_exists(f1(f1(f1(b,a),a),a)),
inference(hyper,[status(thm)],[665,626]),
[iquote('hyper,665,626')] ).
cnf(1474,plain,
f1(b,a) = b,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[310,13,18]),16]),
[iquote('hyper,310,13,18,unit_del,16')] ).
cnf(1504,plain,
there_exists(b),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[701]),1474,1474,1474]),
[iquote('back_demod,701,demod,1474,1474,1474')] ).
cnf(1583,plain,
b = a,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1504,14,18])]),
[iquote('hyper,1504,14,18,flip.1')] ).
cnf(1585,plain,
$false,
inference(binary,[status(thm)],[1583,16]),
[iquote('binary,1583.1,16.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : CAT019-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n022.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 02:00:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.92 ----- Otter 3.3f, August 2004 -----
% 1.70/1.92 The process was started by sandbox on n022.cluster.edu,
% 1.70/1.92 Wed Jul 27 02:00:35 2022
% 1.70/1.92 The command was "./otter". The process ID is 17645.
% 1.70/1.92
% 1.70/1.92 set(prolog_style_variables).
% 1.70/1.92 set(auto).
% 1.70/1.92 dependent: set(auto1).
% 1.70/1.92 dependent: set(process_input).
% 1.70/1.92 dependent: clear(print_kept).
% 1.70/1.92 dependent: clear(print_new_demod).
% 1.70/1.92 dependent: clear(print_back_demod).
% 1.70/1.92 dependent: clear(print_back_sub).
% 1.70/1.92 dependent: set(control_memory).
% 1.70/1.92 dependent: assign(max_mem, 12000).
% 1.70/1.92 dependent: assign(pick_given_ratio, 4).
% 1.70/1.92 dependent: assign(stats_level, 1).
% 1.70/1.92 dependent: assign(max_seconds, 10800).
% 1.70/1.92 clear(print_given).
% 1.70/1.92
% 1.70/1.92 list(usable).
% 1.70/1.92 0 [] A=A.
% 1.70/1.92 0 [] -e_quivalent(X,Y)|there_exists(X).
% 1.70/1.92 0 [] -e_quivalent(X,Y)|X=Y.
% 1.70/1.92 0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 1.70/1.92 0 [] -there_exists(domain(X))|there_exists(X).
% 1.70/1.92 0 [] -there_exists(codomain(X))|there_exists(X).
% 1.70/1.92 0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 1.70/1.92 0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 1.70/1.92 0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 1.70/1.92 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 1.70/1.92 0 [] compose(X,domain(X))=X.
% 1.70/1.92 0 [] compose(codomain(X),X)=X.
% 1.70/1.92 0 [] -e_quivalent(X,Y)|there_exists(Y).
% 1.70/1.92 0 [] -there_exists(X)| -there_exists(Y)|X!=Y|e_quivalent(X,Y).
% 1.70/1.92 0 [] -there_exists(compose(X,Y))|there_exists(codomain(X)).
% 1.70/1.92 0 [] there_exists(f1(X,Y))|X=Y.
% 1.70/1.92 0 [] X=f1(X,Y)|Y=f1(X,Y)|X=Y.
% 1.70/1.92 0 [] X!=f1(X,Y)|Y!=f1(X,Y)|X=Y.
% 1.70/1.92 0 [] -there_exists(Z)|a!=Z|b=Z.
% 1.70/1.92 0 [] -there_exists(Z)|a=Z|b!=Z.
% 1.70/1.92 0 [] a!=b.
% 1.70/1.92 end_of_list.
% 1.70/1.92
% 1.70/1.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.70/1.92
% 1.70/1.92 This ia a non-Horn set with equality. The strategy will be
% 1.70/1.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.92 deletion, with positive clauses in sos and nonpositive
% 1.70/1.92 clauses in usable.
% 1.70/1.92
% 1.70/1.92 dependent: set(knuth_bendix).
% 1.70/1.92 dependent: set(anl_eq).
% 1.70/1.92 dependent: set(para_from).
% 1.70/1.92 dependent: set(para_into).
% 1.70/1.92 dependent: clear(para_from_right).
% 1.70/1.92 dependent: clear(para_into_right).
% 1.70/1.92 dependent: set(para_from_vars).
% 1.70/1.92 dependent: set(eq_units_both_ways).
% 1.70/1.92 dependent: set(dynamic_demod_all).
% 1.70/1.92 dependent: set(dynamic_demod).
% 1.70/1.92 dependent: set(order_eq).
% 1.70/1.92 dependent: set(back_demod).
% 1.70/1.92 dependent: set(lrpo).
% 1.70/1.92 dependent: set(hyper_res).
% 1.70/1.92 dependent: set(unit_deletion).
% 1.70/1.92 dependent: set(factor).
% 1.70/1.92
% 1.70/1.92 ------------> process usable:
% 1.70/1.92 ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 1.70/1.92 ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 1.70/1.92 ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 1.70/1.92 ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 1.70/1.92 ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 1.70/1.92 ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 1.70/1.92 ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 1.70/1.92 ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 1.70/1.92 ** KEPT (pick-wt=5): 9 [] -e_quivalent(A,B)|there_exists(B).
% 1.70/1.92 Following clause subsumed by 3 during input processing: 0 [] -there_exists(A)| -there_exists(B)|A!=B|e_quivalent(A,B).
% 1.70/1.92 ** KEPT (pick-wt=7): 10 [] -there_exists(compose(A,B))|there_exists(codomain(A)).
% 1.70/1.92 ** KEPT (pick-wt=13): 12 [copy,11,flip.1,flip.2] f1(A,B)!=A|f1(A,B)!=B|A=B.
% 1.70/1.92 ** KEPT (pick-wt=8): 13 [] -there_exists(A)|a!=A|b=A.
% 1.70/1.92 ** KEPT (pick-wt=8): 14 [] -there_exists(A)|a=A|b!=A.
% 1.70/1.92 ** KEPT (pick-wt=3): 16 [copy,15,flip.1] b!=a.
% 1.70/1.92
% 1.70/1.92 ------------> process sos:
% 1.70/1.92 ** KEPT (pick-wt=3): 18 [] A=A.
% 1.70/1.92 ** KEPT (pick-wt=11): 20 [copy,19,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.70/1.92 ---> New Demodulator: 21 [new_demod,20] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.70/1.92 ** KEPT (pick-wt=6): 22 [] compose(A,domain(A))=A.
% 1.70/1.92 ---> New Demodulator: 23 [new_demod,22] compose(A,domain(A))=A.
% 1.70/1.92 ** KEPT (pick-wt=6): 24 [] compose(codomain(A),A)=A.
% 1.70/1.92 ---> New Demodulator: 25 [new_demod,24] compose(codomain(A),A)=A.
% 1.70/1.92 ** KEPT (pick-wt=7): 26 [] there_exists(f1(A,B))|A=B.
% 1.70/1.92 ** KEPT (pick-wt=13): 28 [copy,27,flip.1,flip.2] f1(A,B)=A|f1(A,B)=B|A=B.
% 1.70/1.92 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 1.70/1.92 18 back subsumes 17.
% 1.82/2.08 >>>> Starting back demodulation with 21.
% 1.82/2.08 >>>> Starting back demodulation with 23.
% 1.82/2.08 >>>> Starting back demodulation with 25.
% 1.82/2.08
% 1.82/2.08 ======= end of input processing =======
% 1.82/2.08
% 1.82/2.08 =========== start of search ===========
% 1.82/2.08
% 1.82/2.08
% 1.82/2.08 Resetting weight limit to 8.
% 1.82/2.08
% 1.82/2.08
% 1.82/2.08 Resetting weight limit to 8.
% 1.82/2.08
% 1.82/2.08 sos_size=1317
% 1.82/2.08
% 1.82/2.08 -------- PROOF --------
% 1.82/2.08
% 1.82/2.08 ----> UNIT CONFLICT at 0.15 sec ----> 1585 [binary,1583.1,16.1] $F.
% 1.82/2.08
% 1.82/2.08 Length of proof is 15. Level of proof is 10.
% 1.82/2.08
% 1.82/2.08 ---------------- PROOF ----------------
% 1.82/2.08 % SZS status Unsatisfiable
% 1.82/2.08 % SZS output start Refutation
% See solution above
% 1.82/2.08 ------------ end of proof -------------
% 1.82/2.08
% 1.82/2.08
% 1.82/2.08 Search stopped by max_proofs option.
% 1.82/2.08
% 1.82/2.08
% 1.82/2.08 Search stopped by max_proofs option.
% 1.82/2.08
% 1.82/2.08 ============ end of search ============
% 1.82/2.08
% 1.82/2.08 -------------- statistics -------------
% 1.82/2.08 clauses given 57
% 1.82/2.08 clauses generated 2991
% 1.82/2.08 clauses kept 1551
% 1.82/2.08 clauses forward subsumed 1474
% 1.82/2.08 clauses back subsumed 45
% 1.82/2.08 Kbytes malloced 4882
% 1.82/2.08
% 1.82/2.08 ----------- times (seconds) -----------
% 1.82/2.08 user CPU time 0.15 (0 hr, 0 min, 0 sec)
% 1.82/2.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.08 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/2.08
% 1.82/2.08 That finishes the proof of the theorem.
% 1.82/2.08
% 1.82/2.08 Process 17645 finished Wed Jul 27 02:00:37 2022
% 1.82/2.08 Otter interrupted
% 1.82/2.08 PROOF FOUND
%------------------------------------------------------------------------------