TSTP Solution File: CAT004-3 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT004-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 12:47:45 EDT 2022
% Result : Unsatisfiable 2.66s 2.84s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 21 ( 20 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(13,axiom,
( compose(A,a) != B
| compose(C,a) != B
| A = C ),
file('CAT004-3.p',unknown),
[] ).
cnf(14,axiom,
( compose(A,b) != B
| compose(C,b) != B
| A = C ),
file('CAT004-3.p',unknown),
[] ).
cnf(15,axiom,
h != g,
file('CAT004-3.p',unknown),
[] ).
cnf(20,axiom,
compose(A,compose(B,C)) = compose(compose(A,B),C),
file('CAT004-3.p',unknown),
[] ).
cnf(21,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
[iquote('copy,20,flip.1')] ).
cnf(24,axiom,
compose(A,domain(A)) = A,
file('CAT004-3.p',unknown),
[] ).
cnf(32,axiom,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
file('CAT004-3.p',unknown),
[] ).
cnf(78,plain,
( compose(A,b) != B
| compose(C,compose(D,b)) != B
| A = compose(C,D) ),
inference(para_from,[status(thm),theory(equality)],[21,14]),
[iquote('para_from,21.1.1,14.2.1')] ).
cnf(81,plain,
( compose(A,compose(B,a)) != C
| compose(D,a) != C
| compose(A,B) = D ),
inference(para_from,[status(thm),theory(equality)],[21,13]),
[iquote('para_from,21.1.1,13.1.1')] ).
cnf(119,plain,
compose(A,compose(domain(A),B)) = compose(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[24,21])]),
[iquote('para_from,23.1.1,21.1.1.1,flip.1')] ).
cnf(2212,plain,
compose(h,a) = compose(g,a),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[78,21,32])]),
[iquote('hyper,78,21,32,flip.1')] ).
cnf(2246,plain,
h = g,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2212,81,119]),24])]),
[iquote('hyper,2212,81,119,demod,24,flip.1')] ).
cnf(2248,plain,
$false,
inference(binary,[status(thm)],[2246,15]),
[iquote('binary,2246.1,15.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT004-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 02:08:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.71/1.94 ----- Otter 3.3f, August 2004 -----
% 1.71/1.94 The process was started by sandbox2 on n027.cluster.edu,
% 1.71/1.94 Wed Jul 27 02:08:06 2022
% 1.71/1.94 The command was "./otter". The process ID is 10698.
% 1.71/1.94
% 1.71/1.94 set(prolog_style_variables).
% 1.71/1.94 set(auto).
% 1.71/1.94 dependent: set(auto1).
% 1.71/1.94 dependent: set(process_input).
% 1.71/1.94 dependent: clear(print_kept).
% 1.71/1.94 dependent: clear(print_new_demod).
% 1.71/1.94 dependent: clear(print_back_demod).
% 1.71/1.94 dependent: clear(print_back_sub).
% 1.71/1.94 dependent: set(control_memory).
% 1.71/1.94 dependent: assign(max_mem, 12000).
% 1.71/1.94 dependent: assign(pick_given_ratio, 4).
% 1.71/1.94 dependent: assign(stats_level, 1).
% 1.71/1.94 dependent: assign(max_seconds, 10800).
% 1.71/1.94 clear(print_given).
% 1.71/1.94
% 1.71/1.94 list(usable).
% 1.71/1.94 0 [] A=A.
% 1.71/1.94 0 [] -e_quivalent(X,Y)|there_exists(X).
% 1.71/1.94 0 [] -e_quivalent(X,Y)|X=Y.
% 1.71/1.94 0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 1.71/1.94 0 [] -there_exists(domain(X))|there_exists(X).
% 1.71/1.94 0 [] -there_exists(codomain(X))|there_exists(X).
% 1.71/1.94 0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 1.71/1.94 0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 1.71/1.94 0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 1.71/1.94 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 1.71/1.94 0 [] compose(X,domain(X))=X.
% 1.71/1.94 0 [] compose(codomain(X),X)=X.
% 1.71/1.94 0 [] -e_quivalent(X,Y)|there_exists(Y).
% 1.71/1.94 0 [] -there_exists(X)| -there_exists(Y)|X!=Y|e_quivalent(X,Y).
% 1.71/1.94 0 [] -there_exists(compose(X,Y))|there_exists(codomain(X)).
% 1.71/1.94 0 [] there_exists(f1(X,Y))|X=Y.
% 1.71/1.94 0 [] X=f1(X,Y)|Y=f1(X,Y)|X=Y.
% 1.71/1.94 0 [] X!=f1(X,Y)|Y!=f1(X,Y)|X=Y.
% 1.71/1.94 0 [] there_exists(compose(a,b)).
% 1.71/1.94 0 [] compose(X,a)!=Y|compose(Z,a)!=Y|X=Z.
% 1.71/1.94 0 [] compose(X,b)!=Y|compose(Z,b)!=Y|X=Z.
% 1.71/1.94 0 [] there_exists(h).
% 1.71/1.94 0 [] compose(h,compose(a,b))=compose(g,compose(a,b)).
% 1.71/1.94 0 [] h!=g.
% 1.71/1.94 end_of_list.
% 1.71/1.94
% 1.71/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.71/1.94
% 1.71/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.71/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.94 deletion, with positive clauses in sos and nonpositive
% 1.71/1.94 clauses in usable.
% 1.71/1.94
% 1.71/1.94 dependent: set(knuth_bendix).
% 1.71/1.94 dependent: set(anl_eq).
% 1.71/1.94 dependent: set(para_from).
% 1.71/1.94 dependent: set(para_into).
% 1.71/1.94 dependent: clear(para_from_right).
% 1.71/1.94 dependent: clear(para_into_right).
% 1.71/1.94 dependent: set(para_from_vars).
% 1.71/1.94 dependent: set(eq_units_both_ways).
% 1.71/1.94 dependent: set(dynamic_demod_all).
% 1.71/1.94 dependent: set(dynamic_demod).
% 1.71/1.94 dependent: set(order_eq).
% 1.71/1.94 dependent: set(back_demod).
% 1.71/1.94 dependent: set(lrpo).
% 1.71/1.94 dependent: set(hyper_res).
% 1.71/1.94 dependent: set(unit_deletion).
% 1.71/1.94 dependent: set(factor).
% 1.71/1.94
% 1.71/1.94 ------------> process usable:
% 1.71/1.94 ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 1.71/1.94 ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 1.71/1.94 ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 1.71/1.94 ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 1.71/1.94 ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 1.71/1.94 ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 1.71/1.94 ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 1.71/1.94 ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 1.71/1.94 ** KEPT (pick-wt=5): 9 [] -e_quivalent(A,B)|there_exists(B).
% 1.71/1.94 Following clause subsumed by 3 during input processing: 0 [] -there_exists(A)| -there_exists(B)|A!=B|e_quivalent(A,B).
% 1.71/1.94 ** KEPT (pick-wt=7): 10 [] -there_exists(compose(A,B))|there_exists(codomain(A)).
% 1.71/1.94 ** KEPT (pick-wt=13): 12 [copy,11,flip.1,flip.2] f1(A,B)!=A|f1(A,B)!=B|A=B.
% 1.71/1.94 ** KEPT (pick-wt=13): 13 [] compose(A,a)!=B|compose(C,a)!=B|A=C.
% 1.71/1.94 ** KEPT (pick-wt=13): 14 [] compose(A,b)!=B|compose(C,b)!=B|A=C.
% 1.71/1.94 ** KEPT (pick-wt=3): 15 [] h!=g.
% 1.71/1.94
% 1.71/1.94 ------------> process sos:
% 1.71/1.94 ** KEPT (pick-wt=3): 19 [] A=A.
% 1.71/1.94 ** KEPT (pick-wt=11): 21 [copy,20,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.71/1.94 ---> New Demodulator: 22 [new_demod,21] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.71/1.94 ** KEPT (pick-wt=6): 23 [] compose(A,domain(A))=A.
% 1.71/1.94 ---> New Demodulator: 24 [new_demod,23] compose(A,domain(A))=A.
% 1.71/1.94 ** KEPT (pick-wt=6): 25 [] compose(codomain(A),A)=A.
% 1.71/1.94 ---> New Demodulator: 26 [new_demod,25] compose(codomain(A),A)=A.
% 1.71/1.94 ** KEPT (pick-wt=7): 27 [] there_exists(f1(A,B))|A=B.
% 1.71/1.94 ** KEPT (pick-wt=13): 29 [copy,28,flip.1,flip.2] f1(A,B)=A|f1(A,B)=B|A=B.
% 2.66/2.84 ** KEPT (pick-wt=4): 30 [] there_exists(compose(a,b)).
% 2.66/2.84 ** KEPT (pick-wt=2): 31 [] there_exists(h).
% 2.66/2.84 ** KEPT (pick-wt=11): 32 [] compose(h,compose(a,b))=compose(g,compose(a,b)).
% 2.66/2.84 ---> New Demodulator: 33 [new_demod,32] compose(h,compose(a,b))=compose(g,compose(a,b)).
% 2.66/2.84 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] A=A.
% 2.66/2.84 19 back subsumes 18.
% 2.66/2.84 19 back subsumes 17.
% 2.66/2.84 19 back subsumes 16.
% 2.66/2.84 >>>> Starting back demodulation with 22.
% 2.66/2.84 >>>> Starting back demodulation with 24.
% 2.66/2.84 >>>> Starting back demodulation with 26.
% 2.66/2.84 >>>> Starting back demodulation with 33.
% 2.66/2.84
% 2.66/2.84 ======= end of input processing =======
% 2.66/2.84
% 2.66/2.84 =========== start of search ===========
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Resetting weight limit to 7.
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Resetting weight limit to 7.
% 2.66/2.84
% 2.66/2.84 sos_size=1943
% 2.66/2.84
% 2.66/2.84 -------- PROOF --------
% 2.66/2.84
% 2.66/2.84 ----> UNIT CONFLICT at 0.91 sec ----> 2248 [binary,2246.1,15.1] $F.
% 2.66/2.84
% 2.66/2.84 Length of proof is 6. Level of proof is 4.
% 2.66/2.84
% 2.66/2.84 ---------------- PROOF ----------------
% 2.66/2.84 % SZS status Unsatisfiable
% 2.66/2.84 % SZS output start Refutation
% See solution above
% 2.66/2.84 ------------ end of proof -------------
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Search stopped by max_proofs option.
% 2.66/2.84
% 2.66/2.84
% 2.66/2.84 Search stopped by max_proofs option.
% 2.66/2.84
% 2.66/2.84 ============ end of search ============
% 2.66/2.84
% 2.66/2.84 -------------- statistics -------------
% 2.66/2.84 clauses given 443
% 2.66/2.84 clauses generated 37374
% 2.66/2.84 clauses kept 2227
% 2.66/2.84 clauses forward subsumed 2569
% 2.66/2.85 clauses back subsumed 9
% 2.66/2.85 Kbytes malloced 5859
% 2.66/2.85
% 2.66/2.85 ----------- times (seconds) -----------
% 2.66/2.85 user CPU time 0.91 (0 hr, 0 min, 0 sec)
% 2.66/2.85 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.66/2.85 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.66/2.85
% 2.66/2.85 That finishes the proof of the theorem.
% 2.66/2.85
% 2.66/2.85 Process 10698 finished Wed Jul 27 02:08:09 2022
% 2.66/2.85 Otter interrupted
% 2.66/2.85 PROOF FOUND
%------------------------------------------------------------------------------