TSTP Solution File: CAT001-4 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT001-4 : 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 12:47:44 EDT 2022
% Result : Unsatisfiable 2.12s 2.34s
% Output : Refutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 16 ( 15 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
( compose(compose(a,b),A) != B
| compose(compose(a,b),C) != B
| A = C ),
file('CAT001-4.p',unknown),
[] ).
cnf(10,axiom,
h != g,
file('CAT001-4.p',unknown),
[] ).
cnf(11,axiom,
A = A,
file('CAT001-4.p',unknown),
[] ).
cnf(12,axiom,
compose(A,compose(B,C)) = compose(compose(A,B),C),
file('CAT001-4.p',unknown),
[] ).
cnf(14,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.1')] ).
cnf(21,axiom,
compose(b,h) = compose(b,g),
file('CAT001-4.p',unknown),
[] ).
cnf(23,plain,
( compose(a,compose(b,A)) != B
| compose(a,compose(b,C)) != B
| A = C ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[9]),14,14]),
[iquote('back_demod,9,demod,14,14')] ).
cnf(136,plain,
( compose(a,compose(b,g)) != A
| compose(a,compose(b,B)) != A
| h = B ),
inference(para_into,[status(thm),theory(equality)],[23,21]),
[iquote('para_into,23.1.1.2,21.1.1')] ).
cnf(1404,plain,
h = g,
inference(hyper,[status(thm)],[136,11,11]),
[iquote('hyper,136,11,11')] ).
cnf(1406,plain,
$false,
inference(binary,[status(thm)],[1404,10]),
[iquote('binary,1404.1,10.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : CAT001-4 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 01:50:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.12/2.34 ----- Otter 3.3f, August 2004 -----
% 2.12/2.34 The process was started by sandbox2 on n011.cluster.edu,
% 2.12/2.34 Wed Jul 27 01:50:40 2022
% 2.12/2.34 The command was "./otter". The process ID is 10110.
% 2.12/2.34
% 2.12/2.34 set(prolog_style_variables).
% 2.12/2.34 set(auto).
% 2.12/2.34 dependent: set(auto1).
% 2.12/2.34 dependent: set(process_input).
% 2.12/2.34 dependent: clear(print_kept).
% 2.12/2.34 dependent: clear(print_new_demod).
% 2.12/2.34 dependent: clear(print_back_demod).
% 2.12/2.34 dependent: clear(print_back_sub).
% 2.12/2.34 dependent: set(control_memory).
% 2.12/2.34 dependent: assign(max_mem, 12000).
% 2.12/2.34 dependent: assign(pick_given_ratio, 4).
% 2.12/2.34 dependent: assign(stats_level, 1).
% 2.12/2.34 dependent: assign(max_seconds, 10800).
% 2.12/2.34 clear(print_given).
% 2.12/2.34
% 2.12/2.34 list(usable).
% 2.12/2.34 0 [] A=A.
% 2.12/2.34 0 [] -e_quivalent(X,Y)|there_exists(X).
% 2.12/2.34 0 [] -e_quivalent(X,Y)|X=Y.
% 2.12/2.34 0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 2.12/2.34 0 [] -there_exists(domain(X))|there_exists(X).
% 2.12/2.34 0 [] -there_exists(codomain(X))|there_exists(X).
% 2.12/2.34 0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 2.12/2.34 0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 2.12/2.34 0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 2.12/2.34 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 2.12/2.34 0 [] compose(X,domain(X))=X.
% 2.12/2.34 0 [] compose(codomain(X),X)=X.
% 2.12/2.34 0 [] there_exists(compose(a,b)).
% 2.12/2.34 0 [] compose(compose(a,b),X)!=Y|compose(compose(a,b),Z)!=Y|X=Z.
% 2.12/2.34 0 [] there_exists(compose(b,h)).
% 2.12/2.34 0 [] compose(b,h)=compose(b,g).
% 2.12/2.34 0 [] h!=g.
% 2.12/2.34 end_of_list.
% 2.12/2.34
% 2.12/2.34 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.12/2.34
% 2.12/2.34 This is a Horn set with equality. The strategy will be
% 2.12/2.34 Knuth-Bendix and hyper_res, with positive clauses in
% 2.12/2.34 sos and nonpositive clauses in usable.
% 2.12/2.34
% 2.12/2.34 dependent: set(knuth_bendix).
% 2.12/2.34 dependent: set(anl_eq).
% 2.12/2.34 dependent: set(para_from).
% 2.12/2.34 dependent: set(para_into).
% 2.12/2.34 dependent: clear(para_from_right).
% 2.12/2.34 dependent: clear(para_into_right).
% 2.12/2.34 dependent: set(para_from_vars).
% 2.12/2.34 dependent: set(eq_units_both_ways).
% 2.12/2.34 dependent: set(dynamic_demod_all).
% 2.12/2.34 dependent: set(dynamic_demod).
% 2.12/2.34 dependent: set(order_eq).
% 2.12/2.34 dependent: set(back_demod).
% 2.12/2.34 dependent: set(lrpo).
% 2.12/2.34 dependent: set(hyper_res).
% 2.12/2.34 dependent: clear(order_hyper).
% 2.12/2.34
% 2.12/2.34 ------------> process usable:
% 2.12/2.34 ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 2.12/2.34 ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 2.12/2.34 ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 2.12/2.34 ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 2.12/2.34 ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 2.12/2.34 ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 2.12/2.34 ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 2.12/2.34 ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 2.12/2.34 ** KEPT (pick-wt=17): 9 [] compose(compose(a,b),A)!=B|compose(compose(a,b),C)!=B|A=C.
% 2.12/2.34 ** KEPT (pick-wt=3): 10 [] h!=g.
% 2.12/2.34
% 2.12/2.34 ------------> process sos:
% 2.12/2.34 ** KEPT (pick-wt=3): 11 [] A=A.
% 2.12/2.34 ** KEPT (pick-wt=11): 13 [copy,12,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 2.12/2.34 ---> New Demodulator: 14 [new_demod,13] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 2.12/2.34 ** KEPT (pick-wt=6): 15 [] compose(A,domain(A))=A.
% 2.12/2.34 ---> New Demodulator: 16 [new_demod,15] compose(A,domain(A))=A.
% 2.12/2.34 ** KEPT (pick-wt=6): 17 [] compose(codomain(A),A)=A.
% 2.12/2.34 ---> New Demodulator: 18 [new_demod,17] compose(codomain(A),A)=A.
% 2.12/2.34 ** KEPT (pick-wt=4): 19 [] there_exists(compose(a,b)).
% 2.12/2.34 ** KEPT (pick-wt=4): 20 [] there_exists(compose(b,h)).
% 2.12/2.34 ** KEPT (pick-wt=7): 21 [] compose(b,h)=compose(b,g).
% 2.12/2.34 ---> New Demodulator: 22 [new_demod,21] compose(b,h)=compose(b,g).
% 2.12/2.34 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 2.12/2.34 >>>> Starting back demodulation with 14.
% 2.12/2.34 >> back demodulating 9 with 14.
% 2.12/2.34 >>>> Starting back demodulation with 16.
% 2.12/2.34 >>>> Starting back demodulation with 18.
% 2.12/2.34 >>>> Starting back demodulation with 22.
% 2.12/2.34 >> back demodulating 20 with 22.
% 2.12/2.34
% 2.12/2.34 ======= end of input processing =======
% 2.12/2.34
% 2.12/2.34 =========== start of search ===========
% 2.12/2.34
% 2.12/2.34
% 2.12/2.34 Resetting weight limit to 7.
% 2.12/2.34
% 2.12/2.34
% 2.12/2.34 Resetting weight limit to 7.
% 2.12/2.34
% 2.12/2.34 sos_size=1174
% 2.12/2.34
% 2.12/2.34 -------- PROOF --------
% 2.12/2.34
% 2.12/2.34 ----> UNIT CONFLICT at 0.21 sec ----> 1406 [binary,1404.1,10.1] $F.
% 2.12/2.34
% 2.12/2.34 Length of proof is 4. Level of proof is 4.
% 2.12/2.34
% 2.12/2.34 ---------------- PROOF ----------------
% 2.12/2.34 % SZS status Unsatisfiable
% 2.12/2.34 % SZS output start Refutation
% See solution above
% 2.12/2.34 ------------ end of proof -------------
% 2.12/2.34
% 2.12/2.34
% 2.12/2.34 Search stopped by max_proofs option.
% 2.12/2.34
% 2.12/2.34
% 2.12/2.34 Search stopped by max_proofs option.
% 2.12/2.34
% 2.12/2.34 ============ end of search ============
% 2.12/2.34
% 2.12/2.34 -------------- statistics -------------
% 2.12/2.34 clauses given 291
% 2.12/2.34 clauses generated 12189
% 2.12/2.34 clauses kept 1371
% 2.12/2.34 clauses forward subsumed 1362
% 2.12/2.34 clauses back subsumed 9
% 2.12/2.34 Kbytes malloced 4882
% 2.12/2.34
% 2.12/2.34 ----------- times (seconds) -----------
% 2.12/2.34 user CPU time 0.21 (0 hr, 0 min, 0 sec)
% 2.12/2.34 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.12/2.34 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.12/2.34
% 2.12/2.34 That finishes the proof of the theorem.
% 2.12/2.34
% 2.12/2.34 Process 10110 finished Wed Jul 27 01:50:42 2022
% 2.12/2.34 Otter interrupted
% 2.12/2.34 PROOF FOUND
%------------------------------------------------------------------------------