%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : CAT002-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 2.21s 2.41s
% Output : Refutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 10 unt; 0 nHn; 9 RR)
% Number of literals : 16 ( 15 equ; 6 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 : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(13,axiom,
( compose(a,A) != B
| compose(a,C) != B
| A = C ),
file('CAT002-3.p',unknown),
[] ).
cnf(14,axiom,
( compose(b,A) != B
| compose(b,C) != B
| A = C ),
file('CAT002-3.p',unknown),
[] ).
cnf(15,axiom,
g != h,
file('CAT002-3.p',unknown),
[] ).
cnf(16,plain,
h != g,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(20,axiom,
A = A,
file('CAT002-3.p',unknown),
[] ).
cnf(21,axiom,
compose(A,compose(B,C)) = compose(compose(A,B),C),
file('CAT002-3.p',unknown),
[] ).
cnf(23,plain,
compose(compose(A,B),C) = compose(A,compose(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
[iquote('copy,21,flip.1')] ).
cnf(33,axiom,
compose(compose(a,b),h) = compose(compose(a,b),g),
file('CAT002-3.p',unknown),
[] ).
cnf(34,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[33]),23,23]),
[iquote('copy,33,demod,23,23')] ).
cnf(566,plain,
compose(b,h) = compose(b,g),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[34,13,20])]),
[iquote('hyper,34,13,20,flip.1')] ).
cnf(2156,plain,
h = g,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[566,14,20])]),
[iquote('hyper,566,14,20,flip.1')] ).
cnf(2158,plain,
$false,
inference(binary,[status(thm)],[2156,16]),
[iquote('binary,2156.1,16.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT002-3 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : otter-tptp-script %s
% 0.14/0.33 % Computer : n004.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Jul 27 01:55:36 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.72/1.92 ----- Otter 3.3f, August 2004 -----
% 1.72/1.92 The process was started by sandbox2 on n004.cluster.edu,
% 1.72/1.92 Wed Jul 27 01:55:36 2022
% 1.72/1.92 The command was "./otter". The process ID is 7675.
% 1.72/1.92
% 1.72/1.92 set(prolog_style_variables).
% 1.72/1.92 set(auto).
% 1.72/1.92 dependent: set(auto1).
% 1.72/1.92 dependent: set(process_input).
% 1.72/1.92 dependent: clear(print_kept).
% 1.72/1.92 dependent: clear(print_new_demod).
% 1.72/1.92 dependent: clear(print_back_demod).
% 1.72/1.92 dependent: clear(print_back_sub).
% 1.72/1.92 dependent: set(control_memory).
% 1.72/1.92 dependent: assign(max_mem, 12000).
% 1.72/1.92 dependent: assign(pick_given_ratio, 4).
% 1.72/1.92 dependent: assign(stats_level, 1).
% 1.72/1.92 dependent: assign(max_seconds, 10800).
% 1.72/1.92 clear(print_given).
% 1.72/1.92
% 1.72/1.92 list(usable).
% 1.72/1.92 0 [] A=A.
% 1.72/1.92 0 [] -e_quivalent(X,Y)|there_exists(X).
% 1.72/1.92 0 [] -e_quivalent(X,Y)|X=Y.
% 1.72/1.92 0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 1.72/1.92 0 [] -there_exists(domain(X))|there_exists(X).
% 1.72/1.92 0 [] -there_exists(codomain(X))|there_exists(X).
% 1.72/1.92 0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 1.72/1.92 0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 1.72/1.92 0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 1.72/1.92 0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 1.72/1.92 0 [] compose(X,domain(X))=X.
% 1.72/1.92 0 [] compose(codomain(X),X)=X.
% 1.72/1.92 0 [] -e_quivalent(X,Y)|there_exists(Y).
% 1.72/1.92 0 [] -there_exists(X)| -there_exists(Y)|X!=Y|e_quivalent(X,Y).
% 1.72/1.92 0 [] -there_exists(compose(X,Y))|there_exists(codomain(X)).
% 1.72/1.92 0 [] there_exists(f1(X,Y))|X=Y.
% 1.72/1.92 0 [] X=f1(X,Y)|Y=f1(X,Y)|X=Y.
% 1.72/1.92 0 [] X!=f1(X,Y)|Y!=f1(X,Y)|X=Y.
% 1.72/1.92 0 [] there_exists(compose(a,b)).
% 1.72/1.92 0 [] compose(a,X)!=Y|compose(a,Z)!=Y|X=Z.
% 1.72/1.92 0 [] compose(b,X)!=Y|compose(b,Z)!=Y|X=Z.
% 1.72/1.92 0 [] there_exists(h).
% 1.72/1.92 0 [] compose(compose(a,b),h)=compose(compose(a,b),g).
% 1.72/1.92 0 [] g!=h.
% 1.72/1.92 end_of_list.
% 1.72/1.92
% 1.72/1.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.72/1.92
% 1.72/1.92 This ia a non-Horn set with equality. The strategy will be
% 1.72/1.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.72/1.92 deletion, with positive clauses in sos and nonpositive
% 1.72/1.92 clauses in usable.
% 1.72/1.92
% 1.72/1.92 dependent: set(knuth_bendix).
% 1.72/1.92 dependent: set(anl_eq).
% 1.72/1.92 dependent: set(para_from).
% 1.72/1.92 dependent: set(para_into).
% 1.72/1.92 dependent: clear(para_from_right).
% 1.72/1.92 dependent: clear(para_into_right).
% 1.72/1.92 dependent: set(para_from_vars).
% 1.72/1.92 dependent: set(eq_units_both_ways).
% 1.72/1.92 dependent: set(dynamic_demod_all).
% 1.72/1.92 dependent: set(dynamic_demod).
% 1.72/1.92 dependent: set(order_eq).
% 1.72/1.92 dependent: set(back_demod).
% 1.72/1.92 dependent: set(lrpo).
% 1.72/1.92 dependent: set(hyper_res).
% 1.72/1.92 dependent: set(unit_deletion).
% 1.72/1.92 dependent: set(factor).
% 1.72/1.92
% 1.72/1.92 ------------> process usable:
% 1.72/1.92 ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 1.72/1.92 ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 1.72/1.92 ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 1.72/1.92 ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 1.72/1.92 ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 1.72/1.92 ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 1.72/1.92 ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 1.72/1.92 ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 1.72/1.92 ** KEPT (pick-wt=5): 9 [] -e_quivalent(A,B)|there_exists(B).
% 1.72/1.92 Following clause subsumed by 3 during input processing: 0 [] -there_exists(A)| -there_exists(B)|A!=B|e_quivalent(A,B).
% 1.72/1.92 ** KEPT (pick-wt=7): 10 [] -there_exists(compose(A,B))|there_exists(codomain(A)).
% 1.72/1.92 ** KEPT (pick-wt=13): 12 [copy,11,flip.1,flip.2] f1(A,B)!=A|f1(A,B)!=B|A=B.
% 1.72/1.92 ** KEPT (pick-wt=13): 13 [] compose(a,A)!=B|compose(a,C)!=B|A=C.
% 1.72/1.92 ** KEPT (pick-wt=13): 14 [] compose(b,A)!=B|compose(b,C)!=B|A=C.
% 1.72/1.92 ** KEPT (pick-wt=3): 16 [copy,15,flip.1] h!=g.
% 1.72/1.92
% 1.72/1.92 ------------> process sos:
% 1.72/1.92 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.72/1.92 ** KEPT (pick-wt=11): 22 [copy,21,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.72/1.92 ---> New Demodulator: 23 [new_demod,22] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.72/1.92 ** KEPT (pick-wt=6): 24 [] compose(A,domain(A))=A.
% 1.72/1.92 ---> New Demodulator: 25 [new_demod,24] compose(A,domain(A))=A.
% 1.72/1.92 ** KEPT (pick-wt=6): 26 [] compose(codomain(A),A)=A.
% 1.72/1.92 ---> New Demodulator: 27 [new_demod,26] compose(codomain(A),A)=A.
% 1.72/1.92 ** KEPT (pick-wt=7): 28 [] there_exists(f1(A,B))|A=B.
% 1.72/1.92 ** KEPT (pick-wt=13): 30 [copy,29,flip.1,flip.2] f1(A,B)=A|f1(A,B)=B|A=B.
% 2.21/2.41 ** KEPT (pick-wt=4): 31 [] there_exists(compose(a,b)).
% 2.21/2.41 ** KEPT (pick-wt=2): 32 [] there_exists(h).
% 2.21/2.41 ** KEPT (pick-wt=11): 34 [copy,33,demod,23,23] compose(a,compose(b,h))=compose(a,compose(b,g)).
% 2.21/2.41 ---> New Demodulator: 35 [new_demod,34] compose(a,compose(b,h))=compose(a,compose(b,g)).
% 2.21/2.41 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 2.21/2.41 20 back subsumes 19.
% 2.21/2.41 20 back subsumes 18.
% 2.21/2.41 20 back subsumes 17.
% 2.21/2.41 >>>> Starting back demodulation with 23.
% 2.21/2.41 >>>> Starting back demodulation with 25.
% 2.21/2.41 >>>> Starting back demodulation with 27.
% 2.21/2.41 >>>> Starting back demodulation with 35.
% 2.21/2.41
% 2.21/2.41 ======= end of input processing =======
% 2.21/2.41
% 2.21/2.41 =========== start of search ===========
% 2.21/2.41
% 2.21/2.41
% 2.21/2.41 Resetting weight limit to 7.
% 2.21/2.41
% 2.21/2.41
% 2.21/2.41 Resetting weight limit to 7.
% 2.21/2.41
% 2.21/2.41 sos_size=1878
% 2.21/2.41
% 2.21/2.41 -------- PROOF --------
% 2.21/2.41
% 2.21/2.41 ----> UNIT CONFLICT at 0.48 sec ----> 2158 [binary,2156.1,16.1] $F.
% 2.21/2.41
% 2.21/2.41 Length of proof is 5. Level of proof is 4.
% 2.21/2.41
% 2.21/2.41 ---------------- PROOF ----------------
% 2.21/2.41 % SZS status Unsatisfiable
% 2.21/2.41 % SZS output start Refutation
% See solution above
% 2.21/2.41 ------------ end of proof -------------
% 2.21/2.41
% 2.21/2.41
% 2.21/2.41 Search stopped by max_proofs option.
% 2.21/2.41
% 2.21/2.41
% 2.21/2.41 Search stopped by max_proofs option.
% 2.21/2.41
% 2.21/2.41 ============ end of search ============
% 2.21/2.41
% 2.21/2.41 -------------- statistics -------------
% 2.21/2.41 clauses given 213
% 2.21/2.41 clauses generated 10283
% 2.21/2.41 clauses kept 2139
% 2.21/2.41 clauses forward subsumed 1941
% 2.21/2.41 clauses back subsumed 7
% 2.21/2.41 Kbytes malloced 4882
% 2.21/2.41
% 2.21/2.41 ----------- times (seconds) -----------
% 2.21/2.41 user CPU time 0.48 (0 hr, 0 min, 0 sec)
% 2.21/2.41 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.21/2.41 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.21/2.41
% 2.21/2.41 That finishes the proof of the theorem.
% 2.21/2.41
% 2.21/2.41 Process 7675 finished Wed Jul 27 01:55:38 2022
% 2.21/2.41 Otter interrupted
% 2.21/2.41 PROOF FOUND
%------------------------------------------------------------------------------