TSTP Solution File: HEN010-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN010-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 12:58:00 EDT 2022
% Result : Unsatisfiable 1.73s 1.92s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of clauses : 27 ( 20 unt; 0 nHn; 21 RR)
% Number of literals : 47 ( 7 equ; 22 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 38 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ quotient(A,B,zero)
| less_e_qual(A,B) ),
file('HEN010-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ quotient(A,B,C)
| ~ quotient(B,D,E)
| ~ quotient(A,D,F)
| ~ quotient(F,E,G)
| ~ quotient(C,D,H)
| less_e_qual(G,H) ),
file('HEN010-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN010-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ quotient(A,B,C)
| ~ less_e_qual(C,D)
| ~ quotient(A,D,E)
| less_e_qual(E,B) ),
file('HEN010-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ less_e_qual(A,B)
| ~ quotient(C,B,D)
| ~ quotient(C,A,E)
| less_e_qual(D,E) ),
file('HEN010-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ less_e_qual(A,B)
| ~ quotient(A,C,D)
| ~ quotient(B,C,E)
| less_e_qual(D,E) ),
file('HEN010-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ quotient(identity,A,B)
| ~ quotient(identity,B,C)
| ~ quotient(identity,C,D)
| B = D ),
file('HEN010-2.p',unknown),
[] ).
cnf(12,axiom,
idQa != idQa_Q__idQ_idQa,
file('HEN010-2.p',unknown),
[] ).
cnf(13,plain,
idQa_Q__idQ_idQa != idQa,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.1')] ).
cnf(16,axiom,
less_e_qual(A,identity),
file('HEN010-2.p',unknown),
[] ).
cnf(17,axiom,
quotient(A,B,divide(A,B)),
file('HEN010-2.p',unknown),
[] ).
cnf(20,axiom,
quotient(A,A,zero),
file('HEN010-2.p',unknown),
[] ).
cnf(21,axiom,
quotient(A,zero,A),
file('HEN010-2.p',unknown),
[] ).
cnf(22,axiom,
quotient(identity,a,idQa),
file('HEN010-2.p',unknown),
[] ).
cnf(23,axiom,
quotient(identity,idQa,idQ_idQa),
file('HEN010-2.p',unknown),
[] ).
cnf(24,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('HEN010-2.p',unknown),
[] ).
cnf(72,plain,
less_e_qual(A,A),
inference(hyper,[status(thm)],[20,2]),
[iquote('hyper,20,2')] ).
cnf(89,plain,
less_e_qual(divide(A,a),idQa),
inference(hyper,[status(thm)],[22,10,16,17]),
[iquote('hyper,22,10,16,17')] ).
cnf(94,plain,
less_e_qual(idQa,divide(idQa,a)),
inference(hyper,[status(thm)],[22,4,22,20,21,17]),
[iquote('hyper,22,4,22,20,21,17')] ).
cnf(109,plain,
divide(identity,idQ_idQa) = idQa,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[23,11,22,17])]),
[iquote('hyper,23,11,22,17,flip.1')] ).
cnf(113,plain,
less_e_qual(idQ_idQa,a),
inference(hyper,[status(thm)],[23,8,22,72]),
[iquote('hyper,23,8,22,72')] ).
cnf(142,plain,
less_e_qual(idQa_Q__idQ_idQa,idQa),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[24,10,16,17]),109]),
[iquote('hyper,24,10,16,17,demod,109')] ).
cnf(143,plain,
less_e_qual(divide(idQa,a),idQa_Q__idQ_idQa),
inference(hyper,[status(thm)],[24,9,113,17]),
[iquote('hyper,24,9,113,17')] ).
cnf(286,plain,
divide(idQa,a) = idQa,
inference(hyper,[status(thm)],[94,5,89]),
[iquote('hyper,94,5,89')] ).
cnf(288,plain,
less_e_qual(idQa,idQa_Q__idQ_idQa),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[143]),286]),
[iquote('back_demod,143,demod,286')] ).
cnf(295,plain,
idQa_Q__idQ_idQa = idQa,
inference(hyper,[status(thm)],[288,5,142]),
[iquote('hyper,288,5,142')] ).
cnf(297,plain,
$false,
inference(binary,[status(thm)],[295,13]),
[iquote('binary,295.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : HEN010-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 08:21:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.89 ----- Otter 3.3f, August 2004 -----
% 1.69/1.89 The process was started by sandbox2 on n017.cluster.edu,
% 1.69/1.89 Wed Jul 27 08:21:48 2022
% 1.69/1.89 The command was "./otter". The process ID is 21589.
% 1.69/1.89
% 1.69/1.89 set(prolog_style_variables).
% 1.69/1.89 set(auto).
% 1.69/1.89 dependent: set(auto1).
% 1.69/1.89 dependent: set(process_input).
% 1.69/1.89 dependent: clear(print_kept).
% 1.69/1.89 dependent: clear(print_new_demod).
% 1.69/1.89 dependent: clear(print_back_demod).
% 1.69/1.89 dependent: clear(print_back_sub).
% 1.69/1.89 dependent: set(control_memory).
% 1.69/1.89 dependent: assign(max_mem, 12000).
% 1.69/1.89 dependent: assign(pick_given_ratio, 4).
% 1.69/1.89 dependent: assign(stats_level, 1).
% 1.69/1.89 dependent: assign(max_seconds, 10800).
% 1.69/1.89 clear(print_given).
% 1.69/1.89
% 1.69/1.89 list(usable).
% 1.69/1.89 0 [] A=A.
% 1.69/1.89 0 [] -less_e_qual(X,Y)|quotient(X,Y,zero).
% 1.69/1.89 0 [] -quotient(X,Y,zero)|less_e_qual(X,Y).
% 1.69/1.89 0 [] -quotient(X,Y,Z)|less_e_qual(Z,X).
% 1.69/1.89 0 [] -quotient(X,Y,V1)| -quotient(Y,Z,V2)| -quotient(X,Z,V3)| -quotient(V3,V2,V4)| -quotient(V1,Z,V5)|less_e_qual(V4,V5).
% 1.69/1.89 0 [] less_e_qual(zero,X).
% 1.69/1.89 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.69/1.89 0 [] less_e_qual(X,identity).
% 1.69/1.89 0 [] quotient(X,Y,divide(X,Y)).
% 1.69/1.89 0 [] -quotient(X,Y,Z)| -quotient(X,Y,W)|Z=W.
% 1.69/1.89 0 [] quotient(X,identity,zero).
% 1.69/1.89 0 [] quotient(zero,X,zero).
% 1.69/1.89 0 [] quotient(X,X,zero).
% 1.69/1.89 0 [] quotient(X,zero,X).
% 1.69/1.89 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,Z)|less_e_qual(X,Z).
% 1.69/1.89 0 [] -quotient(X,Y,W1)| -less_e_qual(W1,Z)| -quotient(X,Z,W2)|less_e_qual(W2,Y).
% 1.69/1.89 0 [] -less_e_qual(X,Y)| -quotient(Z,Y,W1)| -quotient(Z,X,W2)|less_e_qual(W1,W2).
% 1.69/1.89 0 [] -less_e_qual(X,Y)| -quotient(X,Z,W1)| -quotient(Y,Z,W2)|less_e_qual(W1,W2).
% 1.69/1.89 0 [] -quotient(identity,X,Y1)| -quotient(identity,Y1,Y2)| -quotient(identity,Y2,Y3)|Y1=Y3.
% 1.69/1.89 0 [] quotient(identity,a,idQa).
% 1.69/1.89 0 [] quotient(identity,idQa,idQ_idQa).
% 1.69/1.89 0 [] quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa).
% 1.69/1.89 0 [] idQa!=idQa_Q__idQ_idQa.
% 1.69/1.89 end_of_list.
% 1.69/1.89
% 1.69/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 1.69/1.89
% 1.69/1.89 This is a Horn set with equality. The strategy will be
% 1.69/1.89 Knuth-Bendix and hyper_res, with positive clauses in
% 1.69/1.89 sos and nonpositive clauses in usable.
% 1.69/1.89
% 1.69/1.89 dependent: set(knuth_bendix).
% 1.69/1.89 dependent: set(anl_eq).
% 1.69/1.89 dependent: set(para_from).
% 1.69/1.89 dependent: set(para_into).
% 1.69/1.89 dependent: clear(para_from_right).
% 1.69/1.89 dependent: clear(para_into_right).
% 1.69/1.89 dependent: set(para_from_vars).
% 1.69/1.89 dependent: set(eq_units_both_ways).
% 1.69/1.89 dependent: set(dynamic_demod_all).
% 1.69/1.89 dependent: set(dynamic_demod).
% 1.69/1.89 dependent: set(order_eq).
% 1.69/1.89 dependent: set(back_demod).
% 1.69/1.89 dependent: set(lrpo).
% 1.69/1.89 dependent: set(hyper_res).
% 1.69/1.89 dependent: clear(order_hyper).
% 1.69/1.89
% 1.69/1.89 ------------> process usable:
% 1.69/1.89 ** KEPT (pick-wt=7): 1 [] -less_e_qual(A,B)|quotient(A,B,zero).
% 1.69/1.89 ** KEPT (pick-wt=7): 2 [] -quotient(A,B,zero)|less_e_qual(A,B).
% 1.69/1.89 ** KEPT (pick-wt=7): 3 [] -quotient(A,B,C)|less_e_qual(C,A).
% 1.69/1.89 ** KEPT (pick-wt=23): 4 [] -quotient(A,B,C)| -quotient(B,D,E)| -quotient(A,D,F)| -quotient(F,E,G)| -quotient(C,D,H)|less_e_qual(G,H).
% 1.69/1.89 ** KEPT (pick-wt=9): 5 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.69/1.89 ** KEPT (pick-wt=11): 6 [] -quotient(A,B,C)| -quotient(A,B,D)|C=D.
% 1.69/1.89 ** KEPT (pick-wt=9): 7 [] -less_e_qual(A,B)| -less_e_qual(B,C)|less_e_qual(A,C).
% 1.69/1.89 ** KEPT (pick-wt=14): 8 [] -quotient(A,B,C)| -less_e_qual(C,D)| -quotient(A,D,E)|less_e_qual(E,B).
% 1.69/1.89 ** KEPT (pick-wt=14): 9 [] -less_e_qual(A,B)| -quotient(C,B,D)| -quotient(C,A,E)|less_e_qual(D,E).
% 1.69/1.89 ** KEPT (pick-wt=14): 10 [] -less_e_qual(A,B)| -quotient(A,C,D)| -quotient(B,C,E)|less_e_qual(D,E).
% 1.69/1.89 ** KEPT (pick-wt=15): 11 [] -quotient(identity,A,B)| -quotient(identity,B,C)| -quotient(identity,C,D)|B=D.
% 1.69/1.89 ** KEPT (pick-wt=3): 13 [copy,12,flip.1] idQa_Q__idQ_idQa!=idQa.
% 1.69/1.89
% 1.69/1.89 ------------> process sos:
% 1.69/1.89 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.69/1.89 ** KEPT (pick-wt=3): 15 [] less_e_qual(zero,A).
% 1.69/1.89 ** KEPT (pick-wt=3): 16 [] less_e_qual(A,identity).
% 1.69/1.89 ** KEPT (pick-wt=6): 17 [] quotient(A,B,divide(A,B)).
% 1.69/1.89 ** KEPT (pick-wt=4): 18 [] quotient(A,identity,zero).
% 1.69/1.89 ** KEPT (pick-wt=4): 19 [] quotient(zero,A,zero).
% 1.69/1.89 ** KEPT (pick-wt=4): 20 [] quotient(A,A,zero).
% 1.69/1.89 ** KEPT (pick-wt=4): 21 [] quotient(A,zero,A).
% 1.69/1.89 ** KEPT (pick-wt=4): 22 [] quotient(identity,a,idQa).
% 1.69/1.89 ** KEPT (pick-wt=4): 23 [] quotient(identity,idQa,idQ_idQa).
% 1.69/1.89 ** KEPT (pick-wt=4): 24 [] quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa).
% 1.69/1.89 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.73/1.92
% 1.73/1.92 ======= end of input processing =======
% 1.73/1.92
% 1.73/1.92 =========== start of search ===========
% 1.73/1.92
% 1.73/1.92 -------- PROOF --------
% 1.73/1.92
% 1.73/1.92 ----> UNIT CONFLICT at 0.03 sec ----> 297 [binary,295.1,13.1] $F.
% 1.73/1.92
% 1.73/1.92 Length of proof is 11. Level of proof is 5.
% 1.73/1.92
% 1.73/1.92 ---------------- PROOF ----------------
% 1.73/1.92 % SZS status Unsatisfiable
% 1.73/1.92 % SZS output start Refutation
% See solution above
% 1.73/1.92 ------------ end of proof -------------
% 1.73/1.92
% 1.73/1.92
% 1.73/1.92 Search stopped by max_proofs option.
% 1.73/1.92
% 1.73/1.92
% 1.73/1.92 Search stopped by max_proofs option.
% 1.73/1.92
% 1.73/1.92 ============ end of search ============
% 1.73/1.92
% 1.73/1.92 -------------- statistics -------------
% 1.73/1.92 clauses given 28
% 1.73/1.92 clauses generated 3644
% 1.73/1.92 clauses kept 279
% 1.73/1.92 clauses forward subsumed 3421
% 1.73/1.92 clauses back subsumed 10
% 1.73/1.92 Kbytes malloced 976
% 1.73/1.92
% 1.73/1.92 ----------- times (seconds) -----------
% 1.73/1.92 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.73/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.73/1.92
% 1.73/1.92 That finishes the proof of the theorem.
% 1.73/1.92
% 1.73/1.92 Process 21589 finished Wed Jul 27 08:21:49 2022
% 1.73/1.92 Otter interrupted
% 1.73/1.92 PROOF FOUND
%------------------------------------------------------------------------------