TSTP Solution File: HEN009-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN009-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 12:57:59 EDT 2022
% Result : Unsatisfiable 1.79s 2.00s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 15 ( 11 unt; 0 nHn; 13 RR)
% Number of literals : 24 ( 3 equ; 10 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ quotient(A,B,zero)
| less_e_qual(A,B) ),
file('HEN009-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN009-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ quotient(A,B,C)
| ~ less_e_qual(C,D)
| ~ quotient(A,D,E)
| less_e_qual(E,B) ),
file('HEN009-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ less_e_qual(A,B)
| ~ quotient(C,B,D)
| ~ quotient(C,A,E)
| less_e_qual(D,E) ),
file('HEN009-2.p',unknown),
[] ).
cnf(11,axiom,
idQa != idQ__idQ_idQa,
file('HEN009-2.p',unknown),
[] ).
cnf(18,axiom,
quotient(A,A,zero),
file('HEN009-2.p',unknown),
[] ).
cnf(20,axiom,
quotient(identity,a,idQa),
file('HEN009-2.p',unknown),
[] ).
cnf(21,axiom,
quotient(identity,idQa,idQ_idQa),
file('HEN009-2.p',unknown),
[] ).
cnf(22,axiom,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('HEN009-2.p',unknown),
[] ).
cnf(59,plain,
less_e_qual(A,A),
inference(hyper,[status(thm)],[18,2]),
[iquote('hyper,18,2')] ).
cnf(90,plain,
less_e_qual(idQ_idQa,a),
inference(hyper,[status(thm)],[21,8,20,59]),
[iquote('hyper,21,8,20,59')] ).
cnf(119,plain,
less_e_qual(idQa,idQ__idQ_idQa),
inference(hyper,[status(thm)],[22,9,90,20]),
[iquote('hyper,22,9,90,20')] ).
cnf(120,plain,
less_e_qual(idQ__idQ_idQa,idQa),
inference(hyper,[status(thm)],[22,8,21,59]),
[iquote('hyper,22,8,21,59')] ).
cnf(152,plain,
idQa = idQ__idQ_idQa,
inference(hyper,[status(thm)],[120,5,119]),
[iquote('hyper,120,5,119')] ).
cnf(154,plain,
$false,
inference(binary,[status(thm)],[152,11]),
[iquote('binary,152.1,11.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN009-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 08:51:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.79/2.00 ----- Otter 3.3f, August 2004 -----
% 1.79/2.00 The process was started by sandbox on n010.cluster.edu,
% 1.79/2.00 Wed Jul 27 08:51:25 2022
% 1.79/2.00 The command was "./otter". The process ID is 16941.
% 1.79/2.00
% 1.79/2.00 set(prolog_style_variables).
% 1.79/2.00 set(auto).
% 1.79/2.00 dependent: set(auto1).
% 1.79/2.00 dependent: set(process_input).
% 1.79/2.00 dependent: clear(print_kept).
% 1.79/2.00 dependent: clear(print_new_demod).
% 1.79/2.00 dependent: clear(print_back_demod).
% 1.79/2.00 dependent: clear(print_back_sub).
% 1.79/2.00 dependent: set(control_memory).
% 1.79/2.00 dependent: assign(max_mem, 12000).
% 1.79/2.00 dependent: assign(pick_given_ratio, 4).
% 1.79/2.00 dependent: assign(stats_level, 1).
% 1.79/2.00 dependent: assign(max_seconds, 10800).
% 1.79/2.00 clear(print_given).
% 1.79/2.00
% 1.79/2.00 list(usable).
% 1.79/2.00 0 [] A=A.
% 1.79/2.00 0 [] -less_e_qual(X,Y)|quotient(X,Y,zero).
% 1.79/2.00 0 [] -quotient(X,Y,zero)|less_e_qual(X,Y).
% 1.79/2.00 0 [] -quotient(X,Y,Z)|less_e_qual(Z,X).
% 1.79/2.00 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).
% 1.79/2.00 0 [] less_e_qual(zero,X).
% 1.79/2.00 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.79/2.00 0 [] less_e_qual(X,identity).
% 1.79/2.00 0 [] quotient(X,Y,divide(X,Y)).
% 1.79/2.00 0 [] -quotient(X,Y,Z)| -quotient(X,Y,W)|Z=W.
% 1.79/2.00 0 [] quotient(X,identity,zero).
% 1.79/2.00 0 [] quotient(zero,X,zero).
% 1.79/2.00 0 [] quotient(X,X,zero).
% 1.79/2.00 0 [] quotient(X,zero,X).
% 1.79/2.00 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,Z)|less_e_qual(X,Z).
% 1.79/2.00 0 [] -quotient(X,Y,W1)| -less_e_qual(W1,Z)| -quotient(X,Z,W2)|less_e_qual(W2,Y).
% 1.79/2.00 0 [] -less_e_qual(X,Y)| -quotient(Z,Y,W1)| -quotient(Z,X,W2)|less_e_qual(W1,W2).
% 1.79/2.00 0 [] -less_e_qual(X,Y)| -quotient(X,Z,W1)| -quotient(Y,Z,W2)|less_e_qual(W1,W2).
% 1.79/2.00 0 [] quotient(identity,a,idQa).
% 1.79/2.00 0 [] quotient(identity,idQa,idQ_idQa).
% 1.79/2.00 0 [] quotient(identity,idQ_idQa,idQ__idQ_idQa).
% 1.79/2.00 0 [] idQa!=idQ__idQ_idQa.
% 1.79/2.00 end_of_list.
% 1.79/2.00
% 1.79/2.00 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 1.79/2.00
% 1.79/2.00 This is a Horn set with equality. The strategy will be
% 1.79/2.00 Knuth-Bendix and hyper_res, with positive clauses in
% 1.79/2.00 sos and nonpositive clauses in usable.
% 1.79/2.00
% 1.79/2.00 dependent: set(knuth_bendix).
% 1.79/2.00 dependent: set(anl_eq).
% 1.79/2.00 dependent: set(para_from).
% 1.79/2.00 dependent: set(para_into).
% 1.79/2.00 dependent: clear(para_from_right).
% 1.79/2.00 dependent: clear(para_into_right).
% 1.79/2.00 dependent: set(para_from_vars).
% 1.79/2.00 dependent: set(eq_units_both_ways).
% 1.79/2.00 dependent: set(dynamic_demod_all).
% 1.79/2.00 dependent: set(dynamic_demod).
% 1.79/2.00 dependent: set(order_eq).
% 1.79/2.00 dependent: set(back_demod).
% 1.79/2.00 dependent: set(lrpo).
% 1.79/2.00 dependent: set(hyper_res).
% 1.79/2.00 dependent: clear(order_hyper).
% 1.79/2.00
% 1.79/2.00 ------------> process usable:
% 1.79/2.00 ** KEPT (pick-wt=7): 1 [] -less_e_qual(A,B)|quotient(A,B,zero).
% 1.79/2.00 ** KEPT (pick-wt=7): 2 [] -quotient(A,B,zero)|less_e_qual(A,B).
% 1.79/2.00 ** KEPT (pick-wt=7): 3 [] -quotient(A,B,C)|less_e_qual(C,A).
% 1.79/2.00 ** 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).
% 1.79/2.00 ** KEPT (pick-wt=9): 5 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.79/2.00 ** KEPT (pick-wt=11): 6 [] -quotient(A,B,C)| -quotient(A,B,D)|C=D.
% 1.79/2.00 ** KEPT (pick-wt=9): 7 [] -less_e_qual(A,B)| -less_e_qual(B,C)|less_e_qual(A,C).
% 1.79/2.00 ** KEPT (pick-wt=14): 8 [] -quotient(A,B,C)| -less_e_qual(C,D)| -quotient(A,D,E)|less_e_qual(E,B).
% 1.79/2.00 ** KEPT (pick-wt=14): 9 [] -less_e_qual(A,B)| -quotient(C,B,D)| -quotient(C,A,E)|less_e_qual(D,E).
% 1.79/2.00 ** KEPT (pick-wt=14): 10 [] -less_e_qual(A,B)| -quotient(A,C,D)| -quotient(B,C,E)|less_e_qual(D,E).
% 1.79/2.00 ** KEPT (pick-wt=3): 11 [] idQa!=idQ__idQ_idQa.
% 1.79/2.00
% 1.79/2.00 ------------> process sos:
% 1.79/2.00 ** KEPT (pick-wt=3): 12 [] A=A.
% 1.79/2.00 ** KEPT (pick-wt=3): 13 [] less_e_qual(zero,A).
% 1.79/2.00 ** KEPT (pick-wt=3): 14 [] less_e_qual(A,identity).
% 1.79/2.00 ** KEPT (pick-wt=6): 15 [] quotient(A,B,divide(A,B)).
% 1.79/2.00 ** KEPT (pick-wt=4): 16 [] quotient(A,identity,zero).
% 1.79/2.00 ** KEPT (pick-wt=4): 17 [] quotient(zero,A,zero).
% 1.79/2.00 ** KEPT (pick-wt=4): 18 [] quotient(A,A,zero).
% 1.79/2.00 ** KEPT (pick-wt=4): 19 [] quotient(A,zero,A).
% 1.79/2.00 ** KEPT (pick-wt=4): 20 [] quotient(identity,a,idQa).
% 1.79/2.00 ** KEPT (pick-wt=4): 21 [] quotient(identity,idQa,idQ_idQa).
% 1.79/2.00 ** KEPT (pick-wt=4): 22 [] quotient(identity,idQ_idQa,idQ__idQ_idQa).
% 1.79/2.00 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 1.79/2.00
% 1.79/2.00 ======= end of input processing =======
% 1.79/2.00
% 1.79/2.00 =========== start of search ===========
% 1.79/2.00
% 1.79/2.00 -------- PROOF --------
% 1.79/2.00
% 1.79/2.00 ----> UNIT CONFLICT at 0.01 sec ----> 154 [binary,152.1,11.1] $F.
% 1.79/2.00
% 1.79/2.00 Length of proof is 5. Level of proof is 4.
% 1.79/2.00
% 1.79/2.00 ---------------- PROOF ----------------
% 1.79/2.00 % SZS status Unsatisfiable
% 1.79/2.00 % SZS output start Refutation
% See solution above
% 1.79/2.00 ------------ end of proof -------------
% 1.79/2.00
% 1.79/2.00
% 1.79/2.00 Search stopped by max_proofs option.
% 1.79/2.00
% 1.79/2.00
% 1.79/2.00 Search stopped by max_proofs option.
% 1.79/2.00
% 1.79/2.00 ============ end of search ============
% 1.79/2.00
% 1.79/2.00 -------------- statistics -------------
% 1.79/2.00 clauses given 15
% 1.79/2.00 clauses generated 2910
% 1.79/2.00 clauses kept 145
% 1.79/2.00 clauses forward subsumed 2804
% 1.79/2.00 clauses back subsumed 8
% 1.79/2.00 Kbytes malloced 976
% 1.79/2.00
% 1.79/2.00 ----------- times (seconds) -----------
% 1.79/2.00 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.79/2.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/2.00 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.79/2.00
% 1.79/2.00 That finishes the proof of the theorem.
% 1.79/2.00
% 1.79/2.00 Process 16941 finished Wed Jul 27 08:51:26 2022
% 1.79/2.00 Otter interrupted
% 1.79/2.00 PROOF FOUND
%------------------------------------------------------------------------------