TSTP Solution File: HEN009-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN009-1 : 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 12:57:59 EDT 2022
% Result : Unsatisfiable 1.79s 2.02s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 66 ( 59 unt; 0 nHn; 38 RR)
% Number of literals : 80 ( 17 equ; 15 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 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 : 56 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| quotient(A,B,zero) ),
file('HEN009-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ quotient(A,B,zero)
| less_e_qual(A,B) ),
file('HEN009-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ quotient(A,B,C)
| less_e_qual(C,A) ),
file('HEN009-1.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('HEN009-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN009-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ quotient(A,B,C)
| ~ quotient(A,B,D)
| C = D ),
file('HEN009-1.p',unknown),
[] ).
cnf(7,axiom,
idQa != idQ__idQ_idQa,
file('HEN009-1.p',unknown),
[] ).
cnf(9,axiom,
less_e_qual(zero,A),
file('HEN009-1.p',unknown),
[] ).
cnf(10,axiom,
less_e_qual(A,identity),
file('HEN009-1.p',unknown),
[] ).
cnf(11,axiom,
quotient(A,B,divide(A,B)),
file('HEN009-1.p',unknown),
[] ).
cnf(12,axiom,
quotient(identity,a,idQa),
file('HEN009-1.p',unknown),
[] ).
cnf(13,axiom,
quotient(identity,idQa,idQ_idQa),
file('HEN009-1.p',unknown),
[] ).
cnf(14,axiom,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('HEN009-1.p',unknown),
[] ).
cnf(15,plain,
quotient(zero,A,zero),
inference(hyper,[status(thm)],[9,1]),
[iquote('hyper,9,1')] ).
cnf(18,plain,
quotient(A,identity,zero),
inference(hyper,[status(thm)],[10,1]),
[iquote('hyper,10,1')] ).
cnf(40,plain,
less_e_qual(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)),
inference(hyper,[status(thm)],[11,4,12,11,13,11]),
[iquote('hyper,11,4,12,11,13,11')] ).
cnf(50,plain,
less_e_qual(divide(A,B),A),
inference(hyper,[status(thm)],[11,3]),
[iquote('hyper,11,3')] ).
cnf(52,plain,
( quotient(A,B,C)
| ~ less_e_qual(divide(A,B),C)
| ~ less_e_qual(C,divide(A,B)) ),
inference(para_into,[status(thm),theory(equality)],[11,5]),
[iquote('para_into,11.1.3,5.3.1')] ).
cnf(56,plain,
less_e_qual(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),divide(idQ_idQa,idQ_idQa)),
inference(hyper,[status(thm)],[14,4,13,11,11,11]),
[iquote('hyper,14,4,13,11,11,11')] ).
cnf(62,plain,
less_e_qual(divide(idQa,divide(idQ_idQa,a)),divide(idQ__idQ_idQa,a)),
inference(hyper,[status(thm)],[14,4,11,12,11,11]),
[iquote('hyper,14,4,11,12,11,11')] ).
cnf(83,plain,
less_e_qual(divide(divide(A,idQ_idQa),idQ__idQ_idQa),zero),
inference(hyper,[status(thm)],[18,4,14,11,11,15]),
[iquote('hyper,18,4,14,11,11,15')] ).
cnf(84,plain,
less_e_qual(divide(idQ_idQa,idQ_idQa),zero),
inference(hyper,[status(thm)],[18,4,13,13,11,15]),
[iquote('hyper,18,4,13,13,11,15')] ).
cnf(85,plain,
less_e_qual(divide(divide(A,idQa),idQ_idQa),zero),
inference(hyper,[status(thm)],[18,4,13,11,11,15]),
[iquote('hyper,18,4,13,11,11,15')] ).
cnf(86,plain,
less_e_qual(divide(idQa,idQa),zero),
inference(hyper,[status(thm)],[18,4,12,12,11,15]),
[iquote('hyper,18,4,12,12,11,15')] ).
cnf(103,plain,
quotient(divide(A,B),A,zero),
inference(hyper,[status(thm)],[50,1]),
[iquote('hyper,50,1')] ).
cnf(123,plain,
divide(idQ_idQa,idQ_idQa) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[84,5,9])]),
[iquote('hyper,84,5,9,flip.1')] ).
cnf(124,plain,
less_e_qual(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[56]),123]),
[iquote('back_demod,56,demod,123')] ).
cnf(128,plain,
divide(idQa,idQa) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[86,5,9])]),
[iquote('hyper,86,5,9,flip.1')] ).
cnf(129,plain,
less_e_qual(divide(idQ_idQa,divide(a,idQa)),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[40]),128]),
[iquote('back_demod,40,demod,128')] ).
cnf(186,plain,
divide(divide(A,B),A) = zero,
inference(hyper,[status(thm)],[103,6,11]),
[iquote('hyper,103,6,11')] ).
cnf(188,plain,
less_e_qual(divide(divide(A,A),zero),zero),
inference(hyper,[status(thm)],[103,4,11,103,11,11]),
[iquote('hyper,103,4,11,103,11,11')] ).
cnf(201,plain,
divide(divide(A,idQ_idQa),idQ__idQ_idQa) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[83,5,9])]),
[iquote('hyper,83,5,9,flip.1')] ).
cnf(204,plain,
divide(divide(A,idQa),idQ_idQa) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[85,5,9])]),
[iquote('hyper,85,5,9,flip.1')] ).
cnf(218,plain,
divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[124,5,9])]),
[iquote('hyper,124,5,9,flip.1')] ).
cnf(234,plain,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[129,5,9])]),
[iquote('hyper,129,5,9,flip.1')] ).
cnf(256,plain,
divide(divide(A,A),zero) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[188,5,9])]),
[iquote('hyper,188,5,9,flip.1')] ).
cnf(264,plain,
quotient(divide(A,idQ_idQa),idQ__idQ_idQa,zero),
inference(para_from,[status(thm),theory(equality)],[201,11]),
[iquote('para_from,201.1.1,11.1.3')] ).
cnf(275,plain,
less_e_qual(divide(A,idQ_idQa),idQ__idQ_idQa),
inference(hyper,[status(thm)],[264,2]),
[iquote('hyper,264,2')] ).
cnf(296,plain,
quotient(divide(A,idQa),idQ_idQa,zero),
inference(para_from,[status(thm),theory(equality)],[204,11]),
[iquote('para_from,204.1.1,11.1.3')] ).
cnf(302,plain,
less_e_qual(divide(A,idQa),idQ_idQa),
inference(hyper,[status(thm)],[296,2]),
[iquote('hyper,296,2')] ).
cnf(358,plain,
quotient(idQ__idQ_idQa,divide(idQa,idQ_idQa),zero),
inference(para_from,[status(thm),theory(equality)],[218,11]),
[iquote('para_from,218.1.1,11.1.3')] ).
cnf(365,plain,
less_e_qual(idQ__idQ_idQa,divide(idQa,idQ_idQa)),
inference(hyper,[status(thm)],[358,2]),
[iquote('hyper,358,2')] ).
cnf(376,plain,
divide(idQa,idQ_idQa) = idQ__idQ_idQa,
inference(hyper,[status(thm)],[365,5,275]),
[iquote('hyper,365,5,275')] ).
cnf(385,plain,
less_e_qual(idQ__idQ_idQa,idQa),
inference(para_from,[status(thm),theory(equality)],[376,50]),
[iquote('para_from,376.1.1,50.1.1')] ).
cnf(440,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(para_from,[status(thm),theory(equality)],[234,11]),
[iquote('para_from,234.1.1,11.1.3')] ).
cnf(449,plain,
less_e_qual(idQ_idQa,divide(a,idQa)),
inference(hyper,[status(thm)],[440,2]),
[iquote('hyper,440,2')] ).
cnf(460,plain,
divide(a,idQa) = idQ_idQa,
inference(hyper,[status(thm)],[449,5,302]),
[iquote('hyper,449,5,302')] ).
cnf(467,plain,
divide(idQ_idQa,a) = zero,
inference(para_from,[status(thm),theory(equality)],[460,186]),
[iquote('para_from,460.1.1,186.1.1.1')] ).
cnf(471,plain,
less_e_qual(divide(idQa,zero),divide(idQ__idQ_idQa,a)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[62]),467]),
[iquote('back_demod,62,demod,467')] ).
cnf(518,plain,
quotient(divide(A,A),zero,zero),
inference(para_from,[status(thm),theory(equality)],[256,11]),
[iquote('para_from,256.1.1,11.1.3')] ).
cnf(523,plain,
less_e_qual(divide(A,A),zero),
inference(hyper,[status(thm)],[518,2]),
[iquote('hyper,518,2')] ).
cnf(531,plain,
divide(A,A) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[523,5,9])]),
[iquote('hyper,523,5,9,flip.1')] ).
cnf(534,plain,
quotient(A,A,zero),
inference(para_from,[status(thm),theory(equality)],[531,11]),
[iquote('para_from,531.1.1,11.1.3')] ).
cnf(537,plain,
less_e_qual(divide(divide(A,divide(A,zero)),zero),zero),
inference(hyper,[status(thm)],[534,4,11,15,11,11]),
[iquote('hyper,534,4,11,15,11,11')] ).
cnf(546,plain,
quotient(divide(idQa,zero),divide(idQ__idQ_idQa,a),zero),
inference(hyper,[status(thm)],[471,1]),
[iquote('hyper,471,1')] ).
cnf(756,plain,
less_e_qual(divide(divide(divide(idQa,zero),idQ__idQ_idQa),zero),zero),
inference(hyper,[status(thm)],[546,4,103,11,11,15]),
[iquote('hyper,546,4,103,11,11,15')] ).
cnf(1140,plain,
quotient(divide(A,divide(A,zero)),zero,zero),
inference(hyper,[status(thm)],[537,52,9]),
[iquote('hyper,537,52,9')] ).
cnf(1149,plain,
less_e_qual(divide(A,divide(A,zero)),zero),
inference(hyper,[status(thm)],[1140,2]),
[iquote('hyper,1140,2')] ).
cnf(1160,plain,
quotient(A,divide(A,zero),zero),
inference(hyper,[status(thm)],[1149,52,9]),
[iquote('hyper,1149,52,9')] ).
cnf(1200,plain,
less_e_qual(A,divide(A,zero)),
inference(hyper,[status(thm)],[1160,2]),
[iquote('hyper,1160,2')] ).
cnf(1221,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[1200,5,50]),
[iquote('hyper,1200,5,50')] ).
cnf(1310,plain,
less_e_qual(divide(idQa,idQ__idQ_idQa),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[756]),1221,1221]),
[iquote('back_demod,756,demod,1221,1221')] ).
cnf(1406,plain,
quotient(idQa,idQ__idQ_idQa,zero),
inference(hyper,[status(thm)],[1310,52,9]),
[iquote('hyper,1310,52,9')] ).
cnf(1417,plain,
less_e_qual(idQa,idQ__idQ_idQa),
inference(hyper,[status(thm)],[1406,2]),
[iquote('hyper,1406,2')] ).
cnf(1428,plain,
idQa = idQ__idQ_idQa,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1417,5,385])]),
[iquote('hyper,1417,5,385,flip.1')] ).
cnf(1430,plain,
$false,
inference(binary,[status(thm)],[1428,7]),
[iquote('binary,1428.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : HEN009-1 : 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 08:21:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.79/2.02 ----- Otter 3.3f, August 2004 -----
% 1.79/2.02 The process was started by sandbox2 on n017.cluster.edu,
% 1.79/2.02 Wed Jul 27 08:21:33 2022
% 1.79/2.02 The command was "./otter". The process ID is 20688.
% 1.79/2.02
% 1.79/2.02 set(prolog_style_variables).
% 1.79/2.02 set(auto).
% 1.79/2.02 dependent: set(auto1).
% 1.79/2.02 dependent: set(process_input).
% 1.79/2.02 dependent: clear(print_kept).
% 1.79/2.02 dependent: clear(print_new_demod).
% 1.79/2.02 dependent: clear(print_back_demod).
% 1.79/2.02 dependent: clear(print_back_sub).
% 1.79/2.02 dependent: set(control_memory).
% 1.79/2.02 dependent: assign(max_mem, 12000).
% 1.79/2.02 dependent: assign(pick_given_ratio, 4).
% 1.79/2.02 dependent: assign(stats_level, 1).
% 1.79/2.02 dependent: assign(max_seconds, 10800).
% 1.79/2.02 clear(print_given).
% 1.79/2.02
% 1.79/2.02 list(usable).
% 1.79/2.02 0 [] A=A.
% 1.79/2.02 0 [] -less_e_qual(X,Y)|quotient(X,Y,zero).
% 1.79/2.02 0 [] -quotient(X,Y,zero)|less_e_qual(X,Y).
% 1.79/2.02 0 [] -quotient(X,Y,Z)|less_e_qual(Z,X).
% 1.79/2.02 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).
% 1.79/2.02 0 [] less_e_qual(zero,X).
% 1.79/2.02 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.79/2.02 0 [] less_e_qual(X,identity).
% 1.79/2.02 0 [] quotient(X,Y,divide(X,Y)).
% 1.79/2.02 0 [] -quotient(X,Y,Z)| -quotient(X,Y,W)|Z=W.
% 1.79/2.02 0 [] quotient(identity,a,idQa).
% 1.79/2.02 0 [] quotient(identity,idQa,idQ_idQa).
% 1.79/2.02 0 [] quotient(identity,idQ_idQa,idQ__idQ_idQa).
% 1.79/2.02 0 [] idQa!=idQ__idQ_idQa.
% 1.79/2.02 end_of_list.
% 1.79/2.02
% 1.79/2.02 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 1.79/2.02
% 1.79/2.02 This is a Horn set with equality. The strategy will be
% 1.79/2.02 Knuth-Bendix and hyper_res, with positive clauses in
% 1.79/2.02 sos and nonpositive clauses in usable.
% 1.79/2.02
% 1.79/2.02 dependent: set(knuth_bendix).
% 1.79/2.02 dependent: set(anl_eq).
% 1.79/2.02 dependent: set(para_from).
% 1.79/2.02 dependent: set(para_into).
% 1.79/2.02 dependent: clear(para_from_right).
% 1.79/2.02 dependent: clear(para_into_right).
% 1.79/2.02 dependent: set(para_from_vars).
% 1.79/2.02 dependent: set(eq_units_both_ways).
% 1.79/2.02 dependent: set(dynamic_demod_all).
% 1.79/2.02 dependent: set(dynamic_demod).
% 1.79/2.02 dependent: set(order_eq).
% 1.79/2.02 dependent: set(back_demod).
% 1.79/2.02 dependent: set(lrpo).
% 1.79/2.02 dependent: set(hyper_res).
% 1.79/2.02 dependent: clear(order_hyper).
% 1.79/2.02
% 1.79/2.02 ------------> process usable:
% 1.79/2.02 ** KEPT (pick-wt=7): 1 [] -less_e_qual(A,B)|quotient(A,B,zero).
% 1.79/2.02 ** KEPT (pick-wt=7): 2 [] -quotient(A,B,zero)|less_e_qual(A,B).
% 1.79/2.02 ** KEPT (pick-wt=7): 3 [] -quotient(A,B,C)|less_e_qual(C,A).
% 1.79/2.02 ** 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).
% 1.79/2.02 ** KEPT (pick-wt=9): 5 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.79/2.02 ** KEPT (pick-wt=11): 6 [] -quotient(A,B,C)| -quotient(A,B,D)|C=D.
% 1.79/2.02 ** KEPT (pick-wt=3): 7 [] idQa!=idQ__idQ_idQa.
% 1.79/2.02
% 1.79/2.02 ------------> process sos:
% 1.79/2.02 ** KEPT (pick-wt=3): 8 [] A=A.
% 1.79/2.02 ** KEPT (pick-wt=3): 9 [] less_e_qual(zero,A).
% 1.79/2.02 ** KEPT (pick-wt=3): 10 [] less_e_qual(A,identity).
% 1.79/2.02 ** KEPT (pick-wt=6): 11 [] quotient(A,B,divide(A,B)).
% 1.79/2.02 ** KEPT (pick-wt=4): 12 [] quotient(identity,a,idQa).
% 1.79/2.02 ** KEPT (pick-wt=4): 13 [] quotient(identity,idQa,idQ_idQa).
% 1.79/2.02 ** KEPT (pick-wt=4): 14 [] quotient(identity,idQ_idQa,idQ__idQ_idQa).
% 1.79/2.02 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 1.79/2.02
% 1.79/2.02 ======= end of input processing =======
% 1.79/2.02
% 1.79/2.02 =========== start of search ===========
% 1.79/2.02
% 1.79/2.02 -------- PROOF --------
% 1.79/2.02
% 1.79/2.02 ----> UNIT CONFLICT at 0.13 sec ----> 1430 [binary,1428.1,7.1] $F.
% 1.79/2.02
% 1.79/2.02 Length of proof is 52. Level of proof is 18.
% 1.79/2.02
% 1.79/2.02 ---------------- PROOF ----------------
% 1.79/2.02 % SZS status Unsatisfiable
% 1.79/2.02 % SZS output start Refutation
% See solution above
% 1.79/2.02 ------------ end of proof -------------
% 1.79/2.02
% 1.79/2.02
% 1.79/2.02 Search stopped by max_proofs option.
% 1.79/2.02
% 1.79/2.02
% 1.79/2.02 Search stopped by max_proofs option.
% 1.79/2.02
% 1.79/2.02 ============ end of search ============
% 1.79/2.02
% 1.79/2.02 -------------- statistics -------------
% 1.79/2.02 clauses given 157
% 1.79/2.02 clauses generated 12950
% 1.79/2.02 clauses kept 1383
% 1.79/2.02 clauses forward subsumed 12070
% 1.79/2.02 clauses back subsumed 71
% 1.79/2.02 Kbytes malloced 1953
% 1.79/2.02
% 1.79/2.02 ----------- times (seconds) -----------
% 1.79/2.02 user CPU time 0.13 (0 hr, 0 min, 0 sec)
% 1.79/2.02 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/2.02 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.79/2.02
% 1.79/2.02 That finishes the proof of the theorem.
% 1.79/2.02
% 1.79/2.02 Process 20688 finished Wed Jul 27 08:21:35 2022
% 1.79/2.02 Otter interrupted
% 1.79/2.02 PROOF FOUND
%------------------------------------------------------------------------------