TSTP Solution File: HEN010-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 2.05s 2.26s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of clauses : 63 ( 57 unt; 0 nHn; 35 RR)
% Number of literals : 75 ( 14 equ; 14 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 : 51 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| quotient(A,B,zero) ),
file('HEN010-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ quotient(A,B,zero)
| less_e_qual(A,B) ),
file('HEN010-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ quotient(A,B,C)
| less_e_qual(C,A) ),
file('HEN010-1.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('HEN010-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN010-1.p',unknown),
[] ).
cnf(7,axiom,
idQa != idQa_Q__idQ_idQa,
file('HEN010-1.p',unknown),
[] ).
cnf(8,plain,
idQa_Q__idQ_idQa != idQa,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(10,axiom,
less_e_qual(zero,A),
file('HEN010-1.p',unknown),
[] ).
cnf(11,axiom,
less_e_qual(A,identity),
file('HEN010-1.p',unknown),
[] ).
cnf(12,axiom,
quotient(A,B,divide(A,B)),
file('HEN010-1.p',unknown),
[] ).
cnf(13,axiom,
quotient(identity,a,idQa),
file('HEN010-1.p',unknown),
[] ).
cnf(14,axiom,
quotient(identity,idQa,idQ_idQa),
file('HEN010-1.p',unknown),
[] ).
cnf(15,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('HEN010-1.p',unknown),
[] ).
cnf(16,plain,
quotient(zero,A,zero),
inference(hyper,[status(thm)],[10,1]),
[iquote('hyper,10,1')] ).
cnf(19,plain,
quotient(A,identity,zero),
inference(hyper,[status(thm)],[11,1]),
[iquote('hyper,11,1')] ).
cnf(41,plain,
less_e_qual(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)),
inference(hyper,[status(thm)],[12,4,13,12,14,12]),
[iquote('hyper,12,4,13,12,14,12')] ).
cnf(51,plain,
less_e_qual(divide(A,B),A),
inference(hyper,[status(thm)],[12,3]),
[iquote('hyper,12,3')] ).
cnf(53,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)],[12,5]),
[iquote('para_into,12.1.3,5.3.1')] ).
cnf(61,plain,
less_e_qual(divide(divide(A,idQ_idQa),idQa_Q__idQ_idQa),divide(divide(A,idQa),idQ_idQa)),
inference(hyper,[status(thm)],[15,4,12,12,12,12]),
[iquote('hyper,15,4,12,12,12,12')] ).
cnf(63,plain,
less_e_qual(idQa_Q__idQ_idQa,idQa),
inference(hyper,[status(thm)],[15,3]),
[iquote('hyper,15,3')] ).
cnf(88,plain,
less_e_qual(divide(divide(A,idQa),idQ_idQa),zero),
inference(hyper,[status(thm)],[19,4,14,12,12,16]),
[iquote('hyper,19,4,14,12,12,16')] ).
cnf(89,plain,
less_e_qual(divide(idQa,idQa),zero),
inference(hyper,[status(thm)],[19,4,13,13,12,16]),
[iquote('hyper,19,4,13,13,12,16')] ).
cnf(91,plain,
less_e_qual(divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),zero),
inference(hyper,[status(thm)],[19,4,12,15,12,16]),
[iquote('hyper,19,4,12,15,12,16')] ).
cnf(120,plain,
quotient(divide(A,B),A,zero),
inference(hyper,[status(thm)],[51,1]),
[iquote('hyper,51,1')] ).
cnf(144,plain,
divide(idQa,idQa) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[89,5,10])]),
[iquote('hyper,89,5,10,flip.1')] ).
cnf(146,plain,
less_e_qual(divide(idQ_idQa,divide(a,idQa)),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),144]),
[iquote('back_demod,41,demod,144')] ).
cnf(218,plain,
less_e_qual(divide(divide(A,A),zero),zero),
inference(hyper,[status(thm)],[120,4,12,120,12,12]),
[iquote('hyper,120,4,12,120,12,12')] ).
cnf(234,plain,
divide(divide(A,idQa),idQ_idQa) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[88,5,10])]),
[iquote('hyper,88,5,10,flip.1')] ).
cnf(235,plain,
less_e_qual(divide(divide(A,idQ_idQa),idQa_Q__idQ_idQa),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[61]),234]),
[iquote('back_demod,61,demod,234')] ).
cnf(240,plain,
divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[91,5,10])]),
[iquote('hyper,91,5,10,flip.1')] ).
cnf(260,plain,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[146,5,10])]),
[iquote('hyper,146,5,10,flip.1')] ).
cnf(284,plain,
divide(divide(A,A),zero) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[218,5,10])]),
[iquote('hyper,218,5,10,flip.1')] ).
cnf(292,plain,
quotient(divide(A,idQa),idQ_idQa,zero),
inference(para_from,[status(thm),theory(equality)],[234,12]),
[iquote('para_from,233.1.1,12.1.3')] ).
cnf(297,plain,
less_e_qual(divide(A,idQa),idQ_idQa),
inference(hyper,[status(thm)],[292,2]),
[iquote('hyper,292,2')] ).
cnf(315,plain,
divide(divide(A,idQ_idQa),idQa_Q__idQ_idQa) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[235,5,10])]),
[iquote('hyper,235,5,10,flip.1')] ).
cnf(356,plain,
quotient(idQa_Q__idQ_idQa,divide(identity,idQ_idQa),zero),
inference(para_from,[status(thm),theory(equality)],[240,12]),
[iquote('para_from,240.1.1,12.1.3')] ).
cnf(361,plain,
less_e_qual(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),
inference(hyper,[status(thm)],[356,2]),
[iquote('hyper,356,2')] ).
cnf(388,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(para_from,[status(thm),theory(equality)],[260,12]),
[iquote('para_from,260.1.1,12.1.3')] ).
cnf(402,plain,
less_e_qual(idQ_idQa,divide(a,idQa)),
inference(hyper,[status(thm)],[388,2]),
[iquote('hyper,388,2')] ).
cnf(413,plain,
divide(a,idQa) = idQ_idQa,
inference(hyper,[status(thm)],[402,5,297]),
[iquote('hyper,402,5,297')] ).
cnf(421,plain,
quotient(idQ_idQa,a,zero),
inference(para_from,[status(thm),theory(equality)],[413,120]),
[iquote('para_from,413.1.1,120.1.1')] ).
cnf(440,plain,
less_e_qual(divide(idQa,zero),divide(divide(identity,idQ_idQa),a)),
inference(hyper,[status(thm)],[421,4,12,13,12,12]),
[iquote('hyper,421,4,12,13,12,12')] ).
cnf(469,plain,
quotient(divide(A,A),zero,zero),
inference(para_from,[status(thm),theory(equality)],[284,12]),
[iquote('para_from,284.1.1,12.1.3')] ).
cnf(478,plain,
less_e_qual(divide(A,A),zero),
inference(hyper,[status(thm)],[469,2]),
[iquote('hyper,469,2')] ).
cnf(486,plain,
divide(A,A) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[478,5,10])]),
[iquote('hyper,478,5,10,flip.1')] ).
cnf(489,plain,
quotient(A,A,zero),
inference(para_from,[status(thm),theory(equality)],[486,12]),
[iquote('para_from,486.1.1,12.1.3')] ).
cnf(490,plain,
less_e_qual(divide(divide(A,divide(A,zero)),zero),zero),
inference(hyper,[status(thm)],[489,4,12,16,12,12]),
[iquote('hyper,489,4,12,16,12,12')] ).
cnf(508,plain,
quotient(divide(A,idQ_idQa),idQa_Q__idQ_idQa,zero),
inference(para_from,[status(thm),theory(equality)],[315,12]),
[iquote('para_from,315.1.1,12.1.3')] ).
cnf(516,plain,
less_e_qual(divide(A,idQ_idQa),idQa_Q__idQ_idQa),
inference(hyper,[status(thm)],[508,2]),
[iquote('hyper,508,2')] ).
cnf(526,plain,
divide(identity,idQ_idQa) = idQa_Q__idQ_idQa,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[516,5,361])]),
[iquote('hyper,516,5,361,flip.1')] ).
cnf(527,plain,
less_e_qual(divide(idQa,zero),divide(idQa_Q__idQ_idQa,a)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[440]),526]),
[iquote('back_demod,440,demod,526')] ).
cnf(573,plain,
quotient(divide(idQa,zero),divide(idQa_Q__idQ_idQa,a),zero),
inference(hyper,[status(thm)],[527,1]),
[iquote('hyper,527,1')] ).
cnf(766,plain,
less_e_qual(divide(divide(divide(idQa,zero),idQa_Q__idQ_idQa),zero),zero),
inference(hyper,[status(thm)],[573,4,120,12,12,16]),
[iquote('hyper,573,4,120,12,12,16')] ).
cnf(959,plain,
quotient(divide(A,divide(A,zero)),zero,zero),
inference(hyper,[status(thm)],[490,53,10]),
[iquote('hyper,490,53,10')] ).
cnf(967,plain,
less_e_qual(divide(A,divide(A,zero)),zero),
inference(hyper,[status(thm)],[959,2]),
[iquote('hyper,959,2')] ).
cnf(995,plain,
quotient(A,divide(A,zero),zero),
inference(hyper,[status(thm)],[967,53,10]),
[iquote('hyper,967,53,10')] ).
cnf(1029,plain,
less_e_qual(A,divide(A,zero)),
inference(hyper,[status(thm)],[995,2]),
[iquote('hyper,995,2')] ).
cnf(1050,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[1029,5,51]),
[iquote('hyper,1029,5,51')] ).
cnf(1125,plain,
less_e_qual(divide(idQa,idQa_Q__idQ_idQa),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[766]),1050,1050]),
[iquote('back_demod,766,demod,1050,1050')] ).
cnf(1231,plain,
quotient(idQa,idQa_Q__idQ_idQa,zero),
inference(hyper,[status(thm)],[1125,53,10]),
[iquote('hyper,1125,53,10')] ).
cnf(1248,plain,
less_e_qual(idQa,idQa_Q__idQ_idQa),
inference(hyper,[status(thm)],[1231,2]),
[iquote('hyper,1231,2')] ).
cnf(1257,plain,
idQa_Q__idQ_idQa = idQa,
inference(hyper,[status(thm)],[1248,5,63]),
[iquote('hyper,1248,5,63')] ).
cnf(1259,plain,
$false,
inference(binary,[status(thm)],[1257,8]),
[iquote('binary,1257.1,8.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : HEN010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 09:07:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.05/2.26 ----- Otter 3.3f, August 2004 -----
% 2.05/2.26 The process was started by sandbox2 on n025.cluster.edu,
% 2.05/2.26 Wed Jul 27 09:07:30 2022
% 2.05/2.26 The command was "./otter". The process ID is 20543.
% 2.05/2.26
% 2.05/2.26 set(prolog_style_variables).
% 2.05/2.26 set(auto).
% 2.05/2.26 dependent: set(auto1).
% 2.05/2.26 dependent: set(process_input).
% 2.05/2.26 dependent: clear(print_kept).
% 2.05/2.26 dependent: clear(print_new_demod).
% 2.05/2.26 dependent: clear(print_back_demod).
% 2.05/2.26 dependent: clear(print_back_sub).
% 2.05/2.26 dependent: set(control_memory).
% 2.05/2.26 dependent: assign(max_mem, 12000).
% 2.05/2.26 dependent: assign(pick_given_ratio, 4).
% 2.05/2.26 dependent: assign(stats_level, 1).
% 2.05/2.26 dependent: assign(max_seconds, 10800).
% 2.05/2.26 clear(print_given).
% 2.05/2.26
% 2.05/2.26 list(usable).
% 2.05/2.26 0 [] A=A.
% 2.05/2.26 0 [] -less_e_qual(X,Y)|quotient(X,Y,zero).
% 2.05/2.26 0 [] -quotient(X,Y,zero)|less_e_qual(X,Y).
% 2.05/2.26 0 [] -quotient(X,Y,Z)|less_e_qual(Z,X).
% 2.05/2.26 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).
% 2.05/2.26 0 [] less_e_qual(zero,X).
% 2.05/2.26 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 2.05/2.26 0 [] less_e_qual(X,identity).
% 2.05/2.26 0 [] quotient(X,Y,divide(X,Y)).
% 2.05/2.26 0 [] -quotient(X,Y,Z)| -quotient(X,Y,W)|Z=W.
% 2.05/2.26 0 [] quotient(identity,a,idQa).
% 2.05/2.26 0 [] quotient(identity,idQa,idQ_idQa).
% 2.05/2.26 0 [] quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa).
% 2.05/2.26 0 [] idQa!=idQa_Q__idQ_idQa.
% 2.05/2.26 end_of_list.
% 2.05/2.26
% 2.05/2.26 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 2.05/2.26
% 2.05/2.26 This is a Horn set with equality. The strategy will be
% 2.05/2.26 Knuth-Bendix and hyper_res, with positive clauses in
% 2.05/2.26 sos and nonpositive clauses in usable.
% 2.05/2.26
% 2.05/2.26 dependent: set(knuth_bendix).
% 2.05/2.26 dependent: set(anl_eq).
% 2.05/2.26 dependent: set(para_from).
% 2.05/2.26 dependent: set(para_into).
% 2.05/2.26 dependent: clear(para_from_right).
% 2.05/2.26 dependent: clear(para_into_right).
% 2.05/2.26 dependent: set(para_from_vars).
% 2.05/2.26 dependent: set(eq_units_both_ways).
% 2.05/2.26 dependent: set(dynamic_demod_all).
% 2.05/2.26 dependent: set(dynamic_demod).
% 2.05/2.26 dependent: set(order_eq).
% 2.05/2.26 dependent: set(back_demod).
% 2.05/2.26 dependent: set(lrpo).
% 2.05/2.26 dependent: set(hyper_res).
% 2.05/2.26 dependent: clear(order_hyper).
% 2.05/2.26
% 2.05/2.26 ------------> process usable:
% 2.05/2.26 ** KEPT (pick-wt=7): 1 [] -less_e_qual(A,B)|quotient(A,B,zero).
% 2.05/2.26 ** KEPT (pick-wt=7): 2 [] -quotient(A,B,zero)|less_e_qual(A,B).
% 2.05/2.26 ** KEPT (pick-wt=7): 3 [] -quotient(A,B,C)|less_e_qual(C,A).
% 2.05/2.26 ** 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).
% 2.05/2.26 ** KEPT (pick-wt=9): 5 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 2.05/2.26 ** KEPT (pick-wt=11): 6 [] -quotient(A,B,C)| -quotient(A,B,D)|C=D.
% 2.05/2.26 ** KEPT (pick-wt=3): 8 [copy,7,flip.1] idQa_Q__idQ_idQa!=idQa.
% 2.05/2.26
% 2.05/2.26 ------------> process sos:
% 2.05/2.26 ** KEPT (pick-wt=3): 9 [] A=A.
% 2.05/2.26 ** KEPT (pick-wt=3): 10 [] less_e_qual(zero,A).
% 2.05/2.26 ** KEPT (pick-wt=3): 11 [] less_e_qual(A,identity).
% 2.05/2.26 ** KEPT (pick-wt=6): 12 [] quotient(A,B,divide(A,B)).
% 2.05/2.26 ** KEPT (pick-wt=4): 13 [] quotient(identity,a,idQa).
% 2.05/2.26 ** KEPT (pick-wt=4): 14 [] quotient(identity,idQa,idQ_idQa).
% 2.05/2.26 ** KEPT (pick-wt=4): 15 [] quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa).
% 2.05/2.26 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 2.05/2.26
% 2.05/2.26 ======= end of input processing =======
% 2.05/2.26
% 2.05/2.26 =========== start of search ===========
% 2.05/2.26
% 2.05/2.26 -------- PROOF --------
% 2.05/2.26
% 2.05/2.26 ----> UNIT CONFLICT at 0.14 sec ----> 1259 [binary,1257.1,8.1] $F.
% 2.05/2.26
% 2.05/2.26 Length of proof is 50. Level of proof is 18.
% 2.05/2.26
% 2.05/2.26 ---------------- PROOF ----------------
% 2.05/2.26 % SZS status Unsatisfiable
% 2.05/2.26 % SZS output start Refutation
% See solution above
% 2.05/2.26 ------------ end of proof -------------
% 2.05/2.26
% 2.05/2.26
% 2.05/2.26 Search stopped by max_proofs option.
% 2.05/2.26
% 2.05/2.26
% 2.05/2.26 Search stopped by max_proofs option.
% 2.05/2.26
% 2.05/2.26 ============ end of search ============
% 2.05/2.26
% 2.05/2.26 -------------- statistics -------------
% 2.05/2.26 clauses given 138
% 2.05/2.26 clauses generated 10833
% 2.05/2.26 clauses kept 1214
% 2.05/2.26 clauses forward subsumed 10070
% 2.05/2.26 clauses back subsumed 65
% 2.05/2.26 Kbytes malloced 1953
% 2.05/2.26
% 2.05/2.26 ----------- times (seconds) -----------
% 2.05/2.26 user CPU time 0.14 (0 hr, 0 min, 0 sec)
% 2.05/2.26 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.05/2.26 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.05/2.26
% 2.05/2.26 That finishes the proof of the theorem.
% 2.05/2.26
% 2.05/2.26 Process 20543 finished Wed Jul 27 09:07:32 2022
% 2.05/2.26 Otter interrupted
% 2.05/2.26 PROOF FOUND
%------------------------------------------------------------------------------