TSTP Solution File: HEN009-3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN009-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 2.64s 2.87s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of clauses : 58 ( 53 unt; 0 nHn; 30 RR)
% Number of literals : 68 ( 26 equ; 12 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| divide(A,B) = zero ),
file('HEN009-3.p',unknown),
[] ).
cnf(2,axiom,
( divide(A,B) != zero
| less_e_qual(A,B) ),
file('HEN009-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN009-3.p',unknown),
[] ).
cnf(6,axiom,
b != d,
file('HEN009-3.p',unknown),
[] ).
cnf(7,plain,
d != b,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(9,axiom,
less_e_qual(divide(A,B),A),
file('HEN009-3.p',unknown),
[] ).
cnf(10,axiom,
less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
file('HEN009-3.p',unknown),
[] ).
cnf(11,axiom,
less_e_qual(zero,A),
file('HEN009-3.p',unknown),
[] ).
cnf(12,axiom,
less_e_qual(A,identity),
file('HEN009-3.p',unknown),
[] ).
cnf(14,axiom,
divide(identity,a) = b,
file('HEN009-3.p',unknown),
[] ).
cnf(15,axiom,
divide(identity,b) = c,
file('HEN009-3.p',unknown),
[] ).
cnf(17,axiom,
divide(identity,c) = d,
file('HEN009-3.p',unknown),
[] ).
cnf(20,plain,
divide(zero,A) = zero,
inference(hyper,[status(thm)],[11,1]),
[iquote('hyper,11,1')] ).
cnf(23,plain,
divide(A,identity) = zero,
inference(hyper,[status(thm)],[12,1]),
[iquote('hyper,12,1')] ).
cnf(26,plain,
divide(divide(A,B),A) = zero,
inference(hyper,[status(thm)],[9,1]),
[iquote('hyper,9,1')] ).
cnf(27,plain,
( less_e_qual(A,B)
| ~ less_e_qual(divide(B,C),A)
| ~ less_e_qual(A,divide(B,C)) ),
inference(para_into,[status(thm),theory(equality)],[9,3]),
[iquote('para_into,9.1.1,3.3.1')] ).
cnf(34,plain,
less_e_qual(divide(b,divide(A,a)),divide(divide(identity,A),a)),
inference(para_into,[status(thm),theory(equality)],[10,14]),
[iquote('para_into,10.1.1.1,13.1.1')] ).
cnf(36,plain,
less_e_qual(divide(divide(A,a),b),zero),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,14]),23,20]),
[iquote('para_into,10.1.1.2,13.1.1,demod,23,20')] ).
cnf(40,plain,
less_e_qual(divide(divide(identity,A),divide(a,A)),divide(b,A)),
inference(para_into,[status(thm),theory(equality)],[10,14]),
[iquote('para_into,10.1.2.1,13.1.1')] ).
cnf(48,plain,
less_e_qual(divide(divide(identity,A),divide(b,A)),divide(c,A)),
inference(para_from,[status(thm),theory(equality)],[15,10]),
[iquote('para_from,15.1.1,10.1.2.1')] ).
cnf(49,plain,
less_e_qual(divide(divide(A,b),c),zero),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[15,10]),23,20]),
[iquote('para_from,15.1.1,10.1.1.2,demod,23,20')] ).
cnf(56,plain,
less_e_qual(divide(divide(A,c),d),zero),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[17,10]),23,20]),
[iquote('para_from,17.1.1,10.1.1.2,demod,23,20')] ).
cnf(62,plain,
less_e_qual(divide(divide(A,B),divide(identity,B)),zero),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[23,10]),20]),
[iquote('para_from,22.1.1,10.1.2.1,demod,20')] ).
cnf(118,plain,
divide(divide(A,a),b) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[36,3,11])]),
[iquote('hyper,36,3,11,flip.1')] ).
cnf(121,plain,
divide(divide(A,b),c) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[49,3,11])]),
[iquote('hyper,49,3,11,flip.1')] ).
cnf(124,plain,
divide(divide(A,c),d) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[56,3,11])]),
[iquote('hyper,56,3,11,flip.1')] ).
cnf(128,plain,
( less_e_qual(A,B)
| ~ less_e_qual(divide(B,C),A)
| ~ less_e_qual(A,D)
| ~ less_e_qual(divide(B,C),D)
| ~ less_e_qual(D,divide(B,C)) ),
inference(para_into,[status(thm),theory(equality)],[27,3]),
[iquote('para_into,27.3.2,3.3.1')] ).
cnf(130,plain,
less_e_qual(divide(A,a),b),
inference(hyper,[status(thm)],[118,2]),
[iquote('hyper,118,2')] ).
cnf(133,plain,
divide(b,b) = zero,
inference(para_into,[status(thm),theory(equality)],[118,14]),
[iquote('para_into,118.1.1.1,13.1.1')] ).
cnf(154,plain,
less_e_qual(divide(A,b),c),
inference(hyper,[status(thm)],[121,2]),
[iquote('hyper,121,2')] ).
cnf(157,plain,
divide(c,c) = zero,
inference(para_into,[status(thm),theory(equality)],[121,15]),
[iquote('para_into,121.1.1.1,15.1.1')] ).
cnf(179,plain,
less_e_qual(divide(A,c),d),
inference(hyper,[status(thm)],[124,2]),
[iquote('hyper,124,2')] ).
cnf(186,plain,
less_e_qual(divide(divide(A,d),divide(c,d)),zero),
inference(para_from,[status(thm),theory(equality)],[124,10]),
[iquote('para_from,124.1.1,10.1.2')] ).
cnf(304,plain,
divide(divide(A,B),divide(identity,B)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[62,3,11])]),
[iquote('hyper,62,3,11,flip.1')] ).
cnf(677,plain,
divide(divide(A,d),divide(c,d)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[186,3,11])]),
[iquote('hyper,186,3,11,flip.1')] ).
cnf(692,plain,
less_e_qual(divide(A,B),divide(identity,B)),
inference(hyper,[status(thm)],[304,2]),
[iquote('hyper,304,2')] ).
cnf(722,plain,
less_e_qual(divide(c,divide(a,b)),zero),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[40,15]),133]),
[iquote('para_into,40.1.1.1,15.1.1,demod,133')] ).
cnf(734,plain,
divide(c,divide(a,b)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[722,3,11])]),
[iquote('hyper,722,3,11,flip.1')] ).
cnf(736,plain,
less_e_qual(c,divide(a,b)),
inference(hyper,[status(thm)],[734,2]),
[iquote('hyper,734,2')] ).
cnf(757,plain,
less_e_qual(c,a),
inference(hyper,[status(thm)],[736,27,154]),
[iquote('hyper,736,27,154')] ).
cnf(817,plain,
divide(c,a) = zero,
inference(hyper,[status(thm)],[757,1]),
[iquote('hyper,757,1')] ).
cnf(859,plain,
less_e_qual(divide(divide(c,A),divide(a,A)),zero),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[817,10]),20]),
[iquote('para_from,817.1.1,10.1.2.1,demod,20')] ).
cnf(1341,plain,
less_e_qual(divide(d,divide(b,c)),zero),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,17]),157]),
[iquote('para_into,48.1.1.1,17.1.1,demod,157')] ).
cnf(1353,plain,
divide(d,divide(b,c)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1341,3,11])]),
[iquote('hyper,1341,3,11,flip.1')] ).
cnf(1377,plain,
less_e_qual(d,divide(b,c)),
inference(hyper,[status(thm)],[1353,2]),
[iquote('hyper,1353,2')] ).
cnf(1407,plain,
less_e_qual(d,b),
inference(hyper,[status(thm)],[1377,27,179]),
[iquote('hyper,1377,27,179')] ).
cnf(2826,plain,
less_e_qual(divide(A,d),divide(c,d)),
inference(hyper,[status(thm)],[677,2]),
[iquote('hyper,677,2')] ).
cnf(2889,plain,
divide(identity,d) = divide(c,d),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2826,3,692])]),
[iquote('hyper,2826,3,692,flip.1')] ).
cnf(2951,plain,
less_e_qual(divide(b,divide(d,a)),divide(divide(c,d),a)),
inference(para_from,[status(thm),theory(equality)],[2889,34]),
[iquote('para_from,2889.1.1,34.1.2.1')] ).
cnf(3933,plain,
divide(divide(c,A),divide(a,A)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[859,3,11])]),
[iquote('hyper,859,3,11,flip.1')] ).
cnf(4456,plain,
less_e_qual(divide(c,A),divide(a,A)),
inference(hyper,[status(thm)],[3933,2]),
[iquote('hyper,3933,2')] ).
cnf(4469,plain,
divide(c,d) = divide(a,d),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4456,3,2826])]),
[iquote('hyper,4456,3,2826,flip.1')] ).
cnf(4470,plain,
less_e_qual(divide(b,divide(d,a)),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2951]),4469,26]),
[iquote('back_demod,2951,demod,4469,26')] ).
cnf(4555,plain,
divide(b,divide(d,a)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4470,3,11])]),
[iquote('hyper,4470,3,11,flip.1')] ).
cnf(4559,plain,
less_e_qual(b,divide(d,a)),
inference(hyper,[status(thm)],[4555,2]),
[iquote('hyper,4555,2')] ).
cnf(4566,plain,
less_e_qual(b,d),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4559,128,692,130,130]),14]),
[iquote('hyper,4559,128,692,130,130,demod,14')] ).
cnf(4576,plain,
d = b,
inference(hyper,[status(thm)],[4566,3,1407]),
[iquote('hyper,4566,3,1407')] ).
cnf(4578,plain,
$false,
inference(binary,[status(thm)],[4576,7]),
[iquote('binary,4576.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : HEN009-3 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 08:57:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.64/2.87 ----- Otter 3.3f, August 2004 -----
% 2.64/2.87 The process was started by sandbox2 on n012.cluster.edu,
% 2.64/2.87 Wed Jul 27 08:57:50 2022
% 2.64/2.87 The command was "./otter". The process ID is 27566.
% 2.64/2.87
% 2.64/2.87 set(prolog_style_variables).
% 2.64/2.87 set(auto).
% 2.64/2.87 dependent: set(auto1).
% 2.64/2.87 dependent: set(process_input).
% 2.64/2.87 dependent: clear(print_kept).
% 2.64/2.87 dependent: clear(print_new_demod).
% 2.64/2.87 dependent: clear(print_back_demod).
% 2.64/2.87 dependent: clear(print_back_sub).
% 2.64/2.87 dependent: set(control_memory).
% 2.64/2.87 dependent: assign(max_mem, 12000).
% 2.64/2.87 dependent: assign(pick_given_ratio, 4).
% 2.64/2.87 dependent: assign(stats_level, 1).
% 2.64/2.87 dependent: assign(max_seconds, 10800).
% 2.64/2.87 clear(print_given).
% 2.64/2.87
% 2.64/2.87 list(usable).
% 2.64/2.87 0 [] A=A.
% 2.64/2.87 0 [] -less_e_qual(X,Y)|divide(X,Y)=zero.
% 2.64/2.87 0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 2.64/2.87 0 [] less_e_qual(divide(X,Y),X).
% 2.64/2.87 0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 2.64/2.87 0 [] less_e_qual(zero,X).
% 2.64/2.87 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 2.64/2.87 0 [] less_e_qual(X,identity).
% 2.64/2.87 0 [] divide(identity,a)!=divide(identity,divide(identity,divide(identity,a))).
% 2.64/2.87 0 [] divide(identity,a)=b.
% 2.64/2.87 0 [] divide(identity,b)=c.
% 2.64/2.87 0 [] divide(identity,c)=d.
% 2.64/2.87 0 [] b!=d.
% 2.64/2.87 end_of_list.
% 2.64/2.87
% 2.64/2.87 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.64/2.87
% 2.64/2.87 This is a Horn set with equality. The strategy will be
% 2.64/2.87 Knuth-Bendix and hyper_res, with positive clauses in
% 2.64/2.87 sos and nonpositive clauses in usable.
% 2.64/2.87
% 2.64/2.87 dependent: set(knuth_bendix).
% 2.64/2.87 dependent: set(anl_eq).
% 2.64/2.87 dependent: set(para_from).
% 2.64/2.87 dependent: set(para_into).
% 2.64/2.87 dependent: clear(para_from_right).
% 2.64/2.87 dependent: clear(para_into_right).
% 2.64/2.87 dependent: set(para_from_vars).
% 2.64/2.87 dependent: set(eq_units_both_ways).
% 2.64/2.87 dependent: set(dynamic_demod_all).
% 2.64/2.87 dependent: set(dynamic_demod).
% 2.64/2.87 dependent: set(order_eq).
% 2.64/2.87 dependent: set(back_demod).
% 2.64/2.87 dependent: set(lrpo).
% 2.64/2.87 dependent: set(hyper_res).
% 2.64/2.87 dependent: clear(order_hyper).
% 2.64/2.87
% 2.64/2.87 ------------> process usable:
% 2.64/2.87 ** KEPT (pick-wt=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 2.64/2.87 ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 2.64/2.87 ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 2.64/2.87 ** KEPT (pick-wt=11): 5 [copy,4,flip.1] divide(identity,divide(identity,divide(identity,a)))!=divide(identity,a).
% 2.64/2.87 ** KEPT (pick-wt=3): 7 [copy,6,flip.1] d!=b.
% 2.64/2.87
% 2.64/2.87 ------------> process sos:
% 2.64/2.87 ** KEPT (pick-wt=3): 8 [] A=A.
% 2.64/2.87 ** KEPT (pick-wt=5): 9 [] less_e_qual(divide(A,B),A).
% 2.64/2.87 ** KEPT (pick-wt=13): 10 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 2.64/2.87 ** KEPT (pick-wt=3): 11 [] less_e_qual(zero,A).
% 2.64/2.87 ** KEPT (pick-wt=3): 12 [] less_e_qual(A,identity).
% 2.64/2.87 ** KEPT (pick-wt=5): 13 [] divide(identity,a)=b.
% 2.64/2.87 ---> New Demodulator: 14 [new_demod,13] divide(identity,a)=b.
% 2.64/2.87 ** KEPT (pick-wt=5): 15 [] divide(identity,b)=c.
% 2.64/2.87 ---> New Demodulator: 16 [new_demod,15] divide(identity,b)=c.
% 2.64/2.87 ** KEPT (pick-wt=5): 17 [] divide(identity,c)=d.
% 2.64/2.87 ---> New Demodulator: 18 [new_demod,17] divide(identity,c)=d.
% 2.64/2.87 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 2.64/2.87 >>>> Starting back demodulation with 14.
% 2.64/2.87 >> back demodulating 5 with 14.
% 2.64/2.87 >>>> Starting back demodulation with 16.
% 2.64/2.87 >>>> Starting back demodulation with 18.
% 2.64/2.87
% 2.64/2.87 ======= end of input processing =======
% 2.64/2.87
% 2.64/2.87 =========== start of search ===========
% 2.64/2.87
% 2.64/2.87
% 2.64/2.87 Resetting weight limit to 11.
% 2.64/2.87
% 2.64/2.87
% 2.64/2.87 Resetting weight limit to 11.
% 2.64/2.87
% 2.64/2.87 sos_size=3238
% 2.64/2.87
% 2.64/2.87
% 2.64/2.87 Resetting weight limit to 10.
% 2.64/2.87
% 2.64/2.87
% 2.64/2.87 Resetting weight limit to 10.
% 2.64/2.87
% 2.64/2.87 sos_size=3143
% 2.64/2.87
% 2.64/2.87 -------- PROOF --------
% 2.64/2.87
% 2.64/2.87 ----> UNIT CONFLICT at 1.12 sec ----> 4578 [binary,4576.1,7.1] $F.
% 2.64/2.87
% 2.64/2.87 Length of proof is 46. Level of proof is 18.
% 2.64/2.87
% 2.64/2.87 ---------------- PROOF ----------------
% 2.64/2.87 % SZS status Unsatisfiable
% 2.64/2.87 % SZS output start Refutation
% See solution above
% 2.64/2.87 ------------ end of proof -------------
% 2.64/2.87
% 2.64/2.87
% 2.64/2.87 Search stopped by max_proofs option.
% 2.64/2.87
% 2.64/2.87
% 2.64/2.87 Search stopped by max_proofs option.
% 2.64/2.87
% 2.64/2.87 ============ end of search ============
% 2.64/2.87
% 2.64/2.87 -------------- statistics -------------
% 2.64/2.87 clauses given 375
% 2.64/2.87 clauses generated 23471
% 2.64/2.87 clauses kept 4431
% 2.64/2.87 clauses forward subsumed 9026
% 2.64/2.87 clauses back subsumed 448
% 2.64/2.87 Kbytes malloced 4882
% 2.64/2.87
% 2.64/2.87 ----------- times (seconds) -----------
% 2.64/2.87 user CPU time 1.12 (0 hr, 0 min, 1 sec)
% 2.64/2.87 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.64/2.87 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.64/2.87
% 2.64/2.87 That finishes the proof of the theorem.
% 2.64/2.87
% 2.64/2.87 Process 27566 finished Wed Jul 27 08:57:53 2022
% 2.64/2.87 Otter interrupted
% 2.64/2.87 PROOF FOUND
%------------------------------------------------------------------------------