TSTP Solution File: HEN009-6 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN009-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 : 11
% Number of leaves : 14
% Syntax : Number of clauses : 39 ( 33 unt; 0 nHn; 18 RR)
% Number of literals : 47 ( 14 equ; 10 neg)
% Maximal clause size : 3 ( 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 : 42 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| divide(A,B) = zero ),
file('HEN009-6.p',unknown),
[] ).
cnf(2,axiom,
( divide(A,B) != zero
| less_e_qual(A,B) ),
file('HEN009-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN009-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ less_e_qual(divide(A,B),C)
| less_e_qual(divide(A,C),B) ),
file('HEN009-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(A,B)
| less_e_qual(divide(A,C),divide(B,C)) ),
file('HEN009-6.p',unknown),
[] ).
cnf(8,axiom,
b != d,
file('HEN009-6.p',unknown),
[] ).
cnf(9,plain,
d != b,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.1')] ).
cnf(11,axiom,
less_e_qual(divide(A,B),A),
file('HEN009-6.p',unknown),
[] ).
cnf(12,axiom,
less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
file('HEN009-6.p',unknown),
[] ).
cnf(13,axiom,
less_e_qual(zero,A),
file('HEN009-6.p',unknown),
[] ).
cnf(14,axiom,
less_e_qual(A,identity),
file('HEN009-6.p',unknown),
[] ).
cnf(19,axiom,
divide(A,A) = zero,
file('HEN009-6.p',unknown),
[] ).
cnf(21,axiom,
divide(identity,a) = b,
file('HEN009-6.p',unknown),
[] ).
cnf(23,axiom,
divide(identity,b) = c,
file('HEN009-6.p',unknown),
[] ).
cnf(26,axiom,
divide(identity,c) = d,
file('HEN009-6.p',unknown),
[] ).
cnf(28,plain,
less_e_qual(divide(A,B),divide(identity,B)),
inference(hyper,[status(thm)],[14,5]),
[iquote('hyper,14,5')] ).
cnf(30,plain,
less_e_qual(divide(divide(A,B),C),divide(A,C)),
inference(hyper,[status(thm)],[11,5]),
[iquote('hyper,11,5')] ).
cnf(33,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)],[11,3]),
[iquote('para_into,11.1.1,3.3.1')] ).
cnf(51,plain,
less_e_qual(A,A),
inference(hyper,[status(thm)],[19,2]),
[iquote('hyper,19,2')] ).
cnf(55,plain,
less_e_qual(divide(A,divide(A,B)),B),
inference(hyper,[status(thm)],[51,4]),
[iquote('hyper,51,4')] ).
cnf(64,plain,
less_e_qual(divide(b,divide(A,a)),divide(divide(identity,A),a)),
inference(para_from,[status(thm),theory(equality)],[21,12]),
[iquote('para_from,21.1.1,12.1.1.1')] ).
cnf(138,plain,
less_e_qual(divide(A,b),c),
inference(para_into,[status(thm),theory(equality)],[28,23]),
[iquote('para_into,28.1.2,23.1.1')] ).
cnf(139,plain,
less_e_qual(divide(A,a),b),
inference(para_into,[status(thm),theory(equality)],[28,21]),
[iquote('para_into,28.1.2,21.1.1')] ).
cnf(150,plain,
less_e_qual(divide(A,c),b),
inference(hyper,[status(thm)],[138,4]),
[iquote('hyper,138,4')] ).
cnf(157,plain,
less_e_qual(divide(A,b),a),
inference(hyper,[status(thm)],[139,4]),
[iquote('hyper,139,4')] ).
cnf(175,plain,
less_e_qual(d,b),
inference(para_into,[status(thm),theory(equality)],[150,26]),
[iquote('para_into,150.1.1,25.1.1')] ).
cnf(179,plain,
divide(d,b) = zero,
inference(hyper,[status(thm)],[175,1]),
[iquote('hyper,175,1')] ).
cnf(187,plain,
less_e_qual(c,a),
inference(para_into,[status(thm),theory(equality)],[157,23]),
[iquote('para_into,157.1.1,23.1.1')] ).
cnf(191,plain,
divide(c,a) = zero,
inference(hyper,[status(thm)],[187,1]),
[iquote('hyper,187,1')] ).
cnf(207,plain,
less_e_qual(divide(divide(d,A),b),zero),
inference(para_from,[status(thm),theory(equality)],[179,30]),
[iquote('para_from,179.1.1,30.1.2')] ).
cnf(230,plain,
divide(A,divide(A,zero)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[55,3,13])]),
[iquote('hyper,55,3,13,flip.1')] ).
cnf(403,plain,
less_e_qual(divide(divide(d,A),zero),b),
inference(hyper,[status(thm)],[207,4]),
[iquote('hyper,207,4')] ).
cnf(411,plain,
less_e_qual(A,divide(A,zero)),
inference(hyper,[status(thm)],[230,2]),
[iquote('hyper,230,2')] ).
cnf(433,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[411,3,11]),
[iquote('hyper,411,3,11')] ).
cnf(437,plain,
less_e_qual(divide(d,A),b),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[403]),433]),
[iquote('back_demod,403,demod,433')] ).
cnf(1881,plain,
less_e_qual(b,divide(d,a)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[64,191]),433,26]),
[iquote('para_into,64.1.1.2,191.1.1,demod,433,26')] ).
cnf(1896,plain,
less_e_qual(b,d),
inference(hyper,[status(thm)],[1881,33,437]),
[iquote('hyper,1881,33,437')] ).
cnf(1903,plain,
d = b,
inference(hyper,[status(thm)],[1896,3,175]),
[iquote('hyper,1896,3,175')] ).
cnf(1905,plain,
$false,
inference(binary,[status(thm)],[1903,9]),
[iquote('binary,1903.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : HEN009-6 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 08:55:10 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 n011.cluster.edu,
% 2.05/2.26 Wed Jul 27 08:55:10 2022
% 2.05/2.26 The command was "./otter". The process ID is 3255.
% 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)|divide(X,Y)=zero.
% 2.05/2.26 0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 2.05/2.26 0 [] less_e_qual(divide(X,Y),X).
% 2.05/2.26 0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 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 [] divide(X,identity)=zero.
% 2.05/2.26 0 [] divide(zero,X)=zero.
% 2.05/2.26 0 [] divide(X,X)=zero.
% 2.05/2.26 0 [] -less_e_qual(divide(X,Y),Z)|less_e_qual(divide(X,Z),Y).
% 2.05/2.26 0 [] -less_e_qual(X,Y)|less_e_qual(divide(X,Z),divide(Y,Z)).
% 2.05/2.26 0 [] divide(identity,a)!=divide(identity,divide(identity,divide(identity,a))).
% 2.05/2.26 0 [] divide(identity,a)=b.
% 2.05/2.26 0 [] divide(identity,b)=c.
% 2.05/2.26 0 [] divide(identity,c)=d.
% 2.05/2.26 0 [] b!=d.
% 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=3.
% 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=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 2.05/2.26 ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 2.05/2.26 ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 2.05/2.26 ** KEPT (pick-wt=10): 4 [] -less_e_qual(divide(A,B),C)|less_e_qual(divide(A,C),B).
% 2.05/2.26 ** KEPT (pick-wt=10): 5 [] -less_e_qual(A,B)|less_e_qual(divide(A,C),divide(B,C)).
% 2.05/2.26 ** KEPT (pick-wt=11): 7 [copy,6,flip.1] divide(identity,divide(identity,divide(identity,a)))!=divide(identity,a).
% 2.05/2.26 ** KEPT (pick-wt=3): 9 [copy,8,flip.1] d!=b.
% 2.05/2.26
% 2.05/2.26 ------------> process sos:
% 2.05/2.26 ** KEPT (pick-wt=3): 10 [] A=A.
% 2.05/2.26 ** KEPT (pick-wt=5): 11 [] less_e_qual(divide(A,B),A).
% 2.05/2.26 ** KEPT (pick-wt=13): 12 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 2.05/2.26 ** KEPT (pick-wt=3): 13 [] less_e_qual(zero,A).
% 2.05/2.26 ** KEPT (pick-wt=3): 14 [] less_e_qual(A,identity).
% 2.05/2.26 ** KEPT (pick-wt=5): 15 [] divide(A,identity)=zero.
% 2.05/2.26 ---> New Demodulator: 16 [new_demod,15] divide(A,identity)=zero.
% 2.05/2.26 ** KEPT (pick-wt=5): 17 [] divide(zero,A)=zero.
% 2.05/2.26 ---> New Demodulator: 18 [new_demod,17] divide(zero,A)=zero.
% 2.05/2.26 ** KEPT (pick-wt=5): 19 [] divide(A,A)=zero.
% 2.05/2.26 ---> New Demodulator: 20 [new_demod,19] divide(A,A)=zero.
% 2.05/2.26 ** KEPT (pick-wt=5): 21 [] divide(identity,a)=b.
% 2.05/2.26 ---> New Demodulator: 22 [new_demod,21] divide(identity,a)=b.
% 2.05/2.26 ** KEPT (pick-wt=5): 23 [] divide(identity,b)=c.
% 2.05/2.26 ---> New Demodulator: 24 [new_demod,23] divide(identity,b)=c.
% 2.05/2.26 ** KEPT (pick-wt=5): 25 [] divide(identity,c)=d.
% 2.05/2.26 ---> New Demodulator: 26 [new_demod,25] divide(identity,c)=d.
% 2.05/2.26 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 2.05/2.26 >>>> Starting back demodulation with 16.
% 2.05/2.26 >>>> Starting back demodulation with 18.
% 2.05/2.26 >>>> Starting back demodulation with 20.
% 2.05/2.26 >>>> Starting back demodulation with 22.
% 2.05/2.26 >> back demodulating 7 with 22.
% 2.05/2.26 >>>> Starting back demodulation with 24.
% 2.05/2.26 >>>> Starting back demodulation with 26.
% 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 0.17 sec ----> 1905 [binary,1903.1,9.1] $F.
% 2.05/2.26
% 2.05/2.26 Length of proof is 24. Level of proof is 10.
% 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 5266
% 2.05/2.26 clauses kept 1816
% 2.05/2.26 clauses forward subsumed 3463
% 2.05/2.26 clauses back subsumed 245
% 2.05/2.26 Kbytes malloced 2929
% 2.05/2.26
% 2.05/2.26 ----------- times (seconds) -----------
% 2.05/2.26 user CPU time 0.17 (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 3255 finished Wed Jul 27 08:55:12 2022
% 2.05/2.26 Otter interrupted
% 2.05/2.26 PROOF FOUND
%------------------------------------------------------------------------------