TSTP Solution File: HEN010-3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN010-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 12:58:00 EDT 2022
% Result : Unsatisfiable 22.25s 22.53s
% Output : Refutation 22.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of clauses : 49 ( 43 unt; 0 nHn; 10 RR)
% Number of literals : 58 ( 29 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 91 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| divide(A,B) = zero ),
file('HEN010-3.p',unknown),
[] ).
cnf(2,axiom,
( divide(A,B) != zero
| less_e_qual(A,B) ),
file('HEN010-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN010-3.p',unknown),
[] ).
cnf(4,axiom,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('HEN010-3.p',unknown),
[] ).
cnf(5,plain,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(6,axiom,
A = A,
file('HEN010-3.p',unknown),
[] ).
cnf(7,axiom,
less_e_qual(divide(A,B),A),
file('HEN010-3.p',unknown),
[] ).
cnf(8,axiom,
less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
file('HEN010-3.p',unknown),
[] ).
cnf(9,axiom,
less_e_qual(zero,A),
file('HEN010-3.p',unknown),
[] ).
cnf(10,axiom,
less_e_qual(A,identity),
file('HEN010-3.p',unknown),
[] ).
cnf(12,plain,
divide(zero,A) = zero,
inference(hyper,[status(thm)],[9,1]),
[iquote('hyper,9,1')] ).
cnf(14,plain,
divide(A,identity) = zero,
inference(hyper,[status(thm)],[10,1]),
[iquote('hyper,10,1')] ).
cnf(18,plain,
divide(divide(A,B),A) = zero,
inference(hyper,[status(thm)],[7,1]),
[iquote('hyper,7,1')] ).
cnf(21,plain,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = zero,
inference(hyper,[status(thm)],[8,1]),
[iquote('hyper,8,1')] ).
cnf(24,plain,
less_e_qual(divide(divide(A,B),zero),divide(divide(A,zero),B)),
inference(para_into,[status(thm),theory(equality)],[8,12]),
[iquote('para_into,8.1.1.2,11.1.1')] ).
cnf(33,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)],[14,8]),12]),
[iquote('para_from,14.1.1,8.1.2.1,demod,12')] ).
cnf(34,plain,
( divide(A,B) = zero
| ~ less_e_qual(divide(B,C),A)
| ~ less_e_qual(A,divide(B,C)) ),
inference(para_into,[status(thm),theory(equality)],[18,3]),
[iquote('para_into,17.1.1.1,3.3.1')] ).
cnf(35,plain,
less_e_qual(divide(divide(A,A),divide(B,A)),zero),
inference(para_from,[status(thm),theory(equality)],[18,8]),
[iquote('para_from,17.1.1,8.1.2')] ).
cnf(37,plain,
less_e_qual(divide(divide(A,B),zero),divide(divide(A,divide(B,C)),B)),
inference(para_from,[status(thm),theory(equality)],[18,8]),
[iquote('para_from,17.1.1,8.1.1.2')] ).
cnf(47,plain,
divide(divide(A,B),divide(identity,B)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[33,3,9])]),
[iquote('hyper,33,3,9,flip.1')] ).
cnf(50,plain,
divide(divide(A,A),divide(B,A)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[35,3,9])]),
[iquote('hyper,35,3,9,flip.1')] ).
cnf(52,plain,
less_e_qual(divide(A,B),divide(identity,B)),
inference(hyper,[status(thm)],[47,2]),
[iquote('hyper,47,2')] ).
cnf(79,plain,
less_e_qual(divide(A,A),divide(B,A)),
inference(hyper,[status(thm)],[50,2]),
[iquote('hyper,50,2')] ).
cnf(90,plain,
divide(A,A) = zero,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[79,3,7]),18])]),
[iquote('hyper,79,3,7,demod,18,flip.1')] ).
cnf(115,plain,
divide(divide(divide(divide(A,B),C),divide(A,C)),zero) = zero,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[21,18]),12]),
[iquote('para_into,21.1.1.2.1,17.1.1,demod,12')] ).
cnf(149,plain,
less_e_qual(divide(divide(A,divide(A,zero)),zero),zero),
inference(para_into,[status(thm),theory(equality)],[24,90]),
[iquote('para_into,24.1.2,90.1.1')] ).
cnf(157,plain,
divide(divide(A,divide(A,zero)),zero) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[149,3,9])]),
[iquote('hyper,149,3,9,flip.1')] ).
cnf(202,plain,
less_e_qual(divide(A,divide(A,zero)),zero),
inference(hyper,[status(thm)],[157,2]),
[iquote('hyper,157,2')] ).
cnf(223,plain,
divide(A,divide(A,zero)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[202,3,9])]),
[iquote('hyper,202,3,9,flip.1')] ).
cnf(225,plain,
less_e_qual(A,divide(A,zero)),
inference(hyper,[status(thm)],[223,2]),
[iquote('hyper,223,2')] ).
cnf(234,plain,
divide(divide(divide(A,divide(divide(A,B),zero)),divide(B,divide(divide(A,B),zero))),zero) = zero,
inference(para_from,[status(thm),theory(equality)],[223,21]),
[iquote('para_from,223.1.1,21.1.1.2')] ).
cnf(290,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[225,3,7]),
[iquote('hyper,225,3,7')] ).
cnf(297,plain,
divide(divide(A,divide(A,B)),divide(B,divide(A,B))) = zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[234]),290,290,290]),
[iquote('back_demod,234,demod,290,290,290')] ).
cnf(330,plain,
divide(divide(divide(A,B),C),divide(A,C)) = zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[115]),290]),
[iquote('back_demod,115,demod,290')] ).
cnf(348,plain,
less_e_qual(divide(A,B),divide(divide(A,divide(B,C)),B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),290]),
[iquote('back_demod,37,demod,290')] ).
cnf(1382,plain,
less_e_qual(divide(divide(A,B),C),divide(A,C)),
inference(hyper,[status(thm)],[330,2]),
[iquote('hyper,330,2')] ).
cnf(1541,plain,
divide(divide(A,B),divide(A,divide(B,C))) = zero,
inference(hyper,[status(thm)],[348,34,1382]),
[iquote('hyper,348,34,1382')] ).
cnf(1553,plain,
divide(divide(A,divide(B,C)),B) = divide(A,B),
inference(hyper,[status(thm)],[348,3,1382]),
[iquote('hyper,348,3,1382')] ).
cnf(3366,plain,
( divide(A,B) = zero
| ~ less_e_qual(A,divide(B,C)) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1541,1]),290]),
[iquote('para_into,1541.1.1.2,1.2.1,demod,290')] ).
cnf(3776,plain,
( zero != zero
| less_e_qual(A,B)
| ~ less_e_qual(A,divide(B,C)) ),
inference(para_from,[status(thm),theory(equality)],[3366,2]),
[iquote('para_from,3366.1.1,2.1.1')] ).
cnf(4254,plain,
less_e_qual(divide(divide(A,B),divide(C,B)),divide(A,C)),
inference(hyper,[status(thm)],[3776,6,8]),
[iquote('hyper,3776,6,8')] ).
cnf(4471,plain,
less_e_qual(divide(A,divide(A,B)),divide(B,divide(A,B))),
inference(hyper,[status(thm)],[297,2]),
[iquote('hyper,297,2')] ).
cnf(4487,plain,
divide(divide(A,divide(A,B)),B) = zero,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[297,1553]),12])]),
[iquote('para_from,297.1.1,1553.1.1.1,demod,12,flip.1')] ).
cnf(4492,plain,
less_e_qual(divide(A,divide(A,B)),B),
inference(hyper,[status(thm)],[4487,2]),
[iquote('hyper,4487,2')] ).
cnf(4514,plain,
less_e_qual(divide(A,B),divide(A,divide(C,divide(C,B)))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[4487,4254]),290]),
[iquote('para_from,4487.1.1,4254.1.1.2,demod,290')] ).
cnf(4824,plain,
divide(A,divide(identity,A)) = divide(identity,divide(identity,A)),
inference(hyper,[status(thm)],[4471,3,52]),
[iquote('hyper,4471,3,52')] ).
cnf(4870,plain,
divide(A,divide(A,divide(A,B))) = divide(A,B),
inference(hyper,[status(thm)],[4514,3,4492]),
[iquote('hyper,4514,3,4492')] ).
cnf(5021,plain,
divide(identity,a) != divide(identity,a),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[4824,5]),4870]),
[iquote('para_from,4824.1.1,5.1.1,demod,4870')] ).
cnf(5022,plain,
$false,
inference(binary,[status(thm)],[5021,6]),
[iquote('binary,5021.1,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN010-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n007.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 08:42:31 EDT 2022
% 0.13/0.33 % CPUTime :
% 22.25/22.53 ----- Otter 3.3f, August 2004 -----
% 22.25/22.53 The process was started by sandbox2 on n007.cluster.edu,
% 22.25/22.53 Wed Jul 27 08:42:31 2022
% 22.25/22.53 The command was "./otter". The process ID is 5615.
% 22.25/22.53
% 22.25/22.53 set(prolog_style_variables).
% 22.25/22.53 set(auto).
% 22.25/22.53 dependent: set(auto1).
% 22.25/22.53 dependent: set(process_input).
% 22.25/22.53 dependent: clear(print_kept).
% 22.25/22.53 dependent: clear(print_new_demod).
% 22.25/22.53 dependent: clear(print_back_demod).
% 22.25/22.53 dependent: clear(print_back_sub).
% 22.25/22.53 dependent: set(control_memory).
% 22.25/22.53 dependent: assign(max_mem, 12000).
% 22.25/22.53 dependent: assign(pick_given_ratio, 4).
% 22.25/22.53 dependent: assign(stats_level, 1).
% 22.25/22.53 dependent: assign(max_seconds, 10800).
% 22.25/22.53 clear(print_given).
% 22.25/22.53
% 22.25/22.53 list(usable).
% 22.25/22.53 0 [] A=A.
% 22.25/22.53 0 [] -less_e_qual(X,Y)|divide(X,Y)=zero.
% 22.25/22.53 0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 22.25/22.53 0 [] less_e_qual(divide(X,Y),X).
% 22.25/22.53 0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 22.25/22.53 0 [] less_e_qual(zero,X).
% 22.25/22.53 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 22.25/22.53 0 [] less_e_qual(X,identity).
% 22.25/22.53 0 [] divide(identity,a)!=divide(divide(identity,a),divide(identity,divide(identity,a))).
% 22.25/22.53 end_of_list.
% 22.25/22.53
% 22.25/22.53 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 22.25/22.53
% 22.25/22.53 This is a Horn set with equality. The strategy will be
% 22.25/22.53 Knuth-Bendix and hyper_res, with positive clauses in
% 22.25/22.53 sos and nonpositive clauses in usable.
% 22.25/22.53
% 22.25/22.53 dependent: set(knuth_bendix).
% 22.25/22.53 dependent: set(anl_eq).
% 22.25/22.53 dependent: set(para_from).
% 22.25/22.53 dependent: set(para_into).
% 22.25/22.53 dependent: clear(para_from_right).
% 22.25/22.53 dependent: clear(para_into_right).
% 22.25/22.53 dependent: set(para_from_vars).
% 22.25/22.53 dependent: set(eq_units_both_ways).
% 22.25/22.53 dependent: set(dynamic_demod_all).
% 22.25/22.53 dependent: set(dynamic_demod).
% 22.25/22.53 dependent: set(order_eq).
% 22.25/22.53 dependent: set(back_demod).
% 22.25/22.53 dependent: set(lrpo).
% 22.25/22.53 dependent: set(hyper_res).
% 22.25/22.53 dependent: clear(order_hyper).
% 22.25/22.53
% 22.25/22.53 ------------> process usable:
% 22.25/22.53 ** KEPT (pick-wt=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 22.25/22.53 ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 22.25/22.53 ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 22.25/22.53 ** KEPT (pick-wt=13): 5 [copy,4,flip.1] divide(divide(identity,a),divide(identity,divide(identity,a)))!=divide(identity,a).
% 22.25/22.53
% 22.25/22.53 ------------> process sos:
% 22.25/22.53 ** KEPT (pick-wt=3): 6 [] A=A.
% 22.25/22.53 ** KEPT (pick-wt=5): 7 [] less_e_qual(divide(A,B),A).
% 22.25/22.53 ** KEPT (pick-wt=13): 8 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 22.25/22.53 ** KEPT (pick-wt=3): 9 [] less_e_qual(zero,A).
% 22.25/22.53 ** KEPT (pick-wt=3): 10 [] less_e_qual(A,identity).
% 22.25/22.53 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 22.25/22.53
% 22.25/22.53 ======= end of input processing =======
% 22.25/22.53
% 22.25/22.53 =========== start of search ===========
% 22.25/22.53
% 22.25/22.53
% 22.25/22.53 Resetting weight limit to 14.
% 22.25/22.53
% 22.25/22.53
% 22.25/22.53 Resetting weight limit to 14.
% 22.25/22.53
% 22.25/22.53 sos_size=3118
% 22.25/22.53
% 22.25/22.53
% 22.25/22.53 Resetting weight limit to 13.
% 22.25/22.53
% 22.25/22.53
% 22.25/22.53 Resetting weight limit to 13.
% 22.25/22.53
% 22.25/22.53 sos_size=3122
% 22.25/22.53
% 22.25/22.53
% 22.25/22.53 Resetting weight limit to 12.
% 22.25/22.53
% 22.25/22.53
% 22.25/22.53 Resetting weight limit to 12.
% 22.25/22.53
% 22.25/22.53 sos_size=2990
% 22.25/22.53
% 22.25/22.53 -- HEY sandbox2, WE HAVE A PROOF!! --
% 22.25/22.53
% 22.25/22.53 ----> UNIT CONFLICT at 20.60 sec ----> 5022 [binary,5021.1,6.1] $F.
% 22.25/22.53
% 22.25/22.53 Length of proof is 39. Level of proof is 20.
% 22.25/22.53
% 22.25/22.53 ---------------- PROOF ----------------
% 22.25/22.53 % SZS status Unsatisfiable
% 22.25/22.53 % SZS output start Refutation
% See solution above
% 22.25/22.53 ------------ end of proof -------------
% 22.25/22.53
% 22.25/22.53
% 22.25/22.53 Search stopped by max_proofs option.
% 22.25/22.53
% 22.25/22.53
% 22.25/22.53 Search stopped by max_proofs option.
% 22.25/22.53
% 22.25/22.53 ============ end of search ============
% 22.25/22.53
% 22.25/22.53 -------------- statistics -------------
% 22.25/22.53 clauses given 438
% 22.25/22.53 clauses generated 1195492
% 22.25/22.53 clauses kept 4872
% 22.25/22.53 clauses forward subsumed 1046941
% 22.25/22.53 clauses back subsumed 1204
% 22.25/22.53 Kbytes malloced 4882
% 22.25/22.53
% 22.25/22.53 ----------- times (seconds) -----------
% 22.25/22.53 user CPU time 20.60 (0 hr, 0 min, 20 sec)
% 22.25/22.53 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 22.25/22.53 wall-clock time 22 (0 hr, 0 min, 22 sec)
% 22.25/22.53
% 22.25/22.53 That finishes the proof of the theorem.
% 22.25/22.53
% 22.25/22.53 Process 5615 finished Wed Jul 27 08:42:53 2022
% 22.25/22.53 Otter interrupted
% 22.25/22.53 PROOF FOUND
%------------------------------------------------------------------------------