%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN005-6 : 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 12:57:56 EDT 2022
% Result : Unsatisfiable 1.91s 2.11s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 15 unt; 0 nHn; 12 RR)
% Number of literals : 22 ( 8 equ; 5 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| divide(A,B) = zero ),
file('HEN005-6.p',unknown),
[] ).
cnf(2,axiom,
( divide(A,B) != zero
| less_e_qual(A,B) ),
file('HEN005-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN005-6.p',unknown),
[] ).
cnf(4,axiom,
~ less_e_qual(a,c),
file('HEN005-6.p',unknown),
[] ).
cnf(7,axiom,
less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
file('HEN005-6.p',unknown),
[] ).
cnf(8,axiom,
less_e_qual(zero,A),
file('HEN005-6.p',unknown),
[] ).
cnf(13,axiom,
divide(zero,A) = zero,
file('HEN005-6.p',unknown),
[] ).
cnf(14,axiom,
less_e_qual(a,b),
file('HEN005-6.p',unknown),
[] ).
cnf(15,axiom,
less_e_qual(b,c),
file('HEN005-6.p',unknown),
[] ).
cnf(18,plain,
divide(a,b) = zero,
inference(hyper,[status(thm)],[14,1]),
[iquote('hyper,14,1')] ).
cnf(22,plain,
divide(b,c) = zero,
inference(hyper,[status(thm)],[15,1]),
[iquote('hyper,15,1')] ).
cnf(45,plain,
less_e_qual(divide(divide(a,A),divide(b,A)),zero),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,18]),13]),
[iquote('para_into,7.1.2.1,18.1.1,demod,13')] ).
cnf(73,plain,
divide(divide(a,A),divide(b,A)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[45,3,8])]),
[iquote('hyper,45,3,8,flip.1')] ).
cnf(113,plain,
less_e_qual(divide(a,A),divide(b,A)),
inference(hyper,[status(thm)],[73,2]),
[iquote('hyper,73,2')] ).
cnf(129,plain,
less_e_qual(divide(a,c),zero),
inference(para_into,[status(thm),theory(equality)],[113,22]),
[iquote('para_into,113.1.2,22.1.1')] ).
cnf(133,plain,
divide(a,c) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[129,3,8])]),
[iquote('hyper,129,3,8,flip.1')] ).
cnf(147,plain,
less_e_qual(a,c),
inference(hyper,[status(thm)],[133,2]),
[iquote('hyper,133,2')] ).
cnf(148,plain,
$false,
inference(binary,[status(thm)],[147,4]),
[iquote('binary,147.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : HEN005-6 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % 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 09:06:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.91/2.11 ----- Otter 3.3f, August 2004 -----
% 1.91/2.11 The process was started by sandbox2 on n025.cluster.edu,
% 1.91/2.11 Wed Jul 27 09:06:45 2022
% 1.91/2.11 The command was "./otter". The process ID is 18131.
% 1.91/2.11
% 1.91/2.11 set(prolog_style_variables).
% 1.91/2.11 set(auto).
% 1.91/2.11 dependent: set(auto1).
% 1.91/2.11 dependent: set(process_input).
% 1.91/2.11 dependent: clear(print_kept).
% 1.91/2.11 dependent: clear(print_new_demod).
% 1.91/2.11 dependent: clear(print_back_demod).
% 1.91/2.11 dependent: clear(print_back_sub).
% 1.91/2.11 dependent: set(control_memory).
% 1.91/2.11 dependent: assign(max_mem, 12000).
% 1.91/2.11 dependent: assign(pick_given_ratio, 4).
% 1.91/2.11 dependent: assign(stats_level, 1).
% 1.91/2.11 dependent: assign(max_seconds, 10800).
% 1.91/2.11 clear(print_given).
% 1.91/2.11
% 1.91/2.11 list(usable).
% 1.91/2.11 0 [] A=A.
% 1.91/2.11 0 [] -less_e_qual(X,Y)|divide(X,Y)=zero.
% 1.91/2.11 0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 1.91/2.11 0 [] less_e_qual(divide(X,Y),X).
% 1.91/2.11 0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 1.91/2.11 0 [] less_e_qual(zero,X).
% 1.91/2.11 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.91/2.11 0 [] less_e_qual(X,identity).
% 1.91/2.11 0 [] divide(X,identity)=zero.
% 1.91/2.11 0 [] divide(zero,X)=zero.
% 1.91/2.11 0 [] less_e_qual(a,b).
% 1.91/2.11 0 [] less_e_qual(b,c).
% 1.91/2.11 0 [] -less_e_qual(a,c).
% 1.91/2.11 end_of_list.
% 1.91/2.11
% 1.91/2.11 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.91/2.11
% 1.91/2.11 This is a Horn set with equality. The strategy will be
% 1.91/2.11 Knuth-Bendix and hyper_res, with positive clauses in
% 1.91/2.11 sos and nonpositive clauses in usable.
% 1.91/2.11
% 1.91/2.11 dependent: set(knuth_bendix).
% 1.91/2.11 dependent: set(anl_eq).
% 1.91/2.11 dependent: set(para_from).
% 1.91/2.11 dependent: set(para_into).
% 1.91/2.11 dependent: clear(para_from_right).
% 1.91/2.11 dependent: clear(para_into_right).
% 1.91/2.11 dependent: set(para_from_vars).
% 1.91/2.11 dependent: set(eq_units_both_ways).
% 1.91/2.11 dependent: set(dynamic_demod_all).
% 1.91/2.11 dependent: set(dynamic_demod).
% 1.91/2.11 dependent: set(order_eq).
% 1.91/2.11 dependent: set(back_demod).
% 1.91/2.11 dependent: set(lrpo).
% 1.91/2.11 dependent: set(hyper_res).
% 1.91/2.11 dependent: clear(order_hyper).
% 1.91/2.11
% 1.91/2.11 ------------> process usable:
% 1.91/2.11 ** KEPT (pick-wt=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 1.91/2.11 ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 1.91/2.11 ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.91/2.11 ** KEPT (pick-wt=3): 4 [] -less_e_qual(a,c).
% 1.91/2.11
% 1.91/2.11 ------------> process sos:
% 1.91/2.11 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.91/2.11 ** KEPT (pick-wt=5): 6 [] less_e_qual(divide(A,B),A).
% 1.91/2.11 ** KEPT (pick-wt=13): 7 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 1.91/2.11 ** KEPT (pick-wt=3): 8 [] less_e_qual(zero,A).
% 1.91/2.11 ** KEPT (pick-wt=3): 9 [] less_e_qual(A,identity).
% 1.91/2.11 ** KEPT (pick-wt=5): 10 [] divide(A,identity)=zero.
% 1.91/2.11 ---> New Demodulator: 11 [new_demod,10] divide(A,identity)=zero.
% 1.91/2.11 ** KEPT (pick-wt=5): 12 [] divide(zero,A)=zero.
% 1.91/2.11 ---> New Demodulator: 13 [new_demod,12] divide(zero,A)=zero.
% 1.91/2.11 ** KEPT (pick-wt=3): 14 [] less_e_qual(a,b).
% 1.91/2.11 ** KEPT (pick-wt=3): 15 [] less_e_qual(b,c).
% 1.91/2.11 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.91/2.11 >>>> Starting back demodulation with 11.
% 1.91/2.11 >>>> Starting back demodulation with 13.
% 1.91/2.11
% 1.91/2.11 ======= end of input processing =======
% 1.91/2.11
% 1.91/2.11 =========== start of search ===========
% 1.91/2.11
% 1.91/2.11 -------- PROOF --------
% 1.91/2.11
% 1.91/2.11 ----> UNIT CONFLICT at 0.01 sec ----> 148 [binary,147.1,4.1] $F.
% 1.91/2.11
% 1.91/2.11 Length of proof is 8. Level of proof is 7.
% 1.91/2.11
% 1.91/2.11 ---------------- PROOF ----------------
% 1.91/2.11 % SZS status Unsatisfiable
% 1.91/2.11 % SZS output start Refutation
% See solution above
% 1.91/2.11 ------------ end of proof -------------
% 1.91/2.11
% 1.91/2.11
% 1.91/2.11 Search stopped by max_proofs option.
% 1.91/2.11
% 1.91/2.11
% 1.91/2.11 Search stopped by max_proofs option.
% 1.91/2.11
% 1.91/2.11 ============ end of search ============
% 1.91/2.11
% 1.91/2.11 -------------- statistics -------------
% 1.91/2.11 clauses given 32
% 1.91/2.11 clauses generated 329
% 1.91/2.11 clauses kept 135
% 1.91/2.11 clauses forward subsumed 211
% 1.91/2.11 clauses back subsumed 5
% 1.91/2.11 Kbytes malloced 976
% 1.91/2.11
% 1.91/2.11 ----------- times (seconds) -----------
% 1.91/2.11 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.91/2.11 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.11 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.91/2.11
% 1.91/2.11 That finishes the proof of the theorem.
% 1.91/2.11
% 1.91/2.11 Process 18131 finished Wed Jul 27 09:06:47 2022
% 1.91/2.11 Otter interrupted
% 1.91/2.11 PROOF FOUND
%------------------------------------------------------------------------------