TSTP Solution File: HEN010-4 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN010-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 1.74s 1.98s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 16 unt; 0 nHn; 6 RR)
% Number of literals : 25 ( 10 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 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 : 30 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( divide(A,B) != zero
| less_e_qual(A,B) ),
file('HEN010-4.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN010-4.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(divide(A,B),C)
| less_e_qual(divide(A,C),B) ),
file('HEN010-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ less_e_qual(A,B)
| less_e_qual(divide(C,B),divide(C,A)) ),
file('HEN010-4.p',unknown),
[] ).
cnf(8,axiom,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('HEN010-4.p',unknown),
[] ).
cnf(9,plain,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
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('HEN010-4.p',unknown),
[] ).
cnf(12,axiom,
less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
file('HEN010-4.p',unknown),
[] ).
cnf(13,axiom,
less_e_qual(zero,A),
file('HEN010-4.p',unknown),
[] ).
cnf(20,axiom,
divide(A,A) = zero,
file('HEN010-4.p',unknown),
[] ).
cnf(24,axiom,
divide(identity,divide(identity,divide(identity,A))) = divide(identity,A),
file('HEN010-4.p',unknown),
[] ).
cnf(30,plain,
less_e_qual(divide(A,B),divide(A,divide(B,C))),
inference(hyper,[status(thm)],[11,6]),
[iquote('hyper,11,6')] ).
cnf(57,plain,
less_e_qual(A,A),
inference(hyper,[status(thm)],[20,2]),
[iquote('hyper,19,2')] ).
cnf(61,plain,
less_e_qual(divide(A,divide(A,B)),B),
inference(hyper,[status(thm)],[57,5]),
[iquote('hyper,57,5')] ).
cnf(168,plain,
divide(A,divide(A,zero)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[61,3,13])]),
[iquote('hyper,61,3,13,flip.1')] ).
cnf(216,plain,
less_e_qual(A,divide(A,zero)),
inference(hyper,[status(thm)],[168,2]),
[iquote('hyper,168,2')] ).
cnf(243,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[216,3,11]),
[iquote('hyper,216,3,11')] ).
cnf(268,plain,
divide(divide(A,B),B) = divide(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[30,3,12]),20,243])]),
[iquote('hyper,30,3,12,demod,20,243,flip.1')] ).
cnf(1014,plain,
divide(divide(identity,A),divide(identity,divide(identity,A))) = divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[268,24]),24]),
[iquote('para_into,268.1.1.1,23.1.1,demod,24')] ).
cnf(1016,plain,
$false,
inference(binary,[status(thm)],[1014,9]),
[iquote('binary,1014.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.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 08:55:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.88 ----- Otter 3.3f, August 2004 -----
% 1.68/1.88 The process was started by sandbox on n004.cluster.edu,
% 1.68/1.88 Wed Jul 27 08:55:51 2022
% 1.68/1.88 The command was "./otter". The process ID is 6235.
% 1.68/1.88
% 1.68/1.88 set(prolog_style_variables).
% 1.68/1.88 set(auto).
% 1.68/1.88 dependent: set(auto1).
% 1.68/1.88 dependent: set(process_input).
% 1.68/1.88 dependent: clear(print_kept).
% 1.68/1.88 dependent: clear(print_new_demod).
% 1.68/1.88 dependent: clear(print_back_demod).
% 1.68/1.88 dependent: clear(print_back_sub).
% 1.68/1.88 dependent: set(control_memory).
% 1.68/1.88 dependent: assign(max_mem, 12000).
% 1.68/1.88 dependent: assign(pick_given_ratio, 4).
% 1.68/1.88 dependent: assign(stats_level, 1).
% 1.68/1.88 dependent: assign(max_seconds, 10800).
% 1.68/1.88 clear(print_given).
% 1.68/1.88
% 1.68/1.88 list(usable).
% 1.68/1.88 0 [] A=A.
% 1.68/1.88 0 [] -less_e_qual(X,Y)|divide(X,Y)=zero.
% 1.68/1.88 0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 1.68/1.88 0 [] less_e_qual(divide(X,Y),X).
% 1.68/1.88 0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 1.68/1.88 0 [] less_e_qual(zero,X).
% 1.68/1.88 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.68/1.88 0 [] less_e_qual(X,identity).
% 1.68/1.88 0 [] divide(X,identity)=zero.
% 1.68/1.88 0 [] divide(zero,X)=zero.
% 1.68/1.88 0 [] divide(X,X)=zero.
% 1.68/1.88 0 [] divide(a,zero)=a.
% 1.68/1.88 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,Z)|less_e_qual(X,Z).
% 1.68/1.88 0 [] -less_e_qual(divide(X,Y),Z)|less_e_qual(divide(X,Z),Y).
% 1.68/1.88 0 [] -less_e_qual(X,Y)|less_e_qual(divide(Z,Y),divide(Z,X)).
% 1.68/1.88 0 [] -less_e_qual(X,Y)|less_e_qual(divide(X,Z),divide(Y,Z)).
% 1.68/1.88 0 [] divide(identity,divide(identity,divide(identity,X)))=divide(identity,X).
% 1.68/1.88 0 [] divide(identity,a)!=divide(divide(identity,a),divide(identity,divide(identity,a))).
% 1.68/1.88 end_of_list.
% 1.68/1.88
% 1.68/1.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.68/1.88
% 1.68/1.88 This is a Horn set with equality. The strategy will be
% 1.68/1.88 Knuth-Bendix and hyper_res, with positive clauses in
% 1.68/1.88 sos and nonpositive clauses in usable.
% 1.68/1.88
% 1.68/1.88 dependent: set(knuth_bendix).
% 1.68/1.88 dependent: set(anl_eq).
% 1.68/1.88 dependent: set(para_from).
% 1.68/1.88 dependent: set(para_into).
% 1.68/1.88 dependent: clear(para_from_right).
% 1.68/1.88 dependent: clear(para_into_right).
% 1.68/1.88 dependent: set(para_from_vars).
% 1.68/1.88 dependent: set(eq_units_both_ways).
% 1.68/1.88 dependent: set(dynamic_demod_all).
% 1.68/1.88 dependent: set(dynamic_demod).
% 1.68/1.88 dependent: set(order_eq).
% 1.68/1.88 dependent: set(back_demod).
% 1.68/1.88 dependent: set(lrpo).
% 1.68/1.88 dependent: set(hyper_res).
% 1.68/1.88 dependent: clear(order_hyper).
% 1.68/1.88
% 1.68/1.88 ------------> process usable:
% 1.68/1.88 ** KEPT (pick-wt=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 1.68/1.88 ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 1.68/1.88 ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.68/1.88 ** KEPT (pick-wt=9): 4 [] -less_e_qual(A,B)| -less_e_qual(B,C)|less_e_qual(A,C).
% 1.68/1.88 ** KEPT (pick-wt=10): 5 [] -less_e_qual(divide(A,B),C)|less_e_qual(divide(A,C),B).
% 1.68/1.88 ** KEPT (pick-wt=10): 6 [] -less_e_qual(A,B)|less_e_qual(divide(C,B),divide(C,A)).
% 1.68/1.88 ** KEPT (pick-wt=10): 7 [] -less_e_qual(A,B)|less_e_qual(divide(A,C),divide(B,C)).
% 1.68/1.88 ** KEPT (pick-wt=13): 9 [copy,8,flip.1] divide(divide(identity,a),divide(identity,divide(identity,a)))!=divide(identity,a).
% 1.68/1.88
% 1.68/1.88 ------------> process sos:
% 1.68/1.88 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.68/1.88 ** KEPT (pick-wt=5): 11 [] less_e_qual(divide(A,B),A).
% 1.68/1.88 ** KEPT (pick-wt=13): 12 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 1.68/1.88 ** KEPT (pick-wt=3): 13 [] less_e_qual(zero,A).
% 1.68/1.88 ** KEPT (pick-wt=3): 14 [] less_e_qual(A,identity).
% 1.68/1.88 ** KEPT (pick-wt=5): 15 [] divide(A,identity)=zero.
% 1.68/1.88 ---> New Demodulator: 16 [new_demod,15] divide(A,identity)=zero.
% 1.68/1.88 ** KEPT (pick-wt=5): 17 [] divide(zero,A)=zero.
% 1.68/1.88 ---> New Demodulator: 18 [new_demod,17] divide(zero,A)=zero.
% 1.68/1.88 ** KEPT (pick-wt=5): 19 [] divide(A,A)=zero.
% 1.68/1.88 ---> New Demodulator: 20 [new_demod,19] divide(A,A)=zero.
% 1.68/1.88 ** KEPT (pick-wt=5): 21 [] divide(a,zero)=a.
% 1.68/1.88 ---> New Demodulator: 22 [new_demod,21] divide(a,zero)=a.
% 1.68/1.88 ** KEPT (pick-wt=11): 23 [] divide(identity,divide(identity,divide(identity,A)))=divide(identity,A).
% 1.68/1.88 ---> New Demodulator: 24 [new_demod,23] divide(identity,divide(identity,divide(identity,A)))=divide(identity,A).
% 1.68/1.88 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.68/1.88 >>>> Starting back demodulation with 16.
% 1.68/1.88 >>>> Starting back demodulation with 18.
% 1.68/1.88 >>>> Starting back demodulation with 20.
% 1.68/1.88 >>>> Starting back demodulation with 22.
% 1.68/1.88 >>>> Starting back demodulation with 24.
% 1.74/1.98
% 1.74/1.98 ======= end of input processing =======
% 1.74/1.98
% 1.74/1.98 =========== start of search ===========
% 1.74/1.98
% 1.74/1.98 -------- PROOF --------
% 1.74/1.98
% 1.74/1.98 ----> UNIT CONFLICT at 0.09 sec ----> 1016 [binary,1014.1,9.1] $F.
% 1.74/1.98
% 1.74/1.98 Length of proof is 9. Level of proof is 7.
% 1.74/1.98
% 1.74/1.98 ---------------- PROOF ----------------
% 1.74/1.98 % SZS status Unsatisfiable
% 1.74/1.98 % SZS output start Refutation
% See solution above
% 1.74/1.98 ------------ end of proof -------------
% 1.74/1.98
% 1.74/1.98
% 1.74/1.98 Search stopped by max_proofs option.
% 1.74/1.98
% 1.74/1.98
% 1.74/1.98 Search stopped by max_proofs option.
% 1.74/1.98
% 1.74/1.98 ============ end of search ============
% 1.74/1.98
% 1.74/1.98 -------------- statistics -------------
% 1.74/1.98 clauses given 80
% 1.74/1.98 clauses generated 3704
% 1.74/1.98 clauses kept 962
% 1.74/1.98 clauses forward subsumed 2831
% 1.74/1.98 clauses back subsumed 121
% 1.74/1.98 Kbytes malloced 1953
% 1.74/1.98
% 1.74/1.98 ----------- times (seconds) -----------
% 1.74/1.98 user CPU time 0.09 (0 hr, 0 min, 0 sec)
% 1.74/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.98 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.98
% 1.74/1.98 That finishes the proof of the theorem.
% 1.74/1.98
% 1.74/1.98 Process 6235 finished Wed Jul 27 08:55:52 2022
% 1.74/1.98 Otter interrupted
% 1.74/1.98 PROOF FOUND
%------------------------------------------------------------------------------