TSTP Solution File: NUM283-1.005 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM283-1.005 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 13:07:57 EDT 2022
% Result : Unsatisfiable 1.93s 2.10s
% Output : Refutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of clauses : 47 ( 44 unt; 0 nHn; 21 RR)
% Number of literals : 52 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 121 ( 22 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 37 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ sum(A,B,C)
| sum(A,s(B),s(C)) ),
file('NUM283-1.005.p',unknown),
[] ).
cnf(2,axiom,
( ~ sum(A,B,C)
| ~ product(D,B,A)
| product(s(D),B,C) ),
file('NUM283-1.005.p',unknown),
[] ).
cnf(3,axiom,
( ~ factorial(A,B)
| ~ product(s(A),B,C)
| factorial(s(A),C) ),
file('NUM283-1.005.p',unknown),
[] ).
cnf(4,axiom,
~ factorial(s(s(s(s(s(n0))))),A),
file('NUM283-1.005.p',unknown),
[] ).
cnf(5,axiom,
sum(A,n0,A),
file('NUM283-1.005.p',unknown),
[] ).
cnf(6,axiom,
product(s(n0),A,A),
file('NUM283-1.005.p',unknown),
[] ).
cnf(7,axiom,
factorial(n0,s(n0)),
file('NUM283-1.005.p',unknown),
[] ).
cnf(8,plain,
sum(A,s(n0),s(A)),
inference(hyper,[status(thm)],[5,1]),
[iquote('hyper,5,1')] ).
cnf(9,plain,
factorial(s(n0),s(n0)),
inference(hyper,[status(thm)],[6,3,7]),
[iquote('hyper,6,3,7')] ).
cnf(11,plain,
product(s(s(n0)),s(n0),s(s(n0))),
inference(hyper,[status(thm)],[8,2,6]),
[iquote('hyper,8,2,6')] ).
cnf(12,plain,
sum(A,s(s(n0)),s(s(A))),
inference(hyper,[status(thm)],[8,1]),
[iquote('hyper,8,1')] ).
cnf(15,plain,
product(s(s(n0)),s(s(n0)),s(s(s(s(n0))))),
inference(hyper,[status(thm)],[12,2,6]),
[iquote('hyper,12,2,6')] ).
cnf(16,plain,
sum(A,s(s(s(n0))),s(s(s(A)))),
inference(hyper,[status(thm)],[12,1]),
[iquote('hyper,12,1')] ).
cnf(18,plain,
factorial(s(s(n0)),s(s(n0))),
inference(hyper,[status(thm)],[11,3,9]),
[iquote('hyper,11,3,9')] ).
cnf(20,plain,
product(s(s(s(n0))),s(s(n0)),s(s(s(s(s(s(n0))))))),
inference(hyper,[status(thm)],[15,2,12]),
[iquote('hyper,15,2,12')] ).
cnf(23,plain,
sum(A,s(s(s(s(n0)))),s(s(s(s(A))))),
inference(hyper,[status(thm)],[16,1]),
[iquote('hyper,16,1')] ).
cnf(28,plain,
sum(A,s(s(s(s(s(n0))))),s(s(s(s(s(A)))))),
inference(hyper,[status(thm)],[23,1]),
[iquote('hyper,23,1')] ).
cnf(31,plain,
factorial(s(s(s(n0))),s(s(s(s(s(s(n0))))))),
inference(hyper,[status(thm)],[20,3,18]),
[iquote('hyper,20,3,18')] ).
cnf(35,plain,
sum(A,s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(A))))))),
inference(hyper,[status(thm)],[28,1]),
[iquote('hyper,28,1')] ).
cnf(40,plain,
product(s(s(n0)),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))),
inference(hyper,[status(thm)],[35,2,6]),
[iquote('hyper,35,2,6')] ).
cnf(41,plain,
sum(A,s(s(s(s(s(s(s(n0))))))),s(s(s(s(s(s(s(A)))))))),
inference(hyper,[status(thm)],[35,1]),
[iquote('hyper,35,1')] ).
cnf(48,plain,
sum(A,s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(s(s(s(s(A))))))))),
inference(hyper,[status(thm)],[41,1]),
[iquote('hyper,41,1')] ).
cnf(54,plain,
product(s(s(s(n0))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))),
inference(hyper,[status(thm)],[40,2,35]),
[iquote('hyper,40,2,35')] ).
cnf(56,plain,
sum(A,s(s(s(s(s(s(s(s(s(n0))))))))),s(s(s(s(s(s(s(s(s(A)))))))))),
inference(hyper,[status(thm)],[48,1]),
[iquote('hyper,48,1')] ).
cnf(63,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(s(s(s(s(s(s(s(A))))))))))),
inference(hyper,[status(thm)],[56,1]),
[iquote('hyper,56,1')] ).
cnf(71,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(n0))))))))))),s(s(s(s(s(s(s(s(s(s(s(A)))))))))))),
inference(hyper,[status(thm)],[63,1]),
[iquote('hyper,63,1')] ).
cnf(77,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(A))))))))))))),
inference(hyper,[status(thm)],[71,1]),
[iquote('hyper,71,1')] ).
cnf(78,plain,
product(s(s(s(s(n0)))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))))))))),
inference(hyper,[status(thm)],[54,2,35]),
[iquote('hyper,54,2,35')] ).
cnf(87,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(A)))))))))))))),
inference(hyper,[status(thm)],[77,1]),
[iquote('hyper,77,1')] ).
cnf(94,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(A))))))))))))))),
inference(hyper,[status(thm)],[87,1]),
[iquote('hyper,87,1')] ).
cnf(102,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(A)))))))))))))))),
inference(hyper,[status(thm)],[94,1]),
[iquote('hyper,94,1')] ).
cnf(111,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(A))))))))))))))))),
inference(hyper,[status(thm)],[102,1]),
[iquote('hyper,102,1')] ).
cnf(112,plain,
factorial(s(s(s(s(n0)))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))))))))),
inference(hyper,[status(thm)],[78,3,31]),
[iquote('hyper,78,3,31')] ).
cnf(121,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(A)))))))))))))))))),
inference(hyper,[status(thm)],[111,1]),
[iquote('hyper,111,1')] ).
cnf(128,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(A))))))))))))))))))),
inference(hyper,[status(thm)],[121,1]),
[iquote('hyper,121,1')] ).
cnf(138,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(A)))))))))))))))))))),
inference(hyper,[status(thm)],[128,1]),
[iquote('hyper,128,1')] ).
cnf(145,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(A))))))))))))))))))))),
inference(hyper,[status(thm)],[138,1]),
[iquote('hyper,138,1')] ).
cnf(154,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(A)))))))))))))))))))))),
inference(hyper,[status(thm)],[145,1]),
[iquote('hyper,145,1')] ).
cnf(164,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(A))))))))))))))))))))))),
inference(hyper,[status(thm)],[154,1]),
[iquote('hyper,154,1')] ).
cnf(173,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(A)))))))))))))))))))))))),
inference(hyper,[status(thm)],[164,1]),
[iquote('hyper,164,1')] ).
cnf(179,plain,
sum(A,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(A))))))))))))))))))))))))),
inference(hyper,[status(thm)],[173,1]),
[iquote('hyper,173,1')] ).
cnf(191,plain,
product(s(s(n0)),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))))))))))))))))))))))))))))))))),
inference(hyper,[status(thm)],[179,2,6]),
[iquote('hyper,179,2,6')] ).
cnf(274,plain,
product(s(s(s(n0))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
inference(hyper,[status(thm)],[191,2,179]),
[iquote('hyper,191,2,179')] ).
cnf(385,plain,
product(s(s(s(s(n0)))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
inference(hyper,[status(thm)],[274,2,179]),
[iquote('hyper,274,2,179')] ).
cnf(528,plain,
product(s(s(s(s(s(n0))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
inference(hyper,[status(thm)],[385,2,179]),
[iquote('hyper,385,2,179')] ).
cnf(720,plain,
factorial(s(s(s(s(s(n0))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
inference(hyper,[status(thm)],[528,3,112]),
[iquote('hyper,528,3,112')] ).
cnf(721,plain,
$false,
inference(binary,[status(thm)],[720,4]),
[iquote('binary,720.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM283-1.005 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 09:47:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.93/2.10 ----- Otter 3.3f, August 2004 -----
% 1.93/2.10 The process was started by sandbox on n009.cluster.edu,
% 1.93/2.10 Wed Jul 27 09:47:21 2022
% 1.93/2.10 The command was "./otter". The process ID is 31208.
% 1.93/2.10
% 1.93/2.10 set(prolog_style_variables).
% 1.93/2.10 set(auto).
% 1.93/2.10 dependent: set(auto1).
% 1.93/2.10 dependent: set(process_input).
% 1.93/2.10 dependent: clear(print_kept).
% 1.93/2.10 dependent: clear(print_new_demod).
% 1.93/2.10 dependent: clear(print_back_demod).
% 1.93/2.10 dependent: clear(print_back_sub).
% 1.93/2.10 dependent: set(control_memory).
% 1.93/2.10 dependent: assign(max_mem, 12000).
% 1.93/2.10 dependent: assign(pick_given_ratio, 4).
% 1.93/2.10 dependent: assign(stats_level, 1).
% 1.93/2.10 dependent: assign(max_seconds, 10800).
% 1.93/2.10 clear(print_given).
% 1.93/2.10
% 1.93/2.10 list(usable).
% 1.93/2.10 0 [] sum(X,n0,X).
% 1.93/2.10 0 [] -sum(X,Y,Z)|sum(X,s(Y),s(Z)).
% 1.93/2.10 0 [] product(s(n0),X,X).
% 1.93/2.10 0 [] -sum(R,Y,Z)| -product(X,Y,R)|product(s(X),Y,Z).
% 1.93/2.10 0 [] factorial(n0,s(n0)).
% 1.93/2.10 0 [] -factorial(X,Z)| -product(s(X),Z,Y)|factorial(s(X),Y).
% 1.93/2.10 0 [] -factorial(s(s(s(s(s(n0))))),Result).
% 1.93/2.10 end_of_list.
% 1.93/2.10
% 1.93/2.10 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.93/2.10
% 1.93/2.10 This is a Horn set without equality. The strategy will
% 1.93/2.10 be hyperresolution, with satellites in sos and nuclei
% 1.93/2.10 in usable.
% 1.93/2.10
% 1.93/2.10 dependent: set(hyper_res).
% 1.93/2.10 dependent: clear(order_hyper).
% 1.93/2.10
% 1.93/2.10 ------------> process usable:
% 1.93/2.10 ** KEPT (pick-wt=10): 1 [] -sum(A,B,C)|sum(A,s(B),s(C)).
% 1.93/2.10 ** KEPT (pick-wt=13): 2 [] -sum(A,B,C)| -product(D,B,A)|product(s(D),B,C).
% 1.93/2.10 ** KEPT (pick-wt=12): 3 [] -factorial(A,B)| -product(s(A),B,C)|factorial(s(A),C).
% 1.93/2.10 ** KEPT (pick-wt=8): 4 [] -factorial(s(s(s(s(s(n0))))),A).
% 1.93/2.10
% 1.93/2.10 ------------> process sos:
% 1.93/2.10 ** KEPT (pick-wt=4): 5 [] sum(A,n0,A).
% 1.93/2.10 ** KEPT (pick-wt=5): 6 [] product(s(n0),A,A).
% 1.93/2.10 ** KEPT (pick-wt=4): 7 [] factorial(n0,s(n0)).
% 1.93/2.10
% 1.93/2.10 ======= end of input processing =======
% 1.93/2.10
% 1.93/2.10 =========== start of search ===========
% 1.93/2.10
% 1.93/2.10 -------- PROOF --------
% 1.93/2.10
% 1.93/2.10 ----> UNIT CONFLICT at 0.10 sec ----> 721 [binary,720.1,4.1] $F.
% 1.93/2.10
% 1.93/2.10 Length of proof is 39. Level of proof is 29.
% 1.93/2.10
% 1.93/2.10 ---------------- PROOF ----------------
% 1.93/2.10 % SZS status Unsatisfiable
% 1.93/2.10 % SZS output start Refutation
% See solution above
% 1.93/2.10 ------------ end of proof -------------
% 1.93/2.10
% 1.93/2.10
% 1.93/2.10 Search stopped by max_proofs option.
% 1.93/2.10
% 1.93/2.10
% 1.93/2.10 Search stopped by max_proofs option.
% 1.93/2.10
% 1.93/2.10 ============ end of search ============
% 1.93/2.10
% 1.93/2.10 -------------- statistics -------------
% 1.93/2.10 clauses given 641
% 1.93/2.10 clauses generated 713
% 1.93/2.10 clauses kept 720
% 1.93/2.10 clauses forward subsumed 0
% 1.93/2.10 clauses back subsumed 0
% 1.93/2.10 Kbytes malloced 1953
% 1.93/2.10
% 1.93/2.10 ----------- times (seconds) -----------
% 1.93/2.10 user CPU time 0.10 (0 hr, 0 min, 0 sec)
% 1.93/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.93/2.10
% 1.93/2.10 That finishes the proof of the theorem.
% 1.93/2.10
% 1.93/2.10 Process 31208 finished Wed Jul 27 09:47:23 2022
% 1.93/2.10 Otter interrupted
% 1.93/2.10 PROOF FOUND
%------------------------------------------------------------------------------