TSTP Solution File: FLD043-5 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD043-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 12:53:48 EDT 2022
% Result : Unsatisfiable 3.50s 3.74s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 19
% Syntax : Number of clauses : 58 ( 38 unt; 0 nHn; 58 RR)
% Number of literals : 100 ( 0 equ; 43 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( sum(A,B,C)
| ~ sum(A,D,E)
| ~ sum(D,F,B)
| ~ sum(E,F,C) ),
file('FLD043-5.p',unknown),
[] ).
cnf(2,axiom,
( sum(A,B,C)
| ~ sum(D,E,A)
| ~ sum(E,B,F)
| ~ sum(D,F,C) ),
file('FLD043-5.p',unknown),
[] ).
cnf(3,axiom,
( sum(additive_identity,A,A)
| ~ defined(A) ),
file('FLD043-5.p',unknown),
[] ).
cnf(4,axiom,
( sum(additive_inverse(A),A,additive_identity)
| ~ defined(A) ),
file('FLD043-5.p',unknown),
[] ).
cnf(5,axiom,
( sum(A,B,C)
| ~ sum(B,A,C) ),
file('FLD043-5.p',unknown),
[] ).
cnf(6,axiom,
( product(A,B,C)
| ~ product(A,D,E)
| ~ product(D,F,B)
| ~ product(E,F,C) ),
file('FLD043-5.p',unknown),
[] ).
cnf(7,axiom,
( product(A,B,C)
| ~ product(D,E,A)
| ~ product(E,B,F)
| ~ product(D,F,C) ),
file('FLD043-5.p',unknown),
[] ).
cnf(8,axiom,
( product(multiplicative_identity,A,A)
| ~ defined(A) ),
file('FLD043-5.p',unknown),
[] ).
cnf(10,axiom,
( product(A,B,C)
| ~ product(B,A,C) ),
file('FLD043-5.p',unknown),
[] ).
cnf(11,axiom,
( sum(A,B,C)
| ~ sum(D,E,F)
| ~ product(F,G,C)
| ~ product(D,G,A)
| ~ product(E,G,B) ),
file('FLD043-5.p',unknown),
[] ).
cnf(12,axiom,
( product(A,B,C)
| ~ sum(D,E,A)
| ~ product(D,B,F)
| ~ product(E,B,G)
| ~ sum(F,G,C) ),
file('FLD043-5.p',unknown),
[] ).
cnf(14,axiom,
( defined(additive_inverse(A))
| ~ defined(A) ),
file('FLD043-5.p',unknown),
[] ).
cnf(15,axiom,
( defined(multiply(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD043-5.p',unknown),
[] ).
cnf(17,axiom,
( sum(A,B,add(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD043-5.p',unknown),
[] ).
cnf(18,axiom,
( product(A,B,multiply(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD043-5.p',unknown),
[] ).
cnf(25,axiom,
~ product(additive_identity,a,additive_identity),
file('FLD043-5.p',unknown),
[] ).
cnf(27,plain,
( sum(A,B,B)
| ~ sum(A,C,C)
| ~ sum(C,D,B) ),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.3.4')] ).
cnf(35,plain,
( sum(A,B,B)
| ~ sum(C,D,D)
| ~ product(D,E,B)
| ~ product(C,E,A) ),
inference(factor,[status(thm)],[11]),
[iquote('factor,11.3.5')] ).
cnf(38,plain,
( product(A,B,C)
| ~ sum(D,D,A)
| ~ product(D,B,E)
| ~ sum(E,E,C) ),
inference(factor,[status(thm)],[12]),
[iquote('factor,12.3.4')] ).
cnf(40,plain,
( defined(multiply(A,A))
| ~ defined(A) ),
inference(factor,[status(thm)],[15]),
[iquote('factor,15.2.3')] ).
cnf(42,plain,
( product(A,A,multiply(A,A))
| ~ defined(A) ),
inference(factor,[status(thm)],[18]),
[iquote('factor,18.2.3')] ).
cnf(49,axiom,
defined(additive_identity),
file('FLD043-5.p',unknown),
[] ).
cnf(50,axiom,
defined(multiplicative_identity),
file('FLD043-5.p',unknown),
[] ).
cnf(51,axiom,
defined(a),
file('FLD043-5.p',unknown),
[] ).
cnf(53,plain,
product(additive_identity,additive_identity,multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[49,42]),
[iquote('hyper,49,42')] ).
cnf(55,plain,
defined(multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[49,40]),
[iquote('hyper,49,40')] ).
cnf(58,plain,
defined(additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[49,14]),
[iquote('hyper,49,14')] ).
cnf(60,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[49,8]),
[iquote('hyper,49,8')] ).
cnf(61,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(hyper,[status(thm)],[49,4]),
[iquote('hyper,49,4')] ).
cnf(62,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[49,3]),
[iquote('hyper,49,3')] ).
cnf(71,plain,
sum(additive_identity,multiplicative_identity,add(additive_identity,multiplicative_identity)),
inference(hyper,[status(thm)],[50,17,49]),
[iquote('hyper,50,17,49')] ).
cnf(82,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(hyper,[status(thm)],[50,3]),
[iquote('hyper,50,3')] ).
cnf(91,plain,
product(additive_identity,a,multiply(additive_identity,a)),
inference(hyper,[status(thm)],[51,18,49]),
[iquote('hyper,51,18,49')] ).
cnf(109,plain,
product(multiplicative_identity,a,a),
inference(hyper,[status(thm)],[51,8]),
[iquote('hyper,51,8')] ).
cnf(110,plain,
sum(additive_inverse(a),a,additive_identity),
inference(hyper,[status(thm)],[51,4]),
[iquote('hyper,51,4')] ).
cnf(111,plain,
sum(additive_identity,a,a),
inference(hyper,[status(thm)],[51,3]),
[iquote('hyper,51,3')] ).
cnf(149,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[58,3]),
[iquote('hyper,58,3')] ).
cnf(318,plain,
sum(additive_identity,multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[55,3]),
[iquote('hyper,55,3')] ).
cnf(392,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[60,10]),
[iquote('hyper,60,10')] ).
cnf(400,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[61,5]),
[iquote('hyper,61,5')] ).
cnf(1040,plain,
sum(multiply(additive_identity,additive_identity),additive_identity,additive_identity),
inference(hyper,[status(thm)],[82,35,60,53]),
[iquote('hyper,82,35,60,53')] ).
cnf(1043,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(hyper,[status(thm)],[82,5]),
[iquote('hyper,82,5')] ).
cnf(2838,plain,
sum(a,additive_identity,a),
inference(hyper,[status(thm)],[111,5]),
[iquote('hyper,111,5')] ).
cnf(3601,plain,
sum(add(additive_identity,multiplicative_identity),additive_identity,multiplicative_identity),
inference(hyper,[status(thm)],[1043,2,71,82]),
[iquote('hyper,1043,2,71,82')] ).
cnf(3628,plain,
sum(a,additive_inverse(a),additive_identity),
inference(hyper,[status(thm)],[110,5]),
[iquote('hyper,110,5')] ).
cnf(8969,plain,
sum(multiply(additive_identity,a),a,a),
inference(hyper,[status(thm)],[91,35,82,109]),
[iquote('hyper,91,35,82,109')] ).
cnf(8971,plain,
product(a,additive_identity,multiply(additive_identity,a)),
inference(hyper,[status(thm)],[91,10]),
[iquote('hyper,91,10')] ).
cnf(9469,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[149,1,62,400]),
[iquote('hyper,149,1,62,400')] ).
cnf(9480,plain,
product(additive_identity,multiplicative_identity,additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[9469,38,62,392]),
[iquote('hyper,9469,38,62,392')] ).
cnf(9513,plain,
product(multiplicative_identity,additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[9480,6,60,392]),
[iquote('hyper,9480,6,60,392')] ).
cnf(9758,plain,
product(add(additive_identity,multiplicative_identity),additive_identity,additive_identity),
inference(hyper,[status(thm)],[1040,12,71,53,60]),
[iquote('hyper,1040,12,71,53,60')] ).
cnf(10049,plain,
sum(multiply(additive_identity,a),additive_identity,additive_identity),
inference(hyper,[status(thm)],[8969,27,3628]),
[iquote('hyper,8969,27,3628')] ).
cnf(10176,plain,
product(multiplicative_identity,additive_identity,multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[318,12,3601,9758,53]),
[iquote('hyper,318,12,3601,9758,53')] ).
cnf(10214,plain,
product(multiply(additive_identity,additive_identity),multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[10176,7,9480,9513]),
[iquote('hyper,10176,7,9480,9513')] ).
cnf(10237,plain,
product(additive_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[10214,6,53,392]),
[iquote('hyper,10214,6,53,392')] ).
cnf(10261,plain,
product(a,additive_identity,additive_identity),
inference(hyper,[status(thm)],[10237,12,2838,8971,10049]),
[iquote('hyper,10237,12,2838,8971,10049')] ).
cnf(10304,plain,
product(additive_identity,a,additive_identity),
inference(hyper,[status(thm)],[10261,10]),
[iquote('hyper,10261,10')] ).
cnf(10305,plain,
$false,
inference(binary,[status(thm)],[10304,25]),
[iquote('binary,10304.1,25.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : FLD043-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 03:09:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.58/1.79 ----- Otter 3.3f, August 2004 -----
% 1.58/1.79 The process was started by sandbox2 on n005.cluster.edu,
% 1.58/1.79 Wed Jul 27 03:09:35 2022
% 1.58/1.79 The command was "./otter". The process ID is 4253.
% 1.58/1.79
% 1.58/1.79 set(prolog_style_variables).
% 1.58/1.79 set(auto).
% 1.58/1.79 dependent: set(auto1).
% 1.58/1.79 dependent: set(process_input).
% 1.58/1.79 dependent: clear(print_kept).
% 1.58/1.79 dependent: clear(print_new_demod).
% 1.58/1.79 dependent: clear(print_back_demod).
% 1.58/1.79 dependent: clear(print_back_sub).
% 1.58/1.79 dependent: set(control_memory).
% 1.58/1.79 dependent: assign(max_mem, 12000).
% 1.58/1.79 dependent: assign(pick_given_ratio, 4).
% 1.58/1.79 dependent: assign(stats_level, 1).
% 1.58/1.79 dependent: assign(max_seconds, 10800).
% 1.58/1.79 clear(print_given).
% 1.58/1.79
% 1.58/1.79 list(usable).
% 1.58/1.79 0 [] sum(X,V,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W).
% 1.58/1.79 0 [] sum(U,Z,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W).
% 1.58/1.79 0 [] sum(additive_identity,X,X)| -defined(X).
% 1.58/1.79 0 [] sum(additive_inverse(X),X,additive_identity)| -defined(X).
% 1.58/1.79 0 [] sum(Y,X,Z)| -sum(X,Y,Z).
% 1.58/1.79 0 [] product(X,V,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W).
% 1.58/1.79 0 [] product(U,Z,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W).
% 1.58/1.79 0 [] product(multiplicative_identity,X,X)| -defined(X).
% 1.58/1.79 0 [] product(multiplicative_inverse(X),X,multiplicative_identity)|sum(additive_identity,X,additive_identity)| -defined(X).
% 1.58/1.79 0 [] product(Y,X,Z)| -product(X,Y,Z).
% 1.58/1.79 0 [] sum(C,D,B)| -sum(X,Y,A)| -product(A,Z,B)| -product(X,Z,C)| -product(Y,Z,D).
% 1.58/1.79 0 [] product(A,Z,B)| -sum(X,Y,A)| -product(X,Z,C)| -product(Y,Z,D)| -sum(C,D,B).
% 1.58/1.79 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.58/1.79 0 [] defined(additive_identity).
% 1.58/1.79 0 [] defined(additive_inverse(X))| -defined(X).
% 1.58/1.79 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.58/1.79 0 [] defined(multiplicative_identity).
% 1.58/1.79 0 [] defined(multiplicative_inverse(X))| -defined(X)|sum(additive_identity,X,additive_identity).
% 1.58/1.79 0 [] sum(X,Y,add(X,Y))| -defined(X)| -defined(Y).
% 1.58/1.79 0 [] product(X,Y,multiply(X,Y))| -defined(X)| -defined(Y).
% 1.58/1.79 0 [] sum(additive_identity,X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.58/1.79 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.58/1.79 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.58/1.79 0 [] less_or_e_qual(U,V)| -less_or_e_qual(X,Y)| -sum(X,Z,U)| -sum(Y,Z,V).
% 1.58/1.79 0 [] less_or_e_qual(additive_identity,Z)| -less_or_e_qual(additive_identity,X)| -less_or_e_qual(additive_identity,Y)| -product(X,Y,Z).
% 1.58/1.79 0 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.58/1.79 0 [] defined(a).
% 1.58/1.79 0 [] -product(additive_identity,a,additive_identity).
% 1.58/1.79 end_of_list.
% 1.58/1.79
% 1.58/1.79 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.58/1.79
% 1.58/1.79 This is a non-Horn set without equality. The strategy will
% 1.58/1.79 be ordered hyper_res, unit deletion, and factoring, with
% 1.58/1.79 satellites in sos and with nuclei in usable.
% 1.58/1.79
% 1.58/1.79 dependent: set(hyper_res).
% 1.58/1.79 dependent: set(factor).
% 1.58/1.79 dependent: set(unit_deletion).
% 1.58/1.79
% 1.58/1.79 ------------> process usable:
% 1.58/1.79 ** KEPT (pick-wt=16): 1 [] sum(A,B,C)| -sum(A,D,E)| -sum(D,F,B)| -sum(E,F,C).
% 1.58/1.79 ** KEPT (pick-wt=16): 2 [] sum(A,B,C)| -sum(D,E,A)| -sum(E,B,F)| -sum(D,F,C).
% 1.58/1.79 ** KEPT (pick-wt=6): 3 [] sum(additive_identity,A,A)| -defined(A).
% 1.58/1.79 ** KEPT (pick-wt=7): 4 [] sum(additive_inverse(A),A,additive_identity)| -defined(A).
% 1.58/1.79 ** KEPT (pick-wt=8): 5 [] sum(A,B,C)| -sum(B,A,C).
% 1.58/1.79 ** KEPT (pick-wt=16): 6 [] product(A,B,C)| -product(A,D,E)| -product(D,F,B)| -product(E,F,C).
% 1.58/1.79 ** KEPT (pick-wt=16): 7 [] product(A,B,C)| -product(D,E,A)| -product(E,B,F)| -product(D,F,C).
% 1.58/1.79 ** KEPT (pick-wt=6): 8 [] product(multiplicative_identity,A,A)| -defined(A).
% 1.58/1.79 ** KEPT (pick-wt=11): 9 [] product(multiplicative_inverse(A),A,multiplicative_identity)|sum(additive_identity,A,additive_identity)| -defined(A).
% 1.58/1.79 ** KEPT (pick-wt=8): 10 [] product(A,B,C)| -product(B,A,C).
% 1.58/1.79 ** KEPT (pick-wt=20): 11 [] sum(A,B,C)| -sum(D,E,F)| -product(F,G,C)| -product(D,G,A)| -product(E,G,B).
% 1.58/1.79 ** KEPT (pick-wt=20): 12 [] product(A,B,C)| -sum(D,E,A)| -product(D,B,F)| -product(E,B,G)| -sum(F,G,C).
% 1.58/1.79 ** KEPT (pick-wt=8): 13 [] defined(add(A,B))| -defined(A)| -defined(B).
% 1.58/1.79 ** KEPT (pick-wt=5): 14 [] defined(additive_inverse(A))| -defined(A).
% 1.58/1.79 ** KEPT (pick-wt=8): 15 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 1.58/1.79 ** KEPT (pick-wt=9): 16 [] defined(multiplicative_inverse(A))| -defined(A)|sum(additive_identity,A,additive_identity).
% 3.50/3.74 ** KEPT (pick-wt=10): 17 [] sum(A,B,add(A,B))| -defined(A)| -defined(B).
% 3.50/3.74 ** KEPT (pick-wt=10): 18 [] product(A,B,multiply(A,B))| -defined(A)| -defined(B).
% 3.50/3.74 ** KEPT (pick-wt=10): 19 [] sum(additive_identity,A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 3.50/3.74 ** KEPT (pick-wt=9): 20 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 3.50/3.74 ** KEPT (pick-wt=10): 21 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 3.50/3.74 ** KEPT (pick-wt=14): 22 [] less_or_e_qual(A,B)| -less_or_e_qual(C,D)| -sum(C,E,A)| -sum(D,E,B).
% 3.50/3.74 ** KEPT (pick-wt=13): 23 [] less_or_e_qual(additive_identity,A)| -less_or_e_qual(additive_identity,B)| -less_or_e_qual(additive_identity,C)| -product(B,C,A).
% 3.50/3.74 ** KEPT (pick-wt=4): 24 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 3.50/3.74 ** KEPT (pick-wt=4): 25 [] -product(additive_identity,a,additive_identity).
% 3.50/3.74
% 3.50/3.74 ------------> process sos:
% 3.50/3.74 ** KEPT (pick-wt=2): 49 [] defined(additive_identity).
% 3.50/3.74 ** KEPT (pick-wt=2): 50 [] defined(multiplicative_identity).
% 3.50/3.74 ** KEPT (pick-wt=2): 51 [] defined(a).
% 3.50/3.74
% 3.50/3.74 ======= end of input processing =======
% 3.50/3.74
% 3.50/3.74 =========== start of search ===========
% 3.50/3.74
% 3.50/3.74
% 3.50/3.74 Resetting weight limit to 7.
% 3.50/3.74
% 3.50/3.74
% 3.50/3.74 Resetting weight limit to 7.
% 3.50/3.74
% 3.50/3.74 sos_size=8644
% 3.50/3.74
% 3.50/3.74 -------- PROOF --------
% 3.50/3.74
% 3.50/3.74 ----> UNIT CONFLICT at 1.95 sec ----> 10305 [binary,10304.1,25.1] $F.
% 3.50/3.74
% 3.50/3.74 Length of proof is 38. Level of proof is 9.
% 3.50/3.74
% 3.50/3.74 ---------------- PROOF ----------------
% 3.50/3.74 % SZS status Unsatisfiable
% 3.50/3.74 % SZS output start Refutation
% See solution above
% 3.50/3.74 ------------ end of proof -------------
% 3.50/3.74
% 3.50/3.74
% 3.50/3.74 Search stopped by max_proofs option.
% 3.50/3.74
% 3.50/3.74
% 3.50/3.74 Search stopped by max_proofs option.
% 3.50/3.74
% 3.50/3.74 ============ end of search ============
% 3.50/3.74
% 3.50/3.74 -------------- statistics -------------
% 3.50/3.74 clauses given 809
% 3.50/3.74 clauses generated 967850
% 3.50/3.74 clauses kept 10304
% 3.50/3.74 clauses forward subsumed 11909
% 3.50/3.74 clauses back subsumed 104
% 3.50/3.74 Kbytes malloced 5859
% 3.50/3.74
% 3.50/3.74 ----------- times (seconds) -----------
% 3.50/3.74 user CPU time 1.95 (0 hr, 0 min, 1 sec)
% 3.50/3.74 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.50/3.74 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 3.50/3.74
% 3.50/3.74 That finishes the proof of the theorem.
% 3.50/3.74
% 3.50/3.74 Process 4253 finished Wed Jul 27 03:09:39 2022
% 3.50/3.74 Otter interrupted
% 3.50/3.74 PROOF FOUND
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