TSTP Solution File: FLD040-3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD040-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 1.99s 2.18s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 26 ( 16 unt; 1 nHn; 26 RR)
% Number of literals : 46 ( 0 equ; 21 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 : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 32 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( sum(A,B,C)
| ~ sum(D,E,A)
| ~ sum(E,B,F)
| ~ sum(D,F,C) ),
file('FLD040-3.p',unknown),
[] ).
cnf(3,axiom,
( sum(additive_identity,A,A)
| ~ defined(A) ),
file('FLD040-3.p',unknown),
[] ).
cnf(4,axiom,
( sum(additive_inverse(A),A,additive_identity)
| ~ defined(A) ),
file('FLD040-3.p',unknown),
[] ).
cnf(5,axiom,
( sum(A,B,C)
| ~ sum(B,A,C) ),
file('FLD040-3.p',unknown),
[] ).
cnf(8,axiom,
( product(multiplicative_identity,A,A)
| ~ defined(A) ),
file('FLD040-3.p',unknown),
[] ).
cnf(9,axiom,
( product(multiplicative_inverse(A),A,multiplicative_identity)
| sum(additive_identity,A,additive_identity)
| ~ defined(A) ),
file('FLD040-3.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('FLD040-3.p',unknown),
[] ).
cnf(24,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('FLD040-3.p',unknown),
[] ).
cnf(25,axiom,
~ sum(additive_identity,a,additive_identity),
file('FLD040-3.p',unknown),
[] ).
cnf(28,plain,
( sum(A,B,A)
| ~ sum(C,D,A)
| ~ sum(D,B,D) ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.2.4')] ).
cnf(29,plain,
( sum(A,B,B)
| ~ sum(C,C,A)
| ~ sum(C,B,B) ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.3.4')] ).
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(50,axiom,
defined(multiplicative_identity),
file('FLD040-3.p',unknown),
[] ).
cnf(51,axiom,
defined(a),
file('FLD040-3.p',unknown),
[] ).
cnf(52,axiom,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
file('FLD040-3.p',unknown),
[] ).
cnf(83,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(hyper,[status(thm)],[50,3]),
[iquote('hyper,50,3')] ).
cnf(109,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[51,9]),25]),
[iquote('hyper,51,9,unit_del,25')] ).
cnf(110,plain,
product(multiplicative_identity,a,a),
inference(hyper,[status(thm)],[51,8]),
[iquote('hyper,51,8')] ).
cnf(111,plain,
sum(additive_inverse(a),a,additive_identity),
inference(hyper,[status(thm)],[51,4]),
[iquote('hyper,51,4')] ).
cnf(1196,plain,
sum(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity),
inference(hyper,[status(thm)],[83,29,52]),
[iquote('hyper,83,29,52')] ).
cnf(1198,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(hyper,[status(thm)],[83,5]),
[iquote('hyper,83,5')] ).
cnf(8541,plain,
sum(multiplicative_identity,a,a),
inference(hyper,[status(thm)],[1196,35,110,109]),
[iquote('hyper,1196,35,110,109')] ).
cnf(8553,plain,
sum(a,multiplicative_identity,a),
inference(hyper,[status(thm)],[8541,5]),
[iquote('hyper,8541,5')] ).
cnf(8566,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[8553,28,111]),
[iquote('hyper,8553,28,111')] ).
cnf(8611,plain,
sum(additive_identity,additive_identity,multiplicative_identity),
inference(hyper,[status(thm)],[8566,2,1198,83]),
[iquote('hyper,8566,2,1198,83')] ).
cnf(8612,plain,
$false,
inference(binary,[status(thm)],[8611,24]),
[iquote('binary,8611.1,24.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : FLD040-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 03:12:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.74/1.95 ----- Otter 3.3f, August 2004 -----
% 1.74/1.95 The process was started by sandbox2 on n022.cluster.edu,
% 1.74/1.95 Wed Jul 27 03:12:20 2022
% 1.74/1.95 The command was "./otter". The process ID is 16108.
% 1.74/1.95
% 1.74/1.95 set(prolog_style_variables).
% 1.74/1.95 set(auto).
% 1.74/1.95 dependent: set(auto1).
% 1.74/1.95 dependent: set(process_input).
% 1.74/1.95 dependent: clear(print_kept).
% 1.74/1.95 dependent: clear(print_new_demod).
% 1.74/1.95 dependent: clear(print_back_demod).
% 1.74/1.95 dependent: clear(print_back_sub).
% 1.74/1.95 dependent: set(control_memory).
% 1.74/1.95 dependent: assign(max_mem, 12000).
% 1.74/1.95 dependent: assign(pick_given_ratio, 4).
% 1.74/1.95 dependent: assign(stats_level, 1).
% 1.74/1.95 dependent: assign(max_seconds, 10800).
% 1.74/1.95 clear(print_given).
% 1.74/1.95
% 1.74/1.95 list(usable).
% 1.74/1.95 0 [] sum(X,V,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W).
% 1.74/1.95 0 [] sum(U,Z,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W).
% 1.74/1.95 0 [] sum(additive_identity,X,X)| -defined(X).
% 1.74/1.95 0 [] sum(additive_inverse(X),X,additive_identity)| -defined(X).
% 1.74/1.95 0 [] sum(Y,X,Z)| -sum(X,Y,Z).
% 1.74/1.95 0 [] product(X,V,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W).
% 1.74/1.95 0 [] product(U,Z,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W).
% 1.74/1.95 0 [] product(multiplicative_identity,X,X)| -defined(X).
% 1.74/1.95 0 [] product(multiplicative_inverse(X),X,multiplicative_identity)|sum(additive_identity,X,additive_identity)| -defined(X).
% 1.74/1.95 0 [] product(Y,X,Z)| -product(X,Y,Z).
% 1.74/1.95 0 [] sum(C,D,B)| -sum(X,Y,A)| -product(A,Z,B)| -product(X,Z,C)| -product(Y,Z,D).
% 1.74/1.95 0 [] product(A,Z,B)| -sum(X,Y,A)| -product(X,Z,C)| -product(Y,Z,D)| -sum(C,D,B).
% 1.74/1.95 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.74/1.95 0 [] defined(additive_identity).
% 1.74/1.95 0 [] defined(additive_inverse(X))| -defined(X).
% 1.74/1.95 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.74/1.95 0 [] defined(multiplicative_identity).
% 1.74/1.95 0 [] defined(multiplicative_inverse(X))| -defined(X)|sum(additive_identity,X,additive_identity).
% 1.74/1.95 0 [] sum(X,Y,add(X,Y))| -defined(X)| -defined(Y).
% 1.74/1.95 0 [] product(X,Y,multiply(X,Y))| -defined(X)| -defined(Y).
% 1.74/1.95 0 [] sum(additive_identity,X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.74/1.95 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.74/1.95 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.74/1.95 0 [] less_or_e_qual(U,V)| -less_or_e_qual(X,Y)| -sum(X,Z,U)| -sum(Y,Z,V).
% 1.74/1.95 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).
% 1.74/1.95 0 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.74/1.95 0 [] defined(a).
% 1.74/1.95 0 [] -sum(additive_identity,a,additive_identity).
% 1.74/1.95 0 [] sum(additive_identity,additive_identity,multiplicative_inverse(a)).
% 1.74/1.95 end_of_list.
% 1.74/1.95
% 1.74/1.95 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.74/1.95
% 1.74/1.95 This is a non-Horn set without equality. The strategy will
% 1.74/1.95 be ordered hyper_res, unit deletion, and factoring, with
% 1.74/1.95 satellites in sos and with nuclei in usable.
% 1.74/1.95
% 1.74/1.95 dependent: set(hyper_res).
% 1.74/1.95 dependent: set(factor).
% 1.74/1.95 dependent: set(unit_deletion).
% 1.74/1.95
% 1.74/1.95 ------------> process usable:
% 1.74/1.95 ** KEPT (pick-wt=16): 1 [] sum(A,B,C)| -sum(A,D,E)| -sum(D,F,B)| -sum(E,F,C).
% 1.74/1.95 ** KEPT (pick-wt=16): 2 [] sum(A,B,C)| -sum(D,E,A)| -sum(E,B,F)| -sum(D,F,C).
% 1.74/1.95 ** KEPT (pick-wt=6): 3 [] sum(additive_identity,A,A)| -defined(A).
% 1.74/1.95 ** KEPT (pick-wt=7): 4 [] sum(additive_inverse(A),A,additive_identity)| -defined(A).
% 1.74/1.95 ** KEPT (pick-wt=8): 5 [] sum(A,B,C)| -sum(B,A,C).
% 1.74/1.95 ** KEPT (pick-wt=16): 6 [] product(A,B,C)| -product(A,D,E)| -product(D,F,B)| -product(E,F,C).
% 1.74/1.95 ** KEPT (pick-wt=16): 7 [] product(A,B,C)| -product(D,E,A)| -product(E,B,F)| -product(D,F,C).
% 1.74/1.95 ** KEPT (pick-wt=6): 8 [] product(multiplicative_identity,A,A)| -defined(A).
% 1.74/1.95 ** KEPT (pick-wt=11): 9 [] product(multiplicative_inverse(A),A,multiplicative_identity)|sum(additive_identity,A,additive_identity)| -defined(A).
% 1.74/1.95 ** KEPT (pick-wt=8): 10 [] product(A,B,C)| -product(B,A,C).
% 1.74/1.95 ** 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).
% 1.74/1.95 ** 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).
% 1.74/1.95 ** KEPT (pick-wt=8): 13 [] defined(add(A,B))| -defined(A)| -defined(B).
% 1.74/1.95 ** KEPT (pick-wt=5): 14 [] defined(additive_inverse(A))| -defined(A).
% 1.74/1.95 ** KEPT (pick-wt=8): 15 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 1.99/2.18 ** KEPT (pick-wt=9): 16 [] defined(multiplicative_inverse(A))| -defined(A)|sum(additive_identity,A,additive_identity).
% 1.99/2.18 ** KEPT (pick-wt=10): 17 [] sum(A,B,add(A,B))| -defined(A)| -defined(B).
% 1.99/2.18 ** KEPT (pick-wt=10): 18 [] product(A,B,multiply(A,B))| -defined(A)| -defined(B).
% 1.99/2.18 ** KEPT (pick-wt=10): 19 [] sum(additive_identity,A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 1.99/2.18 ** KEPT (pick-wt=9): 20 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 1.99/2.18 ** KEPT (pick-wt=10): 21 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 1.99/2.18 ** 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).
% 1.99/2.18 ** 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).
% 1.99/2.18 ** KEPT (pick-wt=4): 24 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.99/2.18 ** KEPT (pick-wt=4): 25 [] -sum(additive_identity,a,additive_identity).
% 1.99/2.18
% 1.99/2.18 ------------> process sos:
% 1.99/2.18 ** KEPT (pick-wt=2): 49 [] defined(additive_identity).
% 1.99/2.18 ** KEPT (pick-wt=2): 50 [] defined(multiplicative_identity).
% 1.99/2.18 ** KEPT (pick-wt=2): 51 [] defined(a).
% 1.99/2.18 ** KEPT (pick-wt=5): 52 [] sum(additive_identity,additive_identity,multiplicative_inverse(a)).
% 1.99/2.18
% 1.99/2.18 ======= end of input processing =======
% 1.99/2.18
% 1.99/2.18 =========== start of search ===========
% 1.99/2.18
% 1.99/2.18
% 1.99/2.18 Resetting weight limit to 6.
% 1.99/2.18
% 1.99/2.18
% 1.99/2.18 Resetting weight limit to 6.
% 1.99/2.18
% 1.99/2.18 sos_size=8285
% 1.99/2.18
% 1.99/2.18 -------- PROOF --------
% 1.99/2.18
% 1.99/2.18 ----> UNIT CONFLICT at 0.22 sec ----> 8612 [binary,8611.1,24.1] $F.
% 1.99/2.18
% 1.99/2.18 Length of proof is 13. Level of proof is 6.
% 1.99/2.18
% 1.99/2.18 ---------------- PROOF ----------------
% 1.99/2.18 % SZS status Unsatisfiable
% 1.99/2.18 % SZS output start Refutation
% See solution above
% 1.99/2.18 ------------ end of proof -------------
% 1.99/2.18
% 1.99/2.18
% 1.99/2.18 Search stopped by max_proofs option.
% 1.99/2.18
% 1.99/2.18
% 1.99/2.18 Search stopped by max_proofs option.
% 1.99/2.18
% 1.99/2.18 ============ end of search ============
% 1.99/2.18
% 1.99/2.18 -------------- statistics -------------
% 1.99/2.18 clauses given 145
% 1.99/2.18 clauses generated 40733
% 1.99/2.18 clauses kept 8611
% 1.99/2.18 clauses forward subsumed 2041
% 1.99/2.18 clauses back subsumed 438
% 1.99/2.18 Kbytes malloced 4882
% 1.99/2.18
% 1.99/2.18 ----------- times (seconds) -----------
% 1.99/2.18 user CPU time 0.22 (0 hr, 0 min, 0 sec)
% 1.99/2.18 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.99/2.18 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.99/2.18
% 1.99/2.18 That finishes the proof of the theorem.
% 1.99/2.18
% 1.99/2.18 Process 16108 finished Wed Jul 27 03:12:22 2022
% 1.99/2.18 Otter interrupted
% 1.99/2.18 PROOF FOUND
%------------------------------------------------------------------------------