%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD013-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 12:53:42 EDT 2022
% Result : Unsatisfiable 1.89s 2.09s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 17 ( 13 unt; 0 nHn; 17 RR)
% Number of literals : 25 ( 0 equ; 9 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( sum(A,B,C)
| ~ sum(A,D,E)
| ~ sum(D,F,B)
| ~ sum(E,F,C) ),
file('FLD013-4.p',unknown),
[] ).
cnf(2,axiom,
( sum(A,B,C)
| ~ sum(D,E,A)
| ~ sum(E,B,F)
| ~ sum(D,F,C) ),
file('FLD013-4.p',unknown),
[] ).
cnf(3,axiom,
( sum(additive_identity,A,A)
| ~ defined(A) ),
file('FLD013-4.p',unknown),
[] ).
cnf(5,axiom,
( sum(A,B,C)
| ~ sum(B,A,C) ),
file('FLD013-4.p',unknown),
[] ).
cnf(25,axiom,
~ sum(d,b,u),
file('FLD013-4.p',unknown),
[] ).
cnf(49,axiom,
defined(additive_identity),
file('FLD013-4.p',unknown),
[] ).
cnf(51,axiom,
defined(a),
file('FLD013-4.p',unknown),
[] ).
cnf(56,axiom,
sum(additive_identity,a,b),
file('FLD013-4.p',unknown),
[] ).
cnf(57,axiom,
sum(additive_identity,c,d),
file('FLD013-4.p',unknown),
[] ).
cnf(58,axiom,
sum(a,c,u),
file('FLD013-4.p',unknown),
[] ).
cnf(69,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[49,3]),
[iquote('hyper,49,3')] ).
cnf(118,plain,
sum(additive_identity,a,a),
inference(hyper,[status(thm)],[51,3]),
[iquote('hyper,51,3')] ).
cnf(575,plain,
sum(c,additive_identity,d),
inference(hyper,[status(thm)],[57,5]),
[iquote('hyper,57,5')] ).
cnf(787,plain,
sum(c,a,u),
inference(hyper,[status(thm)],[58,5]),
[iquote('hyper,58,5')] ).
cnf(4914,plain,
sum(additive_identity,b,a),
inference(hyper,[status(thm)],[118,1,69,56]),
[iquote('hyper,118,1,69,56')] ).
cnf(11814,plain,
sum(d,b,u),
inference(hyper,[status(thm)],[4914,2,575,787]),
[iquote('hyper,4914,2,575,787')] ).
cnf(11815,plain,
$false,
inference(binary,[status(thm)],[11814,25]),
[iquote('binary,11814.1,25.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : FLD013-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.32 % Computer : n029.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Jul 27 03:25:29 EDT 2022
% 0.12/0.32 % CPUTime :
% 1.59/1.80 ----- Otter 3.3f, August 2004 -----
% 1.59/1.80 The process was started by sandbox on n029.cluster.edu,
% 1.59/1.80 Wed Jul 27 03:25:29 2022
% 1.59/1.80 The command was "./otter". The process ID is 25542.
% 1.59/1.80
% 1.59/1.80 set(prolog_style_variables).
% 1.59/1.80 set(auto).
% 1.59/1.80 dependent: set(auto1).
% 1.59/1.80 dependent: set(process_input).
% 1.59/1.80 dependent: clear(print_kept).
% 1.59/1.80 dependent: clear(print_new_demod).
% 1.59/1.80 dependent: clear(print_back_demod).
% 1.59/1.80 dependent: clear(print_back_sub).
% 1.59/1.80 dependent: set(control_memory).
% 1.59/1.80 dependent: assign(max_mem, 12000).
% 1.59/1.80 dependent: assign(pick_given_ratio, 4).
% 1.59/1.80 dependent: assign(stats_level, 1).
% 1.59/1.80 dependent: assign(max_seconds, 10800).
% 1.59/1.80 clear(print_given).
% 1.59/1.80
% 1.59/1.80 list(usable).
% 1.59/1.80 0 [] sum(X,V,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W).
% 1.59/1.80 0 [] sum(U,Z,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W).
% 1.59/1.80 0 [] sum(additive_identity,X,X)| -defined(X).
% 1.59/1.80 0 [] sum(additive_inverse(X),X,additive_identity)| -defined(X).
% 1.59/1.80 0 [] sum(Y,X,Z)| -sum(X,Y,Z).
% 1.59/1.80 0 [] product(X,V,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W).
% 1.59/1.80 0 [] product(U,Z,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W).
% 1.59/1.80 0 [] product(multiplicative_identity,X,X)| -defined(X).
% 1.59/1.80 0 [] product(multiplicative_inverse(X),X,multiplicative_identity)|sum(additive_identity,X,additive_identity)| -defined(X).
% 1.59/1.80 0 [] product(Y,X,Z)| -product(X,Y,Z).
% 1.59/1.80 0 [] sum(C,D,B)| -sum(X,Y,A)| -product(A,Z,B)| -product(X,Z,C)| -product(Y,Z,D).
% 1.59/1.80 0 [] product(A,Z,B)| -sum(X,Y,A)| -product(X,Z,C)| -product(Y,Z,D)| -sum(C,D,B).
% 1.59/1.80 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.59/1.80 0 [] defined(additive_identity).
% 1.59/1.80 0 [] defined(additive_inverse(X))| -defined(X).
% 1.59/1.80 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.59/1.80 0 [] defined(multiplicative_identity).
% 1.59/1.80 0 [] defined(multiplicative_inverse(X))| -defined(X)|sum(additive_identity,X,additive_identity).
% 1.59/1.80 0 [] sum(X,Y,add(X,Y))| -defined(X)| -defined(Y).
% 1.59/1.80 0 [] product(X,Y,multiply(X,Y))| -defined(X)| -defined(Y).
% 1.59/1.80 0 [] sum(additive_identity,X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.59/1.80 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.59/1.80 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.59/1.80 0 [] less_or_e_qual(U,V)| -less_or_e_qual(X,Y)| -sum(X,Z,U)| -sum(Y,Z,V).
% 1.59/1.80 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).
% 1.59/1.80 0 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.59/1.80 0 [] defined(a).
% 1.59/1.80 0 [] defined(b).
% 1.59/1.80 0 [] defined(c).
% 1.59/1.80 0 [] defined(d).
% 1.59/1.80 0 [] defined(u).
% 1.59/1.80 0 [] sum(additive_identity,a,b).
% 1.59/1.80 0 [] sum(additive_identity,c,d).
% 1.59/1.80 0 [] sum(a,c,u).
% 1.59/1.80 0 [] -sum(d,b,u).
% 1.59/1.80 end_of_list.
% 1.59/1.80
% 1.59/1.80 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.59/1.80
% 1.59/1.80 This is a non-Horn set without equality. The strategy will
% 1.59/1.80 be ordered hyper_res, unit deletion, and factoring, with
% 1.59/1.80 satellites in sos and with nuclei in usable.
% 1.59/1.80
% 1.59/1.80 dependent: set(hyper_res).
% 1.59/1.80 dependent: set(factor).
% 1.59/1.80 dependent: set(unit_deletion).
% 1.59/1.80
% 1.59/1.80 ------------> process usable:
% 1.59/1.80 ** KEPT (pick-wt=16): 1 [] sum(A,B,C)| -sum(A,D,E)| -sum(D,F,B)| -sum(E,F,C).
% 1.59/1.80 ** KEPT (pick-wt=16): 2 [] sum(A,B,C)| -sum(D,E,A)| -sum(E,B,F)| -sum(D,F,C).
% 1.59/1.80 ** KEPT (pick-wt=6): 3 [] sum(additive_identity,A,A)| -defined(A).
% 1.59/1.80 ** KEPT (pick-wt=7): 4 [] sum(additive_inverse(A),A,additive_identity)| -defined(A).
% 1.59/1.80 ** KEPT (pick-wt=8): 5 [] sum(A,B,C)| -sum(B,A,C).
% 1.59/1.80 ** KEPT (pick-wt=16): 6 [] product(A,B,C)| -product(A,D,E)| -product(D,F,B)| -product(E,F,C).
% 1.59/1.80 ** KEPT (pick-wt=16): 7 [] product(A,B,C)| -product(D,E,A)| -product(E,B,F)| -product(D,F,C).
% 1.59/1.80 ** KEPT (pick-wt=6): 8 [] product(multiplicative_identity,A,A)| -defined(A).
% 1.59/1.80 ** KEPT (pick-wt=11): 9 [] product(multiplicative_inverse(A),A,multiplicative_identity)|sum(additive_identity,A,additive_identity)| -defined(A).
% 1.59/1.80 ** KEPT (pick-wt=8): 10 [] product(A,B,C)| -product(B,A,C).
% 1.59/1.80 ** 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).
% 1.59/1.80 ** 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).
% 1.59/1.80 ** KEPT (pick-wt=8): 13 [] defined(add(A,B))| -defined(A)| -defined(B).
% 1.59/1.80 ** KEPT (pick-wt=5): 14 [] defined(additive_inverse(A))| -defined(A).
% 1.59/1.80 ** KEPT (pick-wt=8): 15 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 1.89/2.09 ** KEPT (pick-wt=9): 16 [] defined(multiplicative_inverse(A))| -defined(A)|sum(additive_identity,A,additive_identity).
% 1.89/2.09 ** KEPT (pick-wt=10): 17 [] sum(A,B,add(A,B))| -defined(A)| -defined(B).
% 1.89/2.09 ** KEPT (pick-wt=10): 18 [] product(A,B,multiply(A,B))| -defined(A)| -defined(B).
% 1.89/2.09 ** KEPT (pick-wt=10): 19 [] sum(additive_identity,A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 1.89/2.09 ** KEPT (pick-wt=9): 20 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 1.89/2.09 ** KEPT (pick-wt=10): 21 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 1.89/2.09 ** 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).
% 1.89/2.09 ** 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).
% 1.89/2.09 ** KEPT (pick-wt=4): 24 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.89/2.09 ** KEPT (pick-wt=4): 25 [] -sum(d,b,u).
% 1.89/2.09
% 1.89/2.09 ------------> process sos:
% 1.89/2.09 ** KEPT (pick-wt=2): 49 [] defined(additive_identity).
% 1.89/2.09 ** KEPT (pick-wt=2): 50 [] defined(multiplicative_identity).
% 1.89/2.09 ** KEPT (pick-wt=2): 51 [] defined(a).
% 1.89/2.09 ** KEPT (pick-wt=2): 52 [] defined(b).
% 1.89/2.09 ** KEPT (pick-wt=2): 53 [] defined(c).
% 1.89/2.09 ** KEPT (pick-wt=2): 54 [] defined(d).
% 1.89/2.09 ** KEPT (pick-wt=2): 55 [] defined(u).
% 1.89/2.09 ** KEPT (pick-wt=4): 56 [] sum(additive_identity,a,b).
% 1.89/2.09 ** KEPT (pick-wt=4): 57 [] sum(additive_identity,c,d).
% 1.89/2.09 ** KEPT (pick-wt=4): 58 [] sum(a,c,u).
% 1.89/2.09
% 1.89/2.09 ======= end of input processing =======
% 1.89/2.09
% 1.89/2.09 =========== start of search ===========
% 1.89/2.09
% 1.89/2.09
% 1.89/2.09 Resetting weight limit to 6.
% 1.89/2.09
% 1.89/2.09
% 1.89/2.09 Resetting weight limit to 6.
% 1.89/2.09
% 1.89/2.09 sos_size=9406
% 1.89/2.09
% 1.89/2.09 -------- PROOF --------
% 1.89/2.09
% 1.89/2.09 ----> UNIT CONFLICT at 0.28 sec ----> 11815 [binary,11814.1,25.1] $F.
% 1.89/2.09
% 1.89/2.09 Length of proof is 6. Level of proof is 3.
% 1.89/2.09
% 1.89/2.09 ---------------- PROOF ----------------
% 1.89/2.09 % SZS status Unsatisfiable
% 1.89/2.09 % SZS output start Refutation
% See solution above
% 1.89/2.09 ------------ end of proof -------------
% 1.89/2.09
% 1.89/2.09
% 1.89/2.09 Search stopped by max_proofs option.
% 1.89/2.09
% 1.89/2.09
% 1.89/2.09 Search stopped by max_proofs option.
% 1.89/2.09
% 1.89/2.09 ============ end of search ============
% 1.89/2.09
% 1.89/2.09 -------------- statistics -------------
% 1.89/2.09 clauses given 188
% 1.89/2.09 clauses generated 76490
% 1.89/2.09 clauses kept 11814
% 1.89/2.09 clauses forward subsumed 2058
% 1.89/2.09 clauses back subsumed 21
% 1.89/2.09 Kbytes malloced 4882
% 1.89/2.09
% 1.89/2.09 ----------- times (seconds) -----------
% 1.89/2.09 user CPU time 0.28 (0 hr, 0 min, 0 sec)
% 1.89/2.09 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.89/2.09 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.89/2.09
% 1.89/2.09 That finishes the proof of the theorem.
% 1.89/2.09
% 1.89/2.09 Process 25542 finished Wed Jul 27 03:25:31 2022
% 1.89/2.09 Otter interrupted
% 1.89/2.09 PROOF FOUND
%------------------------------------------------------------------------------