TSTP Solution File: FLD067-4 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD067-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 12:53:54 EDT 2022
% Result : Unsatisfiable 1.94s 2.13s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of clauses : 31 ( 22 unt; 1 nHn; 31 RR)
% Number of literals : 48 ( 0 equ; 17 neg)
% Maximal clause size : 4 ( 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; 4 con; 0-1 aty)
% Number of variables : 25 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( sum(A,B,C)
| ~ sum(D,E,A)
| ~ sum(E,B,F)
| ~ sum(D,F,C) ),
file('FLD067-4.p',unknown),
[] ).
cnf(3,axiom,
( sum(additive_identity,A,A)
| ~ defined(A) ),
file('FLD067-4.p',unknown),
[] ).
cnf(4,axiom,
( sum(additive_inverse(A),A,additive_identity)
| ~ defined(A) ),
file('FLD067-4.p',unknown),
[] ).
cnf(5,axiom,
( sum(A,B,C)
| ~ sum(B,A,C) ),
file('FLD067-4.p',unknown),
[] ).
cnf(19,axiom,
( sum(additive_identity,A,B)
| ~ less_or_e_qual(A,B)
| ~ less_or_e_qual(B,A) ),
file('FLD067-4.p',unknown),
[] ).
cnf(21,axiom,
( less_or_e_qual(A,B)
| less_or_e_qual(B,A)
| ~ defined(A)
| ~ defined(B) ),
file('FLD067-4.p',unknown),
[] ).
cnf(22,axiom,
( less_or_e_qual(A,B)
| ~ less_or_e_qual(C,D)
| ~ sum(C,E,A)
| ~ sum(D,E,B) ),
file('FLD067-4.p',unknown),
[] ).
cnf(25,axiom,
~ less_or_e_qual(additive_identity,u),
file('FLD067-4.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(44,plain,
( less_or_e_qual(A,A)
| ~ defined(A) ),
inference(factor_simp,[status(thm)],[inference(factor,[status(thm)],[21])]),
[iquote('factor,21.1.2,factor_simp')] ).
cnf(49,axiom,
defined(additive_identity),
file('FLD067-4.p',unknown),
[] ).
cnf(51,axiom,
defined(a),
file('FLD067-4.p',unknown),
[] ).
cnf(52,axiom,
defined(b),
file('FLD067-4.p',unknown),
[] ).
cnf(53,axiom,
defined(u),
file('FLD067-4.p',unknown),
[] ).
cnf(54,axiom,
less_or_e_qual(a,b),
file('FLD067-4.p',unknown),
[] ).
cnf(55,axiom,
sum(b,additive_inverse(a),u),
file('FLD067-4.p',unknown),
[] ).
cnf(56,plain,
less_or_e_qual(additive_identity,additive_identity),
inference(hyper,[status(thm)],[49,44]),
[iquote('hyper,49,44')] ).
cnf(114,plain,
sum(additive_inverse(a),a,additive_identity),
inference(hyper,[status(thm)],[51,4]),
[iquote('hyper,51,4')] ).
cnf(115,plain,
sum(additive_identity,a,a),
inference(hyper,[status(thm)],[51,3]),
[iquote('hyper,51,3')] ).
cnf(152,plain,
sum(additive_identity,b,b),
inference(hyper,[status(thm)],[52,3]),
[iquote('hyper,52,3')] ).
cnf(161,plain,
less_or_e_qual(u,additive_identity),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[53,21,49]),25]),
[iquote('hyper,53,21,49,unit_del,25')] ).
cnf(199,plain,
sum(additive_identity,u,u),
inference(hyper,[status(thm)],[53,3]),
[iquote('hyper,53,3')] ).
cnf(8724,plain,
sum(b,additive_identity,b),
inference(hyper,[status(thm)],[152,5]),
[iquote('hyper,152,5')] ).
cnf(10051,plain,
sum(u,a,b),
inference(hyper,[status(thm)],[114,2,55,8724]),
[iquote('hyper,114,2,55,8724')] ).
cnf(10052,plain,
less_or_e_qual(b,a),
inference(hyper,[status(thm)],[10051,22,161,115]),
[iquote('hyper,10051,22,161,115')] ).
cnf(10054,plain,
sum(a,u,b),
inference(hyper,[status(thm)],[10051,5]),
[iquote('hyper,10051,5')] ).
cnf(10058,plain,
sum(additive_identity,b,a),
inference(hyper,[status(thm)],[10052,19,54]),
[iquote('hyper,10052,19,54')] ).
cnf(10079,plain,
sum(a,u,a),
inference(hyper,[status(thm)],[10058,2,115,10054]),
[iquote('hyper,10058,2,115,10054')] ).
cnf(10135,plain,
sum(additive_identity,u,additive_identity),
inference(hyper,[status(thm)],[10079,28,114]),
[iquote('hyper,10079,28,114')] ).
cnf(10156,plain,
less_or_e_qual(additive_identity,u),
inference(hyper,[status(thm)],[10135,22,56,199]),
[iquote('hyper,10135,22,56,199')] ).
cnf(10157,plain,
$false,
inference(binary,[status(thm)],[10156,25]),
[iquote('binary,10156.1,25.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : FLD067-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 02:45:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.91 ----- Otter 3.3f, August 2004 -----
% 1.68/1.91 The process was started by sandbox2 on n017.cluster.edu,
% 1.68/1.91 Wed Jul 27 02:45:33 2022
% 1.68/1.91 The command was "./otter". The process ID is 18086.
% 1.68/1.91
% 1.68/1.91 set(prolog_style_variables).
% 1.68/1.91 set(auto).
% 1.68/1.91 dependent: set(auto1).
% 1.68/1.91 dependent: set(process_input).
% 1.68/1.91 dependent: clear(print_kept).
% 1.68/1.91 dependent: clear(print_new_demod).
% 1.68/1.91 dependent: clear(print_back_demod).
% 1.68/1.91 dependent: clear(print_back_sub).
% 1.68/1.91 dependent: set(control_memory).
% 1.68/1.91 dependent: assign(max_mem, 12000).
% 1.68/1.91 dependent: assign(pick_given_ratio, 4).
% 1.68/1.91 dependent: assign(stats_level, 1).
% 1.68/1.91 dependent: assign(max_seconds, 10800).
% 1.68/1.91 clear(print_given).
% 1.68/1.91
% 1.68/1.91 list(usable).
% 1.68/1.91 0 [] sum(X,V,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W).
% 1.68/1.91 0 [] sum(U,Z,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W).
% 1.68/1.91 0 [] sum(additive_identity,X,X)| -defined(X).
% 1.68/1.91 0 [] sum(additive_inverse(X),X,additive_identity)| -defined(X).
% 1.68/1.91 0 [] sum(Y,X,Z)| -sum(X,Y,Z).
% 1.68/1.91 0 [] product(X,V,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W).
% 1.68/1.91 0 [] product(U,Z,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W).
% 1.68/1.91 0 [] product(multiplicative_identity,X,X)| -defined(X).
% 1.68/1.91 0 [] product(multiplicative_inverse(X),X,multiplicative_identity)|sum(additive_identity,X,additive_identity)| -defined(X).
% 1.68/1.91 0 [] product(Y,X,Z)| -product(X,Y,Z).
% 1.68/1.91 0 [] sum(C,D,B)| -sum(X,Y,A)| -product(A,Z,B)| -product(X,Z,C)| -product(Y,Z,D).
% 1.68/1.91 0 [] product(A,Z,B)| -sum(X,Y,A)| -product(X,Z,C)| -product(Y,Z,D)| -sum(C,D,B).
% 1.68/1.91 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.68/1.91 0 [] defined(additive_identity).
% 1.68/1.91 0 [] defined(additive_inverse(X))| -defined(X).
% 1.68/1.91 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.68/1.91 0 [] defined(multiplicative_identity).
% 1.68/1.91 0 [] defined(multiplicative_inverse(X))| -defined(X)|sum(additive_identity,X,additive_identity).
% 1.68/1.91 0 [] sum(X,Y,add(X,Y))| -defined(X)| -defined(Y).
% 1.68/1.91 0 [] product(X,Y,multiply(X,Y))| -defined(X)| -defined(Y).
% 1.68/1.91 0 [] sum(additive_identity,X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.68/1.91 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.68/1.91 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.68/1.91 0 [] less_or_e_qual(U,V)| -less_or_e_qual(X,Y)| -sum(X,Z,U)| -sum(Y,Z,V).
% 1.68/1.91 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).
% 1.68/1.91 0 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.68/1.91 0 [] defined(a).
% 1.68/1.91 0 [] defined(b).
% 1.68/1.91 0 [] defined(u).
% 1.68/1.91 0 [] less_or_e_qual(a,b).
% 1.68/1.91 0 [] sum(b,additive_inverse(a),u).
% 1.68/1.91 0 [] -less_or_e_qual(additive_identity,u).
% 1.68/1.91 end_of_list.
% 1.68/1.91
% 1.68/1.91 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.68/1.91
% 1.68/1.91 This is a non-Horn set without equality. The strategy will
% 1.68/1.91 be ordered hyper_res, unit deletion, and factoring, with
% 1.68/1.91 satellites in sos and with nuclei in usable.
% 1.68/1.91
% 1.68/1.91 dependent: set(hyper_res).
% 1.68/1.91 dependent: set(factor).
% 1.68/1.91 dependent: set(unit_deletion).
% 1.68/1.91
% 1.68/1.91 ------------> process usable:
% 1.68/1.91 ** KEPT (pick-wt=16): 1 [] sum(A,B,C)| -sum(A,D,E)| -sum(D,F,B)| -sum(E,F,C).
% 1.68/1.91 ** KEPT (pick-wt=16): 2 [] sum(A,B,C)| -sum(D,E,A)| -sum(E,B,F)| -sum(D,F,C).
% 1.68/1.91 ** KEPT (pick-wt=6): 3 [] sum(additive_identity,A,A)| -defined(A).
% 1.68/1.91 ** KEPT (pick-wt=7): 4 [] sum(additive_inverse(A),A,additive_identity)| -defined(A).
% 1.68/1.91 ** KEPT (pick-wt=8): 5 [] sum(A,B,C)| -sum(B,A,C).
% 1.68/1.91 ** KEPT (pick-wt=16): 6 [] product(A,B,C)| -product(A,D,E)| -product(D,F,B)| -product(E,F,C).
% 1.68/1.91 ** KEPT (pick-wt=16): 7 [] product(A,B,C)| -product(D,E,A)| -product(E,B,F)| -product(D,F,C).
% 1.68/1.91 ** KEPT (pick-wt=6): 8 [] product(multiplicative_identity,A,A)| -defined(A).
% 1.68/1.91 ** KEPT (pick-wt=11): 9 [] product(multiplicative_inverse(A),A,multiplicative_identity)|sum(additive_identity,A,additive_identity)| -defined(A).
% 1.68/1.91 ** KEPT (pick-wt=8): 10 [] product(A,B,C)| -product(B,A,C).
% 1.68/1.91 ** 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).
% 1.68/1.91 ** 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).
% 1.68/1.91 ** KEPT (pick-wt=8): 13 [] defined(add(A,B))| -defined(A)| -defined(B).
% 1.68/1.91 ** KEPT (pick-wt=5): 14 [] defined(additive_inverse(A))| -defined(A).
% 1.68/1.91 ** KEPT (pick-wt=8): 15 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 1.94/2.13 ** KEPT (pick-wt=9): 16 [] defined(multiplicative_inverse(A))| -defined(A)|sum(additive_identity,A,additive_identity).
% 1.94/2.13 ** KEPT (pick-wt=10): 17 [] sum(A,B,add(A,B))| -defined(A)| -defined(B).
% 1.94/2.13 ** KEPT (pick-wt=10): 18 [] product(A,B,multiply(A,B))| -defined(A)| -defined(B).
% 1.94/2.13 ** KEPT (pick-wt=10): 19 [] sum(additive_identity,A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 1.94/2.13 ** KEPT (pick-wt=9): 20 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 1.94/2.13 ** KEPT (pick-wt=10): 21 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 1.94/2.13 ** 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).
% 1.94/2.13 ** 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).
% 1.94/2.13 ** KEPT (pick-wt=4): 24 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.94/2.13 ** KEPT (pick-wt=3): 25 [] -less_or_e_qual(additive_identity,u).
% 1.94/2.13
% 1.94/2.13 ------------> process sos:
% 1.94/2.13 ** KEPT (pick-wt=2): 49 [] defined(additive_identity).
% 1.94/2.13 ** KEPT (pick-wt=2): 50 [] defined(multiplicative_identity).
% 1.94/2.13 ** KEPT (pick-wt=2): 51 [] defined(a).
% 1.94/2.13 ** KEPT (pick-wt=2): 52 [] defined(b).
% 1.94/2.13 ** KEPT (pick-wt=2): 53 [] defined(u).
% 1.94/2.13 ** KEPT (pick-wt=3): 54 [] less_or_e_qual(a,b).
% 1.94/2.13 ** KEPT (pick-wt=5): 55 [] sum(b,additive_inverse(a),u).
% 1.94/2.13
% 1.94/2.13 ======= end of input processing =======
% 1.94/2.13
% 1.94/2.13 =========== start of search ===========
% 1.94/2.13
% 1.94/2.13
% 1.94/2.13 Resetting weight limit to 6.
% 1.94/2.13
% 1.94/2.13
% 1.94/2.13 Resetting weight limit to 6.
% 1.94/2.13
% 1.94/2.13 sos_size=9401
% 1.94/2.13
% 1.94/2.13 -------- PROOF --------
% 1.94/2.13
% 1.94/2.13 ----> UNIT CONFLICT at 0.22 sec ----> 10157 [binary,10156.1,25.1] $F.
% 1.94/2.13
% 1.94/2.13 Length of proof is 16. Level of proof is 8.
% 1.94/2.13
% 1.94/2.13 ---------------- PROOF ----------------
% 1.94/2.13 % SZS status Unsatisfiable
% 1.94/2.13 % SZS output start Refutation
% See solution above
% 1.94/2.13 ------------ end of proof -------------
% 1.94/2.13
% 1.94/2.13
% 1.94/2.13 Search stopped by max_proofs option.
% 1.94/2.13
% 1.94/2.13
% 1.94/2.13 Search stopped by max_proofs option.
% 1.94/2.13
% 1.94/2.13 ============ end of search ============
% 1.94/2.13
% 1.94/2.13 -------------- statistics -------------
% 1.94/2.13 clauses given 135
% 1.94/2.13 clauses generated 24829
% 1.94/2.13 clauses kept 10156
% 1.94/2.13 clauses forward subsumed 2837
% 1.94/2.13 clauses back subsumed 37
% 1.94/2.13 Kbytes malloced 4882
% 1.94/2.13
% 1.94/2.13 ----------- times (seconds) -----------
% 1.94/2.13 user CPU time 0.22 (0 hr, 0 min, 0 sec)
% 1.94/2.13 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.13 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.94/2.13
% 1.94/2.13 That finishes the proof of the theorem.
% 1.94/2.13
% 1.94/2.13 Process 18086 finished Wed Jul 27 02:45:34 2022
% 1.94/2.13 Otter interrupted
% 1.94/2.13 PROOF FOUND
%------------------------------------------------------------------------------