TSTP Solution File: FLD060-4 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD060-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 12:53:53 EDT 2022
% Result : Unsatisfiable 41.48s 41.65s
% Output : Refutation 41.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of clauses : 53 ( 38 unt; 1 nHn; 53 RR)
% Number of literals : 82 ( 0 equ; 29 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( sum(additive_identity,A,A)
| ~ defined(A) ),
file('FLD060-4.p',unknown),
[] ).
cnf(4,axiom,
( sum(additive_inverse(A),A,additive_identity)
| ~ defined(A) ),
file('FLD060-4.p',unknown),
[] ).
cnf(5,axiom,
( sum(A,B,C)
| ~ sum(B,A,C) ),
file('FLD060-4.p',unknown),
[] ).
cnf(8,axiom,
( product(multiplicative_identity,A,A)
| ~ defined(A) ),
file('FLD060-4.p',unknown),
[] ).
cnf(10,axiom,
( product(A,B,C)
| ~ product(B,A,C) ),
file('FLD060-4.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('FLD060-4.p',unknown),
[] ).
cnf(14,axiom,
( defined(additive_inverse(A))
| ~ defined(A) ),
file('FLD060-4.p',unknown),
[] ).
cnf(17,axiom,
( sum(A,B,add(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD060-4.p',unknown),
[] ).
cnf(18,axiom,
( product(A,B,multiply(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD060-4.p',unknown),
[] ).
cnf(20,axiom,
( less_or_e_qual(A,B)
| ~ less_or_e_qual(A,C)
| ~ less_or_e_qual(C,B) ),
file('FLD060-4.p',unknown),
[] ).
cnf(21,axiom,
( less_or_e_qual(A,B)
| less_or_e_qual(B,A)
| ~ defined(A)
| ~ defined(B) ),
file('FLD060-4.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('FLD060-4.p',unknown),
[] ).
cnf(25,axiom,
~ less_or_e_qual(u,v),
file('FLD060-4.p',unknown),
[] ).
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(36,plain,
( sum(A,A,B)
| ~ sum(C,C,D)
| ~ product(D,E,B)
| ~ product(C,E,A) ),
inference(factor,[status(thm)],[11]),
[iquote('factor,11.4.5')] ).
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('FLD060-4.p',unknown),
[] ).
cnf(50,axiom,
defined(multiplicative_identity),
file('FLD060-4.p',unknown),
[] ).
cnf(51,axiom,
defined(a),
file('FLD060-4.p',unknown),
[] ).
cnf(52,axiom,
defined(b),
file('FLD060-4.p',unknown),
[] ).
cnf(53,axiom,
defined(u),
file('FLD060-4.p',unknown),
[] ).
cnf(55,axiom,
less_or_e_qual(a,b),
file('FLD060-4.p',unknown),
[] ).
cnf(56,axiom,
sum(a,a,u),
file('FLD060-4.p',unknown),
[] ).
cnf(57,axiom,
sum(b,b,v),
file('FLD060-4.p',unknown),
[] ).
cnf(58,plain,
less_or_e_qual(additive_identity,additive_identity),
inference(hyper,[status(thm)],[49,44]),
[iquote('hyper,49,44')] ).
cnf(64,plain,
defined(additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[49,14]),
[iquote('hyper,49,14')] ).
cnf(66,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[49,8]),
[iquote('hyper,49,8')] ).
cnf(67,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(hyper,[status(thm)],[49,4]),
[iquote('hyper,49,4')] ).
cnf(68,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[49,3]),
[iquote('hyper,49,3')] ).
cnf(75,plain,
product(additive_identity,multiplicative_identity,multiply(additive_identity,multiplicative_identity)),
inference(hyper,[status(thm)],[50,18,49]),
[iquote('hyper,50,18,49')] ).
cnf(98,plain,
product(a,multiplicative_identity,multiply(a,multiplicative_identity)),
inference(hyper,[status(thm)],[51,18,50]),
[iquote('hyper,51,18,50')] ).
cnf(115,plain,
product(multiplicative_identity,a,a),
inference(hyper,[status(thm)],[51,8]),
[iquote('hyper,51,8')] ).
cnf(117,plain,
sum(additive_identity,a,a),
inference(hyper,[status(thm)],[51,3]),
[iquote('hyper,51,3')] ).
cnf(131,plain,
sum(a,b,add(a,b)),
inference(hyper,[status(thm)],[52,17,51]),
[iquote('hyper,52,17,51')] ).
cnf(199,plain,
product(multiplicative_identity,u,u),
inference(hyper,[status(thm)],[53,8]),
[iquote('hyper,53,8')] ).
cnf(322,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[64,3]),
[iquote('hyper,64,3')] ).
cnf(1030,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[66,10]),
[iquote('hyper,66,10')] ).
cnf(1321,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[67,5]),
[iquote('hyper,67,5')] ).
cnf(4338,plain,
product(a,multiplicative_identity,a),
inference(hyper,[status(thm)],[115,10]),
[iquote('hyper,115,10')] ).
cnf(9990,plain,
product(u,multiplicative_identity,u),
inference(hyper,[status(thm)],[199,10]),
[iquote('hyper,199,10')] ).
cnf(10717,plain,
sum(additive_identity,additive_identity,multiply(additive_identity,multiplicative_identity)),
inference(hyper,[status(thm)],[1030,36,68,75]),
[iquote('hyper,1030,36,68,75')] ).
cnf(10743,plain,
sum(multiply(additive_identity,multiplicative_identity),a,a),
inference(hyper,[status(thm)],[4338,35,117,75]),
[iquote('hyper,4338,35,117,75')] ).
cnf(10747,plain,
sum(additive_identity,a,multiply(a,multiplicative_identity)),
inference(hyper,[status(thm)],[4338,11,117,98,1030]),
[iquote('hyper,4338,11,117,98,1030')] ).
cnf(10776,plain,
sum(multiply(a,multiplicative_identity),a,u),
inference(hyper,[status(thm)],[9990,11,56,98,4338]),
[iquote('hyper,9990,11,56,98,4338')] ).
cnf(10858,plain,
less_or_e_qual(add(a,b),v),
inference(hyper,[status(thm)],[131,22,55,57]),
[iquote('hyper,131,22,55,57')] ).
cnf(10859,plain,
sum(b,a,add(a,b)),
inference(hyper,[status(thm)],[131,5]),
[iquote('hyper,131,5')] ).
cnf(11187,plain,
less_or_e_qual(additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[322,22,58,1321]),
[iquote('hyper,322,22,58,1321')] ).
cnf(11349,plain,
less_or_e_qual(additive_identity,multiply(additive_identity,multiplicative_identity)),
inference(hyper,[status(thm)],[10717,22,11187,67]),
[iquote('hyper,10717,22,11187,67')] ).
cnf(11388,plain,
less_or_e_qual(multiply(a,multiplicative_identity),a),
inference(hyper,[status(thm)],[10747,22,11349,10743]),
[iquote('hyper,10747,22,11349,10743')] ).
cnf(11389,plain,
less_or_e_qual(multiply(a,multiplicative_identity),b),
inference(hyper,[status(thm)],[11388,20,55]),
[iquote('hyper,11388,20,55')] ).
cnf(11413,plain,
less_or_e_qual(u,add(a,b)),
inference(hyper,[status(thm)],[10859,22,11389,10776]),
[iquote('hyper,10859,22,11389,10776')] ).
cnf(11415,plain,
less_or_e_qual(u,v),
inference(hyper,[status(thm)],[11413,20,10858]),
[iquote('hyper,11413,20,10858')] ).
cnf(11416,plain,
$false,
inference(binary,[status(thm)],[11415,25]),
[iquote('binary,11415.1,25.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : FLD060-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 03:17:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.91/2.10 ----- Otter 3.3f, August 2004 -----
% 1.91/2.10 The process was started by sandbox on n020.cluster.edu,
% 1.91/2.10 Wed Jul 27 03:17:38 2022
% 1.91/2.10 The command was "./otter". The process ID is 15071.
% 1.91/2.10
% 1.91/2.10 set(prolog_style_variables).
% 1.91/2.10 set(auto).
% 1.91/2.10 dependent: set(auto1).
% 1.91/2.10 dependent: set(process_input).
% 1.91/2.10 dependent: clear(print_kept).
% 1.91/2.10 dependent: clear(print_new_demod).
% 1.91/2.10 dependent: clear(print_back_demod).
% 1.91/2.10 dependent: clear(print_back_sub).
% 1.91/2.10 dependent: set(control_memory).
% 1.91/2.10 dependent: assign(max_mem, 12000).
% 1.91/2.10 dependent: assign(pick_given_ratio, 4).
% 1.91/2.10 dependent: assign(stats_level, 1).
% 1.91/2.10 dependent: assign(max_seconds, 10800).
% 1.91/2.10 clear(print_given).
% 1.91/2.10
% 1.91/2.10 list(usable).
% 1.91/2.10 0 [] sum(X,V,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W).
% 1.91/2.10 0 [] sum(U,Z,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W).
% 1.91/2.10 0 [] sum(additive_identity,X,X)| -defined(X).
% 1.91/2.10 0 [] sum(additive_inverse(X),X,additive_identity)| -defined(X).
% 1.91/2.10 0 [] sum(Y,X,Z)| -sum(X,Y,Z).
% 1.91/2.10 0 [] product(X,V,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W).
% 1.91/2.10 0 [] product(U,Z,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W).
% 1.91/2.10 0 [] product(multiplicative_identity,X,X)| -defined(X).
% 1.91/2.10 0 [] product(multiplicative_inverse(X),X,multiplicative_identity)|sum(additive_identity,X,additive_identity)| -defined(X).
% 1.91/2.10 0 [] product(Y,X,Z)| -product(X,Y,Z).
% 1.91/2.10 0 [] sum(C,D,B)| -sum(X,Y,A)| -product(A,Z,B)| -product(X,Z,C)| -product(Y,Z,D).
% 1.91/2.10 0 [] product(A,Z,B)| -sum(X,Y,A)| -product(X,Z,C)| -product(Y,Z,D)| -sum(C,D,B).
% 1.91/2.10 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.91/2.10 0 [] defined(additive_identity).
% 1.91/2.10 0 [] defined(additive_inverse(X))| -defined(X).
% 1.91/2.10 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.91/2.10 0 [] defined(multiplicative_identity).
% 1.91/2.10 0 [] defined(multiplicative_inverse(X))| -defined(X)|sum(additive_identity,X,additive_identity).
% 1.91/2.10 0 [] sum(X,Y,add(X,Y))| -defined(X)| -defined(Y).
% 1.91/2.10 0 [] product(X,Y,multiply(X,Y))| -defined(X)| -defined(Y).
% 1.91/2.10 0 [] sum(additive_identity,X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.91/2.10 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.91/2.10 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.91/2.10 0 [] less_or_e_qual(U,V)| -less_or_e_qual(X,Y)| -sum(X,Z,U)| -sum(Y,Z,V).
% 1.91/2.10 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).
% 1.91/2.10 0 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.91/2.10 0 [] defined(a).
% 1.91/2.10 0 [] defined(b).
% 1.91/2.10 0 [] defined(u).
% 1.91/2.10 0 [] defined(v).
% 1.91/2.10 0 [] less_or_e_qual(a,b).
% 1.91/2.10 0 [] sum(a,a,u).
% 1.91/2.10 0 [] sum(b,b,v).
% 1.91/2.10 0 [] -less_or_e_qual(u,v).
% 1.91/2.10 end_of_list.
% 1.91/2.10
% 1.91/2.10 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.91/2.10
% 1.91/2.10 This is a non-Horn set without equality. The strategy will
% 1.91/2.10 be ordered hyper_res, unit deletion, and factoring, with
% 1.91/2.10 satellites in sos and with nuclei in usable.
% 1.91/2.10
% 1.91/2.10 dependent: set(hyper_res).
% 1.91/2.10 dependent: set(factor).
% 1.91/2.10 dependent: set(unit_deletion).
% 1.91/2.10
% 1.91/2.10 ------------> process usable:
% 1.91/2.10 ** KEPT (pick-wt=16): 1 [] sum(A,B,C)| -sum(A,D,E)| -sum(D,F,B)| -sum(E,F,C).
% 1.91/2.10 ** KEPT (pick-wt=16): 2 [] sum(A,B,C)| -sum(D,E,A)| -sum(E,B,F)| -sum(D,F,C).
% 1.91/2.10 ** KEPT (pick-wt=6): 3 [] sum(additive_identity,A,A)| -defined(A).
% 1.91/2.10 ** KEPT (pick-wt=7): 4 [] sum(additive_inverse(A),A,additive_identity)| -defined(A).
% 1.91/2.10 ** KEPT (pick-wt=8): 5 [] sum(A,B,C)| -sum(B,A,C).
% 1.91/2.10 ** KEPT (pick-wt=16): 6 [] product(A,B,C)| -product(A,D,E)| -product(D,F,B)| -product(E,F,C).
% 1.91/2.10 ** KEPT (pick-wt=16): 7 [] product(A,B,C)| -product(D,E,A)| -product(E,B,F)| -product(D,F,C).
% 1.91/2.10 ** KEPT (pick-wt=6): 8 [] product(multiplicative_identity,A,A)| -defined(A).
% 1.91/2.10 ** KEPT (pick-wt=11): 9 [] product(multiplicative_inverse(A),A,multiplicative_identity)|sum(additive_identity,A,additive_identity)| -defined(A).
% 1.91/2.10 ** KEPT (pick-wt=8): 10 [] product(A,B,C)| -product(B,A,C).
% 1.91/2.10 ** 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).
% 1.91/2.10 ** 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).
% 1.91/2.10 ** KEPT (pick-wt=8): 13 [] defined(add(A,B))| -defined(A)| -defined(B).
% 1.91/2.10 ** KEPT (pick-wt=5): 14 [] defined(additive_inverse(A))| -defined(A).
% 1.91/2.10 ** KEPT (pick-wt=8): 15 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 41.48/41.65 ** KEPT (pick-wt=9): 16 [] defined(multiplicative_inverse(A))| -defined(A)|sum(additive_identity,A,additive_identity).
% 41.48/41.65 ** KEPT (pick-wt=10): 17 [] sum(A,B,add(A,B))| -defined(A)| -defined(B).
% 41.48/41.65 ** KEPT (pick-wt=10): 18 [] product(A,B,multiply(A,B))| -defined(A)| -defined(B).
% 41.48/41.65 ** KEPT (pick-wt=10): 19 [] sum(additive_identity,A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 41.48/41.65 ** KEPT (pick-wt=9): 20 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 41.48/41.65 ** KEPT (pick-wt=10): 21 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 41.48/41.65 ** 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).
% 41.48/41.65 ** 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).
% 41.48/41.65 ** KEPT (pick-wt=4): 24 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 41.48/41.65 ** KEPT (pick-wt=3): 25 [] -less_or_e_qual(u,v).
% 41.48/41.65
% 41.48/41.65 ------------> process sos:
% 41.48/41.65 ** KEPT (pick-wt=2): 49 [] defined(additive_identity).
% 41.48/41.65 ** KEPT (pick-wt=2): 50 [] defined(multiplicative_identity).
% 41.48/41.65 ** KEPT (pick-wt=2): 51 [] defined(a).
% 41.48/41.65 ** KEPT (pick-wt=2): 52 [] defined(b).
% 41.48/41.65 ** KEPT (pick-wt=2): 53 [] defined(u).
% 41.48/41.65 ** KEPT (pick-wt=2): 54 [] defined(v).
% 41.48/41.65 ** KEPT (pick-wt=3): 55 [] less_or_e_qual(a,b).
% 41.48/41.65 ** KEPT (pick-wt=4): 56 [] sum(a,a,u).
% 41.48/41.65 ** KEPT (pick-wt=4): 57 [] sum(b,b,v).
% 41.48/41.65
% 41.48/41.65 ======= end of input processing =======
% 41.48/41.65
% 41.48/41.65 =========== start of search ===========
% 41.48/41.65
% 41.48/41.65
% 41.48/41.65 Resetting weight limit to 6.
% 41.48/41.65
% 41.48/41.65
% 41.48/41.65 Resetting weight limit to 6.
% 41.48/41.65
% 41.48/41.65 sos_size=9397
% 41.48/41.65
% 41.48/41.65 -- HEY sandbox, WE HAVE A PROOF!! --
% 41.48/41.65
% 41.48/41.65 ----> UNIT CONFLICT at 39.54 sec ----> 11416 [binary,11415.1,25.1] $F.
% 41.48/41.65
% 41.48/41.65 Length of proof is 31. Level of proof is 8.
% 41.48/41.65
% 41.48/41.65 ---------------- PROOF ----------------
% 41.48/41.65 % SZS status Unsatisfiable
% 41.48/41.65 % SZS output start Refutation
% See solution above
% 41.48/41.65 ------------ end of proof -------------
% 41.48/41.65
% 41.48/41.65
% 41.48/41.65 Search stopped by max_proofs option.
% 41.48/41.65
% 41.48/41.65
% 41.48/41.65 Search stopped by max_proofs option.
% 41.48/41.65
% 41.48/41.65 ============ end of search ============
% 41.48/41.65
% 41.48/41.65 -------------- statistics -------------
% 41.48/41.65 clauses given 3212
% 41.48/41.65 clauses generated 28029090
% 41.48/41.65 clauses kept 11415
% 41.48/41.65 clauses forward subsumed 9079
% 41.48/41.65 clauses back subsumed 47
% 41.48/41.65 Kbytes malloced 5859
% 41.48/41.65
% 41.48/41.65 ----------- times (seconds) -----------
% 41.48/41.65 user CPU time 39.54 (0 hr, 0 min, 39 sec)
% 41.48/41.65 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 41.48/41.65 wall-clock time 42 (0 hr, 0 min, 42 sec)
% 41.48/41.65
% 41.48/41.65 That finishes the proof of the theorem.
% 41.48/41.65
% 41.48/41.65 Process 15071 finished Wed Jul 27 03:18:20 2022
% 41.48/41.65 Otter interrupted
% 41.48/41.65 PROOF FOUND
%------------------------------------------------------------------------------