TSTP Solution File: FLD031-5 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD031-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 12:53:46 EDT 2022
% Result : Unsatisfiable 2.14s 2.37s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of clauses : 22 ( 16 unt; 2 nHn; 22 RR)
% Number of literals : 34 ( 0 equ; 12 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( product(A,B,C)
| ~ product(A,D,E)
| ~ product(D,F,B)
| ~ product(E,F,C) ),
file('FLD031-5.p',unknown),
[] ).
cnf(7,axiom,
( product(A,B,C)
| ~ product(D,E,A)
| ~ product(E,B,F)
| ~ product(D,F,C) ),
file('FLD031-5.p',unknown),
[] ).
cnf(8,axiom,
( product(multiplicative_identity,A,A)
| ~ defined(A) ),
file('FLD031-5.p',unknown),
[] ).
cnf(9,axiom,
( product(multiplicative_inverse(A),A,multiplicative_identity)
| sum(additive_identity,A,additive_identity)
| ~ defined(A) ),
file('FLD031-5.p',unknown),
[] ).
cnf(10,axiom,
( product(A,B,C)
| ~ product(B,A,C) ),
file('FLD031-5.p',unknown),
[] ).
cnf(16,axiom,
( defined(multiplicative_inverse(A))
| ~ defined(A)
| sum(additive_identity,A,additive_identity) ),
file('FLD031-5.p',unknown),
[] ).
cnf(25,axiom,
~ sum(additive_identity,a,additive_identity),
file('FLD031-5.p',unknown),
[] ).
cnf(26,axiom,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
file('FLD031-5.p',unknown),
[] ).
cnf(51,axiom,
defined(multiplicative_identity),
file('FLD031-5.p',unknown),
[] ).
cnf(52,axiom,
defined(a),
file('FLD031-5.p',unknown),
[] ).
cnf(53,axiom,
product(multiplicative_identity,a,multiplicative_identity),
file('FLD031-5.p',unknown),
[] ).
cnf(82,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(hyper,[status(thm)],[51,8]),
[iquote('hyper,51,8')] ).
cnf(100,plain,
defined(multiplicative_inverse(a)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[52,16]),25]),
[iquote('hyper,52,16,unit_del,25')] ).
cnf(110,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[52,9]),25]),
[iquote('hyper,52,9,unit_del,25')] ).
cnf(111,plain,
product(multiplicative_identity,a,a),
inference(hyper,[status(thm)],[52,8]),
[iquote('hyper,52,8')] ).
cnf(152,plain,
product(a,multiplicative_identity,multiplicative_identity),
inference(hyper,[status(thm)],[53,10]),
[iquote('hyper,53,10')] ).
cnf(253,plain,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(hyper,[status(thm)],[100,8]),
[iquote('hyper,100,8')] ).
cnf(3315,plain,
product(a,a,multiplicative_identity),
inference(hyper,[status(thm)],[152,6,111,53]),
[iquote('hyper,152,6,111,53')] ).
cnf(4521,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(hyper,[status(thm)],[110,10]),
[iquote('hyper,110,10')] ).
cnf(8753,plain,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
inference(hyper,[status(thm)],[4521,7,3315,152]),
[iquote('hyper,4521,7,3315,152')] ).
cnf(8842,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
inference(hyper,[status(thm)],[253,6,82,8753]),
[iquote('hyper,253,6,82,8753')] ).
cnf(8843,plain,
$false,
inference(binary,[status(thm)],[8842,26]),
[iquote('binary,8842.1,26.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : FLD031-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n006.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 03:10:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.83/2.04 ----- Otter 3.3f, August 2004 -----
% 1.83/2.04 The process was started by sandbox2 on n006.cluster.edu,
% 1.83/2.04 Wed Jul 27 03:10:17 2022
% 1.83/2.04 The command was "./otter". The process ID is 17130.
% 1.83/2.04
% 1.83/2.04 set(prolog_style_variables).
% 1.83/2.04 set(auto).
% 1.83/2.04 dependent: set(auto1).
% 1.83/2.04 dependent: set(process_input).
% 1.83/2.04 dependent: clear(print_kept).
% 1.83/2.04 dependent: clear(print_new_demod).
% 1.83/2.04 dependent: clear(print_back_demod).
% 1.83/2.04 dependent: clear(print_back_sub).
% 1.83/2.04 dependent: set(control_memory).
% 1.83/2.04 dependent: assign(max_mem, 12000).
% 1.83/2.04 dependent: assign(pick_given_ratio, 4).
% 1.83/2.04 dependent: assign(stats_level, 1).
% 1.83/2.04 dependent: assign(max_seconds, 10800).
% 1.83/2.04 clear(print_given).
% 1.83/2.04
% 1.83/2.04 list(usable).
% 1.83/2.04 0 [] sum(X,V,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W).
% 1.83/2.04 0 [] sum(U,Z,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W).
% 1.83/2.04 0 [] sum(additive_identity,X,X)| -defined(X).
% 1.83/2.04 0 [] sum(additive_inverse(X),X,additive_identity)| -defined(X).
% 1.83/2.04 0 [] sum(Y,X,Z)| -sum(X,Y,Z).
% 1.83/2.04 0 [] product(X,V,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W).
% 1.83/2.04 0 [] product(U,Z,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W).
% 1.83/2.04 0 [] product(multiplicative_identity,X,X)| -defined(X).
% 1.83/2.04 0 [] product(multiplicative_inverse(X),X,multiplicative_identity)|sum(additive_identity,X,additive_identity)| -defined(X).
% 1.83/2.04 0 [] product(Y,X,Z)| -product(X,Y,Z).
% 1.83/2.04 0 [] sum(C,D,B)| -sum(X,Y,A)| -product(A,Z,B)| -product(X,Z,C)| -product(Y,Z,D).
% 1.83/2.04 0 [] product(A,Z,B)| -sum(X,Y,A)| -product(X,Z,C)| -product(Y,Z,D)| -sum(C,D,B).
% 1.83/2.04 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.83/2.04 0 [] defined(additive_identity).
% 1.83/2.04 0 [] defined(additive_inverse(X))| -defined(X).
% 1.83/2.04 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.83/2.04 0 [] defined(multiplicative_identity).
% 1.83/2.04 0 [] defined(multiplicative_inverse(X))| -defined(X)|sum(additive_identity,X,additive_identity).
% 1.83/2.04 0 [] sum(X,Y,add(X,Y))| -defined(X)| -defined(Y).
% 1.83/2.04 0 [] product(X,Y,multiply(X,Y))| -defined(X)| -defined(Y).
% 1.83/2.04 0 [] sum(additive_identity,X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.83/2.04 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.83/2.04 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.83/2.04 0 [] less_or_e_qual(U,V)| -less_or_e_qual(X,Y)| -sum(X,Z,U)| -sum(Y,Z,V).
% 1.83/2.04 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).
% 1.83/2.04 0 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.83/2.04 0 [] defined(a).
% 1.83/2.04 0 [] product(multiplicative_identity,a,multiplicative_identity).
% 1.83/2.04 0 [] -sum(additive_identity,a,additive_identity).
% 1.83/2.04 0 [] -product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)).
% 1.83/2.04 end_of_list.
% 1.83/2.04
% 1.83/2.04 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.83/2.04
% 1.83/2.04 This is a non-Horn set without equality. The strategy will
% 1.83/2.04 be ordered hyper_res, unit deletion, and factoring, with
% 1.83/2.04 satellites in sos and with nuclei in usable.
% 1.83/2.04
% 1.83/2.04 dependent: set(hyper_res).
% 1.83/2.04 dependent: set(factor).
% 1.83/2.04 dependent: set(unit_deletion).
% 1.83/2.04
% 1.83/2.04 ------------> process usable:
% 1.83/2.04 ** KEPT (pick-wt=16): 1 [] sum(A,B,C)| -sum(A,D,E)| -sum(D,F,B)| -sum(E,F,C).
% 1.83/2.04 ** KEPT (pick-wt=16): 2 [] sum(A,B,C)| -sum(D,E,A)| -sum(E,B,F)| -sum(D,F,C).
% 1.83/2.04 ** KEPT (pick-wt=6): 3 [] sum(additive_identity,A,A)| -defined(A).
% 1.83/2.04 ** KEPT (pick-wt=7): 4 [] sum(additive_inverse(A),A,additive_identity)| -defined(A).
% 1.83/2.04 ** KEPT (pick-wt=8): 5 [] sum(A,B,C)| -sum(B,A,C).
% 1.83/2.04 ** KEPT (pick-wt=16): 6 [] product(A,B,C)| -product(A,D,E)| -product(D,F,B)| -product(E,F,C).
% 1.83/2.04 ** KEPT (pick-wt=16): 7 [] product(A,B,C)| -product(D,E,A)| -product(E,B,F)| -product(D,F,C).
% 1.83/2.04 ** KEPT (pick-wt=6): 8 [] product(multiplicative_identity,A,A)| -defined(A).
% 1.83/2.04 ** KEPT (pick-wt=11): 9 [] product(multiplicative_inverse(A),A,multiplicative_identity)|sum(additive_identity,A,additive_identity)| -defined(A).
% 1.83/2.04 ** KEPT (pick-wt=8): 10 [] product(A,B,C)| -product(B,A,C).
% 1.83/2.04 ** 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).
% 1.83/2.04 ** 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).
% 1.83/2.04 ** KEPT (pick-wt=8): 13 [] defined(add(A,B))| -defined(A)| -defined(B).
% 1.83/2.04 ** KEPT (pick-wt=5): 14 [] defined(additive_inverse(A))| -defined(A).
% 2.14/2.37 ** KEPT (pick-wt=8): 15 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 2.14/2.37 ** KEPT (pick-wt=9): 16 [] defined(multiplicative_inverse(A))| -defined(A)|sum(additive_identity,A,additive_identity).
% 2.14/2.37 ** KEPT (pick-wt=10): 17 [] sum(A,B,add(A,B))| -defined(A)| -defined(B).
% 2.14/2.37 ** KEPT (pick-wt=10): 18 [] product(A,B,multiply(A,B))| -defined(A)| -defined(B).
% 2.14/2.37 ** KEPT (pick-wt=10): 19 [] sum(additive_identity,A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 2.14/2.37 ** KEPT (pick-wt=9): 20 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 2.14/2.37 ** KEPT (pick-wt=10): 21 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 2.14/2.37 ** 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).
% 2.14/2.37 ** 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).
% 2.14/2.37 ** KEPT (pick-wt=4): 24 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 2.14/2.37 ** KEPT (pick-wt=4): 25 [] -sum(additive_identity,a,additive_identity).
% 2.14/2.37 ** KEPT (pick-wt=5): 26 [] -product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)).
% 2.14/2.37
% 2.14/2.37 ------------> process sos:
% 2.14/2.37 ** KEPT (pick-wt=2): 50 [] defined(additive_identity).
% 2.14/2.37 ** KEPT (pick-wt=2): 51 [] defined(multiplicative_identity).
% 2.14/2.37 ** KEPT (pick-wt=2): 52 [] defined(a).
% 2.14/2.37 ** KEPT (pick-wt=4): 53 [] product(multiplicative_identity,a,multiplicative_identity).
% 2.14/2.37
% 2.14/2.37 ======= end of input processing =======
% 2.14/2.37
% 2.14/2.37 =========== start of search ===========
% 2.14/2.37
% 2.14/2.37
% 2.14/2.37 Resetting weight limit to 6.
% 2.14/2.37
% 2.14/2.37
% 2.14/2.37 Resetting weight limit to 6.
% 2.14/2.37
% 2.14/2.37 sos_size=8437
% 2.14/2.37
% 2.14/2.37 -------- PROOF --------
% 2.14/2.37
% 2.14/2.37 ----> UNIT CONFLICT at 0.33 sec ----> 8843 [binary,8842.1,26.1] $F.
% 2.14/2.37
% 2.14/2.37 Length of proof is 10. Level of proof is 4.
% 2.14/2.37
% 2.14/2.37 ---------------- PROOF ----------------
% 2.14/2.37 % SZS status Unsatisfiable
% 2.14/2.37 % SZS output start Refutation
% See solution above
% 2.14/2.37 ------------ end of proof -------------
% 2.14/2.37
% 2.14/2.37
% 2.14/2.37 Search stopped by max_proofs option.
% 2.14/2.37
% 2.14/2.37
% 2.14/2.37 Search stopped by max_proofs option.
% 2.14/2.37
% 2.14/2.37 ============ end of search ============
% 2.14/2.37
% 2.14/2.37 -------------- statistics -------------
% 2.14/2.37 clauses given 267
% 2.14/2.37 clauses generated 79997
% 2.14/2.37 clauses kept 8842
% 2.14/2.37 clauses forward subsumed 5739
% 2.14/2.37 clauses back subsumed 38
% 2.14/2.37 Kbytes malloced 4882
% 2.14/2.37
% 2.14/2.37 ----------- times (seconds) -----------
% 2.14/2.37 user CPU time 0.33 (0 hr, 0 min, 0 sec)
% 2.14/2.37 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.14/2.37 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.14/2.37
% 2.14/2.37 That finishes the proof of the theorem.
% 2.14/2.37
% 2.14/2.37 Process 17130 finished Wed Jul 27 03:10:19 2022
% 2.14/2.37 Otter interrupted
% 2.14/2.37 PROOF FOUND
%------------------------------------------------------------------------------