TSTP Solution File: FLD071-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD071-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 12:53:55 EDT 2022
% Result : Unsatisfiable 1.80s 2.00s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 6 ( 5 unt; 0 nHn; 6 RR)
% Number of literals : 8 ( 0 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(18,axiom,
( less_or_e_qual(additive_identity,multiply(A,B))
| ~ less_or_e_qual(additive_identity,A)
| ~ less_or_e_qual(additive_identity,B) ),
file('FLD071-1.p',unknown),
[] ).
cnf(26,axiom,
~ less_or_e_qual(additive_identity,multiply(a,b)),
file('FLD071-1.p',unknown),
[] ).
cnf(50,axiom,
less_or_e_qual(additive_identity,a),
file('FLD071-1.p',unknown),
[] ).
cnf(51,axiom,
less_or_e_qual(additive_identity,b),
file('FLD071-1.p',unknown),
[] ).
cnf(348,plain,
less_or_e_qual(additive_identity,multiply(a,b)),
inference(hyper,[status(thm)],[51,18,50]),
[iquote('hyper,51,18,50')] ).
cnf(349,plain,
$false,
inference(binary,[status(thm)],[348,26]),
[iquote('binary,348.1,26.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : FLD071-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.14 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 03:14:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.80/1.99 ----- Otter 3.3f, August 2004 -----
% 1.80/1.99 The process was started by sandbox on n008.cluster.edu,
% 1.80/1.99 Wed Jul 27 03:14:38 2022
% 1.80/1.99 The command was "./otter". The process ID is 11398.
% 1.80/1.99
% 1.80/1.99 set(prolog_style_variables).
% 1.80/1.99 set(auto).
% 1.80/1.99 dependent: set(auto1).
% 1.80/1.99 dependent: set(process_input).
% 1.80/1.99 dependent: clear(print_kept).
% 1.80/1.99 dependent: clear(print_new_demod).
% 1.80/1.99 dependent: clear(print_back_demod).
% 1.80/1.99 dependent: clear(print_back_sub).
% 1.80/1.99 dependent: set(control_memory).
% 1.80/1.99 dependent: assign(max_mem, 12000).
% 1.80/1.99 dependent: assign(pick_given_ratio, 4).
% 1.80/1.99 dependent: assign(stats_level, 1).
% 1.80/1.99 dependent: assign(max_seconds, 10800).
% 1.80/1.99 clear(print_given).
% 1.80/1.99
% 1.80/1.99 list(usable).
% 1.80/1.99 0 [] e_qualish(add(X,add(Y,Z)),add(add(X,Y),Z))| -defined(X)| -defined(Y)| -defined(Z).
% 1.80/1.99 0 [] e_qualish(add(additive_identity,X),X)| -defined(X).
% 1.80/1.99 0 [] e_qualish(add(X,additive_inverse(X)),additive_identity)| -defined(X).
% 1.80/1.99 0 [] e_qualish(add(X,Y),add(Y,X))| -defined(X)| -defined(Y).
% 1.80/1.99 0 [] e_qualish(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z))| -defined(X)| -defined(Y)| -defined(Z).
% 1.80/1.99 0 [] e_qualish(multiply(multiplicative_identity,X),X)| -defined(X).
% 1.80/1.99 0 [] e_qualish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)| -defined(X)|e_qualish(X,additive_identity).
% 1.80/1.99 0 [] e_qualish(multiply(X,Y),multiply(Y,X))| -defined(X)| -defined(Y).
% 1.80/1.99 0 [] e_qualish(add(multiply(X,Z),multiply(Y,Z)),multiply(add(X,Y),Z))| -defined(X)| -defined(Y)| -defined(Z).
% 1.80/1.99 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.80/1.99 0 [] defined(additive_identity).
% 1.80/1.99 0 [] defined(additive_inverse(X))| -defined(X).
% 1.80/1.99 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.80/1.99 0 [] defined(multiplicative_identity).
% 1.80/1.99 0 [] defined(multiplicative_inverse(X))| -defined(X)|e_qualish(X,additive_identity).
% 1.80/1.99 0 [] e_qualish(X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.80/1.99 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.80/1.99 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.80/1.99 0 [] less_or_e_qual(add(X,Z),add(Y,Z))| -defined(Z)| -less_or_e_qual(X,Y).
% 1.80/1.99 0 [] less_or_e_qual(additive_identity,multiply(Y,Z))| -less_or_e_qual(additive_identity,Y)| -less_or_e_qual(additive_identity,Z).
% 1.80/1.99 0 [] e_qualish(X,X)| -defined(X).
% 1.80/1.99 0 [] e_qualish(X,Y)| -e_qualish(Y,X).
% 1.80/1.99 0 [] e_qualish(X,Z)| -e_qualish(X,Y)| -e_qualish(Y,Z).
% 1.80/1.99 0 [] e_qualish(add(X,Z),add(Y,Z))| -defined(Z)| -e_qualish(X,Y).
% 1.80/1.99 0 [] e_qualish(multiply(X,Z),multiply(Y,Z))| -defined(Z)| -e_qualish(X,Y).
% 1.80/1.99 0 [] less_or_e_qual(Y,Z)| -less_or_e_qual(X,Z)| -e_qualish(X,Y).
% 1.80/1.99 0 [] -e_qualish(additive_identity,multiplicative_identity).
% 1.80/1.99 0 [] defined(a).
% 1.80/1.99 0 [] defined(b).
% 1.80/1.99 0 [] less_or_e_qual(additive_identity,a).
% 1.80/1.99 0 [] less_or_e_qual(additive_identity,b).
% 1.80/1.99 0 [] -less_or_e_qual(additive_identity,multiply(a,b)).
% 1.80/1.99 end_of_list.
% 1.80/1.99
% 1.80/1.99 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.80/1.99
% 1.80/1.99 This is a non-Horn set without equality. The strategy will
% 1.80/1.99 be ordered hyper_res, unit deletion, and factoring, with
% 1.80/1.99 satellites in sos and with nuclei in usable.
% 1.80/1.99
% 1.80/1.99 dependent: set(hyper_res).
% 1.80/1.99 dependent: set(factor).
% 1.80/1.99 dependent: set(unit_deletion).
% 1.80/1.99
% 1.80/1.99 ------------> process usable:
% 1.80/1.99 ** KEPT (pick-wt=17): 1 [] e_qualish(add(A,add(B,C)),add(add(A,B),C))| -defined(A)| -defined(B)| -defined(C).
% 1.80/1.99 ** KEPT (pick-wt=7): 2 [] e_qualish(add(additive_identity,A),A)| -defined(A).
% 1.80/1.99 ** KEPT (pick-wt=8): 3 [] e_qualish(add(A,additive_inverse(A)),additive_identity)| -defined(A).
% 1.80/1.99 ** KEPT (pick-wt=11): 4 [] e_qualish(add(A,B),add(B,A))| -defined(A)| -defined(B).
% 1.80/1.99 ** KEPT (pick-wt=17): 5 [] e_qualish(multiply(A,multiply(B,C)),multiply(multiply(A,B),C))| -defined(A)| -defined(B)| -defined(C).
% 1.80/1.99 ** KEPT (pick-wt=7): 6 [] e_qualish(multiply(multiplicative_identity,A),A)| -defined(A).
% 1.80/1.99 ** KEPT (pick-wt=11): 7 [] e_qualish(multiply(A,multiplicative_inverse(A)),multiplicative_identity)| -defined(A)|e_qualish(A,additive_identity).
% 1.80/1.99 ** KEPT (pick-wt=11): 8 [] e_qualish(multiply(A,B),multiply(B,A))| -defined(A)| -defined(B).
% 1.80/1.99 ** KEPT (pick-wt=19): 9 [] e_qualish(add(multiply(A,B),multiply(C,B)),multiply(add(A,C),B))| -defined(A)| -defined(C)| -defined(B).
% 1.80/1.99 ** KEPT (pick-wt=8): 10 [] defined(add(A,B))| -defined(A)| -defined(B).
% 1.80/1.99 ** KEPT (pick-wt=5): 11 [] defined(additive_inverse(A))| -defined(A).
% 1.80/2.00 ** KEPT (pick-wt=8): 12 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 1.80/2.00 ** KEPT (pick-wt=8): 13 [] defined(multiplicative_inverse(A))| -defined(A)|e_qualish(A,additive_identity).
% 1.80/2.00 ** KEPT (pick-wt=9): 14 [] e_qualish(A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 1.80/2.00 ** KEPT (pick-wt=9): 15 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 1.80/2.00 ** KEPT (pick-wt=10): 16 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 1.80/2.00 ** KEPT (pick-wt=12): 17 [] less_or_e_qual(add(A,B),add(C,B))| -defined(B)| -less_or_e_qual(A,C).
% 1.80/2.00 ** KEPT (pick-wt=11): 18 [] less_or_e_qual(additive_identity,multiply(A,B))| -less_or_e_qual(additive_identity,A)| -less_or_e_qual(additive_identity,B).
% 1.80/2.00 ** KEPT (pick-wt=5): 19 [] e_qualish(A,A)| -defined(A).
% 1.80/2.00 ** KEPT (pick-wt=6): 20 [] e_qualish(A,B)| -e_qualish(B,A).
% 1.80/2.00 ** KEPT (pick-wt=9): 21 [] e_qualish(A,B)| -e_qualish(A,C)| -e_qualish(C,B).
% 1.80/2.00 ** KEPT (pick-wt=12): 22 [] e_qualish(add(A,B),add(C,B))| -defined(B)| -e_qualish(A,C).
% 1.80/2.00 ** KEPT (pick-wt=12): 23 [] e_qualish(multiply(A,B),multiply(C,B))| -defined(B)| -e_qualish(A,C).
% 1.80/2.00 ** KEPT (pick-wt=9): 24 [] less_or_e_qual(A,B)| -less_or_e_qual(C,B)| -e_qualish(C,A).
% 1.80/2.00 ** KEPT (pick-wt=3): 25 [] -e_qualish(additive_identity,multiplicative_identity).
% 1.80/2.00 ** KEPT (pick-wt=5): 26 [] -less_or_e_qual(additive_identity,multiply(a,b)).
% 1.80/2.00
% 1.80/2.00 ------------> process sos:
% 1.80/2.00 ** KEPT (pick-wt=2): 46 [] defined(additive_identity).
% 1.80/2.00 ** KEPT (pick-wt=2): 47 [] defined(multiplicative_identity).
% 1.80/2.00 ** KEPT (pick-wt=2): 48 [] defined(a).
% 1.80/2.00 ** KEPT (pick-wt=2): 49 [] defined(b).
% 1.80/2.00 ** KEPT (pick-wt=3): 50 [] less_or_e_qual(additive_identity,a).
% 1.80/2.00 ** KEPT (pick-wt=3): 51 [] less_or_e_qual(additive_identity,b).
% 1.80/2.00
% 1.80/2.00 ======= end of input processing =======
% 1.80/2.00
% 1.80/2.00 =========== start of search ===========
% 1.80/2.00
% 1.80/2.00 -------- PROOF --------
% 1.80/2.00
% 1.80/2.00 ----> UNIT CONFLICT at 0.01 sec ----> 349 [binary,348.1,26.1] $F.
% 1.80/2.00
% 1.80/2.00 Length of proof is 1. Level of proof is 1.
% 1.80/2.00
% 1.80/2.00 ---------------- PROOF ----------------
% 1.80/2.00 % SZS status Unsatisfiable
% 1.80/2.00 % SZS output start Refutation
% See solution above
% 1.80/2.00 ------------ end of proof -------------
% 1.80/2.00
% 1.80/2.00
% 1.80/2.00 Search stopped by max_proofs option.
% 1.80/2.00
% 1.80/2.00
% 1.80/2.00 Search stopped by max_proofs option.
% 1.80/2.00
% 1.80/2.00 ============ end of search ============
% 1.80/2.00
% 1.80/2.00 -------------- statistics -------------
% 1.80/2.00 clauses given 6
% 1.80/2.00 clauses generated 648
% 1.80/2.00 clauses kept 348
% 1.80/2.00 clauses forward subsumed 330
% 1.80/2.00 clauses back subsumed 0
% 1.80/2.00 Kbytes malloced 976
% 1.80/2.00
% 1.80/2.00 ----------- times (seconds) -----------
% 1.80/2.00 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.80/2.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/2.00 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.80/2.00
% 1.80/2.00 That finishes the proof of the theorem.
% 1.80/2.00
% 1.80/2.00 Process 11398 finished Wed Jul 27 03:14:40 2022
% 1.80/2.00 Otter interrupted
% 1.80/2.00 PROOF FOUND
%------------------------------------------------------------------------------