TSTP Solution File: BOO013-3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO013-3 : TPTP v8.1.0. Released v1.0.0.
% 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 12:47:34 EDT 2022
% Result : Unsatisfiable 2.20s 2.36s
% Output : Refutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of clauses : 20 ( 17 unt; 0 nHn; 15 RR)
% Number of literals : 27 ( 6 equ; 9 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ sum(A,B,C)
| sum(B,A,C) ),
file('BOO013-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum(A,B,C)
| ~ sum(D,B,E)
| ~ product(A,D,F)
| ~ product(C,E,G)
| sum(F,B,G) ),
file('BOO013-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| C = D ),
file('BOO013-3.p',unknown),
[] ).
cnf(13,axiom,
y != z,
file('BOO013-3.p',unknown),
[] ).
cnf(14,plain,
z != y,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(16,axiom,
sum(A,B,add(A,B)),
file('BOO013-3.p',unknown),
[] ).
cnf(19,axiom,
sum(A,additive_identity,A),
file('BOO013-3.p',unknown),
[] ).
cnf(20,axiom,
product(multiplicative_identity,A,A),
file('BOO013-3.p',unknown),
[] ).
cnf(28,axiom,
sum(x,y,multiplicative_identity),
file('BOO013-3.p',unknown),
[] ).
cnf(29,axiom,
sum(x,z,multiplicative_identity),
file('BOO013-3.p',unknown),
[] ).
cnf(30,axiom,
product(x,y,additive_identity),
file('BOO013-3.p',unknown),
[] ).
cnf(31,axiom,
product(x,z,additive_identity),
file('BOO013-3.p',unknown),
[] ).
cnf(41,plain,
add(A,additive_identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[16,11,19])]),
[iquote('hyper,16,11,19,flip.1')] ).
cnf(58,plain,
sum(A,B,add(B,A)),
inference(hyper,[status(thm)],[16,1]),
[iquote('hyper,16,1')] ).
cnf(89,plain,
sum(additive_identity,z,add(y,z)),
inference(hyper,[status(thm)],[30,10,29,16,20]),
[iquote('hyper,30,10,29,16,20')] ).
cnf(1470,plain,
sum(additive_identity,y,add(y,z)),
inference(hyper,[status(thm)],[58,10,28,31,20]),
[iquote('hyper,58,10,28,31,20')] ).
cnf(2159,plain,
add(y,z) = z,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[89,11,58]),41])]),
[iquote('hyper,89,11,58,demod,41,flip.1')] ).
cnf(2160,plain,
sum(additive_identity,y,z),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1470]),2159]),
[iquote('back_demod,1470,demod,2159')] ).
cnf(2308,plain,
z = y,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2160,11,58]),41])]),
[iquote('hyper,2160,11,58,demod,41,flip.1')] ).
cnf(2310,plain,
$false,
inference(binary,[status(thm)],[2308,14]),
[iquote('binary,2308.1,14.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO013-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % 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 02:37:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.99/2.16 ----- Otter 3.3f, August 2004 -----
% 1.99/2.16 The process was started by sandbox on n020.cluster.edu,
% 1.99/2.16 Wed Jul 27 02:37:23 2022
% 1.99/2.16 The command was "./otter". The process ID is 6321.
% 1.99/2.16
% 1.99/2.16 set(prolog_style_variables).
% 1.99/2.16 set(auto).
% 1.99/2.16 dependent: set(auto1).
% 1.99/2.16 dependent: set(process_input).
% 1.99/2.16 dependent: clear(print_kept).
% 1.99/2.16 dependent: clear(print_new_demod).
% 1.99/2.16 dependent: clear(print_back_demod).
% 1.99/2.16 dependent: clear(print_back_sub).
% 1.99/2.16 dependent: set(control_memory).
% 1.99/2.16 dependent: assign(max_mem, 12000).
% 1.99/2.16 dependent: assign(pick_given_ratio, 4).
% 1.99/2.16 dependent: assign(stats_level, 1).
% 1.99/2.16 dependent: assign(max_seconds, 10800).
% 1.99/2.16 clear(print_given).
% 1.99/2.16
% 1.99/2.16 list(usable).
% 1.99/2.16 0 [] A=A.
% 1.99/2.16 0 [] sum(X,Y,add(X,Y)).
% 1.99/2.16 0 [] product(X,Y,multiply(X,Y)).
% 1.99/2.16 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.99/2.16 0 [] -product(X,Y,Z)|product(Y,X,Z).
% 1.99/2.16 0 [] sum(additive_identity,X,X).
% 1.99/2.16 0 [] sum(X,additive_identity,X).
% 1.99/2.16 0 [] product(multiplicative_identity,X,X).
% 1.99/2.16 0 [] product(X,multiplicative_identity,X).
% 1.99/2.16 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.99/2.16 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.99/2.16 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.99/2.16 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.99/2.16 0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -sum(X,V3,V4)|product(V1,V2,V4).
% 1.99/2.16 0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(X,V3,V4).
% 1.99/2.16 0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -sum(V3,X,V4)|product(V1,V2,V4).
% 1.99/2.16 0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(V3,X,V4).
% 1.99/2.16 0 [] sum(inverse(X),X,multiplicative_identity).
% 1.99/2.16 0 [] sum(X,inverse(X),multiplicative_identity).
% 1.99/2.16 0 [] product(inverse(X),X,additive_identity).
% 1.99/2.16 0 [] product(X,inverse(X),additive_identity).
% 1.99/2.16 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.99/2.16 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.99/2.16 0 [] inverse(inverse(X))=X.
% 1.99/2.16 0 [] sum(x,y,multiplicative_identity).
% 1.99/2.16 0 [] sum(x,z,multiplicative_identity).
% 1.99/2.16 0 [] product(x,y,additive_identity).
% 1.99/2.16 0 [] product(x,z,additive_identity).
% 1.99/2.16 0 [] y!=z.
% 1.99/2.16 end_of_list.
% 1.99/2.16
% 1.99/2.16 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.99/2.16
% 1.99/2.16 This is a Horn set with equality. The strategy will be
% 1.99/2.16 Knuth-Bendix and hyper_res, with positive clauses in
% 1.99/2.16 sos and nonpositive clauses in usable.
% 1.99/2.16
% 1.99/2.16 dependent: set(knuth_bendix).
% 1.99/2.16 dependent: set(anl_eq).
% 1.99/2.16 dependent: set(para_from).
% 1.99/2.16 dependent: set(para_into).
% 1.99/2.16 dependent: clear(para_from_right).
% 1.99/2.16 dependent: clear(para_into_right).
% 1.99/2.16 dependent: set(para_from_vars).
% 1.99/2.16 dependent: set(eq_units_both_ways).
% 1.99/2.16 dependent: set(dynamic_demod_all).
% 1.99/2.16 dependent: set(dynamic_demod).
% 1.99/2.16 dependent: set(order_eq).
% 1.99/2.16 dependent: set(back_demod).
% 1.99/2.16 dependent: set(lrpo).
% 1.99/2.16 dependent: set(hyper_res).
% 1.99/2.16 dependent: clear(order_hyper).
% 1.99/2.16
% 1.99/2.16 ------------> process usable:
% 1.99/2.16 ** KEPT (pick-wt=8): 1 [] -sum(A,B,C)|sum(B,A,C).
% 1.99/2.16 ** KEPT (pick-wt=8): 2 [] -product(A,B,C)|product(B,A,C).
% 1.99/2.16 ** KEPT (pick-wt=20): 3 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -product(A,F,G)|sum(C,E,G).
% 1.99/2.16 ** KEPT (pick-wt=20): 4 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -sum(C,E,G)|product(A,F,G).
% 1.99/2.16 ** KEPT (pick-wt=20): 5 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -product(F,B,G)|sum(C,E,G).
% 1.99/2.16 ** KEPT (pick-wt=20): 6 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -sum(C,E,G)|product(F,B,G).
% 1.99/2.16 ** KEPT (pick-wt=20): 7 [] -sum(A,B,C)| -sum(A,D,E)| -product(B,D,F)| -sum(A,F,G)|product(C,E,G).
% 1.99/2.16 ** KEPT (pick-wt=20): 8 [] -sum(A,B,C)| -sum(A,D,E)| -product(B,D,F)| -product(C,E,G)|sum(A,F,G).
% 1.99/2.16 ** KEPT (pick-wt=20): 9 [] -sum(A,B,C)| -sum(D,B,E)| -product(A,D,F)| -sum(F,B,G)|product(C,E,G).
% 1.99/2.16 ** KEPT (pick-wt=20): 10 [] -sum(A,B,C)| -sum(D,B,E)| -product(A,D,F)| -product(C,E,G)|sum(F,B,G).
% 1.99/2.16 ** KEPT (pick-wt=11): 11 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.99/2.16 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.99/2.16 ** KEPT (pick-wt=3): 14 [copy,13,flip.1] z!=y.
% 1.99/2.16
% 1.99/2.16 ------------> process sos:
% 1.99/2.16 ** KEPT (pick-wt=3): 15 [] A=A.
% 1.99/2.16 ** KEPT (pick-wt=6): 16 [] sum(A,B,add(A,B)).
% 1.99/2.16 ** KEPT (pick-wt=6): 17 [] product(A,B,multiply(A,B)).
% 1.99/2.16 ** KEPT (pick-wt=4): 18 [] sum(additive_identity,A,A).
% 2.20/2.36 ** KEPT (pick-wt=4): 19 [] sum(A,additive_identity,A).
% 2.20/2.36 ** KEPT (pick-wt=4): 20 [] product(multiplicative_identity,A,A).
% 2.20/2.36 ** KEPT (pick-wt=4): 21 [] product(A,multiplicative_identity,A).
% 2.20/2.36 ** KEPT (pick-wt=5): 22 [] sum(inverse(A),A,multiplicative_identity).
% 2.20/2.36 ** KEPT (pick-wt=5): 23 [] sum(A,inverse(A),multiplicative_identity).
% 2.20/2.36 ** KEPT (pick-wt=5): 24 [] product(inverse(A),A,additive_identity).
% 2.20/2.36 ** KEPT (pick-wt=5): 25 [] product(A,inverse(A),additive_identity).
% 2.20/2.36 ** KEPT (pick-wt=5): 26 [] inverse(inverse(A))=A.
% 2.20/2.36 ---> New Demodulator: 27 [new_demod,26] inverse(inverse(A))=A.
% 2.20/2.36 ** KEPT (pick-wt=4): 28 [] sum(x,y,multiplicative_identity).
% 2.20/2.36 ** KEPT (pick-wt=4): 29 [] sum(x,z,multiplicative_identity).
% 2.20/2.36 ** KEPT (pick-wt=4): 30 [] product(x,y,additive_identity).
% 2.20/2.36 ** KEPT (pick-wt=4): 31 [] product(x,z,additive_identity).
% 2.20/2.36 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 2.20/2.36 >>>> Starting back demodulation with 27.
% 2.20/2.36
% 2.20/2.36 ======= end of input processing =======
% 2.20/2.36
% 2.20/2.36 =========== start of search ===========
% 2.20/2.36
% 2.20/2.36 -------- PROOF --------
% 2.20/2.36
% 2.20/2.36 ----> UNIT CONFLICT at 0.20 sec ----> 2310 [binary,2308.1,14.1] $F.
% 2.20/2.36
% 2.20/2.36 Length of proof is 8. Level of proof is 4.
% 2.20/2.36
% 2.20/2.36 ---------------- PROOF ----------------
% 2.20/2.36 % SZS status Unsatisfiable
% 2.20/2.36 % SZS output start Refutation
% See solution above
% 2.20/2.36 ------------ end of proof -------------
% 2.20/2.36
% 2.20/2.36
% 2.20/2.36 Search stopped by max_proofs option.
% 2.20/2.36
% 2.20/2.36
% 2.20/2.36 Search stopped by max_proofs option.
% 2.20/2.36
% 2.20/2.36 ============ end of search ============
% 2.20/2.36
% 2.20/2.36 -------------- statistics -------------
% 2.20/2.36 clauses given 67
% 2.20/2.36 clauses generated 22380
% 2.20/2.36 clauses kept 2274
% 2.20/2.36 clauses forward subsumed 20516
% 2.20/2.36 clauses back subsumed 108
% 2.20/2.36 Kbytes malloced 3906
% 2.20/2.36
% 2.20/2.36 ----------- times (seconds) -----------
% 2.20/2.36 user CPU time 0.20 (0 hr, 0 min, 0 sec)
% 2.20/2.36 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.20/2.36 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.20/2.36
% 2.20/2.36 That finishes the proof of the theorem.
% 2.20/2.36
% 2.20/2.36 Process 6321 finished Wed Jul 27 02:37:25 2022
% 2.20/2.36 Otter interrupted
% 2.20/2.36 PROOF FOUND
%------------------------------------------------------------------------------