TSTP Solution File: BOO006-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 12:47:31 EDT 2022
% Result : Unsatisfiable 1.90s 2.09s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of clauses : 24 ( 18 unt; 0 nHn; 8 RR)
% Number of literals : 38 ( 5 equ; 15 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ sum(A,B,C)
| sum(B,A,C) ),
file('BOO006-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| product(B,A,C) ),
file('BOO006-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ product(A,D,E)
| ~ sum(B,D,F)
| ~ product(A,F,G)
| sum(C,E,G) ),
file('BOO006-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ sum(A,B,C)
| ~ sum(D,B,E)
| ~ product(A,D,F)
| ~ sum(F,B,G)
| product(C,E,G) ),
file('BOO006-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| C = D ),
file('BOO006-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('BOO006-1.p',unknown),
[] ).
cnf(13,axiom,
~ product(x,additive_identity,additive_identity),
file('BOO006-1.p',unknown),
[] ).
cnf(15,axiom,
sum(A,B,add(A,B)),
file('BOO006-1.p',unknown),
[] ).
cnf(16,axiom,
product(A,B,multiply(A,B)),
file('BOO006-1.p',unknown),
[] ).
cnf(17,axiom,
sum(additive_identity,A,A),
file('BOO006-1.p',unknown),
[] ).
cnf(18,axiom,
sum(A,additive_identity,A),
file('BOO006-1.p',unknown),
[] ).
cnf(19,axiom,
product(multiplicative_identity,A,A),
file('BOO006-1.p',unknown),
[] ).
cnf(20,axiom,
product(A,multiplicative_identity,A),
file('BOO006-1.p',unknown),
[] ).
cnf(21,axiom,
sum(inverse(A),A,multiplicative_identity),
file('BOO006-1.p',unknown),
[] ).
cnf(36,plain,
add(additive_identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[15,11,17])]),
[iquote('hyper,15,11,17,flip.1')] ).
cnf(51,plain,
sum(A,B,add(B,A)),
inference(hyper,[status(thm)],[15,1]),
[iquote('hyper,15,1')] ).
cnf(59,plain,
product(multiplicative_identity,add(multiplicative_identity,A),multiplicative_identity),
inference(hyper,[status(thm)],[21,9,21,15,20]),
[iquote('hyper,21,9,21,15,20')] ).
cnf(112,plain,
multiply(A,multiplicative_identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[16,12,20])]),
[iquote('hyper,16,12,20,flip.1')] ).
cnf(278,plain,
product(A,B,multiply(B,A)),
inference(hyper,[status(thm)],[16,2]),
[iquote('hyper,16,2')] ).
cnf(1040,plain,
sum(multiply(A,B),A,multiply(A,add(multiplicative_identity,B))),
inference(hyper,[status(thm)],[51,3,16,20,16]),
[iquote('hyper,51,3,16,20,16')] ).
cnf(1050,plain,
add(multiplicative_identity,A) = multiplicative_identity,
inference(hyper,[status(thm)],[59,12,19]),
[iquote('hyper,59,12,19')] ).
cnf(1055,plain,
sum(multiply(A,B),A,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1040]),1050,112]),
[iquote('back_demod,1040,demod,1050,112')] ).
cnf(1351,plain,
product(A,additive_identity,additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1055,9,51,18,278]),36]),
[iquote('hyper,1055,9,51,18,278,demod,36')] ).
cnf(1352,plain,
$false,
inference(binary,[status(thm)],[1351,13]),
[iquote('binary,1351.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : BOO006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 02:46:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.73/1.93 ----- Otter 3.3f, August 2004 -----
% 1.73/1.93 The process was started by sandbox2 on n027.cluster.edu,
% 1.73/1.93 Wed Jul 27 02:46:21 2022
% 1.73/1.93 The command was "./otter". The process ID is 22320.
% 1.73/1.93
% 1.73/1.93 set(prolog_style_variables).
% 1.73/1.93 set(auto).
% 1.73/1.93 dependent: set(auto1).
% 1.73/1.93 dependent: set(process_input).
% 1.73/1.93 dependent: clear(print_kept).
% 1.73/1.93 dependent: clear(print_new_demod).
% 1.73/1.93 dependent: clear(print_back_demod).
% 1.73/1.93 dependent: clear(print_back_sub).
% 1.73/1.93 dependent: set(control_memory).
% 1.73/1.93 dependent: assign(max_mem, 12000).
% 1.73/1.93 dependent: assign(pick_given_ratio, 4).
% 1.73/1.93 dependent: assign(stats_level, 1).
% 1.73/1.93 dependent: assign(max_seconds, 10800).
% 1.73/1.93 clear(print_given).
% 1.73/1.93
% 1.73/1.93 list(usable).
% 1.73/1.93 0 [] A=A.
% 1.73/1.93 0 [] sum(X,Y,add(X,Y)).
% 1.73/1.93 0 [] product(X,Y,multiply(X,Y)).
% 1.73/1.93 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.73/1.93 0 [] -product(X,Y,Z)|product(Y,X,Z).
% 1.73/1.93 0 [] sum(additive_identity,X,X).
% 1.73/1.93 0 [] sum(X,additive_identity,X).
% 1.73/1.93 0 [] product(multiplicative_identity,X,X).
% 1.73/1.93 0 [] product(X,multiplicative_identity,X).
% 1.73/1.93 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.73/1.93 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.73/1.93 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.73/1.93 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.73/1.93 0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -sum(X,V3,V4)|product(V1,V2,V4).
% 1.73/1.93 0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(X,V3,V4).
% 1.73/1.93 0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -sum(V3,X,V4)|product(V1,V2,V4).
% 1.73/1.93 0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(V3,X,V4).
% 1.73/1.93 0 [] sum(inverse(X),X,multiplicative_identity).
% 1.73/1.93 0 [] sum(X,inverse(X),multiplicative_identity).
% 1.73/1.93 0 [] product(inverse(X),X,additive_identity).
% 1.73/1.93 0 [] product(X,inverse(X),additive_identity).
% 1.73/1.93 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.73/1.93 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.73/1.93 0 [] -product(x,additive_identity,additive_identity).
% 1.73/1.93 end_of_list.
% 1.73/1.93
% 1.73/1.93 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.73/1.93
% 1.73/1.93 This is a Horn set with equality. The strategy will be
% 1.73/1.93 Knuth-Bendix and hyper_res, with positive clauses in
% 1.73/1.93 sos and nonpositive clauses in usable.
% 1.73/1.93
% 1.73/1.93 dependent: set(knuth_bendix).
% 1.73/1.93 dependent: set(anl_eq).
% 1.73/1.93 dependent: set(para_from).
% 1.73/1.93 dependent: set(para_into).
% 1.73/1.93 dependent: clear(para_from_right).
% 1.73/1.93 dependent: clear(para_into_right).
% 1.73/1.93 dependent: set(para_from_vars).
% 1.73/1.93 dependent: set(eq_units_both_ways).
% 1.73/1.93 dependent: set(dynamic_demod_all).
% 1.73/1.93 dependent: set(dynamic_demod).
% 1.73/1.93 dependent: set(order_eq).
% 1.73/1.93 dependent: set(back_demod).
% 1.73/1.93 dependent: set(lrpo).
% 1.73/1.93 dependent: set(hyper_res).
% 1.73/1.93 dependent: clear(order_hyper).
% 1.73/1.93
% 1.73/1.93 ------------> process usable:
% 1.73/1.93 ** KEPT (pick-wt=8): 1 [] -sum(A,B,C)|sum(B,A,C).
% 1.73/1.93 ** KEPT (pick-wt=8): 2 [] -product(A,B,C)|product(B,A,C).
% 1.73/1.93 ** 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).
% 1.73/1.93 ** 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).
% 1.73/1.93 ** 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).
% 1.73/1.93 ** 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).
% 1.73/1.93 ** 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).
% 1.73/1.93 ** 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).
% 1.73/1.93 ** 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).
% 1.73/1.93 ** 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).
% 1.73/1.93 ** KEPT (pick-wt=11): 11 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.73/1.93 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.73/1.93 ** KEPT (pick-wt=4): 13 [] -product(x,additive_identity,additive_identity).
% 1.73/1.93
% 1.73/1.93 ------------> process sos:
% 1.73/1.93 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.73/1.93 ** KEPT (pick-wt=6): 15 [] sum(A,B,add(A,B)).
% 1.73/1.93 ** KEPT (pick-wt=6): 16 [] product(A,B,multiply(A,B)).
% 1.73/1.93 ** KEPT (pick-wt=4): 17 [] sum(additive_identity,A,A).
% 1.73/1.93 ** KEPT (pick-wt=4): 18 [] sum(A,additive_identity,A).
% 1.73/1.93 ** KEPT (pick-wt=4): 19 [] product(multiplicative_identity,A,A).
% 1.90/2.09 ** KEPT (pick-wt=4): 20 [] product(A,multiplicative_identity,A).
% 1.90/2.09 ** KEPT (pick-wt=5): 21 [] sum(inverse(A),A,multiplicative_identity).
% 1.90/2.09 ** KEPT (pick-wt=5): 22 [] sum(A,inverse(A),multiplicative_identity).
% 1.90/2.09 ** KEPT (pick-wt=5): 23 [] product(inverse(A),A,additive_identity).
% 1.90/2.09 ** KEPT (pick-wt=5): 24 [] product(A,inverse(A),additive_identity).
% 1.90/2.09 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.90/2.09
% 1.90/2.09 ======= end of input processing =======
% 1.90/2.09
% 1.90/2.09 =========== start of search ===========
% 1.90/2.09
% 1.90/2.09 -------- PROOF --------
% 1.90/2.09
% 1.90/2.09 ----> UNIT CONFLICT at 0.16 sec ----> 1352 [binary,1351.1,13.1] $F.
% 1.90/2.09
% 1.90/2.09 Length of proof is 9. Level of proof is 4.
% 1.90/2.09
% 1.90/2.09 ---------------- PROOF ----------------
% 1.90/2.09 % SZS status Unsatisfiable
% 1.90/2.09 % SZS output start Refutation
% See solution above
% 1.90/2.09 ------------ end of proof -------------
% 1.90/2.09
% 1.90/2.09
% 1.90/2.09 Search stopped by max_proofs option.
% 1.90/2.09
% 1.90/2.09
% 1.90/2.09 Search stopped by max_proofs option.
% 1.90/2.09
% 1.90/2.09 ============ end of search ============
% 1.90/2.09
% 1.90/2.09 -------------- statistics -------------
% 1.90/2.09 clauses given 44
% 1.90/2.09 clauses generated 24820
% 1.90/2.09 clauses kept 1328
% 1.90/2.09 clauses forward subsumed 24155
% 1.90/2.09 clauses back subsumed 75
% 1.90/2.09 Kbytes malloced 2929
% 1.90/2.09
% 1.90/2.09 ----------- times (seconds) -----------
% 1.90/2.09 user CPU time 0.16 (0 hr, 0 min, 0 sec)
% 1.90/2.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.90/2.09 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.90/2.09
% 1.90/2.09 That finishes the proof of the theorem.
% 1.90/2.09
% 1.90/2.09 Process 22320 finished Wed Jul 27 02:46:23 2022
% 1.90/2.09 Otter interrupted
% 1.90/2.09 PROOF FOUND
%------------------------------------------------------------------------------