TSTP Solution File: RNG008-5 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG008-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 13:12:02 EDT 2022
% Result : Unsatisfiable 2.13s 2.35s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of clauses : 51 ( 41 unt; 0 nHn; 29 RR)
% Number of literals : 80 ( 11 equ; 30 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(C,D,F)
| sum(A,E,F) ),
file('RNG008-5.p',unknown),
[] ).
cnf(2,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(A,E,F)
| sum(C,D,F) ),
file('RNG008-5.p',unknown),
[] ).
cnf(3,axiom,
( ~ sum(A,B,C)
| sum(B,A,C) ),
file('RNG008-5.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('RNG008-5.p',unknown),
[] ).
cnf(5,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('RNG008-5.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(A,B,C)
| ~ product(A,D,E)
| ~ sum(B,D,F)
| ~ sum(C,E,G)
| product(A,F,G) ),
file('RNG008-5.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(A,B,C)
| ~ product(D,B,E)
| ~ sum(A,D,F)
| ~ product(F,B,G)
| sum(C,E,G) ),
file('RNG008-5.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(A,B,C)
| ~ product(D,B,E)
| ~ sum(A,D,F)
| ~ sum(C,E,G)
| product(F,B,G) ),
file('RNG008-5.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| C = D ),
file('RNG008-5.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('RNG008-5.p',unknown),
[] ).
cnf(12,axiom,
~ product(b,a,c),
file('RNG008-5.p',unknown),
[] ).
cnf(14,axiom,
sum(additive_identity,A,A),
file('RNG008-5.p',unknown),
[] ).
cnf(15,axiom,
sum(A,additive_identity,A),
file('RNG008-5.p',unknown),
[] ).
cnf(16,axiom,
product(A,B,multiply(A,B)),
file('RNG008-5.p',unknown),
[] ).
cnf(17,axiom,
sum(A,B,add(A,B)),
file('RNG008-5.p',unknown),
[] ).
cnf(18,axiom,
sum(additive_inverse(A),A,additive_identity),
file('RNG008-5.p',unknown),
[] ).
cnf(19,axiom,
sum(A,additive_inverse(A),additive_identity),
file('RNG008-5.p',unknown),
[] ).
cnf(20,axiom,
sum(additive_inverse(additive_inverse(A)),additive_identity,A),
file('RNG008-5.p',unknown),
[] ).
cnf(22,axiom,
product(additive_identity,A,additive_identity),
file('RNG008-5.p',unknown),
[] ).
cnf(24,axiom,
product(A,additive_inverse(B),additive_inverse(multiply(A,B))),
file('RNG008-5.p',unknown),
[] ).
cnf(25,axiom,
product(A,A,A),
file('RNG008-5.p',unknown),
[] ).
cnf(26,axiom,
product(a,b,c),
file('RNG008-5.p',unknown),
[] ).
cnf(40,plain,
multiply(additive_identity,A) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[16,11,22])]),
[iquote('hyper,16,11,22,flip.1')] ).
cnf(48,plain,
multiply(A,A) = A,
inference(hyper,[status(thm)],[25,11,16]),
[iquote('hyper,25,11,16')] ).
cnf(52,plain,
product(A,multiply(B,multiply(A,B)),multiply(A,B)),
inference(hyper,[status(thm)],[25,4,16,16]),
[iquote('hyper,25,4,16,16')] ).
cnf(57,plain,
product(c,b,c),
inference(hyper,[status(thm)],[26,5,26,25]),
[iquote('hyper,26,5,26,25')] ).
cnf(61,plain,
product(c,A,multiply(a,multiply(b,A))),
inference(hyper,[status(thm)],[26,5,16,16]),
[iquote('hyper,26,5,16,16')] ).
cnf(62,plain,
product(a,c,c),
inference(hyper,[status(thm)],[26,4,25,26]),
[iquote('hyper,26,4,25,26')] ).
cnf(65,plain,
product(a,multiply(b,c),c),
inference(hyper,[status(thm)],[26,4,16,25]),
[iquote('hyper,26,4,16,25')] ).
cnf(87,plain,
multiply(a,c) = c,
inference(hyper,[status(thm)],[62,11,16]),
[iquote('hyper,62,11,16')] ).
cnf(100,plain,
add(A,additive_identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[17,10,15])]),
[iquote('hyper,17,10,15,flip.1')] ).
cnf(102,plain,
add(additive_identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[17,10,14])]),
[iquote('hyper,17,10,14,flip.1')] ).
cnf(108,plain,
product(add(c,b),b,add(c,b)),
inference(hyper,[status(thm)],[17,9,57,25,17]),
[iquote('hyper,17,9,57,25,17')] ).
cnf(148,plain,
product(a,add(c,a),add(c,a)),
inference(hyper,[status(thm)],[17,7,62,25,17]),
[iquote('hyper,17,7,62,25,17')] ).
cnf(189,plain,
sum(A,B,add(B,A)),
inference(hyper,[status(thm)],[17,3]),
[iquote('hyper,17,3')] ).
cnf(197,plain,
additive_inverse(additive_identity) = additive_identity,
inference(hyper,[status(thm)],[18,10,15]),
[iquote('hyper,18,10,15')] ).
cnf(274,plain,
additive_inverse(additive_inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[20,10,17]),100]),
[iquote('hyper,20,10,17,demod,100')] ).
cnf(308,plain,
sum(additive_inverse(A),additive_inverse(A),additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[24,8,25,24,19]),274,48,40,197]),
[iquote('hyper,24,8,25,24,19,demod,274,48,40,197')] ).
cnf(366,plain,
multiply(a,multiply(b,c)) = c,
inference(hyper,[status(thm)],[65,11,16]),
[iquote('hyper,65,11,16')] ).
cnf(713,plain,
sum(A,A,additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[308,274]),274]),
[iquote('para_into,308.1.1,273.1.1,demod,274')] ).
cnf(757,plain,
sum(add(A,B),B,A),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[713,2,17,189]),102]),
[iquote('hyper,713,2,17,189,demod,102')] ).
cnf(771,plain,
sum(A,add(A,B),B),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[713,1,17,189]),100]),
[iquote('hyper,713,1,17,189,demod,100')] ).
cnf(3575,plain,
product(add(c,b),c,additive_identity),
inference(hyper,[status(thm)],[108,7,25,757,713]),
[iquote('hyper,108,7,25,757,713')] ).
cnf(3584,plain,
product(b,c,c),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[3575,9,61,771,189]),366,102]),
[iquote('hyper,3575,9,61,771,189,demod,366,102')] ).
cnf(3618,plain,
multiply(b,c) = c,
inference(hyper,[status(thm)],[3584,11,16]),
[iquote('hyper,3584,11,16')] ).
cnf(3715,plain,
product(c,a,multiply(b,a)),
inference(hyper,[status(thm)],[3584,5,61,52]),
[iquote('hyper,3584,5,61,52')] ).
cnf(3926,plain,
product(add(b,c),a,additive_identity),
inference(hyper,[status(thm)],[3715,9,16,17,713]),
[iquote('hyper,3715,9,16,17,713')] ).
cnf(4045,plain,
product(c,add(c,a),additive_identity),
inference(hyper,[status(thm)],[148,9,25,757,713]),
[iquote('hyper,148,9,25,757,713')] ).
cnf(4049,plain,
product(c,a,c),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4045,7,61,771,189]),3618,87,102]),
[iquote('hyper,4045,7,61,771,189,demod,3618,87,102')] ).
cnf(4067,plain,
product(b,a,c),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4049,9,3926,757,189]),100]),
[iquote('hyper,4049,9,3926,757,189,demod,100')] ).
cnf(4068,plain,
$false,
inference(binary,[status(thm)],[4067,12]),
[iquote('binary,4067.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : RNG008-5 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.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 02:11:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.94 ----- Otter 3.3f, August 2004 -----
% 1.72/1.94 The process was started by sandbox on n004.cluster.edu,
% 1.72/1.94 Wed Jul 27 02:11:21 2022
% 1.72/1.94 The command was "./otter". The process ID is 19371.
% 1.72/1.94
% 1.72/1.94 set(prolog_style_variables).
% 1.72/1.94 set(auto).
% 1.72/1.94 dependent: set(auto1).
% 1.72/1.94 dependent: set(process_input).
% 1.72/1.94 dependent: clear(print_kept).
% 1.72/1.94 dependent: clear(print_new_demod).
% 1.72/1.94 dependent: clear(print_back_demod).
% 1.72/1.94 dependent: clear(print_back_sub).
% 1.72/1.94 dependent: set(control_memory).
% 1.72/1.94 dependent: assign(max_mem, 12000).
% 1.72/1.94 dependent: assign(pick_given_ratio, 4).
% 1.72/1.94 dependent: assign(stats_level, 1).
% 1.72/1.94 dependent: assign(max_seconds, 10800).
% 1.72/1.94 clear(print_given).
% 1.72/1.94
% 1.72/1.94 list(usable).
% 1.72/1.94 0 [] A=A.
% 1.72/1.94 0 [] sum(additive_identity,X,X).
% 1.72/1.94 0 [] sum(X,additive_identity,X).
% 1.72/1.94 0 [] product(X,Y,multiply(X,Y)).
% 1.72/1.94 0 [] sum(X,Y,add(X,Y)).
% 1.72/1.94 0 [] sum(additive_inverse(X),X,additive_identity).
% 1.72/1.94 0 [] sum(X,additive_inverse(X),additive_identity).
% 1.72/1.94 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 1.72/1.94 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 1.72/1.94 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.72/1.94 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.72/1.94 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.72/1.94 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.72/1.94 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.72/1.94 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.72/1.94 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.72/1.94 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.72/1.94 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.72/1.94 0 [] sum(additive_inverse(additive_identity),additive_identity,additive_identity).
% 1.72/1.94 0 [] sum(additive_inverse(additive_inverse(X)),additive_identity,X).
% 1.72/1.94 0 [] product(X,additive_identity,additive_identity).
% 1.72/1.94 0 [] product(additive_identity,X,additive_identity).
% 1.72/1.94 0 [] sum(additive_inverse(X),additive_inverse(Y),additive_inverse(add(X,Y))).
% 1.72/1.94 0 [] product(X,additive_inverse(Y),additive_inverse(multiply(X,Y))).
% 1.72/1.94 0 [] product(X,X,X).
% 1.72/1.94 0 [] product(a,b,c).
% 1.72/1.94 0 [] -product(b,a,c).
% 1.72/1.94 end_of_list.
% 1.72/1.94
% 1.72/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.72/1.94
% 1.72/1.94 This is a Horn set with equality. The strategy will be
% 1.72/1.94 Knuth-Bendix and hyper_res, with positive clauses in
% 1.72/1.94 sos and nonpositive clauses in usable.
% 1.72/1.94
% 1.72/1.94 dependent: set(knuth_bendix).
% 1.72/1.94 dependent: set(anl_eq).
% 1.72/1.94 dependent: set(para_from).
% 1.72/1.94 dependent: set(para_into).
% 1.72/1.94 dependent: clear(para_from_right).
% 1.72/1.94 dependent: clear(para_into_right).
% 1.72/1.94 dependent: set(para_from_vars).
% 1.72/1.94 dependent: set(eq_units_both_ways).
% 1.72/1.94 dependent: set(dynamic_demod_all).
% 1.72/1.94 dependent: set(dynamic_demod).
% 1.72/1.94 dependent: set(order_eq).
% 1.72/1.94 dependent: set(back_demod).
% 1.72/1.94 dependent: set(lrpo).
% 1.72/1.94 dependent: set(hyper_res).
% 1.72/1.94 dependent: clear(order_hyper).
% 1.72/1.94
% 1.72/1.94 ------------> process usable:
% 1.72/1.94 ** KEPT (pick-wt=16): 1 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 1.72/1.94 ** KEPT (pick-wt=16): 2 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 1.72/1.94 ** KEPT (pick-wt=8): 3 [] -sum(A,B,C)|sum(B,A,C).
% 1.72/1.94 ** KEPT (pick-wt=16): 4 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.72/1.94 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.72/1.94 ** KEPT (pick-wt=20): 6 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -product(A,F,G)|sum(C,E,G).
% 1.72/1.94 ** KEPT (pick-wt=20): 7 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -sum(C,E,G)|product(A,F,G).
% 1.72/1.94 ** KEPT (pick-wt=20): 8 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -product(F,B,G)|sum(C,E,G).
% 1.72/1.94 ** KEPT (pick-wt=20): 9 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -sum(C,E,G)|product(F,B,G).
% 1.72/1.94 ** KEPT (pick-wt=11): 10 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.72/1.94 ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.72/1.94 ** KEPT (pick-wt=4): 12 [] -product(b,a,c).
% 1.72/1.94
% 1.72/1.94 ------------> process sos:
% 1.72/1.94 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.72/1.94 ** KEPT (pick-wt=4): 14 [] sum(additive_identity,A,A).
% 1.72/1.94 ** KEPT (pick-wt=4): 15 [] sum(A,additive_identity,A).
% 1.72/1.94 ** KEPT (pick-wt=6): 16 [] product(A,B,multiply(A,B)).
% 1.72/1.94 ** KEPT (pick-wt=6): 17 [] sum(A,B,add(A,B)).
% 1.72/1.94 ** KEPT (pick-wt=5): 18 [] sum(additive_inverse(A),A,additive_identity).
% 2.13/2.35 ** KEPT (pick-wt=5): 19 [] sum(A,additive_inverse(A),additive_identity).
% 2.13/2.35 Following clause subsumed by 18 during input processing: 0 [] sum(additive_inverse(additive_identity),additive_identity,additive_identity).
% 2.13/2.35 ** KEPT (pick-wt=6): 20 [] sum(additive_inverse(additive_inverse(A)),additive_identity,A).
% 2.13/2.35 ** KEPT (pick-wt=4): 21 [] product(A,additive_identity,additive_identity).
% 2.13/2.35 ** KEPT (pick-wt=4): 22 [] product(additive_identity,A,additive_identity).
% 2.13/2.35 ** KEPT (pick-wt=9): 23 [] sum(additive_inverse(A),additive_inverse(B),additive_inverse(add(A,B))).
% 2.13/2.35 ** KEPT (pick-wt=8): 24 [] product(A,additive_inverse(B),additive_inverse(multiply(A,B))).
% 2.13/2.35 ** KEPT (pick-wt=4): 25 [] product(A,A,A).
% 2.13/2.35 ** KEPT (pick-wt=4): 26 [] product(a,b,c).
% 2.13/2.35 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 2.13/2.35
% 2.13/2.35 ======= end of input processing =======
% 2.13/2.35
% 2.13/2.35 =========== start of search ===========
% 2.13/2.35
% 2.13/2.35
% 2.13/2.35 Resetting weight limit to 10.
% 2.13/2.35
% 2.13/2.35
% 2.13/2.35 Resetting weight limit to 10.
% 2.13/2.35
% 2.13/2.35 sos_size=2873
% 2.13/2.35
% 2.13/2.35
% 2.13/2.35 Resetting weight limit to 8.
% 2.13/2.35
% 2.13/2.35
% 2.13/2.35 Resetting weight limit to 8.
% 2.13/2.35
% 2.13/2.35 sos_size=2371
% 2.13/2.35
% 2.13/2.35 -------- PROOF --------
% 2.13/2.35
% 2.13/2.35 ----> UNIT CONFLICT at 0.41 sec ----> 4068 [binary,4067.1,12.1] $F.
% 2.13/2.35
% 2.13/2.35 Length of proof is 28. Level of proof is 10.
% 2.13/2.35
% 2.13/2.35 ---------------- PROOF ----------------
% 2.13/2.35 % SZS status Unsatisfiable
% 2.13/2.35 % SZS output start Refutation
% See solution above
% 2.13/2.35 ------------ end of proof -------------
% 2.13/2.35
% 2.13/2.35
% 2.13/2.35 Search stopped by max_proofs option.
% 2.13/2.35
% 2.13/2.35
% 2.13/2.35 Search stopped by max_proofs option.
% 2.13/2.35
% 2.13/2.35 ============ end of search ============
% 2.13/2.35
% 2.13/2.35 -------------- statistics -------------
% 2.13/2.35 clauses given 119
% 2.13/2.35 clauses generated 50443
% 2.13/2.35 clauses kept 4016
% 2.13/2.35 clauses forward subsumed 36729
% 2.13/2.35 clauses back subsumed 40
% 2.13/2.35 Kbytes malloced 4882
% 2.13/2.35
% 2.13/2.35 ----------- times (seconds) -----------
% 2.13/2.35 user CPU time 0.41 (0 hr, 0 min, 0 sec)
% 2.13/2.35 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.13/2.35 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.13/2.35
% 2.13/2.35 That finishes the proof of the theorem.
% 2.13/2.35
% 2.13/2.35 Process 19371 finished Wed Jul 27 02:11:23 2022
% 2.13/2.35 Otter interrupted
% 2.13/2.35 PROOF FOUND
%------------------------------------------------------------------------------