TSTP Solution File: RNG008-6 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG008-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 2.80s 3.00s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of clauses : 58 ( 46 unt; 0 nHn; 30 RR)
% Number of literals : 93 ( 11 equ; 36 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 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 : 104 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(C,D,F)
| sum(A,E,F) ),
file('RNG008-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(A,E,F)
| sum(C,D,F) ),
file('RNG008-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ sum(A,B,C)
| sum(B,A,C) ),
file('RNG008-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('RNG008-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('RNG008-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(A,B,C)
| ~ product(A,D,E)
| ~ sum(B,D,F)
| ~ product(A,F,G)
| sum(C,E,G) ),
file('RNG008-6.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('RNG008-6.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('RNG008-6.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('RNG008-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| C = D ),
file('RNG008-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('RNG008-6.p',unknown),
[] ).
cnf(12,axiom,
~ product(b,a,c),
file('RNG008-6.p',unknown),
[] ).
cnf(14,axiom,
sum(additive_identity,A,A),
file('RNG008-6.p',unknown),
[] ).
cnf(15,axiom,
sum(A,additive_identity,A),
file('RNG008-6.p',unknown),
[] ).
cnf(16,axiom,
product(A,B,multiply(A,B)),
file('RNG008-6.p',unknown),
[] ).
cnf(17,axiom,
sum(A,B,add(A,B)),
file('RNG008-6.p',unknown),
[] ).
cnf(18,axiom,
sum(additive_inverse(A),A,additive_identity),
file('RNG008-6.p',unknown),
[] ).
cnf(19,axiom,
sum(A,additive_inverse(A),additive_identity),
file('RNG008-6.p',unknown),
[] ).
cnf(20,axiom,
product(A,additive_identity,additive_identity),
file('RNG008-6.p',unknown),
[] ).
cnf(21,axiom,
product(additive_identity,A,additive_identity),
file('RNG008-6.p',unknown),
[] ).
cnf(22,axiom,
product(A,A,A),
file('RNG008-6.p',unknown),
[] ).
cnf(23,axiom,
product(a,b,c),
file('RNG008-6.p',unknown),
[] ).
cnf(42,plain,
( product(A,B,C)
| ~ product(D,E,multiply(A,B))
| ~ product(D,E,C) ),
inference(para_into,[status(thm),theory(equality)],[16,11]),
[iquote('para_into,16.1.3,11.3.1')] ).
cnf(45,plain,
multiply(A,A) = A,
inference(hyper,[status(thm)],[22,11,16]),
[iquote('hyper,22,11,16')] ).
cnf(49,plain,
product(A,multiply(B,multiply(A,B)),multiply(A,B)),
inference(hyper,[status(thm)],[22,4,16,16]),
[iquote('hyper,22,4,16,16')] ).
cnf(54,plain,
product(c,b,c),
inference(hyper,[status(thm)],[23,5,23,22]),
[iquote('hyper,23,5,23,22')] ).
cnf(58,plain,
product(c,A,multiply(a,multiply(b,A))),
inference(hyper,[status(thm)],[23,5,16,16]),
[iquote('hyper,23,5,16,16')] ).
cnf(59,plain,
product(a,c,c),
inference(hyper,[status(thm)],[23,4,22,23]),
[iquote('hyper,23,4,22,23')] ).
cnf(85,plain,
product(multiply(c,a),c,c),
inference(hyper,[status(thm)],[59,5,16,22]),
[iquote('hyper,59,5,16,22')] ).
cnf(88,plain,
product(A,c,multiply(multiply(A,a),c)),
inference(hyper,[status(thm)],[59,4,16,16]),
[iquote('hyper,59,4,16,16')] ).
cnf(97,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(99,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(105,plain,
product(add(c,b),b,add(c,b)),
inference(hyper,[status(thm)],[17,9,54,22,17]),
[iquote('hyper,17,9,54,22,17')] ).
cnf(145,plain,
product(a,add(c,a),add(c,a)),
inference(hyper,[status(thm)],[17,7,59,22,17]),
[iquote('hyper,17,7,59,22,17')] ).
cnf(186,plain,
sum(A,B,add(B,A)),
inference(hyper,[status(thm)],[17,3]),
[iquote('hyper,17,3')] ).
cnf(194,plain,
additive_inverse(additive_identity) = additive_identity,
inference(hyper,[status(thm)],[18,10,15]),
[iquote('hyper,18,10,15')] ).
cnf(205,plain,
sum(multiply(additive_inverse(A),A),A,additive_identity),
inference(hyper,[status(thm)],[18,8,16,22,21]),
[iquote('hyper,18,8,16,22,21')] ).
cnf(217,plain,
sum(multiply(A,additive_inverse(A)),A,additive_identity),
inference(hyper,[status(thm)],[18,6,16,22,20]),
[iquote('hyper,18,6,16,22,20')] ).
cnf(220,plain,
sum(additive_identity,A,additive_inverse(additive_inverse(A))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[18,2,18,17]),97]),
[iquote('hyper,18,2,18,17,demod,97')] ).
cnf(255,plain,
sum(A,multiply(A,additive_inverse(A)),additive_identity),
inference(hyper,[status(thm)],[19,6,22,16,20]),
[iquote('hyper,19,6,22,16,20')] ).
cnf(464,plain,
multiply(multiply(c,a),c) = c,
inference(hyper,[status(thm)],[85,11,16]),
[iquote('hyper,85,11,16')] ).
cnf(654,plain,
sum(A,add(B,additive_inverse(A)),B),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[186,1,19,186]),97]),
[iquote('hyper,186,1,19,186,demod,97')] ).
cnf(676,plain,
additive_inverse(additive_inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[220,10,186]),97])]),
[iquote('hyper,220,10,186,demod,97,flip.1')] ).
cnf(965,plain,
sum(additive_identity,A,multiply(A,additive_inverse(A))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[205,2,18,186]),676,99]),
[iquote('hyper,205,2,18,186,demod,676,99')] ).
cnf(1271,plain,
sum(add(A,multiply(B,additive_inverse(B))),B,A),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[217,2,17,186]),99]),
[iquote('hyper,217,2,17,186,demod,99')] ).
cnf(1810,plain,
multiply(A,additive_inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[965,10,654]),194,97,194,97])]),
[iquote('hyper,965,10,654,demod,194,97,194,97,flip.1')] ).
cnf(1812,plain,
sum(A,A,additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[965,2,965,255]),1810,1810,194,45]),
[iquote('hyper,965,2,965,255,demod,1810,1810,194,45')] ).
cnf(1817,plain,
sum(A,add(A,B),B),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[965,1,255,17]),1810,1810]),
[iquote('hyper,965,1,255,17,demod,1810,1810')] ).
cnf(1852,plain,
sum(add(A,B),B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1271]),1810]),
[iquote('back_demod,1271,demod,1810')] ).
cnf(2074,plain,
product(add(c,b),c,additive_identity),
inference(hyper,[status(thm)],[105,7,22,1852,1812]),
[iquote('hyper,105,7,22,1852,1812')] ).
cnf(2081,plain,
product(b,c,c),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2074,9,88,1817,186]),464,99]),
[iquote('hyper,2074,9,88,1817,186,demod,464,99')] ).
cnf(2136,plain,
multiply(multiply(b,a),c) = c,
inference(hyper,[status(thm)],[2081,11,88]),
[iquote('hyper,2081,11,88')] ).
cnf(2186,plain,
product(c,a,multiply(b,a)),
inference(hyper,[status(thm)],[2081,5,58,49]),
[iquote('hyper,2081,5,58,49')] ).
cnf(2244,plain,
multiply(c,a) = multiply(b,a),
inference(hyper,[status(thm)],[2186,11,16]),
[iquote('hyper,2186,11,16')] ).
cnf(2290,plain,
product(c,add(c,a),additive_identity),
inference(hyper,[status(thm)],[145,9,22,1852,1812]),
[iquote('hyper,145,9,22,1852,1812')] ).
cnf(2300,plain,
product(c,a,c),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2290,7,88,1817,186]),2244,2136,99]),
[iquote('hyper,2290,7,88,1817,186,demod,2244,2136,99')] ).
cnf(2338,plain,
product(b,a,c),
inference(hyper,[status(thm)],[2300,42,2186]),
[iquote('hyper,2300,42,2186')] ).
cnf(2339,plain,
$false,
inference(binary,[status(thm)],[2338,12]),
[iquote('binary,2338.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG008-6 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 02:22:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.13 ----- Otter 3.3f, August 2004 -----
% 1.95/2.13 The process was started by sandbox on n025.cluster.edu,
% 1.95/2.13 Wed Jul 27 02:22:45 2022
% 1.95/2.13 The command was "./otter". The process ID is 18487.
% 1.95/2.13
% 1.95/2.13 set(prolog_style_variables).
% 1.95/2.13 set(auto).
% 1.95/2.13 dependent: set(auto1).
% 1.95/2.13 dependent: set(process_input).
% 1.95/2.13 dependent: clear(print_kept).
% 1.95/2.13 dependent: clear(print_new_demod).
% 1.95/2.13 dependent: clear(print_back_demod).
% 1.95/2.13 dependent: clear(print_back_sub).
% 1.95/2.13 dependent: set(control_memory).
% 1.95/2.13 dependent: assign(max_mem, 12000).
% 1.95/2.13 dependent: assign(pick_given_ratio, 4).
% 1.95/2.13 dependent: assign(stats_level, 1).
% 1.95/2.13 dependent: assign(max_seconds, 10800).
% 1.95/2.13 clear(print_given).
% 1.95/2.13
% 1.95/2.13 list(usable).
% 1.95/2.13 0 [] A=A.
% 1.95/2.13 0 [] sum(additive_identity,X,X).
% 1.95/2.13 0 [] sum(X,additive_identity,X).
% 1.95/2.13 0 [] product(X,Y,multiply(X,Y)).
% 1.95/2.13 0 [] sum(X,Y,add(X,Y)).
% 1.95/2.13 0 [] sum(additive_inverse(X),X,additive_identity).
% 1.95/2.13 0 [] sum(X,additive_inverse(X),additive_identity).
% 1.95/2.13 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 1.95/2.13 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 1.95/2.13 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.95/2.13 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.95/2.13 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.95/2.13 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.95/2.13 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.95/2.13 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.95/2.13 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.95/2.13 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.95/2.13 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.95/2.13 0 [] product(X,additive_identity,additive_identity).
% 1.95/2.13 0 [] product(additive_identity,X,additive_identity).
% 1.95/2.13 0 [] product(X,X,X).
% 1.95/2.13 0 [] product(a,b,c).
% 1.95/2.13 0 [] -product(b,a,c).
% 1.95/2.13 end_of_list.
% 1.95/2.13
% 1.95/2.13 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.95/2.13
% 1.95/2.13 This is a Horn set with equality. The strategy will be
% 1.95/2.13 Knuth-Bendix and hyper_res, with positive clauses in
% 1.95/2.13 sos and nonpositive clauses in usable.
% 1.95/2.13
% 1.95/2.13 dependent: set(knuth_bendix).
% 1.95/2.13 dependent: set(anl_eq).
% 1.95/2.13 dependent: set(para_from).
% 1.95/2.13 dependent: set(para_into).
% 1.95/2.13 dependent: clear(para_from_right).
% 1.95/2.13 dependent: clear(para_into_right).
% 1.95/2.13 dependent: set(para_from_vars).
% 1.95/2.13 dependent: set(eq_units_both_ways).
% 1.95/2.13 dependent: set(dynamic_demod_all).
% 1.95/2.13 dependent: set(dynamic_demod).
% 1.95/2.13 dependent: set(order_eq).
% 1.95/2.13 dependent: set(back_demod).
% 1.95/2.13 dependent: set(lrpo).
% 1.95/2.13 dependent: set(hyper_res).
% 1.95/2.13 dependent: clear(order_hyper).
% 1.95/2.13
% 1.95/2.13 ------------> process usable:
% 1.95/2.13 ** KEPT (pick-wt=16): 1 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 1.95/2.13 ** KEPT (pick-wt=16): 2 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 1.95/2.13 ** KEPT (pick-wt=8): 3 [] -sum(A,B,C)|sum(B,A,C).
% 1.95/2.13 ** KEPT (pick-wt=16): 4 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.95/2.13 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.95/2.13 ** 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).
% 1.95/2.13 ** 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).
% 1.95/2.13 ** 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).
% 1.95/2.13 ** 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).
% 1.95/2.13 ** KEPT (pick-wt=11): 10 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.95/2.13 ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.95/2.13 ** KEPT (pick-wt=4): 12 [] -product(b,a,c).
% 1.95/2.13
% 1.95/2.13 ------------> process sos:
% 1.95/2.13 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.95/2.13 ** KEPT (pick-wt=4): 14 [] sum(additive_identity,A,A).
% 1.95/2.13 ** KEPT (pick-wt=4): 15 [] sum(A,additive_identity,A).
% 1.95/2.13 ** KEPT (pick-wt=6): 16 [] product(A,B,multiply(A,B)).
% 1.95/2.13 ** KEPT (pick-wt=6): 17 [] sum(A,B,add(A,B)).
% 1.95/2.13 ** KEPT (pick-wt=5): 18 [] sum(additive_inverse(A),A,additive_identity).
% 1.95/2.13 ** KEPT (pick-wt=5): 19 [] sum(A,additive_inverse(A),additive_identity).
% 1.95/2.13 ** KEPT (pick-wt=4): 20 [] product(A,additive_identity,additive_identity).
% 1.95/2.13 ** KEPT (pick-wt=4): 21 [] product(additive_identity,A,additive_identity).
% 1.95/2.13 ** KEPT (pick-wt=4): 22 [] product(A,A,A).
% 1.95/2.13 ** KEPT (pick-wt=4): 23 [] product(a,b,c).
% 2.80/3.00 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 2.80/3.00
% 2.80/3.00 ======= end of input processing =======
% 2.80/3.00
% 2.80/3.00 =========== start of search ===========
% 2.80/3.00
% 2.80/3.00
% 2.80/3.00 Resetting weight limit to 8.
% 2.80/3.00
% 2.80/3.00
% 2.80/3.00 Resetting weight limit to 8.
% 2.80/3.00
% 2.80/3.00 sos_size=1613
% 2.80/3.00
% 2.80/3.00 -------- PROOF --------
% 2.80/3.00
% 2.80/3.00 ----> UNIT CONFLICT at 0.87 sec ----> 2339 [binary,2338.1,12.1] $F.
% 2.80/3.00
% 2.80/3.00 Length of proof is 35. Level of proof is 12.
% 2.80/3.00
% 2.80/3.00 ---------------- PROOF ----------------
% 2.80/3.00 % SZS status Unsatisfiable
% 2.80/3.00 % SZS output start Refutation
% See solution above
% 2.80/3.00 ------------ end of proof -------------
% 2.80/3.00
% 2.80/3.00
% 2.80/3.00 Search stopped by max_proofs option.
% 2.80/3.00
% 2.80/3.00
% 2.80/3.00 Search stopped by max_proofs option.
% 2.80/3.00
% 2.80/3.00 ============ end of search ============
% 2.80/3.00
% 2.80/3.00 -------------- statistics -------------
% 2.80/3.00 clauses given 169
% 2.80/3.00 clauses generated 227696
% 2.80/3.00 clauses kept 2261
% 2.80/3.00 clauses forward subsumed 87060
% 2.80/3.00 clauses back subsumed 18
% 2.80/3.00 Kbytes malloced 4882
% 2.80/3.00
% 2.80/3.00 ----------- times (seconds) -----------
% 2.80/3.00 user CPU time 0.87 (0 hr, 0 min, 0 sec)
% 2.80/3.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.80/3.00 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.80/3.00
% 2.80/3.00 That finishes the proof of the theorem.
% 2.80/3.00
% 2.80/3.00 Process 18487 finished Wed Jul 27 02:22:48 2022
% 2.80/3.00 Otter interrupted
% 2.80/3.00 PROOF FOUND
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