TSTP Solution File: RNG004-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 13:12:00 EDT 2022
% Result : Unsatisfiable 1.89s 2.05s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of clauses : 39 ( 32 unt; 0 nHn; 31 RR)
% Number of literals : 59 ( 12 equ; 22 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(A,E,F)
| sum(C,D,F) ),
file('RNG004-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ sum(A,B,C)
| sum(B,A,C) ),
file('RNG004-1.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('RNG004-1.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('RNG004-1.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('RNG004-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| C = D ),
file('RNG004-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('RNG004-1.p',unknown),
[] ).
cnf(12,axiom,
c != d,
file('RNG004-1.p',unknown),
[] ).
cnf(13,plain,
d != c,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.1')] ).
cnf(15,axiom,
sum(additive_identity,A,A),
file('RNG004-1.p',unknown),
[] ).
cnf(16,axiom,
sum(A,additive_identity,A),
file('RNG004-1.p',unknown),
[] ).
cnf(17,axiom,
product(A,B,multiply(A,B)),
file('RNG004-1.p',unknown),
[] ).
cnf(18,axiom,
sum(A,B,add(A,B)),
file('RNG004-1.p',unknown),
[] ).
cnf(19,axiom,
sum(additive_inverse(A),A,additive_identity),
file('RNG004-1.p',unknown),
[] ).
cnf(21,axiom,
product(a,b,c),
file('RNG004-1.p',unknown),
[] ).
cnf(22,axiom,
product(additive_inverse(a),additive_inverse(b),d),
file('RNG004-1.p',unknown),
[] ).
cnf(42,plain,
multiply(a,b) = c,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[17,11,21])]),
[iquote('hyper,17,11,21,flip.1')] ).
cnf(43,plain,
sum(c,multiply(additive_identity,b),c),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[17,8,21,17,16]),42]),
[iquote('hyper,17,8,21,17,16,demod,42')] ).
cnf(49,plain,
sum(c,multiply(a,additive_identity),c),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[17,6,21,17,16]),42]),
[iquote('hyper,17,6,21,17,16,demod,42')] ).
cnf(50,plain,
sum(multiply(a,additive_inverse(b)),c,multiply(a,additive_identity)),
inference(hyper,[status(thm)],[17,6,17,21,19]),
[iquote('hyper,17,6,17,21,19')] ).
cnf(84,plain,
add(A,additive_identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[18,10,16])]),
[iquote('hyper,18,10,16,flip.1')] ).
cnf(86,plain,
add(additive_identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[18,10,15])]),
[iquote('hyper,18,10,15,flip.1')] ).
cnf(119,plain,
sum(A,B,add(B,A)),
inference(hyper,[status(thm)],[18,3]),
[iquote('hyper,18,3')] ).
cnf(152,plain,
sum(d,multiply(a,additive_inverse(b)),multiply(additive_identity,additive_inverse(b))),
inference(hyper,[status(thm)],[22,8,17,19,17]),
[iquote('hyper,22,8,17,19,17')] ).
cnf(202,plain,
sum(additive_identity,multiply(additive_identity,b),additive_identity),
inference(hyper,[status(thm)],[43,2,19,19]),
[iquote('hyper,43,2,19,19')] ).
cnf(254,plain,
sum(additive_identity,multiply(a,additive_identity),additive_identity),
inference(hyper,[status(thm)],[49,2,19,19]),
[iquote('hyper,49,2,19,19')] ).
cnf(427,plain,
multiply(additive_identity,b) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[202,10,119]),84]),
[iquote('hyper,202,10,119,demod,84')] ).
cnf(445,plain,
product(additive_identity,b,additive_identity),
inference(para_from,[status(thm),theory(equality)],[427,17]),
[iquote('para_from,427.1.1,17.1.3')] ).
cnf(450,plain,
product(additive_identity,additive_identity,multiply(additive_identity,additive_inverse(b))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[445,7,17,19,119]),86]),
[iquote('hyper,445,7,17,19,119,demod,86')] ).
cnf(452,plain,
product(additive_identity,b,multiply(additive_identity,additive_identity)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[445,7,17,15,119]),86]),
[iquote('hyper,445,7,17,15,119,demod,86')] ).
cnf(474,plain,
multiply(a,additive_identity) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[254,10,119]),84]),
[iquote('hyper,254,10,119,demod,84')] ).
cnf(476,plain,
sum(multiply(a,additive_inverse(b)),c,additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[50]),474]),
[iquote('back_demod,50,demod,474')] ).
cnf(546,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[452,11,445])]),
[iquote('hyper,452,11,445,flip.1')] ).
cnf(558,plain,
product(additive_identity,additive_identity,additive_identity),
inference(para_from,[status(thm),theory(equality)],[546,17]),
[iquote('para_from,546.1.1,17.1.3')] ).
cnf(1668,plain,
multiply(additive_identity,additive_inverse(b)) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[450,11,558])]),
[iquote('hyper,450,11,558,flip.1')] ).
cnf(1669,plain,
sum(d,multiply(a,additive_inverse(b)),additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[152]),1668]),
[iquote('back_demod,152,demod,1668')] ).
cnf(1708,plain,
sum(additive_identity,c,d),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1669,2,476,119]),86]),
[iquote('hyper,1669,2,476,119,demod,86')] ).
cnf(1720,plain,
d = c,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1708,10,119]),84])]),
[iquote('hyper,1708,10,119,demod,84,flip.1')] ).
cnf(1722,plain,
$false,
inference(binary,[status(thm)],[1720,13]),
[iquote('binary,1720.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.33 % Computer : n009.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Jul 27 02:11:06 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.71/1.90 ----- Otter 3.3f, August 2004 -----
% 1.71/1.90 The process was started by sandbox2 on n009.cluster.edu,
% 1.71/1.90 Wed Jul 27 02:11:06 2022
% 1.71/1.90 The command was "./otter". The process ID is 9039.
% 1.71/1.90
% 1.71/1.90 set(prolog_style_variables).
% 1.71/1.90 set(auto).
% 1.71/1.90 dependent: set(auto1).
% 1.71/1.90 dependent: set(process_input).
% 1.71/1.90 dependent: clear(print_kept).
% 1.71/1.90 dependent: clear(print_new_demod).
% 1.71/1.90 dependent: clear(print_back_demod).
% 1.71/1.90 dependent: clear(print_back_sub).
% 1.71/1.90 dependent: set(control_memory).
% 1.71/1.90 dependent: assign(max_mem, 12000).
% 1.71/1.90 dependent: assign(pick_given_ratio, 4).
% 1.71/1.90 dependent: assign(stats_level, 1).
% 1.71/1.90 dependent: assign(max_seconds, 10800).
% 1.71/1.90 clear(print_given).
% 1.71/1.90
% 1.71/1.90 list(usable).
% 1.71/1.90 0 [] A=A.
% 1.71/1.90 0 [] sum(additive_identity,X,X).
% 1.71/1.90 0 [] sum(X,additive_identity,X).
% 1.71/1.90 0 [] product(X,Y,multiply(X,Y)).
% 1.71/1.90 0 [] sum(X,Y,add(X,Y)).
% 1.71/1.90 0 [] sum(additive_inverse(X),X,additive_identity).
% 1.71/1.90 0 [] sum(X,additive_inverse(X),additive_identity).
% 1.71/1.90 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 1.71/1.90 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 1.71/1.90 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.71/1.90 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.71/1.90 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.71/1.90 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.71/1.90 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.71/1.90 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.71/1.90 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.71/1.90 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.71/1.90 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.71/1.90 0 [] product(a,b,c).
% 1.71/1.90 0 [] product(additive_inverse(a),additive_inverse(b),d).
% 1.71/1.90 0 [] c!=d.
% 1.71/1.90 end_of_list.
% 1.71/1.90
% 1.71/1.90 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.71/1.90
% 1.71/1.90 This is a Horn set with equality. The strategy will be
% 1.71/1.90 Knuth-Bendix and hyper_res, with positive clauses in
% 1.71/1.90 sos and nonpositive clauses in usable.
% 1.71/1.90
% 1.71/1.90 dependent: set(knuth_bendix).
% 1.71/1.90 dependent: set(anl_eq).
% 1.71/1.90 dependent: set(para_from).
% 1.71/1.90 dependent: set(para_into).
% 1.71/1.90 dependent: clear(para_from_right).
% 1.71/1.90 dependent: clear(para_into_right).
% 1.71/1.90 dependent: set(para_from_vars).
% 1.71/1.90 dependent: set(eq_units_both_ways).
% 1.71/1.90 dependent: set(dynamic_demod_all).
% 1.71/1.90 dependent: set(dynamic_demod).
% 1.71/1.90 dependent: set(order_eq).
% 1.71/1.90 dependent: set(back_demod).
% 1.71/1.90 dependent: set(lrpo).
% 1.71/1.90 dependent: set(hyper_res).
% 1.71/1.90 dependent: clear(order_hyper).
% 1.71/1.90
% 1.71/1.90 ------------> process usable:
% 1.71/1.90 ** KEPT (pick-wt=16): 1 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 1.71/1.90 ** KEPT (pick-wt=16): 2 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 1.71/1.90 ** KEPT (pick-wt=8): 3 [] -sum(A,B,C)|sum(B,A,C).
% 1.71/1.90 ** KEPT (pick-wt=16): 4 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.71/1.90 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.71/1.90 ** 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).
% 1.71/1.90 ** 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).
% 1.71/1.90 ** 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).
% 1.71/1.90 ** 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).
% 1.71/1.90 ** KEPT (pick-wt=11): 10 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.71/1.90 ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.71/1.90 ** KEPT (pick-wt=3): 13 [copy,12,flip.1] d!=c.
% 1.71/1.90
% 1.71/1.90 ------------> process sos:
% 1.71/1.90 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.71/1.90 ** KEPT (pick-wt=4): 15 [] sum(additive_identity,A,A).
% 1.71/1.90 ** KEPT (pick-wt=4): 16 [] sum(A,additive_identity,A).
% 1.71/1.90 ** KEPT (pick-wt=6): 17 [] product(A,B,multiply(A,B)).
% 1.71/1.90 ** KEPT (pick-wt=6): 18 [] sum(A,B,add(A,B)).
% 1.71/1.90 ** KEPT (pick-wt=5): 19 [] sum(additive_inverse(A),A,additive_identity).
% 1.71/1.90 ** KEPT (pick-wt=5): 20 [] sum(A,additive_inverse(A),additive_identity).
% 1.71/1.90 ** KEPT (pick-wt=4): 21 [] product(a,b,c).
% 1.71/1.90 ** KEPT (pick-wt=6): 22 [] product(additive_inverse(a),additive_inverse(b),d).
% 1.71/1.90 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.71/1.90
% 1.71/1.90 ======= end of input processing =======
% 1.71/1.90
% 1.71/1.90 =========== start of search ===========
% 1.89/2.05
% 1.89/2.05
% 1.89/2.05 Resetting weight limit to 8.
% 1.89/2.05
% 1.89/2.05
% 1.89/2.05 Resetting weight limit to 8.
% 1.89/2.05
% 1.89/2.05 sos_size=1335
% 1.89/2.05
% 1.89/2.05 -------- PROOF --------
% 1.89/2.05
% 1.89/2.05 ----> UNIT CONFLICT at 0.15 sec ----> 1722 [binary,1720.1,13.1] $F.
% 1.89/2.05
% 1.89/2.05 Length of proof is 23. Level of proof is 12.
% 1.89/2.05
% 1.89/2.05 ---------------- PROOF ----------------
% 1.89/2.05 % SZS status Unsatisfiable
% 1.89/2.05 % SZS output start Refutation
% See solution above
% 1.89/2.05 ------------ end of proof -------------
% 1.89/2.05
% 1.89/2.05
% 1.89/2.05 Search stopped by max_proofs option.
% 1.89/2.05
% 1.89/2.05
% 1.89/2.05 Search stopped by max_proofs option.
% 1.89/2.05
% 1.89/2.05 ============ end of search ============
% 1.89/2.05
% 1.89/2.05 -------------- statistics -------------
% 1.89/2.05 clauses given 83
% 1.89/2.05 clauses generated 12789
% 1.89/2.05 clauses kept 1678
% 1.89/2.05 clauses forward subsumed 9778
% 1.89/2.05 clauses back subsumed 24
% 1.89/2.05 Kbytes malloced 4882
% 1.89/2.05
% 1.89/2.05 ----------- times (seconds) -----------
% 1.89/2.05 user CPU time 0.15 (0 hr, 0 min, 0 sec)
% 1.89/2.05 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.89/2.05 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.89/2.05
% 1.89/2.05 That finishes the proof of the theorem.
% 1.89/2.05
% 1.89/2.05 Process 9039 finished Wed Jul 27 02:11:08 2022
% 1.89/2.05 Otter interrupted
% 1.89/2.05 PROOF FOUND
%------------------------------------------------------------------------------