TSTP Solution File: RNG001-3 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG001-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 2.36s 2.56s
% Output : Refutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 22 ( 18 unt; 0 nHn; 8 RR)
% Number of literals : 36 ( 0 equ; 15 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(C,D,F)
| sum(A,E,F) ),
file('RNG001-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(A,E,F)
| sum(C,D,F) ),
file('RNG001-3.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('RNG001-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(A,B,C)
| ~ product(A,D,E)
| ~ sum(B,D,F)
| ~ sum(C,E,G)
| product(A,F,G) ),
file('RNG001-3.p',unknown),
[] ).
cnf(5,axiom,
~ product(a,additive_identity,additive_identity),
file('RNG001-3.p',unknown),
[] ).
cnf(6,axiom,
sum(additive_identity,A,A),
file('RNG001-3.p',unknown),
[] ).
cnf(7,axiom,
sum(additive_inverse(A),A,additive_identity),
file('RNG001-3.p',unknown),
[] ).
cnf(8,axiom,
product(A,B,multiply(A,B)),
file('RNG001-3.p',unknown),
[] ).
cnf(9,plain,
sum(additive_inverse(additive_inverse(A)),additive_identity,A),
inference(hyper,[status(thm)],[7,1,7,6]),
[iquote('hyper,7,1,7,6')] ).
cnf(10,plain,
sum(additive_inverse(additive_identity),A,A),
inference(hyper,[status(thm)],[7,1,6,6]),
[iquote('hyper,7,1,6,6')] ).
cnf(11,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[10,2,7,7]),
[iquote('hyper,10,2,7,7')] ).
cnf(13,plain,
sum(additive_inverse(additive_identity),additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[11,2,6,10]),
[iquote('hyper,11,2,6,10')] ).
cnf(21,plain,
sum(multiply(A,additive_inverse(additive_identity)),multiply(A,B),multiply(A,B)),
inference(hyper,[status(thm)],[8,3,8,8,10]),
[iquote('hyper,8,3,8,8,10')] ).
cnf(23,plain,
sum(multiply(A,additive_identity),multiply(A,B),multiply(A,B)),
inference(hyper,[status(thm)],[8,3,8,8,6]),
[iquote('hyper,8,3,8,8,6')] ).
cnf(26,plain,
sum(A,additive_identity,A),
inference(hyper,[status(thm)],[9,2,9,6]),
[iquote('hyper,9,2,9,6')] ).
cnf(31,plain,
sum(additive_inverse(additive_inverse(additive_inverse(A))),A,additive_identity),
inference(hyper,[status(thm)],[9,1,7,6]),
[iquote('hyper,9,1,7,6')] ).
cnf(201,plain,
product(A,additive_inverse(additive_identity),multiply(A,additive_identity)),
inference(hyper,[status(thm)],[21,4,8,8,26]),
[iquote('hyper,21,4,8,8,26')] ).
cnf(324,plain,
sum(additive_identity,multiply(A,additive_identity),additive_identity),
inference(hyper,[status(thm)],[23,2,31,31]),
[iquote('hyper,23,2,31,31')] ).
cnf(395,plain,
sum(A,multiply(B,additive_identity),A),
inference(hyper,[status(thm)],[324,2,26,26]),
[iquote('hyper,324,2,26,26')] ).
cnf(550,plain,
sum(multiply(A,additive_identity),multiply(B,additive_identity),additive_identity),
inference(hyper,[status(thm)],[395,2,6,395]),
[iquote('hyper,395,2,6,395')] ).
cnf(4382,plain,
product(A,additive_identity,additive_identity),
inference(hyper,[status(thm)],[550,4,201,201,13]),
[iquote('hyper,550,4,201,201,13')] ).
cnf(4383,plain,
$false,
inference(binary,[status(thm)],[4382,5]),
[iquote('binary,4382.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG001-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 02:20:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.36/2.56 ----- Otter 3.3f, August 2004 -----
% 2.36/2.56 The process was started by sandbox2 on n015.cluster.edu,
% 2.36/2.56 Wed Jul 27 02:20:26 2022
% 2.36/2.56 The command was "./otter". The process ID is 20728.
% 2.36/2.56
% 2.36/2.56 set(prolog_style_variables).
% 2.36/2.56 set(auto).
% 2.36/2.56 dependent: set(auto1).
% 2.36/2.56 dependent: set(process_input).
% 2.36/2.56 dependent: clear(print_kept).
% 2.36/2.56 dependent: clear(print_new_demod).
% 2.36/2.56 dependent: clear(print_back_demod).
% 2.36/2.56 dependent: clear(print_back_sub).
% 2.36/2.56 dependent: set(control_memory).
% 2.36/2.56 dependent: assign(max_mem, 12000).
% 2.36/2.56 dependent: assign(pick_given_ratio, 4).
% 2.36/2.56 dependent: assign(stats_level, 1).
% 2.36/2.56 dependent: assign(max_seconds, 10800).
% 2.36/2.56 clear(print_given).
% 2.36/2.56
% 2.36/2.56 list(usable).
% 2.36/2.56 0 [] sum(additive_identity,X,X).
% 2.36/2.56 0 [] sum(additive_inverse(X),X,additive_identity).
% 2.36/2.56 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 2.36/2.56 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 2.36/2.56 0 [] product(X,Y,multiply(X,Y)).
% 2.36/2.56 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 2.36/2.56 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 2.36/2.56 0 [] -product(a,additive_identity,additive_identity).
% 2.36/2.56 end_of_list.
% 2.36/2.56
% 2.36/2.56 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=5.
% 2.36/2.56
% 2.36/2.56 This is a Horn set without equality. The strategy will
% 2.36/2.56 be hyperresolution, with satellites in sos and nuclei
% 2.36/2.56 in usable.
% 2.36/2.56
% 2.36/2.56 dependent: set(hyper_res).
% 2.36/2.56 dependent: clear(order_hyper).
% 2.36/2.56
% 2.36/2.56 ------------> process usable:
% 2.36/2.56 ** KEPT (pick-wt=16): 1 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 2.36/2.56 ** KEPT (pick-wt=16): 2 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 2.36/2.56 ** 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).
% 2.36/2.56 ** 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).
% 2.36/2.56 ** KEPT (pick-wt=4): 5 [] -product(a,additive_identity,additive_identity).
% 2.36/2.56
% 2.36/2.56 ------------> process sos:
% 2.36/2.56 ** KEPT (pick-wt=4): 6 [] sum(additive_identity,A,A).
% 2.36/2.56 ** KEPT (pick-wt=5): 7 [] sum(additive_inverse(A),A,additive_identity).
% 2.36/2.56 ** KEPT (pick-wt=6): 8 [] product(A,B,multiply(A,B)).
% 2.36/2.56
% 2.36/2.56 ======= end of input processing =======
% 2.36/2.56
% 2.36/2.56 =========== start of search ===========
% 2.36/2.56
% 2.36/2.56 -------- PROOF --------
% 2.36/2.56
% 2.36/2.56 ----> UNIT CONFLICT at 0.51 sec ----> 4383 [binary,4382.1,5.1] $F.
% 2.36/2.56
% 2.36/2.56 Length of proof is 13. Level of proof is 6.
% 2.36/2.56
% 2.36/2.56 ---------------- PROOF ----------------
% 2.36/2.56 % SZS status Unsatisfiable
% 2.36/2.56 % SZS output start Refutation
% See solution above
% 2.36/2.56 ------------ end of proof -------------
% 2.36/2.56
% 2.36/2.56
% 2.36/2.56 Search stopped by max_proofs option.
% 2.36/2.56
% 2.36/2.56
% 2.36/2.56 Search stopped by max_proofs option.
% 2.36/2.56
% 2.36/2.56 ============ end of search ============
% 2.36/2.56
% 2.36/2.56 -------------- statistics -------------
% 2.36/2.56 clauses given 99
% 2.36/2.56 clauses generated 154943
% 2.36/2.56 clauses kept 4382
% 2.36/2.56 clauses forward subsumed 150569
% 2.36/2.56 clauses back subsumed 563
% 2.36/2.56 Kbytes malloced 2929
% 2.36/2.56
% 2.36/2.56 ----------- times (seconds) -----------
% 2.36/2.56 user CPU time 0.51 (0 hr, 0 min, 0 sec)
% 2.36/2.56 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.36/2.56 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.36/2.56
% 2.36/2.56 That finishes the proof of the theorem.
% 2.36/2.56
% 2.36/2.56 Process 20728 finished Wed Jul 27 02:20:28 2022
% 2.36/2.56 Otter interrupted
% 2.36/2.56 PROOF FOUND
%------------------------------------------------------------------------------