TSTP Solution File: RNG001-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG001-2 : 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 13:12:00 EDT 2022
% Result : Unsatisfiable 133.14s 133.39s
% Output : Refutation 133.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 36 ( 30 unt; 0 nHn; 9 RR)
% Number of literals : 58 ( 0 equ; 23 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(C,D,F)
| sum(A,E,F) ),
file('RNG001-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(A,E,F)
| sum(C,D,F) ),
file('RNG001-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(A,B,C)
| ~ product(A,D,E)
| ~ sum(B,D,F)
| ~ product(A,F,G)
| sum(C,E,G) ),
file('RNG001-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(A,B,C)
| ~ product(A,D,E)
| ~ sum(B,D,F)
| ~ sum(C,E,G)
| product(A,F,G) ),
file('RNG001-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(A,B,C)
| ~ product(D,B,E)
| ~ sum(A,D,F)
| ~ product(F,B,G)
| sum(C,E,G) ),
file('RNG001-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(A,B,C)
| ~ product(D,B,E)
| ~ sum(A,D,F)
| ~ sum(C,E,G)
| product(F,B,G) ),
file('RNG001-2.p',unknown),
[] ).
cnf(12,axiom,
~ product(a,additive_identity,additive_identity),
file('RNG001-2.p',unknown),
[] ).
cnf(13,axiom,
sum(additive_identity,A,A),
file('RNG001-2.p',unknown),
[] ).
cnf(14,axiom,
sum(A,additive_identity,A),
file('RNG001-2.p',unknown),
[] ).
cnf(15,axiom,
product(A,B,multiply(A,B)),
file('RNG001-2.p',unknown),
[] ).
cnf(16,axiom,
sum(A,B,add(A,B)),
file('RNG001-2.p',unknown),
[] ).
cnf(17,axiom,
sum(additive_inverse(A),A,additive_identity),
file('RNG001-2.p',unknown),
[] ).
cnf(18,axiom,
sum(A,additive_inverse(A),additive_identity),
file('RNG001-2.p',unknown),
[] ).
cnf(23,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[17,3,14,14]),
[iquote('hyper,17,3,14,14')] ).
cnf(28,plain,
sum(multiply(A,B),multiply(additive_identity,B),multiply(A,B)),
inference(hyper,[status(thm)],[15,9,15,15,14]),
[iquote('hyper,15,9,15,15,14')] ).
cnf(31,plain,
sum(multiply(A,B),multiply(A,additive_identity),multiply(A,B)),
inference(hyper,[status(thm)],[15,7,15,15,14]),
[iquote('hyper,15,7,15,15,14')] ).
cnf(47,plain,
sum(multiply(A,additive_identity),multiply(A,additive_identity),multiply(A,additive_inverse(additive_identity))),
inference(hyper,[status(thm)],[23,7,15,15,15]),
[iquote('hyper,23,7,15,15,15')] ).
cnf(138,plain,
sum(add(additive_identity,A),additive_identity,A),
inference(hyper,[status(thm)],[16,3,14,13]),
[iquote('hyper,16,3,14,13')] ).
cnf(184,plain,
sum(additive_identity,add(A,additive_identity),A),
inference(hyper,[status(thm)],[16,2,13,14]),
[iquote('hyper,16,2,13,14')] ).
cnf(772,plain,
sum(additive_identity,multiply(additive_identity,A),additive_identity),
inference(hyper,[status(thm)],[28,3,17,17]),
[iquote('hyper,28,3,17,17')] ).
cnf(826,plain,
sum(multiply(additive_identity,A),additive_identity,additive_identity),
inference(hyper,[status(thm)],[28,2,18,18]),
[iquote('hyper,28,2,18,18')] ).
cnf(2214,plain,
sum(additive_identity,multiply(A,additive_identity),additive_identity),
inference(hyper,[status(thm)],[31,3,17,17]),
[iquote('hyper,31,3,17,17')] ).
cnf(2339,plain,
sum(multiply(A,additive_identity),additive_identity,additive_identity),
inference(hyper,[status(thm)],[31,2,18,18]),
[iquote('hyper,31,2,18,18')] ).
cnf(3380,plain,
sum(A,multiply(additive_identity,B),A),
inference(hyper,[status(thm)],[772,3,138,138]),
[iquote('hyper,772,3,138,138')] ).
cnf(4396,plain,
sum(multiply(additive_identity,A),B,B),
inference(hyper,[status(thm)],[826,2,184,184]),
[iquote('hyper,826,2,184,184')] ).
cnf(4427,plain,
sum(A,multiply(B,additive_identity),A),
inference(hyper,[status(thm)],[2214,3,138,138]),
[iquote('hyper,2214,3,138,138')] ).
cnf(4456,plain,
sum(additive_identity,add(multiply(A,additive_identity),B),B),
inference(hyper,[status(thm)],[2214,2,16,13]),
[iquote('hyper,2214,2,16,13')] ).
cnf(4471,plain,
sum(multiply(A,additive_identity),B,B),
inference(hyper,[status(thm)],[2339,2,184,184]),
[iquote('hyper,2339,2,184,184')] ).
cnf(4510,plain,
sum(multiply(additive_identity,A),multiply(additive_identity,B),additive_identity),
inference(hyper,[status(thm)],[3380,3,13,3380]),
[iquote('hyper,3380,3,13,3380')] ).
cnf(4559,plain,
product(additive_identity,additive_identity,multiply(A,additive_identity)),
inference(hyper,[status(thm)],[4427,10,15,15,18]),
[iquote('hyper,4427,10,15,15,18')] ).
cnf(4631,plain,
product(A,additive_identity,multiply(B,additive_identity)),
inference(hyper,[status(thm)],[4559,10,15,138,4471]),
[iquote('hyper,4559,10,15,138,4471')] ).
cnf(4638,plain,
product(additive_identity,A,multiply(B,additive_identity)),
inference(hyper,[status(thm)],[4559,8,15,138,4396]),
[iquote('hyper,4559,8,15,138,4396')] ).
cnf(4653,plain,
product(A,additive_identity,multiply(B,additive_inverse(additive_identity))),
inference(hyper,[status(thm)],[4631,10,4631,4471,47]),
[iquote('hyper,4631,10,4631,4471,47')] ).
cnf(4666,plain,
product(additive_identity,A,multiply(B,additive_inverse(additive_identity))),
inference(hyper,[status(thm)],[4638,10,4638,14,47]),
[iquote('hyper,4638,10,4638,14,47')] ).
cnf(5036,plain,
product(A,additive_identity,additive_identity),
inference(hyper,[status(thm)],[4510,10,4666,4653,4456]),
[iquote('hyper,4510,10,4666,4653,4456')] ).
cnf(5037,plain,
$false,
inference(binary,[status(thm)],[5036,12]),
[iquote('binary,5036.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 02:06:21 EDT 2022
% 0.13/0.33 % CPUTime :
% 133.14/133.39 ----- Otter 3.3f, August 2004 -----
% 133.14/133.39 The process was started by sandbox2 on n004.cluster.edu,
% 133.14/133.39 Wed Jul 27 02:06:21 2022
% 133.14/133.39 The command was "./otter". The process ID is 14910.
% 133.14/133.39
% 133.14/133.39 set(prolog_style_variables).
% 133.14/133.39 set(auto).
% 133.14/133.39 dependent: set(auto1).
% 133.14/133.39 dependent: set(process_input).
% 133.14/133.39 dependent: clear(print_kept).
% 133.14/133.39 dependent: clear(print_new_demod).
% 133.14/133.39 dependent: clear(print_back_demod).
% 133.14/133.39 dependent: clear(print_back_sub).
% 133.14/133.39 dependent: set(control_memory).
% 133.14/133.39 dependent: assign(max_mem, 12000).
% 133.14/133.39 dependent: assign(pick_given_ratio, 4).
% 133.14/133.39 dependent: assign(stats_level, 1).
% 133.14/133.39 dependent: assign(max_seconds, 10800).
% 133.14/133.39 clear(print_given).
% 133.14/133.39
% 133.14/133.39 list(usable).
% 133.14/133.39 0 [] -e_qualish(A,B)| -sum(C,D,A)|sum(C,D,B).
% 133.14/133.39 0 [] sum(additive_identity,X,X).
% 133.14/133.39 0 [] sum(X,additive_identity,X).
% 133.14/133.39 0 [] product(X,Y,multiply(X,Y)).
% 133.14/133.39 0 [] sum(X,Y,add(X,Y)).
% 133.14/133.39 0 [] sum(additive_inverse(X),X,additive_identity).
% 133.14/133.39 0 [] sum(X,additive_inverse(X),additive_identity).
% 133.14/133.39 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 133.14/133.39 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 133.14/133.39 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 133.14/133.39 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 133.14/133.39 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 133.14/133.39 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 133.14/133.39 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 133.14/133.39 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 133.14/133.39 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 133.14/133.39 0 [] -sum(X,Y,U)| -sum(X,Y,V)|e_qualish(U,V).
% 133.14/133.39 0 [] -product(a,additive_identity,additive_identity).
% 133.14/133.39 end_of_list.
% 133.14/133.39
% 133.14/133.39 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=5.
% 133.14/133.39
% 133.14/133.39 This is a Horn set without equality. The strategy will
% 133.14/133.39 be hyperresolution, with satellites in sos and nuclei
% 133.14/133.39 in usable.
% 133.14/133.39
% 133.14/133.39 dependent: set(hyper_res).
% 133.14/133.39 dependent: clear(order_hyper).
% 133.14/133.39
% 133.14/133.39 ------------> process usable:
% 133.14/133.39 ** KEPT (pick-wt=11): 1 [] -e_qualish(A,B)| -sum(C,D,A)|sum(C,D,B).
% 133.14/133.39 ** KEPT (pick-wt=16): 2 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 133.14/133.39 ** KEPT (pick-wt=16): 3 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 133.14/133.39 ** KEPT (pick-wt=8): 4 [] -sum(A,B,C)|sum(B,A,C).
% 133.14/133.39 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 133.14/133.39 ** KEPT (pick-wt=16): 6 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 133.14/133.39 ** KEPT (pick-wt=20): 7 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -product(A,F,G)|sum(C,E,G).
% 133.14/133.39 ** KEPT (pick-wt=20): 8 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -sum(C,E,G)|product(A,F,G).
% 133.14/133.39 ** KEPT (pick-wt=20): 9 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -product(F,B,G)|sum(C,E,G).
% 133.14/133.39 ** KEPT (pick-wt=20): 10 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -sum(C,E,G)|product(F,B,G).
% 133.14/133.39 ** KEPT (pick-wt=11): 11 [] -sum(A,B,C)| -sum(A,B,D)|e_qualish(C,D).
% 133.14/133.39 ** KEPT (pick-wt=4): 12 [] -product(a,additive_identity,additive_identity).
% 133.14/133.39
% 133.14/133.39 ------------> process sos:
% 133.14/133.39 ** KEPT (pick-wt=4): 13 [] sum(additive_identity,A,A).
% 133.14/133.39 ** KEPT (pick-wt=4): 14 [] sum(A,additive_identity,A).
% 133.14/133.39 ** KEPT (pick-wt=6): 15 [] product(A,B,multiply(A,B)).
% 133.14/133.39 ** KEPT (pick-wt=6): 16 [] sum(A,B,add(A,B)).
% 133.14/133.39 ** KEPT (pick-wt=5): 17 [] sum(additive_inverse(A),A,additive_identity).
% 133.14/133.39 ** KEPT (pick-wt=5): 18 [] sum(A,additive_inverse(A),additive_identity).
% 133.14/133.39
% 133.14/133.39 ======= end of input processing =======
% 133.14/133.39
% 133.14/133.39 =========== start of search ===========
% 133.14/133.39
% 133.14/133.39
% 133.14/133.39 Resetting weight limit to 8.
% 133.14/133.39
% 133.14/133.39
% 133.14/133.39 Resetting weight limit to 8.
% 133.14/133.39
% 133.14/133.39 sos_size=4067
% 133.14/133.39
% 133.14/133.39 -- HEY sandbox2, WE HAVE A PROOF!! --
% 133.14/133.39
% 133.14/133.39 ----> UNIT CONFLICT at 131.60 sec ----> 5037 [binary,5036.1,12.1] $F.
% 133.14/133.39
% 133.14/133.39 Length of proof is 22. Level of proof is 7.
% 133.14/133.39
% 133.14/133.39 ---------------- PROOF ----------------
% 133.14/133.39 % SZS status Unsatisfiable
% 133.14/133.39 % SZS output start Refutation
% See solution above
% 133.14/133.39 ------------ end of proof -------------
% 133.14/133.39
% 133.14/133.39
% 133.14/133.39 Search stopped by max_proofs option.
% 133.14/133.39
% 133.14/133.39
% 133.14/133.39 Search stopped by max_proofs option.
% 133.14/133.39
% 133.14/133.39 ============ end of search ============
% 133.14/133.39
% 133.14/133.39 -------------- statistics -------------
% 133.14/133.39 clauses given 555
% 133.14/133.39 clauses generated 74553678
% 133.14/133.39 clauses kept 5036
% 133.14/133.39 clauses forward subsumed 1077098
% 133.14/133.39 clauses back subsumed 611
% 133.14/133.39 Kbytes malloced 5859
% 133.14/133.39
% 133.14/133.39 ----------- times (seconds) -----------
% 133.14/133.39 user CPU time 131.60 (0 hr, 2 min, 11 sec)
% 133.14/133.39 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 133.14/133.39 wall-clock time 133 (0 hr, 2 min, 13 sec)
% 133.14/133.39
% 133.14/133.39 That finishes the proof of the theorem.
% 133.14/133.39
% 133.14/133.39 Process 14910 finished Wed Jul 27 02:08:34 2022
% 133.14/133.39 Otter interrupted
% 133.14/133.39 PROOF FOUND
%------------------------------------------------------------------------------