TSTP Solution File: RNG004-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG004-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 2.14s 2.37s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of clauses : 39 ( 30 unt; 0 nHn; 25 RR)
% Number of literals : 62 ( 15 equ; 25 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(C,D,F)
| sum(A,E,F) ),
file('RNG004-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(A,E,F)
| sum(C,D,F) ),
file('RNG004-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ sum(A,B,C)
| sum(B,A,C) ),
file('RNG004-2.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('RNG004-2.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('RNG004-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| C = D ),
file('RNG004-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('RNG004-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ sum(A,B,C)
| ~ sum(A,D,C)
| B = D ),
file('RNG004-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ sum(A,B,C)
| ~ sum(D,B,C)
| A = D ),
file('RNG004-2.p',unknown),
[] ).
cnf(14,axiom,
c != d,
file('RNG004-2.p',unknown),
[] ).
cnf(15,plain,
d != c,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[14])]),
[iquote('copy,14,flip.1')] ).
cnf(17,axiom,
sum(additive_identity,A,A),
file('RNG004-2.p',unknown),
[] ).
cnf(18,axiom,
sum(A,additive_identity,A),
file('RNG004-2.p',unknown),
[] ).
cnf(19,axiom,
product(A,B,multiply(A,B)),
file('RNG004-2.p',unknown),
[] ).
cnf(20,axiom,
sum(A,B,add(A,B)),
file('RNG004-2.p',unknown),
[] ).
cnf(21,axiom,
sum(additive_inverse(A),A,additive_identity),
file('RNG004-2.p',unknown),
[] ).
cnf(22,axiom,
sum(A,additive_inverse(A),additive_identity),
file('RNG004-2.p',unknown),
[] ).
cnf(23,axiom,
product(a,b,c),
file('RNG004-2.p',unknown),
[] ).
cnf(24,axiom,
product(additive_inverse(a),additive_inverse(b),d),
file('RNG004-2.p',unknown),
[] ).
cnf(58,plain,
multiply(a,b) = c,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[19,11,23])]),
[iquote('hyper,19,11,23,flip.1')] ).
cnf(59,plain,
sum(c,multiply(additive_identity,b),c),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[19,8,23,19,18]),58]),
[iquote('hyper,19,8,23,19,18,demod,58')] ).
cnf(86,plain,
additive_inverse(additive_inverse(A)) = A,
inference(hyper,[status(thm)],[22,13,21]),
[iquote('hyper,22,13,21')] ).
cnf(87,plain,
sum(c,multiply(additive_inverse(a),b),multiply(additive_identity,b)),
inference(hyper,[status(thm)],[22,8,23,19,19]),
[iquote('hyper,22,8,23,19,19')] ).
cnf(112,plain,
add(A,additive_identity) = A,
inference(hyper,[status(thm)],[20,13,18]),
[iquote('hyper,20,13,18')] ).
cnf(114,plain,
add(additive_identity,A) = A,
inference(hyper,[status(thm)],[20,12,17]),
[iquote('hyper,20,12,17')] ).
cnf(118,plain,
add(additive_inverse(A),A) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[20,10,21])]),
[iquote('hyper,20,10,21,flip.1')] ).
cnf(151,plain,
sum(A,B,add(B,A)),
inference(hyper,[status(thm)],[20,3]),
[iquote('hyper,20,3')] ).
cnf(155,plain,
sum(add(A,additive_inverse(B)),B,A),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[20,2,20,21]),112]),
[iquote('hyper,20,2,20,21,demod,112')] ).
cnf(158,plain,
sum(A,add(additive_inverse(A),B),B),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[20,1,22,20]),114]),
[iquote('hyper,20,1,22,20,demod,114')] ).
cnf(199,plain,
sum(d,multiply(additive_inverse(a),additive_identity),d),
inference(hyper,[status(thm)],[24,6,24,19,18]),
[iquote('hyper,24,6,24,19,18')] ).
cnf(204,plain,
sum(d,multiply(additive_inverse(a),b),multiply(additive_inverse(a),additive_identity)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[24,6,19,22,19]),86]),
[iquote('hyper,24,6,19,22,19,demod,86')] ).
cnf(231,plain,
multiply(additive_identity,b) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[59,12,18])]),
[iquote('hyper,59,12,18,flip.1')] ).
cnf(232,plain,
sum(c,multiply(additive_inverse(a),b),additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[87]),231]),
[iquote('back_demod,87,demod,231')] ).
cnf(359,plain,
sum(add(additive_inverse(A),B),A,B),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[151,2,151,21]),114]),
[iquote('hyper,151,2,151,21,demod,114')] ).
cnf(1285,plain,
multiply(additive_inverse(a),additive_identity) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[199,12,158]),118])]),
[iquote('hyper,199,12,158,demod,118,flip.1')] ).
cnf(1286,plain,
sum(d,multiply(additive_inverse(a),b),additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[204]),1285]),
[iquote('back_demod,204,demod,1285')] ).
cnf(1376,plain,
additive_inverse(multiply(additive_inverse(a),b)) = c,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[232,13,155]),114]),
[iquote('hyper,232,13,155,demod,114')] ).
cnf(1975,plain,
d = c,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1286,13,359]),1376,112])]),
[iquote('hyper,1286,13,359,demod,1376,112,flip.1')] ).
cnf(1977,plain,
$false,
inference(binary,[status(thm)],[1975,15]),
[iquote('binary,1975.1,15.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 02:20:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.16 ----- Otter 3.3f, August 2004 -----
% 1.98/2.16 The process was started by sandbox on n020.cluster.edu,
% 1.98/2.16 Wed Jul 27 02:20:08 2022
% 1.98/2.16 The command was "./otter". The process ID is 7315.
% 1.98/2.16
% 1.98/2.16 set(prolog_style_variables).
% 1.98/2.16 set(auto).
% 1.98/2.16 dependent: set(auto1).
% 1.98/2.16 dependent: set(process_input).
% 1.98/2.16 dependent: clear(print_kept).
% 1.98/2.16 dependent: clear(print_new_demod).
% 1.98/2.16 dependent: clear(print_back_demod).
% 1.98/2.16 dependent: clear(print_back_sub).
% 1.98/2.16 dependent: set(control_memory).
% 1.98/2.16 dependent: assign(max_mem, 12000).
% 1.98/2.16 dependent: assign(pick_given_ratio, 4).
% 1.98/2.16 dependent: assign(stats_level, 1).
% 1.98/2.16 dependent: assign(max_seconds, 10800).
% 1.98/2.16 clear(print_given).
% 1.98/2.16
% 1.98/2.16 list(usable).
% 1.98/2.16 0 [] A=A.
% 1.98/2.16 0 [] sum(additive_identity,X,X).
% 1.98/2.16 0 [] sum(X,additive_identity,X).
% 1.98/2.16 0 [] product(X,Y,multiply(X,Y)).
% 1.98/2.16 0 [] sum(X,Y,add(X,Y)).
% 1.98/2.16 0 [] sum(additive_inverse(X),X,additive_identity).
% 1.98/2.16 0 [] sum(X,additive_inverse(X),additive_identity).
% 1.98/2.16 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 1.98/2.16 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 1.98/2.16 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.98/2.16 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.98/2.16 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.98/2.16 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.98/2.16 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.98/2.16 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.98/2.16 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.98/2.16 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.98/2.16 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.98/2.16 0 [] -sum(X,Y,Z)| -sum(X,W,Z)|Y=W.
% 1.98/2.16 0 [] -sum(X,Y,Z)| -sum(W,Y,Z)|X=W.
% 1.98/2.16 0 [] product(a,b,c).
% 1.98/2.16 0 [] product(additive_inverse(a),additive_inverse(b),d).
% 1.98/2.16 0 [] c!=d.
% 1.98/2.16 end_of_list.
% 1.98/2.16
% 1.98/2.16 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.98/2.16
% 1.98/2.16 This is a Horn set with equality. The strategy will be
% 1.98/2.16 Knuth-Bendix and hyper_res, with positive clauses in
% 1.98/2.16 sos and nonpositive clauses in usable.
% 1.98/2.16
% 1.98/2.16 dependent: set(knuth_bendix).
% 1.98/2.16 dependent: set(anl_eq).
% 1.98/2.16 dependent: set(para_from).
% 1.98/2.16 dependent: set(para_into).
% 1.98/2.16 dependent: clear(para_from_right).
% 1.98/2.16 dependent: clear(para_into_right).
% 1.98/2.16 dependent: set(para_from_vars).
% 1.98/2.16 dependent: set(eq_units_both_ways).
% 1.98/2.16 dependent: set(dynamic_demod_all).
% 1.98/2.16 dependent: set(dynamic_demod).
% 1.98/2.16 dependent: set(order_eq).
% 1.98/2.16 dependent: set(back_demod).
% 1.98/2.16 dependent: set(lrpo).
% 1.98/2.16 dependent: set(hyper_res).
% 1.98/2.16 dependent: clear(order_hyper).
% 1.98/2.16
% 1.98/2.16 ------------> process usable:
% 1.98/2.16 ** KEPT (pick-wt=16): 1 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 1.98/2.16 ** KEPT (pick-wt=16): 2 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 1.98/2.16 ** KEPT (pick-wt=8): 3 [] -sum(A,B,C)|sum(B,A,C).
% 1.98/2.16 ** KEPT (pick-wt=16): 4 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.98/2.16 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.98/2.16 ** 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).
% 1.98/2.16 ** 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).
% 1.98/2.16 ** 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).
% 1.98/2.16 ** 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).
% 1.98/2.16 ** KEPT (pick-wt=11): 10 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.98/2.16 ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.98/2.16 ** KEPT (pick-wt=11): 12 [] -sum(A,B,C)| -sum(A,D,C)|B=D.
% 1.98/2.16 ** KEPT (pick-wt=11): 13 [] -sum(A,B,C)| -sum(D,B,C)|A=D.
% 1.98/2.16 ** KEPT (pick-wt=3): 15 [copy,14,flip.1] d!=c.
% 1.98/2.16
% 1.98/2.16 ------------> process sos:
% 1.98/2.16 ** KEPT (pick-wt=3): 16 [] A=A.
% 1.98/2.16 ** KEPT (pick-wt=4): 17 [] sum(additive_identity,A,A).
% 1.98/2.16 ** KEPT (pick-wt=4): 18 [] sum(A,additive_identity,A).
% 1.98/2.16 ** KEPT (pick-wt=6): 19 [] product(A,B,multiply(A,B)).
% 1.98/2.16 ** KEPT (pick-wt=6): 20 [] sum(A,B,add(A,B)).
% 1.98/2.16 ** KEPT (pick-wt=5): 21 [] sum(additive_inverse(A),A,additive_identity).
% 1.98/2.16 ** KEPT (pick-wt=5): 22 [] sum(A,additive_inverse(A),additive_identity).
% 1.98/2.16 ** KEPT (pick-wt=4): 23 [] product(a,b,c).
% 1.98/2.16 ** KEPT (pick-wt=6): 24 [] product(additive_inverse(a),additive_inverse(b),d).
% 2.14/2.37 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 2.14/2.37
% 2.14/2.37 ======= end of input processing =======
% 2.14/2.37
% 2.14/2.37 =========== start of search ===========
% 2.14/2.37
% 2.14/2.37
% 2.14/2.37 Resetting weight limit to 8.
% 2.14/2.37
% 2.14/2.37
% 2.14/2.37 Resetting weight limit to 8.
% 2.14/2.37
% 2.14/2.37 sos_size=1748
% 2.14/2.37
% 2.14/2.37 -------- PROOF --------
% 2.14/2.37
% 2.14/2.37 ----> UNIT CONFLICT at 0.20 sec ----> 1977 [binary,1975.1,15.1] $F.
% 2.14/2.37
% 2.14/2.37 Length of proof is 20. Level of proof is 6.
% 2.14/2.37
% 2.14/2.37 ---------------- PROOF ----------------
% 2.14/2.37 % SZS status Unsatisfiable
% 2.14/2.37 % SZS output start Refutation
% See solution above
% 2.14/2.37 ------------ end of proof -------------
% 2.14/2.37
% 2.14/2.37
% 2.14/2.37 Search stopped by max_proofs option.
% 2.14/2.37
% 2.14/2.37
% 2.14/2.37 Search stopped by max_proofs option.
% 2.14/2.37
% 2.14/2.37 ============ end of search ============
% 2.14/2.37
% 2.14/2.37 -------------- statistics -------------
% 2.14/2.37 clauses given 73
% 2.14/2.37 clauses generated 11914
% 2.14/2.37 clauses kept 1929
% 2.14/2.37 clauses forward subsumed 8715
% 2.14/2.37 clauses back subsumed 18
% 2.14/2.37 Kbytes malloced 4882
% 2.14/2.37
% 2.14/2.37 ----------- times (seconds) -----------
% 2.14/2.37 user CPU time 0.20 (0 hr, 0 min, 0 sec)
% 2.14/2.37 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.14/2.37 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.14/2.37
% 2.14/2.37 That finishes the proof of the theorem.
% 2.14/2.37
% 2.14/2.37 Process 7315 finished Wed Jul 27 02:20:10 2022
% 2.14/2.37 Otter interrupted
% 2.14/2.37 PROOF FOUND
%------------------------------------------------------------------------------