TSTP Solution File: RNG005-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:12:01 EDT 2022
% Result : Unsatisfiable 1.72s 1.98s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of clauses : 27 ( 21 unt; 0 nHn; 20 RR)
% Number of literals : 43 ( 6 equ; 17 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 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 : 41 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(A,E,F)
| sum(C,D,F) ),
file('RNG005-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ sum(A,B,C)
| sum(B,A,C) ),
file('RNG005-1.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('RNG005-1.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('RNG005-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| C = D ),
file('RNG005-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('RNG005-1.p',unknown),
[] ).
cnf(12,axiom,
~ sum(c,d,additive_identity),
file('RNG005-1.p',unknown),
[] ).
cnf(15,axiom,
sum(A,additive_identity,A),
file('RNG005-1.p',unknown),
[] ).
cnf(16,axiom,
product(A,B,multiply(A,B)),
file('RNG005-1.p',unknown),
[] ).
cnf(17,axiom,
sum(A,B,add(A,B)),
file('RNG005-1.p',unknown),
[] ).
cnf(18,axiom,
sum(additive_inverse(A),A,additive_identity),
file('RNG005-1.p',unknown),
[] ).
cnf(19,axiom,
sum(A,additive_inverse(A),additive_identity),
file('RNG005-1.p',unknown),
[] ).
cnf(20,axiom,
product(a,b,d),
file('RNG005-1.p',unknown),
[] ).
cnf(21,axiom,
product(additive_inverse(a),b,c),
file('RNG005-1.p',unknown),
[] ).
cnf(41,plain,
multiply(a,b) = d,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[16,11,20])]),
[iquote('hyper,16,11,20,flip.1')] ).
cnf(42,plain,
sum(d,multiply(additive_identity,b),d),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[16,8,20,16,15]),41]),
[iquote('hyper,16,8,20,16,15,demod,41')] ).
cnf(78,plain,
sum(d,c,multiply(additive_identity,b)),
inference(hyper,[status(thm)],[21,8,20,19,16]),
[iquote('hyper,21,8,20,19,16')] ).
cnf(107,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(111,plain,
product(additive_identity,b,add(c,d)),
inference(hyper,[status(thm)],[17,9,21,20,18]),
[iquote('hyper,17,9,21,20,18')] ).
cnf(162,plain,
sum(A,B,add(B,A)),
inference(hyper,[status(thm)],[17,3]),
[iquote('hyper,17,3')] ).
cnf(193,plain,
sum(additive_identity,multiply(additive_identity,b),additive_identity),
inference(hyper,[status(thm)],[42,2,18,18]),
[iquote('hyper,42,2,18,18')] ).
cnf(354,plain,
multiply(additive_identity,b) = add(d,c),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[78,10,17])]),
[iquote('hyper,78,10,17,flip.1')] ).
cnf(446,plain,
sum(additive_identity,add(d,c),additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[193]),354]),
[iquote('back_demod,193,demod,354')] ).
cnf(464,plain,
add(d,c) = add(c,d),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[111,11,16]),354]),
[iquote('hyper,111,11,16,demod,354')] ).
cnf(503,plain,
sum(additive_identity,add(c,d),additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[446]),464]),
[iquote('back_demod,446,demod,464')] ).
cnf(930,plain,
sum(c,d,additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[503,2,162,17]),107]),
[iquote('hyper,503,2,162,17,demod,107')] ).
cnf(931,plain,
$false,
inference(binary,[status(thm)],[930,12]),
[iquote('binary,930.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 02:11:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.72/1.95 ----- Otter 3.3f, August 2004 -----
% 1.72/1.95 The process was started by sandbox on n008.cluster.edu,
% 1.72/1.95 Wed Jul 27 02:11:38 2022
% 1.72/1.95 The command was "./otter". The process ID is 6198.
% 1.72/1.95
% 1.72/1.95 set(prolog_style_variables).
% 1.72/1.95 set(auto).
% 1.72/1.95 dependent: set(auto1).
% 1.72/1.95 dependent: set(process_input).
% 1.72/1.95 dependent: clear(print_kept).
% 1.72/1.95 dependent: clear(print_new_demod).
% 1.72/1.95 dependent: clear(print_back_demod).
% 1.72/1.95 dependent: clear(print_back_sub).
% 1.72/1.95 dependent: set(control_memory).
% 1.72/1.95 dependent: assign(max_mem, 12000).
% 1.72/1.95 dependent: assign(pick_given_ratio, 4).
% 1.72/1.95 dependent: assign(stats_level, 1).
% 1.72/1.95 dependent: assign(max_seconds, 10800).
% 1.72/1.95 clear(print_given).
% 1.72/1.95
% 1.72/1.95 list(usable).
% 1.72/1.95 0 [] A=A.
% 1.72/1.95 0 [] sum(additive_identity,X,X).
% 1.72/1.95 0 [] sum(X,additive_identity,X).
% 1.72/1.95 0 [] product(X,Y,multiply(X,Y)).
% 1.72/1.95 0 [] sum(X,Y,add(X,Y)).
% 1.72/1.95 0 [] sum(additive_inverse(X),X,additive_identity).
% 1.72/1.95 0 [] sum(X,additive_inverse(X),additive_identity).
% 1.72/1.95 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 1.72/1.95 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 1.72/1.95 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.72/1.95 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.72/1.95 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.72/1.95 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.72/1.95 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.72/1.95 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.72/1.95 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.72/1.95 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.72/1.95 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.72/1.95 0 [] product(a,b,d).
% 1.72/1.95 0 [] product(additive_inverse(a),b,c).
% 1.72/1.95 0 [] -sum(c,d,additive_identity).
% 1.72/1.95 end_of_list.
% 1.72/1.95
% 1.72/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.72/1.95
% 1.72/1.95 This is a Horn set with equality. The strategy will be
% 1.72/1.95 Knuth-Bendix and hyper_res, with positive clauses in
% 1.72/1.95 sos and nonpositive clauses in usable.
% 1.72/1.95
% 1.72/1.95 dependent: set(knuth_bendix).
% 1.72/1.95 dependent: set(anl_eq).
% 1.72/1.95 dependent: set(para_from).
% 1.72/1.95 dependent: set(para_into).
% 1.72/1.95 dependent: clear(para_from_right).
% 1.72/1.95 dependent: clear(para_into_right).
% 1.72/1.95 dependent: set(para_from_vars).
% 1.72/1.95 dependent: set(eq_units_both_ways).
% 1.72/1.95 dependent: set(dynamic_demod_all).
% 1.72/1.95 dependent: set(dynamic_demod).
% 1.72/1.95 dependent: set(order_eq).
% 1.72/1.95 dependent: set(back_demod).
% 1.72/1.95 dependent: set(lrpo).
% 1.72/1.95 dependent: set(hyper_res).
% 1.72/1.95 dependent: clear(order_hyper).
% 1.72/1.95
% 1.72/1.95 ------------> process usable:
% 1.72/1.95 ** KEPT (pick-wt=16): 1 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 1.72/1.95 ** KEPT (pick-wt=16): 2 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 1.72/1.95 ** KEPT (pick-wt=8): 3 [] -sum(A,B,C)|sum(B,A,C).
% 1.72/1.95 ** KEPT (pick-wt=16): 4 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.72/1.95 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.72/1.95 ** 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).
% 1.72/1.95 ** 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).
% 1.72/1.95 ** 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).
% 1.72/1.95 ** 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).
% 1.72/1.95 ** KEPT (pick-wt=11): 10 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.72/1.95 ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.72/1.95 ** KEPT (pick-wt=4): 12 [] -sum(c,d,additive_identity).
% 1.72/1.95
% 1.72/1.95 ------------> process sos:
% 1.72/1.95 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.72/1.95 ** KEPT (pick-wt=4): 14 [] sum(additive_identity,A,A).
% 1.72/1.95 ** KEPT (pick-wt=4): 15 [] sum(A,additive_identity,A).
% 1.72/1.95 ** KEPT (pick-wt=6): 16 [] product(A,B,multiply(A,B)).
% 1.72/1.95 ** KEPT (pick-wt=6): 17 [] sum(A,B,add(A,B)).
% 1.72/1.95 ** KEPT (pick-wt=5): 18 [] sum(additive_inverse(A),A,additive_identity).
% 1.72/1.95 ** KEPT (pick-wt=5): 19 [] sum(A,additive_inverse(A),additive_identity).
% 1.72/1.95 ** KEPT (pick-wt=4): 20 [] product(a,b,d).
% 1.72/1.95 ** KEPT (pick-wt=5): 21 [] product(additive_inverse(a),b,c).
% 1.72/1.95 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.72/1.95
% 1.72/1.95 ======= end of input processing =======
% 1.72/1.95
% 1.72/1.95 =========== start of search ===========
% 1.72/1.98
% 1.72/1.98 -------- PROOF --------
% 1.72/1.98
% 1.72/1.98 ----> UNIT CONFLICT at 0.03 sec ----> 931 [binary,930.1,12.1] $F.
% 1.72/1.98
% 1.72/1.98 Length of proof is 12. Level of proof is 6.
% 1.72/1.98
% 1.72/1.98 ---------------- PROOF ----------------
% 1.72/1.98 % SZS status Unsatisfiable
% 1.72/1.98 % SZS output start Refutation
% See solution above
% 1.72/1.98 ------------ end of proof -------------
% 1.72/1.98
% 1.72/1.98
% 1.72/1.98 Search stopped by max_proofs option.
% 1.72/1.98
% 1.72/1.98
% 1.72/1.98 Search stopped by max_proofs option.
% 1.72/1.98
% 1.72/1.98 ============ end of search ============
% 1.72/1.98
% 1.72/1.98 -------------- statistics -------------
% 1.72/1.98 clauses given 43
% 1.72/1.98 clauses generated 2718
% 1.72/1.98 clauses kept 899
% 1.72/1.98 clauses forward subsumed 2125
% 1.72/1.98 clauses back subsumed 11
% 1.72/1.98 Kbytes malloced 1953
% 1.72/1.98
% 1.72/1.98 ----------- times (seconds) -----------
% 1.72/1.98 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.72/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.98 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.72/1.98
% 1.72/1.98 That finishes the proof of the theorem.
% 1.72/1.98
% 1.72/1.98 Process 6198 finished Wed Jul 27 02:11:40 2022
% 1.72/1.98 Otter interrupted
% 1.72/1.98 PROOF FOUND
%------------------------------------------------------------------------------