TSTP Solution File: RNG041-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG041-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:12:09 EDT 2022
% Result : Unsatisfiable 1.84s 2.11s
% Output : Refutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 13 ( 10 unt; 1 nHn; 10 RR)
% Number of literals : 19 ( 6 equ; 8 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 13 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('RNG041-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('RNG041-1.p',unknown),
[] ).
cnf(12,axiom,
a != additive_identity,
file('RNG041-1.p',unknown),
[] ).
cnf(13,plain,
additive_identity != a,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.1')] ).
cnf(14,axiom,
b != additive_identity,
file('RNG041-1.p',unknown),
[] ).
cnf(48,axiom,
product(additive_identity,A,additive_identity),
file('RNG041-1.p',unknown),
[] ).
cnf(50,axiom,
product(A,multiplicative_identity,A),
file('RNG041-1.p',unknown),
[] ).
cnf(52,axiom,
( product(A,h(A),multiplicative_identity)
| A = additive_identity ),
file('RNG041-1.p',unknown),
[] ).
cnf(54,axiom,
product(a,b,additive_identity),
file('RNG041-1.p',unknown),
[] ).
cnf(250,plain,
product(b,h(b),multiplicative_identity),
inference(hyper,[status(thm)],[52,14]),
[iquote('hyper,52,14')] ).
cnf(329,plain,
product(a,multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[250,4,54,48]),
[iquote('hyper,250,4,54,48')] ).
cnf(348,plain,
additive_identity = a,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[329,11,50])]),
[iquote('hyper,329,11,50,flip.1')] ).
cnf(350,plain,
$false,
inference(binary,[status(thm)],[348,13]),
[iquote('binary,348.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG041-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 02:28:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.84/2.08 ----- Otter 3.3f, August 2004 -----
% 1.84/2.08 The process was started by sandbox on n023.cluster.edu,
% 1.84/2.08 Wed Jul 27 02:28:33 2022
% 1.84/2.08 The command was "./otter". The process ID is 13332.
% 1.84/2.08
% 1.84/2.08 set(prolog_style_variables).
% 1.84/2.08 set(auto).
% 1.84/2.08 dependent: set(auto1).
% 1.84/2.08 dependent: set(process_input).
% 1.84/2.08 dependent: clear(print_kept).
% 1.84/2.08 dependent: clear(print_new_demod).
% 1.84/2.08 dependent: clear(print_back_demod).
% 1.84/2.08 dependent: clear(print_back_sub).
% 1.84/2.08 dependent: set(control_memory).
% 1.84/2.08 dependent: assign(max_mem, 12000).
% 1.84/2.08 dependent: assign(pick_given_ratio, 4).
% 1.84/2.08 dependent: assign(stats_level, 1).
% 1.84/2.08 dependent: assign(max_seconds, 10800).
% 1.84/2.08 clear(print_given).
% 1.84/2.08
% 1.84/2.08 list(usable).
% 1.84/2.08 0 [] A=A.
% 1.84/2.08 0 [] sum(additive_identity,X,X).
% 1.84/2.08 0 [] sum(X,additive_identity,X).
% 1.84/2.08 0 [] product(X,Y,multiply(X,Y)).
% 1.84/2.08 0 [] sum(X,Y,add(X,Y)).
% 1.84/2.08 0 [] sum(additive_inverse(X),X,additive_identity).
% 1.84/2.08 0 [] sum(X,additive_inverse(X),additive_identity).
% 1.84/2.08 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 1.84/2.08 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 1.84/2.08 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.84/2.08 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.84/2.08 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.84/2.08 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.84/2.08 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.84/2.08 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.84/2.08 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.84/2.08 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.84/2.08 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.84/2.08 0 [] product(additive_identity,A,additive_identity).
% 1.84/2.08 0 [] product(A,additive_identity,additive_identity).
% 1.84/2.08 0 [] product(A,multiplicative_identity,A).
% 1.84/2.08 0 [] product(multiplicative_identity,A,A).
% 1.84/2.08 0 [] product(A,h(A),multiplicative_identity)|A=additive_identity.
% 1.84/2.08 0 [] product(h(A),A,multiplicative_identity)|A=additive_identity.
% 1.84/2.08 0 [] product(a,b,additive_identity).
% 1.84/2.08 0 [] a!=additive_identity.
% 1.84/2.08 0 [] b!=additive_identity.
% 1.84/2.08 end_of_list.
% 1.84/2.08
% 1.84/2.08 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.84/2.08
% 1.84/2.08 This ia a non-Horn set with equality. The strategy will be
% 1.84/2.08 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.84/2.08 deletion, with positive clauses in sos and nonpositive
% 1.84/2.08 clauses in usable.
% 1.84/2.08
% 1.84/2.08 dependent: set(knuth_bendix).
% 1.84/2.08 dependent: set(anl_eq).
% 1.84/2.08 dependent: set(para_from).
% 1.84/2.08 dependent: set(para_into).
% 1.84/2.08 dependent: clear(para_from_right).
% 1.84/2.08 dependent: clear(para_into_right).
% 1.84/2.08 dependent: set(para_from_vars).
% 1.84/2.08 dependent: set(eq_units_both_ways).
% 1.84/2.08 dependent: set(dynamic_demod_all).
% 1.84/2.08 dependent: set(dynamic_demod).
% 1.84/2.08 dependent: set(order_eq).
% 1.84/2.08 dependent: set(back_demod).
% 1.84/2.08 dependent: set(lrpo).
% 1.84/2.08 dependent: set(hyper_res).
% 1.84/2.08 dependent: set(unit_deletion).
% 1.84/2.08 dependent: set(factor).
% 1.84/2.08
% 1.84/2.08 ------------> process usable:
% 1.84/2.08 ** KEPT (pick-wt=16): 1 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 1.84/2.08 ** KEPT (pick-wt=16): 2 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 1.84/2.08 ** KEPT (pick-wt=8): 3 [] -sum(A,B,C)|sum(B,A,C).
% 1.84/2.08 ** KEPT (pick-wt=16): 4 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.84/2.08 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.84/2.08 ** 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).
% 1.84/2.08 ** 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).
% 1.84/2.08 ** 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).
% 1.84/2.08 ** 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).
% 1.84/2.08 ** KEPT (pick-wt=11): 10 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.84/2.08 ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.84/2.08 ** KEPT (pick-wt=3): 13 [copy,12,flip.1] additive_identity!=a.
% 1.84/2.08 ** KEPT (pick-wt=3): 14 [] b!=additive_identity.
% 1.84/2.08
% 1.84/2.08 ------------> process sos:
% 1.84/2.08 ** KEPT (pick-wt=3): 41 [] A=A.
% 1.84/2.08 ** KEPT (pick-wt=4): 42 [] sum(additive_identity,A,A).
% 1.84/2.08 ** KEPT (pick-wt=4): 43 [] sum(A,additive_identity,A).
% 1.84/2.08 ** KEPT (pick-wt=6): 44 [] product(A,B,multiply(A,B)).
% 1.84/2.08 ** KEPT (pick-wt=6): 45 [] sum(A,B,add(A,B)).
% 1.84/2.11 ** KEPT (pick-wt=5): 46 [] sum(additive_inverse(A),A,additive_identity).
% 1.84/2.11 ** KEPT (pick-wt=5): 47 [] sum(A,additive_inverse(A),additive_identity).
% 1.84/2.11 ** KEPT (pick-wt=4): 48 [] product(additive_identity,A,additive_identity).
% 1.84/2.11 ** KEPT (pick-wt=4): 49 [] product(A,additive_identity,additive_identity).
% 1.84/2.11 ** KEPT (pick-wt=4): 50 [] product(A,multiplicative_identity,A).
% 1.84/2.11 ** KEPT (pick-wt=4): 51 [] product(multiplicative_identity,A,A).
% 1.84/2.11 ** KEPT (pick-wt=8): 52 [] product(A,h(A),multiplicative_identity)|A=additive_identity.
% 1.84/2.11 ** KEPT (pick-wt=8): 53 [] product(h(A),A,multiplicative_identity)|A=additive_identity.
% 1.84/2.11 ** KEPT (pick-wt=4): 54 [] product(a,b,additive_identity).
% 1.84/2.11 Following clause subsumed by 41 during input processing: 0 [copy,41,flip.1] A=A.
% 1.84/2.11 41 back subsumes 36.
% 1.84/2.11 41 back subsumes 35.
% 1.84/2.11
% 1.84/2.11 ======= end of input processing =======
% 1.84/2.11
% 1.84/2.11 =========== start of search ===========
% 1.84/2.11
% 1.84/2.11 -------- PROOF --------
% 1.84/2.11
% 1.84/2.11 ----> UNIT CONFLICT at 0.03 sec ----> 350 [binary,348.1,13.1] $F.
% 1.84/2.11
% 1.84/2.11 Length of proof is 4. Level of proof is 3.
% 1.84/2.11
% 1.84/2.11 ---------------- PROOF ----------------
% 1.84/2.11 % SZS status Unsatisfiable
% 1.84/2.11 % SZS output start Refutation
% See solution above
% 1.84/2.11 ------------ end of proof -------------
% 1.84/2.11
% 1.84/2.11
% 1.84/2.11 Search stopped by max_proofs option.
% 1.84/2.11
% 1.84/2.11
% 1.84/2.11 Search stopped by max_proofs option.
% 1.84/2.11
% 1.84/2.11 ============ end of search ============
% 1.84/2.11
% 1.84/2.11 -------------- statistics -------------
% 1.84/2.11 clauses given 24
% 1.84/2.11 clauses generated 3039
% 1.84/2.11 clauses kept 336
% 1.84/2.11 clauses forward subsumed 2754
% 1.84/2.11 clauses back subsumed 23
% 1.84/2.11 Kbytes malloced 1953
% 1.84/2.11
% 1.84/2.11 ----------- times (seconds) -----------
% 1.84/2.11 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.84/2.11 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.84/2.11 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.84/2.11
% 1.84/2.11 That finishes the proof of the theorem.
% 1.84/2.11
% 1.84/2.11 Process 13332 finished Wed Jul 27 02:28:35 2022
% 1.84/2.11 Otter interrupted
% 1.84/2.11 PROOF FOUND
%------------------------------------------------------------------------------