TSTP Solution File: SWV376+1 by SOS---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SOS---2.0
% Problem : SWV376+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : sos-script %s
% Computer : n026.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 : 600s
% DateTime : Wed Jul 20 21:38:15 EDT 2022
% Result : Unknown 0.19s 0.36s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV376+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : sos-script %s
% 0.12/0.34 % Computer : n026.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 : 600
% 0.12/0.34 % DateTime : Wed Jun 15 20:56:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.36 ----- Otter 3.2, August 2001 -----
% 0.19/0.36 The process was started by sandbox on n026.cluster.edu,
% 0.19/0.36 Wed Jun 15 20:56:07 2022
% 0.19/0.36 The command was "./sos". The process ID is 7275.
% 0.19/0.36
% 0.19/0.36 set(prolog_style_variables).
% 0.19/0.36 set(auto).
% 0.19/0.36 dependent: set(auto1).
% 0.19/0.36 dependent: set(process_input).
% 0.19/0.36 dependent: clear(print_kept).
% 0.19/0.36 dependent: clear(print_new_demod).
% 0.19/0.36 dependent: clear(print_back_demod).
% 0.19/0.36 dependent: clear(print_back_sub).
% 0.19/0.36 dependent: set(control_memory).
% 0.19/0.36 dependent: assign(max_mem, 12000).
% 0.19/0.36 dependent: assign(pick_given_ratio, 4).
% 0.19/0.36 dependent: assign(stats_level, 1).
% 0.19/0.36 dependent: assign(pick_semantic_ratio, 3).
% 0.19/0.36 dependent: assign(sos_limit, 5000).
% 0.19/0.36 dependent: assign(max_weight, 60).
% 0.19/0.36 clear(print_given).
% 0.19/0.36
% 0.19/0.36 formula_list(usable).
% 0.19/0.36
% 0.19/0.36 ERROR, the 6 terms/operators in the following sequence are OK, but they
% 0.19/0.36 could not be combined into a single term with special operators.
% 0.19/0.36 the
% 0.19/0.36 induction
% 0.19/0.36 principle
% 0.19/0.36 used
% 0.19/0.36 in
% 0.19/0.36 Coq
% 0.19/0.36
% 0.19/0.36 The context of the bad sequence is:
% 0.19/0.36
% 0.19/0.36 /*----
% 0.19/0.36 Explanation about induction
% 0.19/0.36 ===========================
% 0.19/0.36
% 0.19/0.36 In order to prove lemma_not_ok_persistence we use the following induction
% 0.19/0.36 principle: ( ***HERE*** the induction principle used in Coq)
% 0.19/0.36 =====================
% 0.19/0.36 let s/1 be the successor function defined on some set S and let =</2 be the
% 0.19/0.36 predicate that satisfies the following axioms:
% 0.19/0.36
% 0.19/0.36 1) x =< x
% 0.19/0.36 2) x =< y -> x =< s(y)
% 0.19/0.36
% 0.19/0.36 Note that our predicate succ_cpq/2 satisfies those two axioms
% 0.19/0.36
% 0.19/0.36 The induction principle: (V = for eVery
% 0.19/0.36
% 0.19/0.36 Vx ( (P(x) and Vy (x =< y -> (P(y) -> P(s(y)))) -> Vy (x=<y -> P(y)) )
% 0.19/0.36 ======================
% 0.19/0.36
% 0.19/0.36 Let P(x) == ~(ok(x)) and let =</2 == succ/2
% 0.19/0.36
% 0.19/0.36 Then, in order to confirm correctness of lemma_not_ok_persistence we have
% 0.19/0.36 to only verify "Vy (x =< y -> (P(y) -> P(s(y))))" part of the induction
% 0.19/0.36 principle, in other words we need to prove validity of:
% 0.19/0.36
% 0.19/0.36 all(CPQ1, all(CPQ2, succ_cpq(CPQ1, CPQ2) => ( ~(ok(CPQ2)) => ~(ok(s(CPQ2))) ) )), (1)
% 0.19/0.36
% 0.19/0.36 where s(CPQ2) is the immediate successor of CPQ2
% 0.19/0.36
% 0.19/0.36 all(CPQ2, ~(ok(CPQ2)) => ~(ok(s(CPQ2))) ) (2)
% 0.19/0.36
% 0.19/0.36 is a valid formula.
% 0.19/0.36
% 0.19/0.36 ERROR, the 9 terms/operators in the following sequence are OK, but they
% 0.19/0.36 could not be combined into a single term with special operators.
% 0.19/0.36 the
% 0.19/0.36 validity
% 0.19/0.36 of
% 0.19/0.36 formula
% 0.19/0.36 2
% 0.19/0.36 is
% 0.19/0.36 proved
% 0.19/0.36 in
% 0.19/0.36 lemma_not_ok_persistence_induction
% 0.19/0.36
% 0.19/0.36 The context of the bad sequence is:
% 0.19/0.36 ***HERE***
% 0.19/0.36 the validity of formula (2) is proved in lemma_not_ok_persistence_induction,
% 0.19/0.36 so here we have included it as a valid formula
% 0.19/0.36
% 0.19/0.36 lemma_not_ok_persistence_induction proves the validity of formula (1)
% 0.19/0.36 and thus, since (1) is valid we can conclude that the following formula holds:
% 0.19/0.36
% 0.19/0.36 Vx ( P(x) -> Vy (x=<y -> P(y)) )
% 0.19/0.36
% 0.19/0.36 or in our example:
% 0.19/0.36
% 0.19/0.36 all(CPQ, ~(ok(CPQ)) => all(CPQ1, succ(CPQ, CPQ1) => ~(ok(CPQ1)) ) )
% 0.19/0.36
% 0.19/0.36 which completes the inductive proof of lemma_not_ok_persistence
% 0.19/0.36 ----*/
% 0.19/0.36
% 0.19/0.36
% 0.19/0.36
% 0.19/0.36 ( all U V W X Y Z (
% 0.19/0.36 ( succ_cpq(triple(U,V,W),triple(X,Y,Z))
% 0.19/0.36 -> ( -ok(triple(X,Y,Z))
% 0.19/0.36 -> -ok(im_succ_cpq(triple(X,Y,Z))) ) ) ) )
% 0.19/0.36 -> ( all X1 X2 X3 (
% 0.19/0.36 ( -ok(triple(X1,X2,X3))
% 0.19/0.36 -> ( all X4 X5 X6 (
% 0.19/0.36 ( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
% 0.19/0.36 -> -ok(triple(X4,X5,X6)) ) ) ) ) ) ).
% 0.19/0.36
% 0.19/0.36 ======= end of input processing =======
% 0.19/0.36
% 0.19/0.36 2 input errors were found.
% 0.19/0.36
% 0.19/0.36 2 input errors were found.
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