TSTP Solution File: MGT056+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : MGT056+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:06:14 EDT 2022
% Result : Theorem 4.45s 4.68s
% Output : Refutation 4.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of clauses : 36 ( 17 unt; 8 nHn; 30 RR)
% Number of literals : 66 ( 11 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( smaller_or_e_qual(A,B)
| ~ smaller(A,B) ),
file('MGT056+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ greater_or_e_qual(A,B)
| greater(A,B)
| A = B ),
file('MGT056+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ smaller(A,B)
| greater(B,A) ),
file('MGT056+1.p',unknown),
[] ).
cnf(8,axiom,
( smaller(A,B)
| ~ greater(B,A) ),
file('MGT056+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ greater(A,B)
| ~ greater(B,A) ),
file('MGT056+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ greater(A,B)
| ~ greater(B,C)
| greater(A,C) ),
file('MGT056+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ has_endowment(A)
| ~ smaller_or_e_qual(age(A,B),eta)
| has_immunity(A,B) ),
file('MGT056+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ has_endowment(A)
| ~ greater(age(A,B),eta)
| ~ has_immunity(A,B) ),
file('MGT056+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ organization(A)
| ~ has_immunity(A,B)
| ~ has_immunity(A,C)
| hazard_of_mortality(A,B) = hazard_of_mortality(A,C) ),
file('MGT056+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ organization(A)
| ~ has_immunity(A,B)
| has_immunity(A,C)
| greater(hazard_of_mortality(A,C),hazard_of_mortality(A,B)) ),
file('MGT056+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ greater(hazard_of_mortality(dollar_c4,dollar_c1),hazard_of_mortality(dollar_c4,dollar_c2))
| hazard_of_mortality(dollar_c4,dollar_c2) != hazard_of_mortality(dollar_c4,dollar_c3) ),
file('MGT056+1.p',unknown),
[] ).
cnf(20,plain,
( ~ greater(hazard_of_mortality(dollar_c4,dollar_c1),hazard_of_mortality(dollar_c4,dollar_c2))
| hazard_of_mortality(dollar_c4,dollar_c3) != hazard_of_mortality(dollar_c4,dollar_c2) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.2')] ).
cnf(21,plain,
~ greater(A,A),
inference(factor,[status(thm)],[9]),
[iquote('factor,9.1.2')] ).
cnf(23,axiom,
A = A,
file('MGT056+1.p',unknown),
[] ).
cnf(24,axiom,
( smaller(A,B)
| A = B
| greater(A,B) ),
file('MGT056+1.p',unknown),
[] ).
cnf(25,axiom,
organization(dollar_c4),
file('MGT056+1.p',unknown),
[] ).
cnf(26,axiom,
has_endowment(dollar_c4),
file('MGT056+1.p',unknown),
[] ).
cnf(27,axiom,
age(dollar_c4,dollar_c3) = zero,
file('MGT056+1.p',unknown),
[] ).
cnf(29,axiom,
smaller_or_e_qual(age(dollar_c4,dollar_c2),eta),
file('MGT056+1.p',unknown),
[] ).
cnf(30,axiom,
greater(age(dollar_c4,dollar_c1),eta),
file('MGT056+1.p',unknown),
[] ).
cnf(31,axiom,
greater_or_e_qual(eta,sigma),
file('MGT056+1.p',unknown),
[] ).
cnf(32,axiom,
greater(sigma,zero),
file('MGT056+1.p',unknown),
[] ).
cnf(39,plain,
( greater(eta,sigma)
| sigma = eta ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[31,4])]),
[iquote('hyper,31,4,flip.2')] ).
cnf(50,plain,
( A = B
| greater(A,B)
| greater(B,A) ),
inference(hyper,[status(thm)],[24,7]),
[iquote('hyper,24,7')] ).
cnf(112,plain,
( ~ smaller_or_e_qual(zero,eta)
| has_immunity(dollar_c4,dollar_c3) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[27,12]),26]),
[iquote('para_from,27.1.1,12.2.1,unit_del,26')] ).
cnf(119,plain,
has_immunity(dollar_c4,dollar_c2),
inference(hyper,[status(thm)],[29,12,26]),
[iquote('hyper,29,12,26')] ).
cnf(133,plain,
( has_immunity(dollar_c4,A)
| greater(hazard_of_mortality(dollar_c4,A),hazard_of_mortality(dollar_c4,dollar_c2)) ),
inference(hyper,[status(thm)],[119,18,25]),
[iquote('hyper,119,18,25')] ).
cnf(198,plain,
( sigma = eta
| greater(eta,zero) ),
inference(hyper,[status(thm)],[39,10,32]),
[iquote('hyper,39,10,32')] ).
cnf(258,plain,
greater(eta,zero),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[198,32])]),
[iquote('para_from,198.1.1,32.1.1,factor_simp')] ).
cnf(260,plain,
smaller(zero,eta),
inference(hyper,[status(thm)],[258,8]),
[iquote('hyper,258,8')] ).
cnf(274,plain,
smaller_or_e_qual(zero,eta),
inference(hyper,[status(thm)],[260,2]),
[iquote('hyper,260,2')] ).
cnf(287,plain,
has_immunity(dollar_c4,dollar_c3),
inference(hyper,[status(thm)],[274,112]),
[iquote('hyper,274,112')] ).
cnf(296,plain,
hazard_of_mortality(dollar_c4,dollar_c3) = hazard_of_mortality(dollar_c4,dollar_c2),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[287,17,25,119])]),
[iquote('hyper,287,17,25,119,flip.1')] ).
cnf(304,plain,
~ greater(hazard_of_mortality(dollar_c4,dollar_c1),hazard_of_mortality(dollar_c4,dollar_c2)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),296]),23]),
[iquote('back_demod,20,demod,296,unit_del,23')] ).
cnf(973,plain,
( has_endowment(A)
| greater(dollar_c4,A)
| greater(A,dollar_c4) ),
inference(para_from,[status(thm),theory(equality)],[50,26]),
[iquote('para_from,50.1.1,26.1.1')] ).
cnf(4488,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[133,13,973,30]),304,21,21]),
[iquote('hyper,133,13,973,30,unit_del,304,21,21')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT056+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n013.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 03:59:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.89/2.09 ----- Otter 3.3f, August 2004 -----
% 1.89/2.09 The process was started by sandbox2 on n013.cluster.edu,
% 1.89/2.09 Wed Jul 27 03:59:15 2022
% 1.89/2.09 The command was "./otter". The process ID is 7202.
% 1.89/2.09
% 1.89/2.09 set(prolog_style_variables).
% 1.89/2.09 set(auto).
% 1.89/2.09 dependent: set(auto1).
% 1.89/2.09 dependent: set(process_input).
% 1.89/2.09 dependent: clear(print_kept).
% 1.89/2.09 dependent: clear(print_new_demod).
% 1.89/2.09 dependent: clear(print_back_demod).
% 1.89/2.09 dependent: clear(print_back_sub).
% 1.89/2.09 dependent: set(control_memory).
% 1.89/2.09 dependent: assign(max_mem, 12000).
% 1.89/2.09 dependent: assign(pick_given_ratio, 4).
% 1.89/2.09 dependent: assign(stats_level, 1).
% 1.89/2.09 dependent: assign(max_seconds, 10800).
% 1.89/2.09 clear(print_given).
% 1.89/2.09
% 1.89/2.09 formula_list(usable).
% 1.89/2.09 all A (A=A).
% 1.89/2.09 all X Y (smaller_or_e_qual(X,Y)<->smaller(X,Y)|X=Y).
% 1.89/2.09 all X Y (greater_or_e_qual(X,Y)<->greater(X,Y)|X=Y).
% 1.89/2.09 all X Y (smaller(X,Y)<->greater(Y,X)).
% 1.89/2.09 all X Y (-(greater(X,Y)&greater(Y,X))).
% 1.89/2.09 all X Y Z (greater(X,Y)&greater(Y,Z)->greater(X,Z)).
% 1.89/2.09 all X Y (smaller(X,Y)|X=Y|greater(X,Y)).
% 1.89/2.09 all X (has_endowment(X)<-> (all T (organization(X)& (smaller_or_e_qual(age(X,T),eta)->has_immunity(X,T))& (greater(age(X,T),eta)-> -has_immunity(X,T))))).
% 1.89/2.09 all X T0 T (organization(X)&has_immunity(X,T0)&has_immunity(X,T)->hazard_of_mortality(X,T0)=hazard_of_mortality(X,T)).
% 1.89/2.09 all X T0 T (organization(X)&has_immunity(X,T0)& -has_immunity(X,T)->greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0))).
% 1.89/2.09 -(all X T0 T1 T2 (organization(X)&has_endowment(X)&age(X,T0)=zero&smaller_or_e_qual(age(X,T1),eta)&greater(age(X,T2),eta)&greater_or_e_qual(eta,sigma)&greater(sigma,zero)->greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1))&hazard_of_mortality(X,T1)=hazard_of_mortality(X,T0))).
% 1.89/2.09 end_of_list.
% 1.89/2.09
% 1.89/2.09 -------> usable clausifies to:
% 1.89/2.09
% 1.89/2.09 list(usable).
% 1.89/2.09 0 [] A=A.
% 1.89/2.09 0 [] -smaller_or_e_qual(X,Y)|smaller(X,Y)|X=Y.
% 1.89/2.09 0 [] smaller_or_e_qual(X,Y)| -smaller(X,Y).
% 1.89/2.09 0 [] smaller_or_e_qual(X,Y)|X!=Y.
% 1.89/2.09 0 [] -greater_or_e_qual(X,Y)|greater(X,Y)|X=Y.
% 1.89/2.09 0 [] greater_or_e_qual(X,Y)| -greater(X,Y).
% 1.89/2.09 0 [] greater_or_e_qual(X,Y)|X!=Y.
% 1.89/2.09 0 [] -smaller(X,Y)|greater(Y,X).
% 1.89/2.09 0 [] smaller(X,Y)| -greater(Y,X).
% 1.89/2.09 0 [] -greater(X,Y)| -greater(Y,X).
% 1.89/2.09 0 [] -greater(X,Y)| -greater(Y,Z)|greater(X,Z).
% 1.89/2.09 0 [] smaller(X,Y)|X=Y|greater(X,Y).
% 1.89/2.09 0 [] -has_endowment(X)|organization(X).
% 1.89/2.09 0 [] -has_endowment(X)| -smaller_or_e_qual(age(X,T),eta)|has_immunity(X,T).
% 1.89/2.09 0 [] -has_endowment(X)| -greater(age(X,T),eta)| -has_immunity(X,T).
% 1.89/2.09 0 [] has_endowment(X)| -organization(X)|smaller_or_e_qual(age(X,$f1(X)),eta)|greater(age(X,$f1(X)),eta).
% 1.89/2.09 0 [] has_endowment(X)| -organization(X)|smaller_or_e_qual(age(X,$f1(X)),eta)|has_immunity(X,$f1(X)).
% 1.89/2.09 0 [] has_endowment(X)| -organization(X)| -has_immunity(X,$f1(X))|greater(age(X,$f1(X)),eta).
% 1.89/2.09 0 [] -organization(X)| -has_immunity(X,T0)| -has_immunity(X,T)|hazard_of_mortality(X,T0)=hazard_of_mortality(X,T).
% 1.89/2.09 0 [] -organization(X)| -has_immunity(X,T0)|has_immunity(X,T)|greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)).
% 1.89/2.09 0 [] organization($c4).
% 1.89/2.09 0 [] has_endowment($c4).
% 1.89/2.09 0 [] age($c4,$c3)=zero.
% 1.89/2.09 0 [] smaller_or_e_qual(age($c4,$c2),eta).
% 1.89/2.09 0 [] greater(age($c4,$c1),eta).
% 1.89/2.09 0 [] greater_or_e_qual(eta,sigma).
% 1.89/2.09 0 [] greater(sigma,zero).
% 1.89/2.09 0 [] -greater(hazard_of_mortality($c4,$c1),hazard_of_mortality($c4,$c2))|hazard_of_mortality($c4,$c2)!=hazard_of_mortality($c4,$c3).
% 1.89/2.09 end_of_list.
% 1.89/2.09
% 1.89/2.09 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.89/2.09
% 1.89/2.09 This ia a non-Horn set with equality. The strategy will be
% 1.89/2.09 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.89/2.09 deletion, with positive clauses in sos and nonpositive
% 1.89/2.09 clauses in usable.
% 1.89/2.09
% 1.89/2.09 dependent: set(knuth_bendix).
% 1.89/2.09 dependent: set(anl_eq).
% 1.89/2.09 dependent: set(para_from).
% 1.89/2.09 dependent: set(para_into).
% 1.89/2.09 dependent: clear(para_from_right).
% 1.89/2.09 dependent: clear(para_into_right).
% 1.89/2.09 dependent: set(para_from_vars).
% 1.89/2.09 dependent: set(eq_units_both_ways).
% 1.89/2.09 dependent: set(dynamic_demod_all).
% 1.89/2.09 dependent: set(dynamic_demod).
% 1.89/2.09 dependent: set(order_eq).
% 1.89/2.09 dependent: set(back_demod).
% 1.89/2.09 dependent: set(lrpo).
% 1.89/2.09 dependent: set(hyper_res).
% 1.89/2.09 dependent: set(unit_deletion).
% 1.89/2.09 dependent: set(factor).
% 1.89/2.09
% 1.89/2.09 ------------> process usable:
% 1.89/2.09 ** KEPT (pick-wt=9): 1 [] -smaller_or_e_qual(A,B)|smaller(A,B)|A=B.
% 1.89/2.09 ** KEPT (pick-wt=6): 2 [] smaller_or_e_qual(A,B)| -smaller(A,B).
% 4.45/4.68 ** KEPT (pick-wt=6): 3 [] smaller_or_e_qual(A,B)|A!=B.
% 4.45/4.68 ** KEPT (pick-wt=9): 4 [] -greater_or_e_qual(A,B)|greater(A,B)|A=B.
% 4.45/4.68 ** KEPT (pick-wt=6): 5 [] greater_or_e_qual(A,B)| -greater(A,B).
% 4.45/4.68 ** KEPT (pick-wt=6): 6 [] greater_or_e_qual(A,B)|A!=B.
% 4.45/4.68 ** KEPT (pick-wt=6): 7 [] -smaller(A,B)|greater(B,A).
% 4.45/4.68 ** KEPT (pick-wt=6): 8 [] smaller(A,B)| -greater(B,A).
% 4.45/4.68 ** KEPT (pick-wt=6): 9 [] -greater(A,B)| -greater(B,A).
% 4.45/4.68 ** KEPT (pick-wt=9): 10 [] -greater(A,B)| -greater(B,C)|greater(A,C).
% 4.45/4.68 ** KEPT (pick-wt=4): 11 [] -has_endowment(A)|organization(A).
% 4.45/4.68 ** KEPT (pick-wt=10): 12 [] -has_endowment(A)| -smaller_or_e_qual(age(A,B),eta)|has_immunity(A,B).
% 4.45/4.68 ** KEPT (pick-wt=10): 13 [] -has_endowment(A)| -greater(age(A,B),eta)| -has_immunity(A,B).
% 4.45/4.68 ** KEPT (pick-wt=16): 14 [] has_endowment(A)| -organization(A)|smaller_or_e_qual(age(A,$f1(A)),eta)|greater(age(A,$f1(A)),eta).
% 4.45/4.68 ** KEPT (pick-wt=14): 15 [] has_endowment(A)| -organization(A)|smaller_or_e_qual(age(A,$f1(A)),eta)|has_immunity(A,$f1(A)).
% 4.45/4.68 ** KEPT (pick-wt=14): 16 [] has_endowment(A)| -organization(A)| -has_immunity(A,$f1(A))|greater(age(A,$f1(A)),eta).
% 4.45/4.68 ** KEPT (pick-wt=15): 17 [] -organization(A)| -has_immunity(A,B)| -has_immunity(A,C)|hazard_of_mortality(A,B)=hazard_of_mortality(A,C).
% 4.45/4.68 ** KEPT (pick-wt=15): 18 [] -organization(A)| -has_immunity(A,B)|has_immunity(A,C)|greater(hazard_of_mortality(A,C),hazard_of_mortality(A,B)).
% 4.45/4.68 ** KEPT (pick-wt=14): 20 [copy,19,flip.2] -greater(hazard_of_mortality($c4,$c1),hazard_of_mortality($c4,$c2))|hazard_of_mortality($c4,$c3)!=hazard_of_mortality($c4,$c2).
% 4.45/4.68
% 4.45/4.68 ------------> process sos:
% 4.45/4.68 ** KEPT (pick-wt=3): 23 [] A=A.
% 4.45/4.68 ** KEPT (pick-wt=9): 24 [] smaller(A,B)|A=B|greater(A,B).
% 4.45/4.68 ** KEPT (pick-wt=2): 25 [] organization($c4).
% 4.45/4.68 ** KEPT (pick-wt=2): 26 [] has_endowment($c4).
% 4.45/4.68 ** KEPT (pick-wt=5): 27 [] age($c4,$c3)=zero.
% 4.45/4.68 ---> New Demodulator: 28 [new_demod,27] age($c4,$c3)=zero.
% 4.45/4.68 ** KEPT (pick-wt=5): 29 [] smaller_or_e_qual(age($c4,$c2),eta).
% 4.45/4.68 ** KEPT (pick-wt=5): 30 [] greater(age($c4,$c1),eta).
% 4.45/4.68 ** KEPT (pick-wt=3): 31 [] greater_or_e_qual(eta,sigma).
% 4.45/4.68 ** KEPT (pick-wt=3): 32 [] greater(sigma,zero).
% 4.45/4.68 Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] A=A.
% 4.45/4.68 23 back subsumes 22.
% 4.45/4.68 >>>> Starting back demodulation with 28.
% 4.45/4.68
% 4.45/4.68 ======= end of input processing =======
% 4.45/4.68
% 4.45/4.68 =========== start of search ===========
% 4.45/4.68
% 4.45/4.68
% 4.45/4.68 Resetting weight limit to 11.
% 4.45/4.68
% 4.45/4.68
% 4.45/4.68 Resetting weight limit to 11.
% 4.45/4.68
% 4.45/4.68 sos_size=3979
% 4.45/4.68
% 4.45/4.68 -------- PROOF --------
% 4.45/4.68
% 4.45/4.68 -----> EMPTY CLAUSE at 2.59 sec ----> 4488 [hyper,133,13,973,30,unit_del,304,21,21] $F.
% 4.45/4.68
% 4.45/4.68 Length of proof is 15. Level of proof is 8.
% 4.45/4.68
% 4.45/4.68 ---------------- PROOF ----------------
% 4.45/4.68 % SZS status Theorem
% 4.45/4.68 % SZS output start Refutation
% See solution above
% 4.45/4.68 ------------ end of proof -------------
% 4.45/4.68
% 4.45/4.68
% 4.45/4.68 Search stopped by max_proofs option.
% 4.45/4.68
% 4.45/4.68
% 4.45/4.68 Search stopped by max_proofs option.
% 4.45/4.68
% 4.45/4.68 ============ end of search ============
% 4.45/4.68
% 4.45/4.68 -------------- statistics -------------
% 4.45/4.68 clauses given 276
% 4.45/4.68 clauses generated 20383
% 4.45/4.68 clauses kept 4484
% 4.45/4.68 clauses forward subsumed 5681
% 4.45/4.68 clauses back subsumed 524
% 4.45/4.68 Kbytes malloced 4882
% 4.45/4.68
% 4.45/4.68 ----------- times (seconds) -----------
% 4.45/4.68 user CPU time 2.59 (0 hr, 0 min, 2 sec)
% 4.45/4.68 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 4.45/4.68 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 4.45/4.68
% 4.45/4.68 That finishes the proof of the theorem.
% 4.45/4.68
% 4.45/4.68 Process 7202 finished Wed Jul 27 03:59:19 2022
% 4.45/4.68 Otter interrupted
% 4.45/4.68 PROOF FOUND
%------------------------------------------------------------------------------