TSTP Solution File: KLE143+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE143+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 : Sun Jul 17 02:22:26 EDT 2022
% Result : Theorem 8.20s 8.47s
% Output : Refutation 8.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE143+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 07:10:54 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.48/1.02 ============================== Prover9 ===============================
% 0.48/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.48/1.02 Process 17675 was started by sandbox on n012.cluster.edu,
% 0.48/1.02 Thu Jun 16 07:10:55 2022
% 0.48/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17522_n012.cluster.edu".
% 0.48/1.02 ============================== end of head ===========================
% 0.48/1.02
% 0.48/1.02 ============================== INPUT =================================
% 0.48/1.02
% 0.48/1.02 % Reading from file /tmp/Prover9_17522_n012.cluster.edu
% 0.48/1.02
% 0.48/1.02 set(prolog_style_variables).
% 0.48/1.02 set(auto2).
% 0.48/1.02 % set(auto2) -> set(auto).
% 0.48/1.02 % set(auto) -> set(auto_inference).
% 0.48/1.02 % set(auto) -> set(auto_setup).
% 0.48/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.48/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.48/1.02 % set(auto) -> set(auto_limits).
% 0.48/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.48/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.48/1.02 % set(auto) -> set(auto_denials).
% 0.48/1.02 % set(auto) -> set(auto_process).
% 0.48/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.48/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.48/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.48/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.48/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.48/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.48/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.48/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.48/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.48/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.48/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.48/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.48/1.02 % set(auto2) -> assign(stats, some).
% 0.48/1.02 % set(auto2) -> clear(echo_input).
% 0.48/1.02 % set(auto2) -> set(quiet).
% 0.48/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.48/1.02 % set(auto2) -> clear(print_given).
% 0.48/1.02 assign(lrs_ticks,-1).
% 0.48/1.02 assign(sos_limit,10000).
% 0.48/1.02 assign(order,kbo).
% 0.48/1.02 set(lex_order_vars).
% 0.48/1.02 clear(print_given).
% 0.48/1.02
% 0.48/1.02 % formulas(sos). % not echoed (19 formulas)
% 0.48/1.02
% 0.48/1.02 ============================== end of input ==========================
% 0.48/1.02
% 0.48/1.02 % From the command line: assign(max_seconds, 300).
% 0.48/1.02
% 0.48/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.48/1.02
% 0.48/1.02 % Formulas that are not ordinary clauses:
% 0.48/1.02 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(distributivity1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(distributivity2) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 13 (all A all B all C (leq(addition(multiplication(A,C),B),C) -> leq(multiplication(star(A),B),C))) # label(star_induction1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.02 14 (all A all B all C (leq(addition(multiplication(C,A),B),C) -> leq(multiplication(B,star(A)),C))) # label(star_induction2) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 16 (all A all B all C (leq(C,addition(multiplication(A,C),B)) -> leq(C,multiplication(strong_iteration(A),B)))) # label(infty_coinduction) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 19 -(all X0 (leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) & leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 8.20/8.47
% 8.20/8.47 ============================== end of process non-clausal formulas ===
% 8.20/8.47
% 8.20/8.47 ============================== PROCESS INITIAL CLAUSES ===============
% 8.20/8.47
% 8.20/8.47 ============================== PREDICATE ELIMINATION =================
% 8.20/8.47
% 8.20/8.47 ============================== end predicate elimination =============
% 8.20/8.47
% 8.20/8.47 Auto_denials:
% 8.20/8.47 % copying label goals to answer in negative clause
% 8.20/8.47
% 8.20/8.47 Term ordering decisions:
% 8.20/8.47 Function symbol KB weights: one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 8.20/8.47
% 8.20/8.47 ============================== end of process initial clauses ========
% 8.20/8.47
% 8.20/8.47 ============================== CLAUSES FOR SEARCH ====================
% 8.20/8.47
% 8.20/8.47 ============================== end of clauses for search =============
% 8.20/8.47
% 8.20/8.47 ============================== SEARCH ================================
% 8.20/8.47
% 8.20/8.47 % Starting search at 0.01 seconds.
% 8.20/8.47
% 8.20/8.47 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 0.60 sec).
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=39.000, iters=3401
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=35.000, iters=3341
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=33.000, iters=3368
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=32.000, iters=3471
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=29.000, iters=3361
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=26.000, iters=3338
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=25.000, iters=3418
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=24.000, iters=3389
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=23.000, iters=3363
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=22.000, iters=3348
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=21.000, iters=3356
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=20.000, iters=3349
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=19.000, iters=3350
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=18.000, iters=3348
% 8.20/8.47
% 8.20/8.47 Low Water (displace): id=5535, wt=43.000
% 8.20/8.47
% 8.20/8.47 Low Water (displace): id=6152, wt=42.000
% 8.20/8.47
% 8.20/8.47 Low Water (displace): id=5654, wt=40.000
% 8.20/8.47
% 8.20/8.47 Low Water (displace): id=12344, wt=17.000
% 8.20/8.47
% 8.20/8.47 Low Water (displace): id=12406, wt=15.000
% 8.20/8.47
% 8.20/8.47 Low Water (displace): id=12409, wt=14.000
% 8.20/8.47
% 8.20/8.47 Low Water (displace): id=12413, wt=13.000
% 8.20/8.47
% 8.20/8.47 Low Water (displace): id=13279, wt=12.000
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=17.000, iters=3333
% 8.20/8.47
% 8.20/8.47 Low Water (displace): id=15081, wt=11.000
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=16.000, iters=3341
% 8.20/8.47
% 8.20/8.47 Low Water (displace): id=16956, wt=10.000
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=15.000, iters=3334
% 8.20/8.47
% 8.20/8.47 Low Water (keep): wt=14.000, iters=3335
% 8.20/8.47
% 8.20/8.47 ============================== PROOF =================================
% 8.20/8.47 % SZS status Theorem
% 8.20/8.47 % SZS output start Refutation
% 8.20/8.47
% 8.20/8.47 % Proof 1 at 7.20 (+ 0.27) seconds: goals.
% 8.20/8.47 % Length of proof is 45.
% 8.20/8.47 % Level of proof is 7.
% 8.20/8.47 % Maximum clause weight is 17.000.
% 8.20/8.47 % Given clauses 3365.
% 8.20/8.47
% 8.20/8.47 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(distributivity1) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(distributivity2) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 16 (all A all B all C (leq(C,addition(multiplication(A,C),B)) -> leq(C,multiplication(strong_iteration(A),B)))) # label(infty_coinduction) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 8.20/8.47 19 -(all X0 (leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) & leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 8.20/8.47 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 8.20/8.47 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 8.20/8.47 23 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 8.20/8.47 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 8.20/8.47 30 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 8.20/8.47 31 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(30),rewrite([25(5)]),flip(a)].
% 8.20/8.47 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 8.20/8.47 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([25(2)]),flip(a)].
% 8.20/8.47 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 8.20/8.47 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 8.20/8.47 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 8.20/8.47 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 8.20/8.47 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 8.20/8.47 41 -leq(multiplication(strong_iteration(c1),strong_iteration(c1)),strong_iteration(c1)) | -leq(strong_iteration(c1),multiplication(strong_iteration(c1),strong_iteration(c1))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 8.20/8.47 43 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 8.20/8.47 48 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom). [clausify(16)].
% 8.20/8.47 49 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)). [copy(48),rewrite([25(2)])].
% 8.20/8.47 54 addition(A,addition(A,B)) = addition(A,B). [para(35(a,1),21(a,1)),rewrite([25(1),25(2),35(2,R),21(1),25(3)])].
% 8.20/8.47 57 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),38(a,1,1)),rewrite([25(4)]),flip(a)].
% 8.20/8.47 60 addition(A,multiplication(A,multiplication(B,strong_iteration(B)))) = multiplication(A,strong_iteration(B)). [para(31(a,1),38(a,2,2)),rewrite([22(2)])].
% 8.20/8.47 62 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(23(a,1),40(a,1,1)),rewrite([25(4)]),flip(a)].
% 8.20/8.47 69 leq(A,A). [hyper(43,b,21,a)].
% 8.20/8.47 99 -leq(A,addition(B,multiplication(C,multiplication(D,A)))) | leq(A,multiplication(strong_iteration(multiplication(C,D)),B)). [para(36(a,1),49(a,2,2))].
% 8.20/8.47 109 leq(A,addition(A,B)). [hyper(43,b,54,a)].
% 8.20/8.47 111 addition(one,strong_iteration(A)) = strong_iteration(A). [para(31(a,1),54(a,1,2)),rewrite([31(7)])].
% 8.20/8.47 113 leq(A,multiplication(strong_iteration(B),A)). [hyper(49,a,109,a)].
% 8.20/8.47 118 -leq(multiplication(strong_iteration(c1),strong_iteration(c1)),strong_iteration(c1)) # answer(goals). [back_unit_del(41),unit_del(b,113)].
% 8.20/8.47 203 addition(A,addition(B,multiplication(A,multiplication(C,strong_iteration(C))))) = addition(B,multiplication(A,strong_iteration(C))). [para(60(a,1),35(a,2,2)),rewrite([25(4)])].
% 8.20/8.47 240 addition(A,addition(B,addition(one,multiplication(A,B)))) = multiplication(addition(A,one),addition(B,one)). [para(62(a,1),57(a,2,2)),rewrite([35(10,R),35(9),25(8),35(9,R),25(8),35(10,R),25(9)]),flip(a)].
% 8.20/8.47 915 -leq(A,multiplication(B,addition(one,multiplication(C,A)))) | leq(A,multiplication(strong_iteration(multiplication(B,C)),B)). [para(57(a,2),99(a,2)),rewrite([25(3)])].
% 8.20/8.47 6437 addition(one,multiplication(A,multiplication(strong_iteration(A),strong_iteration(A)))) = multiplication(strong_iteration(A),strong_iteration(A)). [para(203(a,1),240(a,1,2)),rewrite([36(7),35(9,R),25(8),38(8),57(6,R),25(5),111(5),25(10),31(10),25(11),31(11)])].
% 8.20/8.47 17734 -leq(A,addition(one,multiplication(B,A))) | leq(A,strong_iteration(B)). [para(23(a,1),915(a,2)),rewrite([23(6),22(7)])].
% 8.20/8.47 21834 $F # answer(goals). [ur(17734,b,118,a),rewrite([6437(14)]),unit_del(a,69)].
% 8.20/8.47
% 8.20/8.47 % SZS output end Refutation
% 8.20/8.47 ============================== end of proof ==========================
% 8.20/8.47
% 8.20/8.47 ============================== STATISTICS ============================
% 8.20/8.47
% 8.20/8.47 Given=3365. Generated=477338. Kept=21804. proofs=1.
% 8.20/8.47 Usable=3181. Sos=9985. Demods=729. Limbo=0, Disabled=8658. Hints=0.
% 8.20/8.47 Megabytes=14.04.
% 8.20/8.47 User_CPU=7.20, System_CPU=0.27, Wall_clock=7.
% 8.20/8.47
% 8.20/8.47 ============================== end of statistics =====================
% 8.20/8.47
% 8.20/8.47 ============================== end of search =========================
% 8.20/8.47
% 8.20/8.47 THEOREM PROVED
% 8.20/8.47 % SZS status Theorem
% 8.20/8.47
% 8.20/8.47 Exiting with 1 proof.
% 8.20/8.47
% 8.20/8.47 Process 17675 exit (max_proofs) Thu Jun 16 07:11:02 2022
% 8.20/8.47 Prover9 interrupted
%------------------------------------------------------------------------------