TSTP Solution File: KLE150+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE150+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 02:22:30 EDT 2022
% Result : Theorem 0.76s 1.03s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE150+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 08:14:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.76/1.02 ============================== Prover9 ===============================
% 0.76/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.02 Process 11042 was started by sandbox2 on n007.cluster.edu,
% 0.76/1.02 Thu Jun 16 08:14:42 2022
% 0.76/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10888_n007.cluster.edu".
% 0.76/1.02 ============================== end of head ===========================
% 0.76/1.02
% 0.76/1.02 ============================== INPUT =================================
% 0.76/1.02
% 0.76/1.02 % Reading from file /tmp/Prover9_10888_n007.cluster.edu
% 0.76/1.02
% 0.76/1.02 set(prolog_style_variables).
% 0.76/1.02 set(auto2).
% 0.76/1.02 % set(auto2) -> set(auto).
% 0.76/1.02 % set(auto) -> set(auto_inference).
% 0.76/1.02 % set(auto) -> set(auto_setup).
% 0.76/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.02 % set(auto) -> set(auto_limits).
% 0.76/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.02 % set(auto) -> set(auto_denials).
% 0.76/1.02 % set(auto) -> set(auto_process).
% 0.76/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.02 % set(auto2) -> assign(stats, some).
% 0.76/1.02 % set(auto2) -> clear(echo_input).
% 0.76/1.02 % set(auto2) -> set(quiet).
% 0.76/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.02 % set(auto2) -> clear(print_given).
% 0.76/1.02 assign(lrs_ticks,-1).
% 0.76/1.02 assign(sos_limit,10000).
% 0.76/1.02 assign(order,kbo).
% 0.76/1.02 set(lex_order_vars).
% 0.76/1.02 clear(print_given).
% 0.76/1.02
% 0.76/1.02 % formulas(sos). % not echoed (19 formulas)
% 0.76/1.02
% 0.76/1.02 ============================== end of input ==========================
% 0.76/1.02
% 0.76/1.02 % From the command line: assign(max_seconds, 300).
% 0.76/1.02
% 0.76/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.02
% 0.76/1.02 % Formulas that are not ordinary clauses:
% 0.76/1.02 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 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].
% 0.76/1.02 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 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].
% 0.76/1.02 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 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].
% 0.76/1.02 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].
% 0.76/1.02 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 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].
% 0.76/1.02 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].
% 0.76/1.03 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.03 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 19 -(all X0 (leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) & leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.03
% 0.76/1.03 ============================== end of process non-clausal formulas ===
% 0.76/1.03
% 0.76/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.03
% 0.76/1.03 ============================== PREDICATE ELIMINATION =================
% 0.76/1.03
% 0.76/1.03 ============================== end predicate elimination =============
% 0.76/1.03
% 0.76/1.03 Auto_denials:
% 0.76/1.03 % copying label goals to answer in negative clause
% 0.76/1.03
% 0.76/1.03 Term ordering decisions:
% 0.76/1.03 Function symbol KB weights: one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 0.76/1.03
% 0.76/1.03 ============================== end of process initial clauses ========
% 0.76/1.03
% 0.76/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.03
% 0.76/1.03 ============================== end of clauses for search =============
% 0.76/1.03
% 0.76/1.03 ============================== SEARCH ================================
% 0.76/1.03
% 0.76/1.03 % Starting search at 0.01 seconds.
% 0.76/1.03
% 0.76/1.03 ============================== PROOF =================================
% 0.76/1.03 % SZS status Theorem
% 0.76/1.03 % SZS output start Refutation
% 0.76/1.03
% 0.76/1.03 % Proof 1 at 0.02 (+ 0.00) seconds: goals.
% 0.76/1.03 % Length of proof is 34.
% 0.76/1.03 % Level of proof is 7.
% 0.76/1.03 % Maximum clause weight is 20.000.
% 0.76/1.03 % Given clauses 43.
% 0.76/1.03
% 0.76/1.03 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.03 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.03 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 19 -(all X0 (leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) & leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.03 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 0.76/1.03 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.76/1.03 24 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(10)].
% 0.76/1.03 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.76/1.03 26 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom). [clausify(11)].
% 0.76/1.03 27 addition(one,multiplication(A,star(A))) = star(A). [copy(26),flip(a)].
% 0.76/1.03 30 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 0.76/1.03 31 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(30),rewrite([25(5)]),flip(a)].
% 0.76/1.03 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.76/1.03 41 -leq(strong_iteration(multiplication(c1,zero)),addition(one,multiplication(c1,zero))) | -leq(addition(one,multiplication(c1,zero)),strong_iteration(multiplication(c1,zero))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 0.76/1.03 42 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(18)].
% 0.76/1.03 43 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 0.76/1.03 44 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction1) # label(axiom). [clausify(13)].
% 0.76/1.03 45 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(44),rewrite([25(2)])].
% 0.76/1.03 55 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)). [para(36(a,1),27(a,1,2))].
% 0.76/1.03 56 addition(one,multiplication(A,multiplication(B,strong_iteration(multiplication(A,B))))) = strong_iteration(multiplication(A,B)). [para(36(a,1),31(a,1,2))].
% 0.76/1.03 69 leq(A,A). [hyper(43,b,21,a)].
% 0.76/1.03 81 leq(star(A),strong_iteration(A)). [para(31(a,1),45(a,1)),rewrite([22(6)]),unit_del(a,69)].
% 0.76/1.03 108 addition(star(A),strong_iteration(A)) = strong_iteration(A). [hyper(42,a,81,a)].
% 0.76/1.03 120 addition(one,multiplication(A,zero)) = star(multiplication(A,zero)). [para(24(a,1),55(a,1,2,2))].
% 0.76/1.03 128 -leq(strong_iteration(multiplication(c1,zero)),star(multiplication(c1,zero))) # answer(goals). [back_rewrite(41),rewrite([120(9),120(14)]),unit_del(b,81)].
% 0.76/1.03 129 strong_iteration(multiplication(c1,zero)) != star(multiplication(c1,zero)) # answer(goals). [ur(43,a,128,a),rewrite([25(9),108(9)])].
% 0.76/1.03 135 strong_iteration(multiplication(A,zero)) = star(multiplication(A,zero)). [para(24(a,1),56(a,1,2,2)),rewrite([120(4)]),flip(a)].
% 0.76/1.03 136 $F # answer(goals). [resolve(135,a,129,a)].
% 0.76/1.03
% 0.76/1.03 % SZS output end Refutation
% 0.76/1.03 ============================== end of proof ==========================
% 0.76/1.03
% 0.76/1.03 ============================== STATISTICS ============================
% 0.76/1.03
% 0.76/1.03 Given=43. Generated=401. Kept=106. proofs=1.
% 0.76/1.03 Usable=38. Sos=57. Demods=44. Limbo=0, Disabled=30. Hints=0.
% 0.76/1.03 Megabytes=0.15.
% 0.76/1.03 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.76/1.03
% 0.76/1.03 ============================== end of statistics =====================
% 0.76/1.03
% 0.76/1.03 ============================== end of search =========================
% 0.76/1.03
% 0.76/1.03 THEOREM PROVED
% 0.76/1.03 % SZS status Theorem
% 0.76/1.03
% 0.76/1.03 Exiting with 1 proof.
% 0.76/1.03
% 0.76/1.03 Process 11042 exit (max_proofs) Thu Jun 16 08:14:42 2022
% 0.76/1.04 Prover9 interrupted
%------------------------------------------------------------------------------