TSTP Solution File: KLE138+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %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 : 600s
% DateTime : Sun Jul 17 02:22:24 EDT 2022
% Result : Theorem 0.38s 0.99s
% Output : Refutation 0.38s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15 % Problem : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.16 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.37 % Computer : n013.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 600
% 0.13/0.37 % DateTime : Thu Jun 16 12:45:29 EDT 2022
% 0.13/0.37 % CPUTime :
% 0.38/0.99 ============================== Prover9 ===============================
% 0.38/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.38/0.99 Process 2704 was started by sandbox2 on n013.cluster.edu,
% 0.38/0.99 Thu Jun 16 12:45:29 2022
% 0.38/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2549_n013.cluster.edu".
% 0.38/0.99 ============================== end of head ===========================
% 0.38/0.99
% 0.38/0.99 ============================== INPUT =================================
% 0.38/0.99
% 0.38/0.99 % Reading from file /tmp/Prover9_2549_n013.cluster.edu
% 0.38/0.99
% 0.38/0.99 set(prolog_style_variables).
% 0.38/0.99 set(auto2).
% 0.38/0.99 % set(auto2) -> set(auto).
% 0.38/0.99 % set(auto) -> set(auto_inference).
% 0.38/0.99 % set(auto) -> set(auto_setup).
% 0.38/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.38/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.38/0.99 % set(auto) -> set(auto_limits).
% 0.38/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.38/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.38/0.99 % set(auto) -> set(auto_denials).
% 0.38/0.99 % set(auto) -> set(auto_process).
% 0.38/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.38/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.38/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.38/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.38/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.38/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.38/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.38/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.38/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.38/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.38/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.38/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.38/0.99 % set(auto2) -> assign(stats, some).
% 0.38/0.99 % set(auto2) -> clear(echo_input).
% 0.38/0.99 % set(auto2) -> set(quiet).
% 0.38/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.38/0.99 % set(auto2) -> clear(print_given).
% 0.38/0.99 assign(lrs_ticks,-1).
% 0.38/0.99 assign(sos_limit,10000).
% 0.38/0.99 assign(order,kbo).
% 0.38/0.99 set(lex_order_vars).
% 0.38/0.99 clear(print_given).
% 0.38/0.99
% 0.38/0.99 % formulas(sos). % not echoed (19 formulas)
% 0.38/0.99
% 0.38/0.99 ============================== end of input ==========================
% 0.38/0.99
% 0.38/0.99 % From the command line: assign(max_seconds, 300).
% 0.38/0.99
% 0.38/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.38/0.99
% 0.38/0.99 % Formulas that are not ordinary clauses:
% 0.38/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 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].
% 0.38/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 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].
% 0.38/0.99 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 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].
% 0.38/0.99 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].
% 0.38/0.99 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 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].
% 0.38/0.99 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].
% 0.38/0.99 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 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].
% 0.38/0.99 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99
% 0.38/0.99 ============================== end of process non-clausal formulas ===
% 0.38/0.99
% 0.38/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.38/0.99
% 0.38/0.99 ============================== PREDICATE ELIMINATION =================
% 0.38/0.99
% 0.38/0.99 ============================== end predicate elimination =============
% 0.38/0.99
% 0.38/0.99 Auto_denials:
% 0.38/0.99 % copying label goals to answer in negative clause
% 0.38/0.99
% 0.38/0.99 Term ordering decisions:
% 0.38/0.99 Function symbol KB weights: one=1. zero=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 0.38/0.99
% 0.38/0.99 ============================== end of process initial clauses ========
% 0.38/0.99
% 0.38/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.38/0.99
% 0.38/0.99 ============================== end of clauses for search =============
% 0.38/0.99
% 0.38/0.99 ============================== SEARCH ================================
% 0.38/0.99
% 0.38/0.99 % Starting search at 0.01 seconds.
% 0.38/0.99
% 0.38/0.99 ============================== PROOF =================================
% 0.38/0.99 % SZS status Theorem
% 0.38/0.99 % SZS output start Refutation
% 0.38/0.99
% 0.38/0.99 % Proof 1 at 0.01 (+ 0.00) seconds: goals.
% 0.38/0.99 % Length of proof is 12.
% 0.38/0.99 % Level of proof is 4.
% 0.38/0.99 % Maximum clause weight is 9.000.
% 0.38/0.99 % Given clauses 9.
% 0.38/0.99
% 0.38/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.38/0.99 19 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.38/0.99 23 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(10)].
% 0.38/0.99 24 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.38/0.99 29 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 0.38/0.99 30 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(29),rewrite([24(5)]),flip(a)].
% 0.38/0.99 40 strong_iteration(zero) != one # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 0.38/0.99 52 strong_iteration(zero) = one. [para(23(a,1),30(a,1,2)),rewrite([19(3)]),flip(a)].
% 0.38/0.99 53 $F # answer(goals). [resolve(52,a,40,a)].
% 0.38/0.99
% 0.38/0.99 % SZS output end Refutation
% 0.38/0.99 ============================== end of proof ==========================
% 0.38/0.99
% 0.38/0.99 ============================== STATISTICS ============================
% 0.38/0.99
% 0.38/0.99 Given=9. Generated=46. Kept=24. proofs=1.
% 0.38/0.99 Usable=9. Sos=13. Demods=17. Limbo=1, Disabled=20. Hints=0.
% 0.38/0.99 Megabytes=0.06.
% 0.38/0.99 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.38/0.99
% 0.38/0.99 ============================== end of statistics =====================
% 0.38/0.99
% 0.38/0.99 ============================== end of search =========================
% 0.38/0.99
% 0.38/0.99 THEOREM PROVED
% 0.38/0.99 % SZS status Theorem
% 0.38/0.99
% 0.38/0.99 Exiting with 1 proof.
% 0.38/0.99
% 0.38/0.99 Process 2704 exit (max_proofs) Thu Jun 16 12:45:29 2022
% 0.38/0.99 Prover9 interrupted
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