TSTP Solution File: KLE040+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE040+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 02:21:56 EDT 2022
% Result : Theorem 0.73s 1.04s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE040+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n022.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 : Thu Jun 16 09:26:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/0.99 ============================== Prover9 ===============================
% 0.45/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.45/0.99 Process 24902 was started by sandbox2 on n022.cluster.edu,
% 0.45/0.99 Thu Jun 16 09:26:33 2022
% 0.45/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24749_n022.cluster.edu".
% 0.45/0.99 ============================== end of head ===========================
% 0.45/0.99
% 0.45/0.99 ============================== INPUT =================================
% 0.45/0.99
% 0.45/0.99 % Reading from file /tmp/Prover9_24749_n022.cluster.edu
% 0.45/0.99
% 0.45/0.99 set(prolog_style_variables).
% 0.45/0.99 set(auto2).
% 0.45/0.99 % set(auto2) -> set(auto).
% 0.45/0.99 % set(auto) -> set(auto_inference).
% 0.45/0.99 % set(auto) -> set(auto_setup).
% 0.45/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.45/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/0.99 % set(auto) -> set(auto_limits).
% 0.45/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/0.99 % set(auto) -> set(auto_denials).
% 0.45/0.99 % set(auto) -> set(auto_process).
% 0.45/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.45/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.45/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.45/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.45/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.45/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.45/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.45/0.99 % set(auto2) -> assign(stats, some).
% 0.45/0.99 % set(auto2) -> clear(echo_input).
% 0.45/0.99 % set(auto2) -> set(quiet).
% 0.45/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.45/0.99 % set(auto2) -> clear(print_given).
% 0.45/0.99 assign(lrs_ticks,-1).
% 0.45/0.99 assign(sos_limit,10000).
% 0.45/0.99 assign(order,kbo).
% 0.45/0.99 set(lex_order_vars).
% 0.45/0.99 clear(print_given).
% 0.45/0.99
% 0.45/0.99 % formulas(sos). % not echoed (17 formulas)
% 0.45/0.99
% 0.45/0.99 ============================== end of input ==========================
% 0.45/0.99
% 0.45/0.99 % From the command line: assign(max_seconds, 300).
% 0.45/0.99
% 0.45/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.00
% 0.45/1.00 % Formulas that are not ordinary clauses:
% 0.45/1.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 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].
% 0.45/1.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 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].
% 0.45/1.00 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 15 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 16 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 17 -(all X0 (leq(multiplication(star(X0),star(X0)),star(X0)) & leq(star(X0),multiplication(star(X0),star(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.04
% 0.73/1.04 ============================== end of process non-clausal formulas ===
% 0.73/1.04
% 0.73/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.04
% 0.73/1.04 ============================== PREDICATE ELIMINATION =================
% 0.73/1.04
% 0.73/1.04 ============================== end predicate elimination =============
% 0.73/1.04
% 0.73/1.04 Auto_denials:
% 0.73/1.04 % copying label goals to answer in negative clause
% 0.73/1.04
% 0.73/1.04 Term ordering decisions:
% 0.73/1.04
% 0.73/1.04 % Assigning unary symbol star kb_weight 0 and highest precedence (8).
% 0.73/1.04 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. star=0.
% 0.73/1.04
% 0.73/1.04 ============================== end of process initial clauses ========
% 0.73/1.04
% 0.73/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.04
% 0.73/1.04 ============================== end of clauses for search =============
% 0.73/1.04
% 0.73/1.04 ============================== SEARCH ================================
% 0.73/1.04
% 0.73/1.04 % Starting search at 0.01 seconds.
% 0.73/1.04
% 0.73/1.04 ============================== PROOF =================================
% 0.73/1.04 % SZS status Theorem
% 0.73/1.04 % SZS output start Refutation
% 0.73/1.04
% 0.73/1.04 % Proof 1 at 0.05 (+ 0.00) seconds: goals.
% 0.73/1.04 % Length of proof is 38.
% 0.73/1.04 % Level of proof is 9.
% 0.73/1.04 % Maximum clause weight is 16.000.
% 0.73/1.04 % Given clauses 87.
% 0.73/1.04
% 0.73/1.04 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 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].
% 0.73/1.04 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 15 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 16 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 17 -(all X0 (leq(multiplication(star(X0),star(X0)),star(X0)) & leq(star(X0),multiplication(star(X0),star(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.04 19 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.73/1.04 20 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.73/1.04 24 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.73/1.04 25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(13)].
% 0.73/1.04 26 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)].
% 0.73/1.04 27 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.73/1.04 28 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(27),rewrite([24(2)]),flip(a)].
% 0.73/1.04 30 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.73/1.04 31 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(30),flip(a)].
% 0.73/1.04 34 -leq(multiplication(star(c1),star(c1)),star(c1)) | -leq(star(c1),multiplication(star(c1),star(c1))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 0.73/1.04 35 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.73/1.04 36 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.73/1.04 37 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom). [clausify(15)].
% 0.73/1.04 38 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(37),rewrite([24(2)])].
% 0.73/1.04 39 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(16)].
% 0.73/1.04 40 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(39),rewrite([24(2)])].
% 0.73/1.04 43 addition(A,addition(A,B)) = addition(A,B). [para(28(a,1),19(a,1)),rewrite([24(1),24(2),28(2,R),19(1),24(3)])].
% 0.73/1.04 46 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(20(a,1),31(a,1,1)),rewrite([24(4)]),flip(a)].
% 0.73/1.04 50 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(35,a,26,a),rewrite([24(6)])].
% 0.73/1.04 77 leq(A,addition(A,B)). [hyper(36,b,43,a)].
% 0.73/1.04 78 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(31(a,1),77(a,2))].
% 0.73/1.04 190 addition(one,addition(star(A),multiplication(star(A),A))) = star(A). [para(50(a,1),28(a,1)),rewrite([28(7),24(6)]),flip(a)].
% 0.73/1.04 349 addition(one,star(A)) = star(A). [para(190(a,1),43(a,1,2)),rewrite([190(9)])].
% 0.73/1.04 352 leq(A,multiplication(A,star(B))). [para(190(a,1),78(a,2,2)),rewrite([20(2)])].
% 0.73/1.04 359 -leq(multiplication(star(c1),star(c1)),star(c1)) # answer(goals). [back_unit_del(34),unit_del(b,352)].
% 0.73/1.04 380 -leq(multiplication(star(c1),addition(one,c1)),star(c1)) # answer(goals). [ur(40,b,359,a),rewrite([46(7,R),24(5)])].
% 0.73/1.04 383 $F # answer(goals). [ur(38,b,380,a),rewrite([24(8),28(8),24(7),28(8,R),24(7),46(7,R),24(6),349(6)]),unit_del(a,25)].
% 0.73/1.04
% 0.73/1.04 % SZS output end Refutation
% 0.73/1.04 ============================== end of proof ==========================
% 0.73/1.04
% 0.73/1.04 ============================== STATISTICS ============================
% 0.73/1.04
% 0.73/1.04 Given=87. Generated=1297. Kept=360. proofs=1.
% 0.73/1.04 Usable=70. Sos=243. Demods=66. Limbo=0, Disabled=65. Hints=0.
% 0.73/1.04 Megabytes=0.38.
% 0.73/1.04 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.73/1.04
% 0.73/1.04 ============================== end of statistics =====================
% 0.73/1.04
% 0.73/1.04 ============================== end of search =========================
% 0.73/1.04
% 0.73/1.04 THEOREM PROVED
% 0.73/1.04 % SZS status Theorem
% 0.73/1.04
% 0.73/1.04 Exiting with 1 proof.
% 0.73/1.04
% 0.73/1.04 Process 24902 exit (max_proofs) Thu Jun 16 09:26:33 2022
% 0.73/1.04 Prover9 interrupted
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