TSTP Solution File: KLE151+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE151+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 02:22:31 EDT 2022
% Result : Theorem 0.49s 1.07s
% Output : Refutation 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE151+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n013.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
% 0.13/0.36 % WCLimit : 600
% 0.13/0.36 % DateTime : Thu Jun 16 07:12:59 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.49/1.06 ============================== Prover9 ===============================
% 0.49/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.49/1.06 Process 8491 was started by sandbox2 on n013.cluster.edu,
% 0.49/1.06 Thu Jun 16 07:12:59 2022
% 0.49/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8338_n013.cluster.edu".
% 0.49/1.06 ============================== end of head ===========================
% 0.49/1.06
% 0.49/1.06 ============================== INPUT =================================
% 0.49/1.06
% 0.49/1.06 % Reading from file /tmp/Prover9_8338_n013.cluster.edu
% 0.49/1.06
% 0.49/1.06 set(prolog_style_variables).
% 0.49/1.06 set(auto2).
% 0.49/1.06 % set(auto2) -> set(auto).
% 0.49/1.06 % set(auto) -> set(auto_inference).
% 0.49/1.06 % set(auto) -> set(auto_setup).
% 0.49/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.49/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.49/1.06 % set(auto) -> set(auto_limits).
% 0.49/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.49/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.49/1.06 % set(auto) -> set(auto_denials).
% 0.49/1.06 % set(auto) -> set(auto_process).
% 0.49/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.49/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.49/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.49/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.49/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.49/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.49/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.49/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.49/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.49/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.49/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.49/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.49/1.06 % set(auto2) -> assign(stats, some).
% 0.49/1.06 % set(auto2) -> clear(echo_input).
% 0.49/1.06 % set(auto2) -> set(quiet).
% 0.49/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.49/1.06 % set(auto2) -> clear(print_given).
% 0.49/1.06 assign(lrs_ticks,-1).
% 0.49/1.06 assign(sos_limit,10000).
% 0.49/1.06 assign(order,kbo).
% 0.49/1.06 set(lex_order_vars).
% 0.49/1.06 clear(print_given).
% 0.49/1.06
% 0.49/1.06 % formulas(sos). % not echoed (19 formulas)
% 0.49/1.06
% 0.49/1.06 ============================== end of input ==========================
% 0.49/1.06
% 0.49/1.06 % From the command line: assign(max_seconds, 300).
% 0.49/1.06
% 0.49/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.49/1.06
% 0.49/1.06 % Formulas that are not ordinary clauses:
% 0.49/1.06 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 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].
% 0.49/1.06 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 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].
% 0.49/1.06 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 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].
% 0.49/1.06 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].
% 0.49/1.06 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 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].
% 0.49/1.06 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].
% 0.49/1.07 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 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].
% 0.49/1.07 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 19 -(all X0 all X1 leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.49/1.07
% 0.49/1.07 ============================== end of process non-clausal formulas ===
% 0.49/1.07
% 0.49/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.49/1.07
% 0.49/1.07 ============================== PREDICATE ELIMINATION =================
% 0.49/1.07
% 0.49/1.07 ============================== end predicate elimination =============
% 0.49/1.07
% 0.49/1.07 Auto_denials:
% 0.49/1.07 % copying label goals to answer in negative clause
% 0.49/1.07
% 0.49/1.07 Term ordering decisions:
% 0.49/1.07 Function symbol KB weights: one=1. zero=1. c1=1. c2=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 0.49/1.07
% 0.49/1.07 ============================== end of process initial clauses ========
% 0.49/1.07
% 0.49/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.49/1.07
% 0.49/1.07 ============================== end of clauses for search =============
% 0.49/1.07
% 0.49/1.07 ============================== SEARCH ================================
% 0.49/1.07
% 0.49/1.07 % Starting search at 0.01 seconds.
% 0.49/1.07
% 0.49/1.07 ============================== PROOF =================================
% 0.49/1.07 % SZS status Theorem
% 0.49/1.07 % SZS output start Refutation
% 0.49/1.07
% 0.49/1.07 % Proof 1 at 0.02 (+ 0.00) seconds: goals.
% 0.49/1.07 % Length of proof is 26.
% 0.49/1.07 % Level of proof is 5.
% 0.49/1.07 % Maximum clause weight is 15.000.
% 0.49/1.07 % Given clauses 20.
% 0.49/1.07
% 0.49/1.07 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 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].
% 0.49/1.07 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 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].
% 0.49/1.07 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 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].
% 0.49/1.07 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 19 -(all X0 all X1 leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.49/1.07 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 0.49/1.07 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.49/1.07 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.49/1.07 30 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 0.49/1.07 31 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(30),rewrite([25(5)]),flip(a)].
% 0.49/1.07 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.49/1.07 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 0.49/1.07 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 0.49/1.07 41 -leq(multiplication(c1,strong_iteration(multiplication(c2,c1))),multiplication(strong_iteration(multiplication(c1,c2)),c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 0.49/1.07 43 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 0.49/1.07 48 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom). [clausify(16)].
% 0.49/1.07 49 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)). [copy(48),rewrite([25(2)])].
% 0.49/1.07 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))].
% 0.49/1.07 57 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),38(a,1,1)),rewrite([25(4)]),flip(a)].
% 0.49/1.07 69 leq(A,A). [hyper(43,b,21,a)].
% 0.49/1.07 95 -leq(multiplication(c1,strong_iteration(multiplication(c2,c1))),multiplication(c1,strong_iteration(multiplication(c2,c1)))) # answer(goals). [ur(49,b,41,a),rewrite([36(17),57(18,R),25(17),56(17)])].
% 0.49/1.07 96 $F # answer(goals). [resolve(95,a,69,a)].
% 0.49/1.07
% 0.49/1.07 % SZS output end Refutation
% 0.49/1.07 ============================== end of proof ==========================
% 0.49/1.07
% 0.49/1.07 ============================== STATISTICS ============================
% 0.49/1.07
% 0.49/1.07 Given=20. Generated=198. Kept=66. proofs=1.
% 0.49/1.07 Usable=20. Sos=45. Demods=33. Limbo=0, Disabled=20. Hints=0.
% 0.49/1.07 Megabytes=0.12.
% 0.49/1.07 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.49/1.07
% 0.49/1.07 ============================== end of statistics =====================
% 0.49/1.07
% 0.49/1.07 ============================== end of search =========================
% 0.49/1.07
% 0.49/1.07 THEOREM PROVED
% 0.49/1.07 % SZS status Theorem
% 0.49/1.07
% 0.49/1.07 Exiting with 1 proof.
% 0.49/1.07
% 0.49/1.07 Process 8491 exit (max_proofs) Thu Jun 16 07:12:59 2022
% 0.49/1.07 Prover9 interrupted
%------------------------------------------------------------------------------