TSTP Solution File: KLE139+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE139+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 02:22:25 EDT 2022
% Result : Theorem 0.92s 1.17s
% Output : Refutation 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE139+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 12:07:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 9791 was started by sandbox2 on n019.cluster.edu,
% 0.43/0.99 Thu Jun 16 12:07:25 2022
% 0.43/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_9638_n019.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_9638_n019.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (19 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.43/0.99 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.92/1.17 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 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].
% 0.92/1.17 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 19 -(all X0 (leq(strong_iteration(X0),addition(multiplication(strong_iteration(X0),X0),one)) & leq(addition(multiplication(strong_iteration(X0),X0),one),strong_iteration(X0)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.92/1.17
% 0.92/1.17 ============================== end of process non-clausal formulas ===
% 0.92/1.17
% 0.92/1.17 ============================== PROCESS INITIAL CLAUSES ===============
% 0.92/1.17
% 0.92/1.17 ============================== PREDICATE ELIMINATION =================
% 0.92/1.17
% 0.92/1.17 ============================== end predicate elimination =============
% 0.92/1.17
% 0.92/1.17 Auto_denials:
% 0.92/1.17 % copying label goals to answer in negative clause
% 0.92/1.17
% 0.92/1.17 Term ordering decisions:
% 0.92/1.17 Function symbol KB weights: one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 0.92/1.17
% 0.92/1.17 ============================== end of process initial clauses ========
% 0.92/1.17
% 0.92/1.17 ============================== CLAUSES FOR SEARCH ====================
% 0.92/1.17
% 0.92/1.17 ============================== end of clauses for search =============
% 0.92/1.17
% 0.92/1.17 ============================== SEARCH ================================
% 0.92/1.17
% 0.92/1.17 % Starting search at 0.01 seconds.
% 0.92/1.17
% 0.92/1.17 ============================== PROOF =================================
% 0.92/1.17 % SZS status Theorem
% 0.92/1.17 % SZS output start Refutation
% 0.92/1.17
% 0.92/1.17 % Proof 1 at 0.18 (+ 0.01) seconds: goals.
% 0.92/1.17 % Length of proof is 54.
% 0.92/1.17 % Level of proof is 8.
% 0.92/1.17 % Maximum clause weight is 18.000.
% 0.92/1.17 % Given clauses 282.
% 0.92/1.17
% 0.92/1.17 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 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].
% 0.92/1.17 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 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].
% 0.92/1.17 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].
% 0.92/1.17 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.17 19 -(all X0 (leq(strong_iteration(X0),addition(multiplication(strong_iteration(X0),X0),one)) & leq(addition(multiplication(strong_iteration(X0),X0),one),strong_iteration(X0)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.92/1.17 20 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.92/1.17 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 0.92/1.17 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.92/1.17 23 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.92/1.17 24 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(10)].
% 0.92/1.17 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.92/1.17 26 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom). [clausify(11)].
% 0.92/1.17 27 addition(one,multiplication(A,star(A))) = star(A). [copy(26),flip(a)].
% 0.92/1.17 28 star(A) = addition(one,multiplication(star(A),A)) # label(star_unfold2) # label(axiom). [clausify(12)].
% 0.92/1.17 29 addition(one,multiplication(star(A),A)) = star(A). [copy(28),flip(a)].
% 0.92/1.17 30 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 0.92/1.17 31 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(30),rewrite([25(5)]),flip(a)].
% 0.92/1.17 32 strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) # label(isolation) # label(axiom). [clausify(17)].
% 0.92/1.17 33 addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A). [copy(32),flip(a)].
% 0.92/1.17 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.92/1.17 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 0.92/1.17 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 0.92/1.17 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 0.92/1.17 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 0.92/1.17 41 -leq(strong_iteration(c1),addition(multiplication(strong_iteration(c1),c1),one)) | -leq(addition(multiplication(strong_iteration(c1),c1),one),strong_iteration(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 0.92/1.17 42 -leq(strong_iteration(c1),addition(one,multiplication(strong_iteration(c1),c1))) | -leq(addition(one,multiplication(strong_iteration(c1),c1)),strong_iteration(c1)) # answer(goals). [copy(41),rewrite([25(8),25(15)])].
% 0.92/1.17 44 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 0.92/1.17 58 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),38(a,1,1)),rewrite([25(4)]),flip(a)].
% 0.92/1.17 62 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(20(a,1),40(a,2,1)),rewrite([24(3),25(3)])].
% 0.92/1.17 64 addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A). [para(27(a,1),40(a,2,1)),rewrite([23(2),36(3)])].
% 0.92/1.17 66 addition(A,multiplication(B,multiplication(strong_iteration(B),A))) = multiplication(strong_iteration(B),A). [para(31(a,1),40(a,2,1)),rewrite([23(2),36(3)])].
% 0.92/1.17 67 addition(multiplication(star(A),B),multiplication(strong_iteration(A),zero)) = multiplication(strong_iteration(A),B). [para(33(a,1),40(a,2,1)),rewrite([36(6),24(5)])].
% 0.92/1.17 68 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(36(a,1),40(a,1,1)),rewrite([25(6)])].
% 0.92/1.17 69 addition(multiplication(A,B),multiplication(C,multiplication(D,B))) = multiplication(addition(A,multiplication(C,D)),B). [para(36(a,1),40(a,1,2))].
% 0.92/1.17 70 leq(A,A). [hyper(44,b,21,a)].
% 0.92/1.17 257 multiplication(star(A),A) = multiplication(A,star(A)). [para(64(a,1),58(a,2)),rewrite([25(4),29(4)]),flip(a)].
% 0.92/1.17 278 multiplication(A,multiplication(strong_iteration(A),zero)) = multiplication(strong_iteration(A),zero). [para(66(a,1),62(a,1)),flip(a)].
% 0.92/1.17 329 addition(multiplication(A,star(A)),multiplication(strong_iteration(A),zero)) = multiplication(strong_iteration(A),A). [para(257(a,1),67(a,1,1))].
% 0.92/1.17 331 addition(multiplication(A,zero),multiplication(B,C)) = multiplication(addition(B,multiplication(A,zero)),C). [para(24(a,1),68(a,1,1,2))].
% 0.92/1.17 363 addition(multiplication(A,B),multiplication(C,zero)) = multiplication(addition(A,multiplication(C,zero)),B). [para(24(a,1),69(a,1,2,2))].
% 0.92/1.17 383 multiplication(addition(A,multiplication(strong_iteration(A),zero)),star(A)) = multiplication(strong_iteration(A),A). [back_rewrite(329),rewrite([363(6)])].
% 0.92/1.17 1573 multiplication(addition(A,multiplication(strong_iteration(A),zero)),B) = multiplication(A,addition(B,multiplication(strong_iteration(A),zero))). [para(278(a,1),38(a,1,1)),rewrite([331(5),25(9)])].
% 0.92/1.17 1610 multiplication(strong_iteration(A),A) = multiplication(A,strong_iteration(A)). [back_rewrite(383),rewrite([1573(6),33(5)]),flip(a)].
% 0.92/1.17 1619 $F # answer(goals). [back_rewrite(42),rewrite([1610(7),31(8),1610(10),31(11)]),merge(b),unit_del(a,70)].
% 0.92/1.17
% 0.92/1.17 % SZS output end Refutation
% 0.92/1.17 ============================== end of proof ==========================
% 0.92/1.17
% 0.92/1.17 ============================== STATISTICS ============================
% 0.92/1.17
% 0.92/1.17 Given=282. Generated=8503. Kept=1588. proofs=1.
% 0.92/1.17 Usable=230. Sos=1137. Demods=300. Limbo=9, Disabled=232. Hints=0.
% 0.92/1.17 Megabytes=1.54.
% 0.92/1.17 User_CPU=0.18, System_CPU=0.01, Wall_clock=0.
% 0.92/1.17
% 0.92/1.17 ============================== end of statistics =====================
% 0.92/1.17
% 0.92/1.17 ============================== end of search =========================
% 0.92/1.17
% 0.92/1.17 THEOREM PROVED
% 0.92/1.17 % SZS status Theorem
% 0.92/1.17
% 0.92/1.17 Exiting with 1 proof.
% 0.92/1.17
% 0.92/1.17 Process 9791 exit (max_proofs) Thu Jun 16 12:07:25 2022
% 0.92/1.18 Prover9 interrupted
%------------------------------------------------------------------------------