TSTP Solution File: KLE039+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE039+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 02:21:55 EDT 2022
% Result : Theorem 0.73s 1.06s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE039+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 09:30:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 11436 was started by sandbox on n019.cluster.edu,
% 0.43/1.00 Thu Jun 16 09:30:25 2022
% 0.43/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11283_n019.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_11283_n019.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (17 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.73/1.06 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].
% 0.73/1.06 17 -(all X0 (leq(star(star(X0)),star(X0)) & leq(star(X0),star(star(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.06
% 0.73/1.06 ============================== end of process non-clausal formulas ===
% 0.73/1.06
% 0.73/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.06
% 0.73/1.06 ============================== PREDICATE ELIMINATION =================
% 0.73/1.06
% 0.73/1.06 ============================== end predicate elimination =============
% 0.73/1.06
% 0.73/1.06 Auto_denials:
% 0.73/1.06 % copying label goals to answer in negative clause
% 0.73/1.06
% 0.73/1.06 Term ordering decisions:
% 0.73/1.06
% 0.73/1.06 % Assigning unary symbol star kb_weight 0 and highest precedence (8).
% 0.73/1.06 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. star=0.
% 0.73/1.06
% 0.73/1.06 ============================== end of process initial clauses ========
% 0.73/1.06
% 0.73/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.06
% 0.73/1.06 ============================== end of clauses for search =============
% 0.73/1.06
% 0.73/1.06 ============================== SEARCH ================================
% 0.73/1.06
% 0.73/1.06 % Starting search at 0.01 seconds.
% 0.73/1.06
% 0.73/1.06 ============================== PROOF =================================
% 0.73/1.06 % SZS status Theorem
% 0.73/1.06 % SZS output start Refutation
% 0.73/1.06
% 0.73/1.06 % Proof 1 at 0.07 (+ 0.00) seconds: goals.
% 0.73/1.06 % Length of proof is 68.
% 0.73/1.06 % Level of proof is 14.
% 0.73/1.06 % Maximum clause weight is 13.000.
% 0.73/1.06 % Given clauses 117.
% 0.73/1.06
% 0.73/1.06 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.06 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].
% 0.73/1.06 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.06 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.06 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.06 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].
% 0.73/1.06 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].
% 0.73/1.06 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.06 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.06 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.06 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].
% 0.73/1.06 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].
% 0.73/1.06 17 -(all X0 (leq(star(star(X0)),star(X0)) & leq(star(X0),star(star(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.06 19 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.73/1.06 20 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.73/1.06 21 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.73/1.06 24 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.73/1.06 25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(13)].
% 0.73/1.06 26 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)].
% 0.73/1.06 27 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.73/1.06 28 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(27),rewrite([24(2)]),flip(a)].
% 0.73/1.06 30 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.73/1.06 31 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(30),flip(a)].
% 0.73/1.06 32 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.73/1.06 33 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(32),flip(a)].
% 0.73/1.06 34 -leq(star(star(c1)),star(c1)) | -leq(star(c1),star(star(c1))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 0.73/1.06 35 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.73/1.06 36 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.73/1.06 37 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom). [clausify(15)].
% 0.73/1.06 38 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(37),rewrite([24(2)])].
% 0.73/1.06 39 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(16)].
% 0.73/1.06 40 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(39),rewrite([24(2)])].
% 0.73/1.06 41 leq(addition(one,star(one)),star(one)). [para(21(a,1),25(a,1,2))].
% 0.73/1.06 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)])].
% 0.73/1.06 46 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(20(a,1),31(a,1,1)),rewrite([24(4)]),flip(a)].
% 0.73/1.06 50 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(35,a,26,a),rewrite([24(6)])].
% 0.73/1.06 52 leq(A,A). [hyper(36,b,19,a)].
% 0.73/1.06 56 -leq(multiplication(A,B),B) | leq(multiplication(star(A),multiplication(A,B)),B). [para(19(a,1),38(a,1))].
% 0.73/1.06 57 -leq(addition(A,B),one) | leq(multiplication(star(B),A),one). [para(20(a,1),38(a,1,2))].
% 0.73/1.06 65 -leq(addition(A,B),B) | leq(multiplication(A,star(one)),B). [para(20(a,1),40(a,1,2))].
% 0.73/1.06 72 addition(one,star(one)) = star(one). [hyper(35,a,41,a),rewrite([24(7),28(7,R),19(6)])].
% 0.73/1.06 77 leq(A,addition(A,B)). [hyper(36,b,43,a)].
% 0.73/1.06 78 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(31(a,1),77(a,2))].
% 0.73/1.06 79 leq(multiplication(A,B),multiplication(addition(A,C),B)). [para(33(a,1),77(a,2))].
% 0.73/1.06 190 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)].
% 0.73/1.06 199 -leq(A,one) | leq(multiplication(star(A),A),one). [para(19(a,1),57(a,1))].
% 0.73/1.06 212 leq(star(one),one). [hyper(199,a,52,a),rewrite([20(4)])].
% 0.73/1.06 219 star(one) = one. [hyper(35,a,212,a),rewrite([24(4),72(4)])].
% 0.73/1.06 222 -leq(addition(A,B),B) | leq(A,B). [back_rewrite(65),rewrite([219(4),20(4)])].
% 0.73/1.06 349 addition(one,star(A)) = star(A). [para(190(a,1),43(a,1,2)),rewrite([190(9)])].
% 0.73/1.06 351 addition(one,multiplication(star(A),addition(A,one))) = star(A). [para(46(a,2),190(a,1,2))].
% 0.73/1.06 352 leq(A,multiplication(A,star(B))). [para(190(a,1),78(a,2,2)),rewrite([20(2)])].
% 0.73/1.06 353 leq(A,multiplication(star(B),A)). [para(190(a,1),79(a,2,1)),rewrite([21(2)])].
% 0.73/1.06 355 leq(one,addition(star(A),multiplication(star(A),A))). [para(190(a,1),222(a,1)),unit_del(a,77)].
% 0.73/1.06 359 addition(A,multiplication(A,star(B))) = multiplication(A,star(B)). [hyper(35,a,352,a)].
% 0.73/1.06 379 addition(star(A),one) = star(A). [para(349(a,1),24(a,1)),flip(a)].
% 0.73/1.06 387 addition(star(A),multiplication(star(A),A)) = star(A). [hyper(35,a,355,a),rewrite([190(6)]),flip(a)].
% 0.73/1.06 389 leq(one,multiplication(star(A),addition(A,one))). [para(46(a,2),355(a,2))].
% 0.73/1.06 400 multiplication(star(A),addition(A,one)) = star(A). [hyper(35,a,389,a),rewrite([351(6)]),flip(a)].
% 0.73/1.06 420 leq(addition(A,one),star(A)). [para(400(a,1),353(a,2))].
% 0.73/1.06 422 multiplication(star(star(A)),star(A)) = star(star(A)). [para(379(a,1),400(a,1,2))].
% 0.73/1.06 429 leq(star(A),star(star(A))). [para(379(a,1),420(a,1))].
% 0.73/1.06 430 -leq(star(star(c1)),star(c1)) # answer(goals). [back_unit_del(34),unit_del(b,429)].
% 0.73/1.06 523 leq(multiplication(star(A),star(A)),star(A)). [para(387(a,1),40(a,1)),unit_del(a,52)].
% 0.73/1.06 546 leq(multiplication(star(star(A)),multiplication(star(A),star(A))),star(A)). [hyper(56,a,523,a)].
% 0.73/1.06 547 multiplication(star(A),star(A)) = star(A). [hyper(35,a,523,a),rewrite([24(5),359(5)])].
% 0.73/1.06 548 leq(star(star(A)),star(A)). [back_rewrite(546),rewrite([547(5),422(4)])].
% 0.73/1.06 549 $F # answer(goals). [resolve(548,a,430,a)].
% 0.73/1.06
% 0.73/1.06 % SZS output end Refutation
% 0.73/1.06 ============================== end of proof ==========================
% 0.73/1.06
% 0.73/1.06 ============================== STATISTICS ============================
% 0.73/1.06
% 0.73/1.06 Given=117. Generated=1888. Kept=526. proofs=1.
% 0.73/1.06 Usable=94. Sos=364. Demods=85. Limbo=1, Disabled=84. Hints=0.
% 0.73/1.06 Megabytes=0.52.
% 0.73/1.06 User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.73/1.06
% 0.73/1.06 ============================== end of statistics =====================
% 0.73/1.06
% 0.73/1.06 ============================== end of search =========================
% 0.73/1.06
% 0.73/1.06 THEOREM PROVED
% 0.73/1.06 % SZS status Theorem
% 0.73/1.06
% 0.73/1.06 Exiting with 1 proof.
% 0.73/1.06
% 0.73/1.06 Process 11436 exit (max_proofs) Thu Jun 16 09:30:25 2022
% 0.73/1.06 Prover9 interrupted
%------------------------------------------------------------------------------