TSTP Solution File: KLE141+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE141+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 0.83s 1.09s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE141+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.32 % Computer : n012.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jun 16 12:55:54 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.42/0.99 ============================== Prover9 ===============================
% 0.42/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.99 Process 32266 was started by sandbox on n012.cluster.edu,
% 0.42/0.99 Thu Jun 16 12:55:55 2022
% 0.42/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32103_n012.cluster.edu".
% 0.42/0.99 ============================== end of head ===========================
% 0.42/0.99
% 0.42/0.99 ============================== INPUT =================================
% 0.42/0.99
% 0.42/0.99 % Reading from file /tmp/Prover9_32103_n012.cluster.edu
% 0.42/0.99
% 0.42/0.99 set(prolog_style_variables).
% 0.42/0.99 set(auto2).
% 0.42/0.99 % set(auto2) -> set(auto).
% 0.42/0.99 % set(auto) -> set(auto_inference).
% 0.42/0.99 % set(auto) -> set(auto_setup).
% 0.42/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.99 % set(auto) -> set(auto_limits).
% 0.42/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.99 % set(auto) -> set(auto_denials).
% 0.42/0.99 % set(auto) -> set(auto_process).
% 0.42/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.99 % set(auto2) -> assign(stats, some).
% 0.42/0.99 % set(auto2) -> clear(echo_input).
% 0.42/0.99 % set(auto2) -> set(quiet).
% 0.42/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.99 % set(auto2) -> clear(print_given).
% 0.42/0.99 assign(lrs_ticks,-1).
% 0.42/0.99 assign(sos_limit,10000).
% 0.42/0.99 assign(order,kbo).
% 0.42/0.99 set(lex_order_vars).
% 0.42/0.99 clear(print_given).
% 0.42/0.99
% 0.42/0.99 % formulas(sos). % not echoed (19 formulas)
% 0.42/0.99
% 0.42/0.99 ============================== end of input ==========================
% 0.42/0.99
% 0.42/0.99 % From the command line: assign(max_seconds, 300).
% 0.42/0.99
% 0.42/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.99
% 0.42/0.99 % Formulas that are not ordinary clauses:
% 0.42/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 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].
% 0.42/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 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].
% 0.42/0.99 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 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].
% 0.42/0.99 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].
% 0.42/0.99 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.99 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].
% 0.42/0.99 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].
% 0.83/1.09 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 19 -(all X0 multiplication(strong_iteration(one),X0) = strong_iteration(one)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.83/1.09
% 0.83/1.09 ============================== end of process non-clausal formulas ===
% 0.83/1.09
% 0.83/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.83/1.09
% 0.83/1.09 ============================== PREDICATE ELIMINATION =================
% 0.83/1.09
% 0.83/1.09 ============================== end predicate elimination =============
% 0.83/1.09
% 0.83/1.09 Auto_denials:
% 0.83/1.09 % copying label goals to answer in negative clause
% 0.83/1.09
% 0.83/1.09 Term ordering decisions:
% 0.83/1.09 Function symbol KB weights: one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 0.83/1.09
% 0.83/1.09 ============================== end of process initial clauses ========
% 0.83/1.09
% 0.83/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.83/1.09
% 0.83/1.09 ============================== end of clauses for search =============
% 0.83/1.09
% 0.83/1.09 ============================== SEARCH ================================
% 0.83/1.09
% 0.83/1.09 % Starting search at 0.01 seconds.
% 0.83/1.09
% 0.83/1.09 ============================== PROOF =================================
% 0.83/1.09 % SZS status Theorem
% 0.83/1.09 % SZS output start Refutation
% 0.83/1.09
% 0.83/1.09 % Proof 1 at 0.11 (+ 0.01) seconds: goals.
% 0.83/1.09 % Length of proof is 76.
% 0.83/1.09 % Level of proof is 16.
% 0.83/1.09 % Maximum clause weight is 15.000.
% 0.83/1.09 % Given clauses 177.
% 0.83/1.09
% 0.83/1.09 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 19 -(all X0 multiplication(strong_iteration(one),X0) = strong_iteration(one)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.83/1.09 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 0.83/1.09 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.83/1.09 23 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.83/1.09 24 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(10)].
% 0.83/1.09 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.83/1.09 26 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom). [clausify(11)].
% 0.83/1.09 27 addition(one,multiplication(A,star(A))) = star(A). [copy(26),flip(a)].
% 0.83/1.09 28 star(A) = addition(one,multiplication(star(A),A)) # label(star_unfold2) # label(axiom). [clausify(12)].
% 0.83/1.09 29 addition(one,multiplication(star(A),A)) = star(A). [copy(28),flip(a)].
% 0.83/1.09 32 strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) # label(isolation) # label(axiom). [clausify(17)].
% 0.83/1.09 33 addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A). [copy(32),flip(a)].
% 0.83/1.09 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.83/1.09 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([25(2)]),flip(a)].
% 0.83/1.09 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.83/1.09 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 0.83/1.09 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 0.83/1.09 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 0.83/1.09 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 0.83/1.09 41 strong_iteration(one) != multiplication(strong_iteration(one),c1) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 0.83/1.09 42 multiplication(strong_iteration(one),c1) != strong_iteration(one) # answer(goals). [copy(41),flip(a)].
% 0.83/1.09 43 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(18)].
% 0.83/1.09 44 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 0.83/1.09 45 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction1) # label(axiom). [clausify(13)].
% 0.83/1.09 46 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(45),rewrite([25(2)])].
% 0.83/1.09 49 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom). [clausify(16)].
% 0.83/1.09 50 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)). [copy(49),rewrite([25(2)])].
% 0.83/1.09 55 addition(A,addition(A,B)) = addition(A,B). [para(35(a,1),21(a,1)),rewrite([25(1),25(2),35(2,R),21(1),25(3)])].
% 0.83/1.09 56 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)). [para(36(a,1),27(a,1,2))].
% 0.83/1.09 58 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),38(a,1,1)),rewrite([25(4)]),flip(a)].
% 0.83/1.09 63 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(23(a,1),40(a,1,1)),rewrite([25(4)]),flip(a)].
% 0.83/1.09 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)])].
% 0.83/1.09 70 leq(A,A). [hyper(44,b,21,a)].
% 0.83/1.09 79 -leq(addition(A,B),one) | leq(multiplication(star(B),A),one). [para(22(a,1),46(a,1,2))].
% 0.83/1.09 97 -leq(A,addition(A,B)) | leq(A,multiplication(strong_iteration(one),B)). [para(23(a,1),50(a,2,2)),rewrite([25(1)])].
% 0.83/1.09 99 -leq(A,star(A)) | leq(A,strong_iteration(star(A))). [para(29(a,1),50(a,2)),rewrite([22(6)])].
% 0.83/1.09 110 leq(A,addition(A,B)). [hyper(44,b,55,a)].
% 0.83/1.09 111 addition(one,star(A)) = star(A). [para(27(a,1),55(a,1,2)),rewrite([27(7)])].
% 0.83/1.09 118 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(38(a,1),110(a,2))].
% 0.83/1.09 120 addition(one,multiplication(A,zero)) = star(multiplication(A,zero)). [para(24(a,1),56(a,1,2,2))].
% 0.83/1.09 195 leq(multiplication(A,B),addition(A,multiplication(A,B))). [para(58(a,1),118(a,2))].
% 0.83/1.09 251 multiplication(star(A),A) = multiplication(A,star(A)). [para(64(a,1),58(a,2)),rewrite([25(4),29(4)]),flip(a)].
% 0.83/1.09 266 leq(multiplication(A,star(A)),star(A)). [para(56(a,1),195(a,2)),rewrite([23(3),23(4),23(4)])].
% 0.83/1.09 279 multiplication(addition(A,one),star(A)) = star(A). [hyper(43,a,266,a),rewrite([25(4),63(4,R)])].
% 0.83/1.09 387 addition(A,star(A)) = star(A). [para(279(a,1),58(a,2,2)),rewrite([25(5),111(5),279(4),25(5),35(5),25(4),35(5,R),25(4),111(4)]),flip(a)].
% 0.83/1.09 396 leq(A,star(A)). [hyper(44,b,387,a)].
% 0.83/1.09 400 leq(A,strong_iteration(star(A))). [hyper(99,a,396,a)].
% 0.83/1.09 401 addition(A,strong_iteration(star(A))) = strong_iteration(star(A)). [hyper(43,a,400,a)].
% 0.83/1.09 520 -leq(A,one) | leq(multiplication(A,star(A)),one). [para(21(a,1),79(a,1)),rewrite([251(4)])].
% 0.83/1.09 597 leq(star(one),one). [hyper(520,a,70,a),rewrite([23(4)])].
% 0.83/1.09 601 star(one) = one. [hyper(43,a,597,a),rewrite([25(4),387(4)])].
% 0.83/1.09 621 star(multiplication(strong_iteration(one),zero)) = strong_iteration(one). [para(601(a,1),33(a,1,1)),rewrite([120(6)])].
% 0.83/1.09 658 addition(A,multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),A). [para(621(a,1),64(a,1,2,2,1)),rewrite([36(8),24(7),621(10)])].
% 0.83/1.09 660 multiplication(strong_iteration(one),strong_iteration(one)) = strong_iteration(one). [para(621(a,1),279(a,1,2)),rewrite([25(6),658(6),22(4),621(10)])].
% 0.83/1.09 662 multiplication(strong_iteration(one),strong_iteration(strong_iteration(one))) = strong_iteration(strong_iteration(one)). [para(621(a,1),401(a,1,2,1)),rewrite([25(8),658(8),621(11)])].
% 0.83/1.09 922 leq(A,multiplication(strong_iteration(one),B)). [hyper(97,a,110,a)].
% 0.83/1.09 923 addition(A,multiplication(strong_iteration(one),B)) = multiplication(strong_iteration(one),B). [hyper(43,a,922,a)].
% 0.83/1.09 925 multiplication(strong_iteration(one),zero) = multiplication(strong_iteration(one),A). [back_rewrite(658),rewrite([923(5)])].
% 0.83/1.09 926 multiplication(strong_iteration(one),zero) = strong_iteration(strong_iteration(one)). [back_rewrite(662),rewrite([925(6,R)])].
% 0.83/1.09 927 strong_iteration(strong_iteration(one)) = strong_iteration(one). [back_rewrite(660),rewrite([925(5,R),926(4)])].
% 0.83/1.09 928 $F # answer(goals). [back_rewrite(42),rewrite([925(4,R),926(4),927(3)]),xx(a)].
% 0.83/1.09
% 0.83/1.09 % SZS output end Refutation
% 0.83/1.09 ============================== end of proof ==========================
% 0.83/1.09
% 0.83/1.09 ============================== STATISTICS ============================
% 0.83/1.09
% 0.83/1.09 Given=177. Generated=3170. Kept=897. proofs=1.
% 0.83/1.09 Usable=158. Sos=626. Demods=159. Limbo=3, Disabled=130. Hints=0.
% 0.83/1.09 Megabytes=0.81.
% 0.83/1.09 User_CPU=0.11, System_CPU=0.01, Wall_clock=0.
% 0.83/1.09
% 0.83/1.09 ============================== end of statistics =====================
% 0.83/1.09
% 0.83/1.09 ============================== end of search =========================
% 0.83/1.09
% 0.83/1.09 THEOREM PROVED
% 0.83/1.09 % SZS status Theorem
% 0.83/1.09
% 0.83/1.09 Exiting with 1 proof.
% 0.83/1.09
% 0.83/1.09 Process 32266 exit (max_proofs) Thu Jun 16 12:55:55 2022
% 0.83/1.09 Prover9 interrupted
%------------------------------------------------------------------------------