TSTP Solution File: KLE142+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE142+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 02:22:26 EDT 2022
% Result : Theorem 0.78s 1.15s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE142+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 09:23:11 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.78/1.06 ============================== Prover9 ===============================
% 0.78/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.78/1.06 Process 18434 was started by sandbox on n003.cluster.edu,
% 0.78/1.06 Thu Jun 16 09:23:12 2022
% 0.78/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18281_n003.cluster.edu".
% 0.78/1.06 ============================== end of head ===========================
% 0.78/1.06
% 0.78/1.06 ============================== INPUT =================================
% 0.78/1.06
% 0.78/1.06 % Reading from file /tmp/Prover9_18281_n003.cluster.edu
% 0.78/1.06
% 0.78/1.06 set(prolog_style_variables).
% 0.78/1.06 set(auto2).
% 0.78/1.06 % set(auto2) -> set(auto).
% 0.78/1.06 % set(auto) -> set(auto_inference).
% 0.78/1.06 % set(auto) -> set(auto_setup).
% 0.78/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.78/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.78/1.06 % set(auto) -> set(auto_limits).
% 0.78/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.78/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.78/1.06 % set(auto) -> set(auto_denials).
% 0.78/1.06 % set(auto) -> set(auto_process).
% 0.78/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.78/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.78/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.78/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.78/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.78/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.78/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.78/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.78/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.78/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.78/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.78/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.78/1.06 % set(auto2) -> assign(stats, some).
% 0.78/1.06 % set(auto2) -> clear(echo_input).
% 0.78/1.06 % set(auto2) -> set(quiet).
% 0.78/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.78/1.06 % set(auto2) -> clear(print_given).
% 0.78/1.06 assign(lrs_ticks,-1).
% 0.78/1.06 assign(sos_limit,10000).
% 0.78/1.06 assign(order,kbo).
% 0.78/1.06 set(lex_order_vars).
% 0.78/1.06 clear(print_given).
% 0.78/1.06
% 0.78/1.06 % formulas(sos). % not echoed (19 formulas)
% 0.78/1.06
% 0.78/1.06 ============================== end of input ==========================
% 0.78/1.06
% 0.78/1.06 % From the command line: assign(max_seconds, 300).
% 0.78/1.06
% 0.78/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.78/1.06
% 0.78/1.06 % Formulas that are not ordinary clauses:
% 0.78/1.06 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.06 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].
% 0.78/1.06 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.06 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.06 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].
% 0.78/1.06 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.06 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.06 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].
% 0.78/1.06 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].
% 0.78/1.06 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.06 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.06 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.06 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].
% 0.78/1.06 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].
% 0.78/1.15 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 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].
% 0.78/1.15 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 19 -(all X0 (leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) & leq(strong_iteration(one),strong_iteration(strong_iteration(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.78/1.15
% 0.78/1.15 ============================== end of process non-clausal formulas ===
% 0.78/1.15
% 0.78/1.15 ============================== PROCESS INITIAL CLAUSES ===============
% 0.78/1.15
% 0.78/1.15 ============================== PREDICATE ELIMINATION =================
% 0.78/1.15
% 0.78/1.15 ============================== end predicate elimination =============
% 0.78/1.15
% 0.78/1.15 Auto_denials:
% 0.78/1.15 % copying label goals to answer in negative clause
% 0.78/1.15
% 0.78/1.15 Term ordering decisions:
% 0.78/1.15 Function symbol KB weights: one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 0.78/1.15
% 0.78/1.15 ============================== end of process initial clauses ========
% 0.78/1.15
% 0.78/1.15 ============================== CLAUSES FOR SEARCH ====================
% 0.78/1.15
% 0.78/1.15 ============================== end of clauses for search =============
% 0.78/1.15
% 0.78/1.15 ============================== SEARCH ================================
% 0.78/1.15
% 0.78/1.15 % Starting search at 0.01 seconds.
% 0.78/1.15
% 0.78/1.15 ============================== PROOF =================================
% 0.78/1.15 % SZS status Theorem
% 0.78/1.15 % SZS output start Refutation
% 0.78/1.15
% 0.78/1.15 % Proof 1 at 0.10 (+ 0.00) seconds: goals.
% 0.78/1.15 % Length of proof is 75.
% 0.78/1.15 % Level of proof is 17.
% 0.78/1.15 % Maximum clause weight is 17.000.
% 0.78/1.15 % Given clauses 158.
% 0.78/1.15
% 0.78/1.15 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 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].
% 0.78/1.15 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 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].
% 0.78/1.15 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 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].
% 0.78/1.15 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].
% 0.78/1.15 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 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].
% 0.78/1.15 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 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].
% 0.78/1.15 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.15 19 -(all X0 (leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) & leq(strong_iteration(one),strong_iteration(strong_iteration(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.78/1.15 20 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.78/1.15 21 addition(A,A) = A # label(idempotence) # label(axiom). [clausify(4)].
% 0.78/1.15 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.78/1.15 23 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.78/1.15 24 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(10)].
% 0.78/1.15 25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.78/1.15 26 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom). [clausify(11)].
% 0.78/1.15 27 addition(one,multiplication(A,star(A))) = star(A). [copy(26),flip(a)].
% 0.78/1.15 30 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 0.78/1.15 31 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(30),rewrite([25(5)]),flip(a)].
% 0.78/1.15 32 strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) # label(isolation) # label(axiom). [clausify(17)].
% 0.78/1.15 33 addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A). [copy(32),flip(a)].
% 0.78/1.15 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.78/1.15 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([25(2)]),flip(a)].
% 0.78/1.15 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.78/1.15 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 0.78/1.15 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 0.78/1.15 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 0.78/1.15 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 0.78/1.15 41 -leq(strong_iteration(strong_iteration(c1)),strong_iteration(one)) | -leq(strong_iteration(one),strong_iteration(strong_iteration(c1))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 0.78/1.15 42 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(18)].
% 0.78/1.15 43 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(18)].
% 0.78/1.15 44 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction1) # label(axiom). [clausify(13)].
% 0.78/1.15 45 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C). [copy(44),rewrite([25(2)])].
% 0.78/1.15 48 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom). [clausify(16)].
% 0.78/1.15 49 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)). [copy(48),rewrite([25(2)])].
% 0.78/1.15 51 star(zero) = one. [para(24(a,1),27(a,1,2)),rewrite([20(3)]),flip(a)].
% 0.78/1.15 54 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)])].
% 0.78/1.15 55 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)). [para(36(a,1),27(a,1,2))].
% 0.78/1.15 57 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),38(a,1,1)),rewrite([25(4)]),flip(a)].
% 0.78/1.15 62 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(23(a,1),40(a,1,1)),rewrite([25(4)]),flip(a)].
% 0.78/1.15 65 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)])].
% 0.78/1.15 67 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)])].
% 0.78/1.15 69 leq(A,A). [hyper(43,b,21,a)].
% 0.78/1.15 79 -leq(addition(A,B),B) | leq(multiplication(star(one),A),B). [para(23(a,1),45(a,1,2))].
% 0.78/1.15 96 -leq(A,addition(A,B)) | leq(A,multiplication(strong_iteration(one),B)). [para(23(a,1),49(a,2,2)),rewrite([25(1)])].
% 0.78/1.15 109 leq(A,addition(A,B)). [hyper(43,b,54,a)].
% 0.78/1.15 110 addition(one,star(A)) = star(A). [para(27(a,1),54(a,1,2)),rewrite([27(7)])].
% 0.78/1.15 112 leq(A,multiplication(strong_iteration(one),B)). [back_unit_del(96),unit_del(a,109)].
% 0.78/1.15 116 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(38(a,1),109(a,2))].
% 0.78/1.15 118 addition(A,multiplication(strong_iteration(one),B)) = multiplication(strong_iteration(one),B). [hyper(42,a,112,a)].
% 0.78/1.15 119 leq(A,strong_iteration(one)). [para(22(a,1),112(a,2))].
% 0.78/1.15 120 -leq(strong_iteration(one),strong_iteration(strong_iteration(c1))) # answer(goals). [back_unit_del(41),unit_del(a,119)].
% 0.78/1.15 130 addition(A,strong_iteration(one)) = strong_iteration(one). [hyper(42,a,119,a)].
% 0.78/1.15 199 leq(multiplication(A,B),addition(A,multiplication(A,B))). [para(57(a,1),116(a,2))].
% 0.78/1.15 283 leq(multiplication(A,star(A)),star(A)). [para(55(a,1),199(a,2)),rewrite([23(3),23(4),23(4)])].
% 0.78/1.15 289 multiplication(addition(A,one),star(A)) = star(A). [hyper(42,a,283,a),rewrite([25(4),62(4,R)])].
% 0.78/1.15 396 addition(A,star(A)) = star(A). [para(289(a,1),57(a,2,2)),rewrite([25(5),110(5),289(4),25(5),35(5),25(4),35(5,R),25(4),110(4)]),flip(a)].
% 0.78/1.15 573 leq(star(one),star(A)). [para(110(a,1),79(a,1)),rewrite([22(7)]),unit_del(a,69)].
% 0.78/1.15 592 leq(star(one),one). [para(51(a,1),573(a,2))].
% 0.78/1.15 594 star(one) = one. [hyper(42,a,592,a),rewrite([25(4),396(4)])].
% 0.78/1.15 614 multiplication(strong_iteration(one),zero) = strong_iteration(one). [para(594(a,1),33(a,1,1)),rewrite([118(6)])].
% 0.78/1.15 615 multiplication(strong_iteration(one),A) = strong_iteration(one). [para(614(a,1),36(a,1,1)),rewrite([24(7),614(7)])].
% 0.78/1.15 622 addition(strong_iteration(one),multiplication(A,B)) = strong_iteration(one). [para(614(a,1),67(a,2,1,2)),rewrite([24(4),615(4),130(7),615(7)])].
% 0.78/1.15 709 multiplication(strong_iteration(A),strong_iteration(one)) = strong_iteration(one). [para(622(a,1),65(a,1)),flip(a)].
% 0.78/1.15 719 leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(A)),B)). [para(709(a,1),49(a,2,2)),rewrite([130(5)]),unit_del(a,69)].
% 0.78/1.15 752 leq(strong_iteration(one),strong_iteration(strong_iteration(A))). [para(22(a,1),719(a,2))].
% 0.78/1.15 753 $F # answer(goals). [resolve(752,a,120,a)].
% 0.78/1.15
% 0.78/1.15 % SZS output end Refutation
% 0.78/1.15 ============================== end of proof ==========================
% 0.78/1.15
% 0.78/1.15 ============================== STATISTICS ============================
% 0.78/1.15
% 0.78/1.15 Given=158. Generated=2997. Kept=723. proofs=1.
% 0.78/1.15 Usable=136. Sos=480. Demods=169. Limbo=1, Disabled=125. Hints=0.
% 0.78/1.15 Megabytes=0.66.
% 0.78/1.15 User_CPU=0.10, System_CPU=0.00, Wall_clock=0.
% 0.78/1.15
% 0.78/1.15 ============================== end of statistics =====================
% 0.78/1.15
% 0.78/1.15 ============================== end of search =========================
% 0.78/1.15
% 0.78/1.15 THEOREM PROVED
% 0.78/1.15 % SZS status Theorem
% 0.78/1.15
% 0.78/1.15 Exiting with 1 proof.
% 0.78/1.15
% 0.78/1.15 Process 18434 exit (max_proofs) Thu Jun 16 09:23:12 2022
% 0.78/1.15 Prover9 interrupted
%------------------------------------------------------------------------------