TSTP Solution File: KLE148+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE148+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 02:22:29 EDT 2022
% Result : Theorem 0.48s 0.82s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : KLE148+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Thu Jun 16 16:23:30 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.48/0.80 ============================== Prover9 ===============================
% 0.48/0.80 Prover9 (32) version 2009-11A, November 2009.
% 0.48/0.80 Process 4235 was started by sandbox on n032.cluster.edu,
% 0.48/0.80 Thu Jun 16 16:23:30 2022
% 0.48/0.80 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4081_n032.cluster.edu".
% 0.48/0.80 ============================== end of head ===========================
% 0.48/0.80
% 0.48/0.80 ============================== INPUT =================================
% 0.48/0.80
% 0.48/0.80 % Reading from file /tmp/Prover9_4081_n032.cluster.edu
% 0.48/0.80
% 0.48/0.80 set(prolog_style_variables).
% 0.48/0.80 set(auto2).
% 0.48/0.80 % set(auto2) -> set(auto).
% 0.48/0.80 % set(auto) -> set(auto_inference).
% 0.48/0.80 % set(auto) -> set(auto_setup).
% 0.48/0.80 % set(auto_setup) -> set(predicate_elim).
% 0.48/0.80 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.48/0.80 % set(auto) -> set(auto_limits).
% 0.48/0.80 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.48/0.80 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.48/0.80 % set(auto) -> set(auto_denials).
% 0.48/0.80 % set(auto) -> set(auto_process).
% 0.48/0.80 % set(auto2) -> assign(new_constants, 1).
% 0.48/0.80 % set(auto2) -> assign(fold_denial_max, 3).
% 0.48/0.80 % set(auto2) -> assign(max_weight, "200.000").
% 0.48/0.80 % set(auto2) -> assign(max_hours, 1).
% 0.48/0.80 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.48/0.80 % set(auto2) -> assign(max_seconds, 0).
% 0.48/0.80 % set(auto2) -> assign(max_minutes, 5).
% 0.48/0.80 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.48/0.80 % set(auto2) -> set(sort_initial_sos).
% 0.48/0.80 % set(auto2) -> assign(sos_limit, -1).
% 0.48/0.80 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.48/0.80 % set(auto2) -> assign(max_megs, 400).
% 0.48/0.80 % set(auto2) -> assign(stats, some).
% 0.48/0.80 % set(auto2) -> clear(echo_input).
% 0.48/0.80 % set(auto2) -> set(quiet).
% 0.48/0.80 % set(auto2) -> clear(print_initial_clauses).
% 0.48/0.80 % set(auto2) -> clear(print_given).
% 0.48/0.80 assign(lrs_ticks,-1).
% 0.48/0.80 assign(sos_limit,10000).
% 0.48/0.80 assign(order,kbo).
% 0.48/0.80 set(lex_order_vars).
% 0.48/0.80 clear(print_given).
% 0.48/0.80
% 0.48/0.80 % formulas(sos). % not echoed (19 formulas)
% 0.48/0.80
% 0.48/0.80 ============================== end of input ==========================
% 0.48/0.80
% 0.48/0.80 % From the command line: assign(max_seconds, 300).
% 0.48/0.80
% 0.48/0.80 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.48/0.80
% 0.48/0.80 % Formulas that are not ordinary clauses:
% 0.48/0.80 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.80 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].
% 0.48/0.80 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.80 4 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.80 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].
% 0.48/0.80 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.80 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.80 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].
% 0.48/0.80 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].
% 0.48/0.80 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.80 11 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.80 12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.80 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].
% 0.48/0.80 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].
% 0.48/0.82 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.82 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].
% 0.48/0.82 17 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.82 18 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.82 19 -(all X0 all X1 (multiplication(X0,X1) = zero -> multiplication(X0,strong_iteration(X1)) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.48/0.82
% 0.48/0.82 ============================== end of process non-clausal formulas ===
% 0.48/0.82
% 0.48/0.82 ============================== PROCESS INITIAL CLAUSES ===============
% 0.48/0.82
% 0.48/0.82 ============================== PREDICATE ELIMINATION =================
% 0.48/0.82
% 0.48/0.82 ============================== end predicate elimination =============
% 0.48/0.82
% 0.48/0.82 Auto_denials:
% 0.48/0.82 % copying label goals to answer in negative clause
% 0.48/0.82
% 0.48/0.82 Term ordering decisions:
% 0.48/0.82 Function symbol KB weights: one=1. zero=1. c1=1. c2=1. multiplication=1. addition=1. star=1. strong_iteration=1.
% 0.48/0.82
% 0.48/0.82 ============================== end of process initial clauses ========
% 0.48/0.82
% 0.48/0.82 ============================== CLAUSES FOR SEARCH ====================
% 0.48/0.82
% 0.48/0.82 ============================== end of clauses for search =============
% 0.48/0.82
% 0.48/0.82 ============================== SEARCH ================================
% 0.48/0.82
% 0.48/0.82 % Starting search at 0.01 seconds.
% 0.48/0.82
% 0.48/0.82 ============================== PROOF =================================
% 0.48/0.82 % SZS status Theorem
% 0.48/0.82 % SZS output start Refutation
% 0.48/0.82
% 0.48/0.82 % Proof 1 at 0.03 (+ 0.00) seconds: goals.
% 0.48/0.82 % Length of proof is 31.
% 0.48/0.82 % Level of proof is 7.
% 0.48/0.82 % Maximum clause weight is 13.000.
% 0.48/0.82 % Given clauses 57.
% 0.48/0.82
% 0.48/0.82 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.82 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.82 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].
% 0.48/0.82 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.82 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].
% 0.48/0.82 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].
% 0.48/0.82 10 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.82 15 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause). [assumption].
% 0.48/0.82 19 -(all X0 all X1 (multiplication(X0,X1) = zero -> multiplication(X0,strong_iteration(X1)) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.48/0.82 20 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.48/0.82 22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.48/0.82 24 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(10)].
% 0.48/0.82 25 multiplication(c1,c2) = zero # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.48/0.82 26 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.48/0.82 31 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom). [clausify(15)].
% 0.48/0.82 32 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A). [copy(31),rewrite([26(5)]),flip(a)].
% 0.48/0.82 37 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.48/0.82 38 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(distributivity1) # label(axiom). [clausify(8)].
% 0.48/0.82 39 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(38),flip(a)].
% 0.48/0.82 40 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(distributivity2) # label(axiom). [clausify(9)].
% 0.48/0.82 41 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(40),flip(a)].
% 0.48/0.82 42 multiplication(c1,strong_iteration(c2)) != c1 # label(goals) # label(negated_conjecture) # answer(goals). [clausify(19)].
% 0.48/0.82 56 multiplication(c1,multiplication(c2,A)) = zero. [para(25(a,1),37(a,1,1)),rewrite([24(2)]),flip(a)].
% 0.48/0.82 59 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(22(a,1),39(a,1,1)),rewrite([26(4)]),flip(a)].
% 0.48/0.82 60 addition(zero,multiplication(c1,A)) = multiplication(c1,addition(A,c2)). [para(25(a,1),39(a,1,1)),rewrite([26(7)])].
% 0.48/0.82 63 addition(A,multiplication(A,multiplication(B,strong_iteration(B)))) = multiplication(A,strong_iteration(B)). [para(32(a,1),39(a,2,2)),rewrite([22(2)])].
% 0.48/0.82 64 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(20(a,1),41(a,2,1)),rewrite([24(3),26(3)])].
% 0.48/0.82 73 multiplication(c1,addition(A,c2)) = multiplication(c1,A). [back_rewrite(60),rewrite([64(4)]),flip(a)].
% 0.48/0.82 152 addition(zero,c1) = c1. [para(25(a,1),59(a,2,2)),rewrite([26(4),73(5),22(3),26(4)]),flip(a)].
% 0.48/0.82 229 multiplication(c1,strong_iteration(c2)) = c1. [para(56(a,1),63(a,1,2)),rewrite([26(3),152(3)]),flip(a)].
% 0.48/0.82 230 $F # answer(goals). [resolve(229,a,42,a)].
% 0.48/0.82
% 0.48/0.82 % SZS output end Refutation
% 0.48/0.82 ============================== end of proof ==========================
% 0.48/0.82
% 0.48/0.82 ============================== STATISTICS ============================
% 0.48/0.82
% 0.48/0.82 Given=57. Generated=740. Kept=200. proofs=1.
% 0.48/0.82 Usable=51. Sos=126. Demods=77. Limbo=6, Disabled=37. Hints=0.
% 0.48/0.82 Megabytes=0.25.
% 0.48/0.82 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.48/0.82
% 0.48/0.82 ============================== end of statistics =====================
% 0.48/0.82
% 0.48/0.82 ============================== end of search =========================
% 0.48/0.82
% 0.48/0.82 THEOREM PROVED
% 0.48/0.82 % SZS status Theorem
% 0.48/0.82
% 0.48/0.82 Exiting with 1 proof.
% 0.48/0.82
% 0.48/0.82 Process 4235 exit (max_proofs) Thu Jun 16 16:23:30 2022
% 0.48/0.82 Prover9 interrupted
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