TSTP Solution File: KLE038+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE038+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 0.76s 1.07s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : KLE038+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n017.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 08:36:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/1.01 ============================== Prover9 ===============================
% 0.46/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.01 Process 22631 was started by sandbox2 on n017.cluster.edu,
% 0.46/1.01 Thu Jun 16 08:36:41 2022
% 0.46/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22478_n017.cluster.edu".
% 0.46/1.01 ============================== end of head ===========================
% 0.46/1.01
% 0.46/1.01 ============================== INPUT =================================
% 0.46/1.01
% 0.46/1.01 % Reading from file /tmp/Prover9_22478_n017.cluster.edu
% 0.46/1.01
% 0.46/1.01 set(prolog_style_variables).
% 0.46/1.01 set(auto2).
% 0.46/1.01 % set(auto2) -> set(auto).
% 0.46/1.01 % set(auto) -> set(auto_inference).
% 0.46/1.01 % set(auto) -> set(auto_setup).
% 0.46/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.01 % set(auto) -> set(auto_limits).
% 0.46/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.01 % set(auto) -> set(auto_denials).
% 0.46/1.01 % set(auto) -> set(auto_process).
% 0.46/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.01 % set(auto2) -> assign(stats, some).
% 0.46/1.01 % set(auto2) -> clear(echo_input).
% 0.46/1.01 % set(auto2) -> set(quiet).
% 0.46/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.01 % set(auto2) -> clear(print_given).
% 0.46/1.01 assign(lrs_ticks,-1).
% 0.46/1.01 assign(sos_limit,10000).
% 0.46/1.01 assign(order,kbo).
% 0.46/1.01 set(lex_order_vars).
% 0.46/1.01 clear(print_given).
% 0.46/1.01
% 0.46/1.01 % formulas(sos). % not echoed (17 formulas)
% 0.46/1.01
% 0.46/1.01 ============================== end of input ==========================
% 0.46/1.01
% 0.46/1.01 % From the command line: assign(max_seconds, 300).
% 0.46/1.01
% 0.46/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.01
% 0.46/1.01 % Formulas that are not ordinary clauses:
% 0.46/1.01 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 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].
% 0.46/1.01 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 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].
% 0.46/1.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 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].
% 0.46/1.01 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].
% 0.46/1.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 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].
% 0.76/1.07 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].
% 0.76/1.07 17 -(all X0 leq(X0,star(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.07
% 0.76/1.07 ============================== end of process non-clausal formulas ===
% 0.76/1.07
% 0.76/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.07
% 0.76/1.07 ============================== PREDICATE ELIMINATION =================
% 0.76/1.07
% 0.76/1.07 ============================== end predicate elimination =============
% 0.76/1.07
% 0.76/1.07 Auto_denials:
% 0.76/1.07 % copying label goals to answer in negative clause
% 0.76/1.07
% 0.76/1.07 Term ordering decisions:
% 0.76/1.07
% 0.76/1.07 % Assigning unary symbol star kb_weight 0 and highest precedence (8).
% 0.76/1.07 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. star=0.
% 0.76/1.07
% 0.76/1.07 ============================== end of process initial clauses ========
% 0.76/1.07
% 0.76/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.07
% 0.76/1.07 ============================== end of clauses for search =============
% 0.76/1.07
% 0.76/1.07 ============================== SEARCH ================================
% 0.76/1.07
% 0.76/1.07 % Starting search at 0.01 seconds.
% 0.76/1.07
% 0.76/1.07 ============================== PROOF =================================
% 0.76/1.07 % SZS status Theorem
% 0.76/1.07 % SZS output start Refutation
% 0.76/1.07
% 0.76/1.07 % Proof 1 at 0.06 (+ 0.01) seconds: goals.
% 0.76/1.07 % Length of proof is 42.
% 0.76/1.07 % Level of proof is 10.
% 0.76/1.07 % Maximum clause weight is 13.000.
% 0.76/1.07 % Given clauses 103.
% 0.76/1.07
% 0.76/1.07 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.07 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].
% 0.76/1.07 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.07 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.07 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.07 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].
% 0.76/1.07 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].
% 0.76/1.07 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.07 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.07 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.07 17 -(all X0 leq(X0,star(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.07 19 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.76/1.07 20 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.76/1.07 21 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.76/1.07 24 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.76/1.07 25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom). [clausify(13)].
% 0.76/1.07 26 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)].
% 0.76/1.07 27 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.76/1.07 28 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(27),rewrite([24(2)]),flip(a)].
% 0.76/1.07 30 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.76/1.07 31 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(30),flip(a)].
% 0.76/1.07 32 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.76/1.07 33 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(32),flip(a)].
% 0.76/1.07 34 -leq(c1,star(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 0.76/1.07 35 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.76/1.07 36 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.76/1.07 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)])].
% 0.76/1.07 47 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(21(a,1),33(a,1,1)),rewrite([24(4)]),flip(a)].
% 0.76/1.07 50 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [hyper(35,a,26,a),rewrite([24(6)])].
% 0.76/1.07 51 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [hyper(35,a,25,a),rewrite([24(6)])].
% 0.76/1.07 53 addition(c1,star(c1)) != star(c1) # answer(goals). [ur(36,a,34,a)].
% 0.76/1.07 78 leq(A,addition(A,B)). [hyper(36,b,43,a)].
% 0.76/1.07 79 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(31(a,1),78(a,2))].
% 0.76/1.07 191 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)].
% 0.76/1.07 214 addition(one,addition(star(A),multiplication(A,star(A)))) = star(A). [para(51(a,1),28(a,1)),rewrite([28(7),24(6)]),flip(a)].
% 0.76/1.07 350 addition(one,star(A)) = star(A). [para(191(a,1),43(a,1,2)),rewrite([191(9)])].
% 0.76/1.07 353 leq(A,multiplication(A,star(B))). [para(191(a,1),79(a,2,2)),rewrite([20(2)])].
% 0.76/1.07 362 leq(addition(A,one),addition(star(B),multiplication(A,star(B)))). [para(47(a,1),353(a,2))].
% 0.76/1.07 445 addition(star(A),multiplication(A,star(A))) = star(A). [para(214(a,1),28(a,1)),rewrite([350(6),24(5)]),flip(a)].
% 0.76/1.07 477 leq(addition(A,one),star(A)). [para(445(a,1),362(a,2))].
% 0.76/1.07 483 addition(A,star(A)) = star(A). [hyper(35,a,477,a),rewrite([24(4),28(4,R),350(3)])].
% 0.76/1.07 484 $F # answer(goals). [resolve(483,a,53,a)].
% 0.76/1.07
% 0.76/1.07 % SZS output end Refutation
% 0.76/1.07 ============================== end of proof ==========================
% 0.76/1.07
% 0.76/1.07 ============================== STATISTICS ============================
% 0.76/1.07
% 0.76/1.07 Given=103. Generated=1743. Kept=461. proofs=1.
% 0.76/1.07 Usable=86. Sos=321. Demods=77. Limbo=0, Disabled=71. Hints=0.
% 0.76/1.07 Megabytes=0.47.
% 0.76/1.07 User_CPU=0.06, System_CPU=0.01, Wall_clock=0.
% 0.76/1.07
% 0.76/1.07 ============================== end of statistics =====================
% 0.76/1.07
% 0.76/1.07 ============================== end of search =========================
% 0.76/1.07
% 0.76/1.07 THEOREM PROVED
% 0.76/1.07 % SZS status Theorem
% 0.76/1.07
% 0.76/1.07 Exiting with 1 proof.
% 0.76/1.07
% 0.76/1.07 Process 22631 exit (max_proofs) Thu Jun 16 08:36:41 2022
% 0.76/1.07 Prover9 interrupted
%------------------------------------------------------------------------------