TSTP Solution File: KLE044-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE044-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 02:21:57 EDT 2022
% Result : Unsatisfiable 5.69s 5.99s
% Output : Refutation 5.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE044-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 13:43:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.30/2.63 ============================== Prover9 ===============================
% 2.30/2.63 Prover9 (32) version 2009-11A, November 2009.
% 2.30/2.63 Process 7389 was started by sandbox2 on n027.cluster.edu,
% 2.30/2.63 Thu Jun 16 13:43:51 2022
% 2.30/2.63 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7219_n027.cluster.edu".
% 2.30/2.63 ============================== end of head ===========================
% 2.30/2.63
% 2.30/2.63 ============================== INPUT =================================
% 2.30/2.63
% 2.30/2.63 % Reading from file /tmp/Prover9_7219_n027.cluster.edu
% 2.30/2.63
% 2.30/2.63 set(prolog_style_variables).
% 2.30/2.63 set(auto2).
% 2.30/2.63 % set(auto2) -> set(auto).
% 2.30/2.63 % set(auto) -> set(auto_inference).
% 2.30/2.63 % set(auto) -> set(auto_setup).
% 2.30/2.63 % set(auto_setup) -> set(predicate_elim).
% 2.30/2.63 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.30/2.63 % set(auto) -> set(auto_limits).
% 2.30/2.63 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.30/2.63 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.30/2.63 % set(auto) -> set(auto_denials).
% 2.30/2.63 % set(auto) -> set(auto_process).
% 2.30/2.63 % set(auto2) -> assign(new_constants, 1).
% 2.30/2.63 % set(auto2) -> assign(fold_denial_max, 3).
% 2.30/2.63 % set(auto2) -> assign(max_weight, "200.000").
% 2.30/2.63 % set(auto2) -> assign(max_hours, 1).
% 2.30/2.63 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.30/2.63 % set(auto2) -> assign(max_seconds, 0).
% 2.30/2.63 % set(auto2) -> assign(max_minutes, 5).
% 2.30/2.63 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.30/2.63 % set(auto2) -> set(sort_initial_sos).
% 2.30/2.63 % set(auto2) -> assign(sos_limit, -1).
% 2.30/2.63 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.30/2.63 % set(auto2) -> assign(max_megs, 400).
% 2.30/2.63 % set(auto2) -> assign(stats, some).
% 2.30/2.63 % set(auto2) -> clear(echo_input).
% 2.30/2.63 % set(auto2) -> set(quiet).
% 2.30/2.63 % set(auto2) -> clear(print_initial_clauses).
% 2.30/2.63 % set(auto2) -> clear(print_given).
% 2.30/2.63 assign(lrs_ticks,-1).
% 2.30/2.63 assign(sos_limit,10000).
% 2.30/2.63 assign(order,kbo).
% 2.30/2.63 set(lex_order_vars).
% 2.30/2.63 clear(print_given).
% 2.30/2.63
% 2.30/2.63 % formulas(sos). % not echoed (21 formulas)
% 2.30/2.63
% 2.30/2.63 ============================== end of input ==========================
% 2.30/2.63
% 2.30/2.63 % From the command line: assign(max_seconds, 300).
% 2.30/2.63
% 2.30/2.63 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.30/2.63
% 2.30/2.63 % Formulas that are not ordinary clauses:
% 2.30/2.63
% 2.30/2.63 ============================== end of process non-clausal formulas ===
% 2.30/2.63
% 2.30/2.63 ============================== PROCESS INITIAL CLAUSES ===============
% 2.30/2.63
% 2.30/2.63 ============================== PREDICATE ELIMINATION =================
% 2.30/2.63
% 2.30/2.63 ============================== end predicate elimination =============
% 2.30/2.63
% 2.30/2.63 Auto_denials:
% 2.30/2.63 % copying label goals to answer in negative clause
% 2.30/2.63
% 2.30/2.63 Term ordering decisions:
% 2.30/2.63
% 2.30/2.63 % Assigning unary symbol star kb_weight 0 and highest precedence (14).
% 2.30/2.63 Function symbol KB weights: true=1. zero=1. one=1. sK1_goals_X0=1. sK2_goals_X0=1. multiplication=1. addition=1. leq=1. tuple=1. ifeq=1. ifeq2=1. ifeq3=1. star=0.
% 2.30/2.63
% 2.30/2.63 ============================== end of process initial clauses ========
% 2.30/2.63
% 2.30/2.63 ============================== CLAUSES FOR SEARCH ====================
% 2.30/2.63
% 2.30/2.63 ============================== end of clauses for search =============
% 2.30/2.63
% 2.30/2.63 ============================== SEARCH ================================
% 2.30/2.63
% 2.30/2.63 % Starting search at 0.01 seconds.
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=45.000, iters=3333
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=41.000, iters=3396
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=37.000, iters=3352
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=36.000, iters=3352
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=35.000, iters=3557
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=33.000, iters=3378
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=31.000, iters=3334
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=30.000, iters=3354
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=29.000, iters=3386
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=28.000, iters=3400
% 2.30/2.63
% 2.30/2.63 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 74 (0.00 of 1.12 sec).
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=27.000, iters=3343
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=25.000, iters=3436
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=24.000, iters=3391
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=23.000, iters=3340
% 2.30/2.63
% 2.30/2.63 Low Water (keep): wt=22.000, iters=3336
% 2.30/2.63
% 2.30/2.63 Low Water (displace): id=5585, wt=51.000
% 2.30/2.63
% 2.30/2.63 Low Water (displace): id=5586, wt=49.000
% 2.30/2.63
% 2.30/2.63 Low Water (displace): id=4600, wt=48.000
% 2.30/2.63
% 2.30/2.63 Low Water (displace): id=5936, wt=45.000
% 2.30/2.63
% 2.30/2.63 Low Water (displace): id=4598, wt=44.000
% 2.30/2.63
% 2.30/2.63 Low Water (displace): id=4623, wt=43.000
% 2.30/2.63
% 2.30/2.63 Low Water (displace): id=4582, wt=42.000
% 2.30/2.63
% 2.30/2.63 Low Water (displace): id=6379, wt=41.000
% 5.69/5.99
% 5.69/5.99 Low Water (keep): wt=21.000, iters=3347
% 5.69/5.99
% 5.69/5.99 Low Water (displace): id=4687, wt=40.000
% 5.69/5.99
% 5.69/5.99 Low Water (displace): id=6487, wt=39.000
% 5.69/5.99
% 5.69/5.99 Low Water (displace): id=12211, wt=20.000
% 5.69/5.99
% 5.69/5.99 Low Water (displace): id=12221, wt=19.000
% 5.69/5.99
% 5.69/5.99 Low Water (displace): id=12240, wt=18.000
% 5.69/5.99
% 5.69/5.99 Low Water (displace): id=12241, wt=15.000
% 5.69/5.99
% 5.69/5.99 Low Water (displace): id=12801, wt=14.000
% 5.69/5.99
% 5.69/5.99 Low Water (displace): id=13706, wt=13.000
% 5.69/5.99
% 5.69/5.99 Low Water (keep): wt=20.000, iters=3351
% 5.69/5.99
% 5.69/5.99 Low Water (keep): wt=19.000, iters=3334
% 5.69/5.99
% 5.69/5.99 Low Water (keep): wt=17.000, iters=4213
% 5.69/5.99
% 5.69/5.99 ============================== PROOF =================================
% 5.69/5.99 % SZS status Unsatisfiable
% 5.69/5.99 % SZS output start Refutation
% 5.69/5.99
% 5.69/5.99 % Proof 1 at 4.91 (+ 0.13) seconds: goals.
% 5.69/5.99 % Length of proof is 128.
% 5.69/5.99 % Level of proof is 27.
% 5.69/5.99 % Maximum clause weight is 20.000.
% 5.69/5.99 % Given clauses 1300.
% 5.69/5.99
% 5.69/5.99 2 addition(A,A) = A # label(additive_idempotence) # label(axiom). [assumption].
% 5.69/5.99 3 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [assumption].
% 5.69/5.99 4 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [assumption].
% 5.69/5.99 7 ifeq3(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 5.69/5.99 8 ifeq2(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 5.69/5.99 9 ifeq(A,A,B,C) = B # label(ifeq_axiom_002) # label(axiom). [assumption].
% 5.69/5.99 10 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [assumption].
% 5.69/5.99 11 addition(A,addition(B,C)) = addition(addition(A,B),C) # label(additive_associativity) # label(axiom). [assumption].
% 5.69/5.99 12 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(11),rewrite([10(4)])].
% 5.69/5.99 13 multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) # label(multiplicative_associativity) # label(axiom). [assumption].
% 5.69/5.99 14 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)). [copy(13),flip(a)].
% 5.69/5.99 15 ifeq2(leq(A,B),true,addition(A,B),B) = B # label(order_1) # label(axiom). [assumption].
% 5.69/5.99 16 ifeq3(addition(A,B),B,leq(A,B),true) = true # label(order) # label(axiom). [assumption].
% 5.69/5.99 17 leq(addition(one,multiplication(A,star(A))),star(A)) = true # label(star_unfold_right) # label(axiom). [assumption].
% 5.69/5.99 18 leq(addition(one,multiplication(star(A),A)),star(A)) = true # label(star_unfold_left) # label(axiom). [assumption].
% 5.69/5.99 19 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [assumption].
% 5.69/5.99 20 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(19),flip(a)].
% 5.69/5.99 21 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [assumption].
% 5.69/5.99 22 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(21),flip(a)].
% 5.69/5.99 23 ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true # label(star_induction_left) # label(axiom). [assumption].
% 5.69/5.99 24 ifeq(leq(addition(A,multiplication(B,C)),C),true,leq(multiplication(star(B),A),C),true) = true. [copy(23),rewrite([10(2)])].
% 5.69/5.99 25 ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true # label(star_induction_right) # label(axiom). [assumption].
% 5.69/5.99 26 ifeq(leq(addition(A,multiplication(B,C)),B),true,leq(multiplication(A,star(C)),B),true) = true. [copy(25),rewrite([10(2)])].
% 5.69/5.99 27 tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 5.69/5.99 28 addition(A,addition(A,B)) = addition(A,B). [para(12(a,1),2(a,1)),rewrite([10(1),10(2),12(2,R),2(1),10(3)])].
% 5.69/5.99 32 leq(A,A) = true. [para(2(a,1),16(a,1,1)),rewrite([7(3)])].
% 5.69/5.99 34 ifeq3(addition(A,addition(B,C)),addition(A,C),leq(B,addition(A,C)),true) = true. [para(12(a,1),16(a,1,1)),rewrite([10(3),10(4)])].
% 5.69/5.99 35 ifeq3(addition(A,addition(B,C)),addition(A,B),leq(C,addition(A,B)),true) = true. [para(12(a,2),16(a,1,1))].
% 5.69/5.99 39 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A). [para(17(a,1),15(a,1,1)),rewrite([10(8),8(10)])].
% 5.69/5.99 40 addition(star(A),addition(one,multiplication(star(A),A))) = star(A). [para(18(a,1),15(a,1,1)),rewrite([10(8),8(10)])].
% 5.69/5.99 42 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(3(a,1),20(a,1,1)),rewrite([10(4)]),flip(a)].
% 5.69/5.99 45 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(4(a,1),22(a,1,1)),rewrite([10(4)]),flip(a)].
% 5.69/5.99 49 ifeq3(multiplication(addition(A,B),C),multiplication(B,C),leq(multiplication(A,C),multiplication(B,C)),true) = true. [para(22(a,1),16(a,1,1))].
% 5.69/5.99 50 ifeq(leq(multiplication(A,B),B),true,leq(multiplication(star(A),multiplication(A,B)),B),true) = true. [para(2(a,1),24(a,1,1,1))].
% 5.69/5.99 52 ifeq(leq(addition(one,multiplication(A,B)),B),true,leq(star(A),B),true) = true. [para(3(a,1),24(a,1,3,1))].
% 5.69/5.99 63 ifeq(leq(addition(one,multiplication(A,B)),A),true,leq(star(B),A),true) = true. [para(4(a,1),26(a,1,3,1))].
% 5.69/5.99 72 leq(A,addition(A,B)) = true. [para(28(a,1),16(a,1,1)),rewrite([7(6)])].
% 5.69/5.99 75 leq(multiplication(A,B),multiplication(A,addition(B,C))) = true. [para(20(a,1),72(a,1,2))].
% 5.69/5.99 104 leq(A,addition(B,A)) = true. [para(2(a,1),34(a,1,1,2)),rewrite([7(6)])].
% 5.69/5.99 109 leq(A,addition(B,addition(A,C))) = true. [para(28(a,1),34(a,1,1,2)),rewrite([7(9)])].
% 5.69/5.99 112 leq(addition(A,B),addition(A,addition(B,C))) = true. [para(12(a,1),104(a,1,2)),rewrite([10(2),12(3,R),10(2)])].
% 5.69/5.99 120 leq(multiplication(A,B),addition(C,multiplication(A,addition(B,D)))) = true. [para(20(a,1),109(a,1,2,2))].
% 5.69/5.99 141 ifeq(leq(multiplication(A,addition(B,one)),A),true,leq(multiplication(A,star(B)),A),true) = true. [para(42(a,2),26(a,1,1,1))].
% 5.69/5.99 149 leq(A,addition(B,multiplication(A,addition(C,one)))) = true. [para(42(a,2),109(a,1,2,2))].
% 5.69/5.99 184 multiplication(addition(A,one),A) = multiplication(A,addition(A,one)). [para(45(a,2),42(a,2)),flip(a)].
% 5.69/5.99 205 ifeq3(star(A),addition(star(A),one),leq(multiplication(A,star(A)),addition(star(A),one)),true) = true. [para(39(a,1),35(a,1,1))].
% 5.69/5.99 206 leq(one,star(A)) = true. [para(39(a,1),109(a,1,2))].
% 5.69/5.99 208 addition(one,star(A)) = star(A). [para(206(a,1),15(a,1,1)),rewrite([8(7)])].
% 5.69/5.99 210 addition(star(A),one) = star(A). [para(208(a,1),10(a,1)),flip(a)].
% 5.69/5.99 211 addition(A,multiplication(A,star(B))) = multiplication(A,star(B)). [para(208(a,1),20(a,2,2)),rewrite([3(2)])].
% 5.69/5.99 212 addition(A,multiplication(star(B),A)) = multiplication(star(B),A). [para(208(a,1),22(a,2,1)),rewrite([4(2)])].
% 5.69/5.99 217 leq(multiplication(A,star(A)),star(A)) = true. [back_rewrite(205),rewrite([210(4),210(7),7(8)])].
% 5.69/5.99 220 addition(star(A),multiplication(star(A),A)) = star(A). [para(40(a,1),12(a,1)),rewrite([210(6),10(5)]),flip(a)].
% 5.69/5.99 225 leq(multiplication(star(A),A),star(A)) = true. [para(40(a,1),35(a,1,1)),rewrite([210(4),210(7),7(8)])].
% 5.69/5.99 235 addition(star(A),multiplication(A,star(A))) = star(A). [para(217(a,1),15(a,1,1)),rewrite([10(6),8(8)])].
% 5.69/5.99 257 leq(multiplication(star(A),star(A)),star(A)) = true. [para(220(a,1),26(a,1,1,1)),rewrite([32(3),9(9)])].
% 5.69/5.99 260 multiplication(star(A),addition(A,one)) = star(A). [para(220(a,1),42(a,2))].
% 5.69/5.99 270 addition(A,star(A)) = star(A). [para(260(a,1),45(a,2,2)),rewrite([210(3),260(4),10(5),12(5,R),208(4)]),flip(a)].
% 5.69/5.99 271 multiplication(star(star(A)),star(A)) = star(star(A)). [para(210(a,1),260(a,1,2))].
% 5.69/5.99 274 addition(A,addition(B,star(A))) = addition(B,star(A)). [para(270(a,1),12(a,2,2)),rewrite([10(2)])].
% 5.69/5.99 280 leq(multiplication(A,B),multiplication(A,star(B))) = true. [para(270(a,1),75(a,1,2,2))].
% 5.69/5.99 309 multiplication(addition(A,one),star(A)) = star(A). [para(235(a,1),45(a,2))].
% 5.69/5.99 351 multiplication(star(A),star(A)) = star(A). [para(257(a,1),15(a,1,1)),rewrite([10(7),211(7),8(7)])].
% 5.69/5.99 352 multiplication(star(A),multiplication(star(A),B)) = multiplication(star(A),B). [para(351(a,1),14(a,1,1)),flip(a)].
% 5.69/5.99 410 leq(multiplication(A,addition(A,one)),star(A)) = true. [para(309(a,1),280(a,1,2)),rewrite([184(3)])].
% 5.69/5.99 430 leq(addition(A,multiplication(A,A)),star(A)) = true. [para(42(a,1),410(a,1,1))].
% 5.69/5.99 433 addition(A,addition(star(A),multiplication(A,A))) = star(A). [para(430(a,1),15(a,1,1)),rewrite([10(6),12(6,R),10(5),8(8)])].
% 5.69/5.99 510 leq(addition(A,B),addition(A,star(B))) = true. [para(270(a,1),112(a,1,2,2))].
% 5.69/5.99 513 leq(addition(A,B),addition(B,star(A))) = true. [para(10(a,1),510(a,1,1))].
% 5.69/5.99 523 leq(multiplication(star(one),A),A) = true. [para(4(a,1),50(a,1,1,1)),rewrite([32(1),4(6),9(8)])].
% 5.69/5.99 531 leq(multiplication(star(addition(A,one)),star(A)),star(A)) = true. [para(309(a,1),50(a,1,1,1)),rewrite([32(3),309(9),9(11)])].
% 5.69/5.99 532 leq(star(star(A)),star(A)) = true. [para(351(a,1),50(a,1,1,1)),rewrite([32(3),351(7),271(6),9(8)])].
% 5.69/5.99 534 leq(star(one),one) = true. [para(3(a,1),523(a,1,1))].
% 5.69/5.99 540 star(one) = one. [para(534(a,1),15(a,1,1)),rewrite([10(6),270(6),8(6)])].
% 5.69/5.99 541 star(star(A)) = star(A). [para(532(a,1),15(a,1,1)),rewrite([10(6),270(6),8(6)])].
% 5.69/5.99 584 leq(A,addition(B,multiplication(A,star(C)))) = true. [para(210(a,1),149(a,1,2,2,2))].
% 5.69/5.99 597 leq(star(addition(A,one)),star(A)) = true. [para(309(a,1),52(a,1,1,1,2)),rewrite([208(3),32(3),9(9)])].
% 5.69/5.99 600 addition(star(A),star(addition(A,one))) = star(A). [para(597(a,1),15(a,1,1)),rewrite([10(7),8(9)])].
% 5.69/5.99 604 leq(A,multiplication(addition(A,B),star(C))) = true. [para(22(a,1),584(a,1,2)),rewrite([10(1)])].
% 5.69/5.99 608 leq(addition(A,one),addition(B,star(A))) = true. [para(309(a,1),584(a,1,2,2))].
% 5.69/5.99 610 ifeq2(leq(star(A),star(addition(A,one))),true,star(A),star(addition(A,one))) = star(addition(A,one)). [para(600(a,1),15(a,1,3))].
% 5.69/5.99 636 leq(A,multiplication(star(A),star(B))) = true. [para(270(a,1),604(a,1,2,1))].
% 5.69/5.99 640 addition(A,multiplication(star(A),star(B))) = multiplication(star(A),star(B)). [para(636(a,1),15(a,1,1)),rewrite([8(10)])].
% 5.69/5.99 644 addition(addition(A,one),star(B)) = addition(A,star(B)). [para(608(a,1),15(a,1,1)),rewrite([12(7),10(6),12(6,R),10(5),12(7,R),274(7),8(9)])].
% 5.69/5.99 904 leq(addition(A,B),addition(A,addition(C,star(B)))) = true. [para(274(a,1),112(a,1,2,2))].
% 5.69/5.99 928 addition(star(A),multiplication(A,A)) = star(A). [para(433(a,1),12(a,1)),rewrite([270(4),10(4)]),flip(a)].
% 5.69/5.99 1039 leq(addition(A,addition(B,one)),addition(B,star(A))) = true. [para(644(a,1),513(a,1,2))].
% 5.69/5.99 1377 multiplication(star(addition(A,one)),star(A)) = star(A). [para(531(a,1),15(a,1,1)),rewrite([10(9),212(9),8(9)])].
% 5.69/5.99 1649 leq(addition(A,B),addition(B,addition(C,star(A)))) = true. [para(10(a,1),904(a,1,1))].
% 5.69/5.99 1753 leq(addition(A,star(B)),addition(star(A),star(B))) = true. [para(210(a,1),1039(a,1,1,2)),rewrite([10(5)])].
% 5.69/5.99 2014 leq(addition(A,B),addition(addition(B,C),star(A))) = true. [para(28(a,1),1649(a,1,1)),rewrite([12(5),10(4),12(4),10(3),12(4,R),10(3),12(5,R),274(5)])].
% 5.69/5.99 2107 addition(A,addition(star(A),star(B))) = addition(star(A),star(B)). [para(1753(a,1),15(a,1,1)),rewrite([12(8),10(7),12(7,R),10(6),12(8,R),10(7),12(7,R),2(6),8(10)])].
% 5.69/5.99 2309 leq(multiplication(addition(A,B),A),star(addition(A,B))) = true. [para(928(a,1),120(a,1,2))].
% 5.69/5.99 2331 leq(addition(A,B),addition(addition(A,C),star(B))) = true. [para(10(a,1),2014(a,1,1))].
% 5.69/5.99 3424 addition(addition(A,B),star(C)) = addition(A,addition(B,star(C))). [para(2331(a,1),15(a,1,1)),rewrite([12(7),12(6),10(5),28(5),12(5),10(4),12(5,R),10(4),12(6,R),10(5),12(5),10(4),270(4),8(9)]),flip(a)].
% 5.69/5.99 5226 leq(multiplication(A,B),multiplication(A,multiplication(star(B),star(C)))) = true. [para(640(a,1),75(a,1,2,2))].
% 5.69/5.99 5453 leq(star(A),star(addition(A,one))) = true. [para(225(a,1),141(a,1,1)),rewrite([1377(7),9(9)])].
% 5.69/5.99 5459 star(addition(A,one)) = star(A). [back_rewrite(610),rewrite([5453(5),8(7)]),flip(a)].
% 5.69/5.99 5851 leq(addition(A,B),addition(A,addition(star(B),star(C)))) = true. [para(2107(a,1),112(a,1,2,2))].
% 5.69/5.99 7260 addition(A,addition(B,star(addition(A,B)))) = star(addition(A,B)). [para(3424(a,1),270(a,1))].
% 5.69/5.99 9282 leq(multiplication(star(A),A),multiplication(star(A),star(B))) = true. [para(352(a,1),5226(a,1,2))].
% 5.69/5.99 9305 multiplication(star(A),addition(A,star(B))) = multiplication(star(A),star(B)). [para(9282(a,1),15(a,1,1)),rewrite([20(8),8(10)])].
% 5.69/5.99 10213 addition(A,star(addition(A,B))) = star(addition(A,B)). [para(7260(a,1),28(a,1,2)),rewrite([7260(7)])].
% 5.69/5.99 10219 leq(A,addition(B,star(addition(A,C)))) = true. [para(7260(a,1),109(a,1,2,2))].
% 5.69/5.99 10258 leq(multiplication(star(addition(A,B)),A),star(addition(A,B))) = true. [para(7260(a,1),2309(a,1,1,1)),rewrite([7260(7),541(6)])].
% 5.69/5.99 10370 addition(A,addition(B,star(addition(A,C)))) = addition(B,star(addition(A,C))). [para(10219(a,1),15(a,1,1)),rewrite([8(10)])].
% 5.69/5.99 10395 addition(A,star(addition(B,A))) = star(addition(B,A)). [back_rewrite(7260),rewrite([10370(4)])].
% 5.69/5.99 10483 leq(addition(A,B),addition(A,star(addition(C,star(B))))) = true. [para(10213(a,1),5851(a,1,2,2)),rewrite([10(3)])].
% 5.69/5.99 10598 leq(multiplication(A,B),multiplication(star(addition(C,A)),B)) = true. [para(10395(a,1),49(a,1,1,1)),rewrite([7(13)])].
% 5.69/5.99 12895 multiplication(star(addition(A,B)),addition(A,one)) = star(addition(A,B)). [para(10258(a,1),15(a,1,1)),rewrite([10(8),42(8,R),8(10)])].
% 5.69/5.99 14320 leq(star(A),star(addition(A,B))) = true. [para(12895(a,1),63(a,1,1,1,2)),rewrite([208(4),32(5),5459(5),9(8)])].
% 5.69/5.99 14347 leq(multiplication(A,addition(B,one)),star(addition(A,B))) = true. [para(12895(a,1),10598(a,1,2)),rewrite([10(4)])].
% 5.69/5.99 14363 addition(star(A),star(addition(A,B))) = star(addition(A,B)). [para(14320(a,1),15(a,1,1)),rewrite([8(9)])].
% 5.69/5.99 15300 leq(addition(A,multiplication(A,B)),star(addition(A,B))) = true. [para(42(a,1),14347(a,1,1))].
% 5.69/5.99 15320 leq(addition(A,star(B)),star(addition(B,A))) = true. [para(14363(a,1),510(a,1,2)),rewrite([12(3),10(2),270(2)])].
% 5.69/5.99 15365 leq(addition(A,star(B)),star(addition(B,star(A)))) = true. [para(14363(a,1),10483(a,1,2)),rewrite([10(2)])].
% 5.69/5.99 15421 addition(star(A),star(addition(B,A))) = star(addition(B,A)). [para(15320(a,1),15(a,1,1)),rewrite([10(5),3424(7),10370(7),10(7),8(9),10(5)])].
% 5.69/5.99 15451 leq(star(addition(A,B)),star(addition(B,star(A)))) = true. [para(14363(a,1),15320(a,1,1)),rewrite([10(5),12(5),10(4),270(4)])].
% 5.69/5.99 15647 addition(multiplication(A,B),star(addition(A,B))) = star(addition(A,B)). [para(15300(a,1),15(a,1,1)),rewrite([10(7),12(7),10(6),10213(6),8(9)])].
% 5.69/5.99 15778 leq(star(addition(A,B)),star(addition(A,star(B)))) = true. [para(10395(a,1),15365(a,1,1)),rewrite([10(5),12(5),10(4),274(5)])].
% 5.69/5.99 15881 leq(star(A),star(addition(B,A))) = true. [para(15421(a,1),16(a,1,1)),rewrite([7(10)])].
% 5.69/5.99 15907 tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),true) != tuple(true,true) # answer(goals). [back_rewrite(27),rewrite([15881(14)])].
% 5.69/5.99 15937 leq(star(addition(A,star(B))),star(addition(B,A))) = true. [para(14363(a,1),15451(a,1,2,1)),rewrite([10(3),12(3),10(2),270(2),541(6)])].
% 5.69/5.99 16075 addition(star(addition(A,B)),star(addition(A,star(B)))) = star(addition(A,star(B))). [para(15778(a,1),15(a,1,1)),rewrite([8(12)])].
% 5.69/5.99 16315 star(addition(A,star(B))) = star(addition(A,B)). [para(15937(a,1),15(a,1,1)),rewrite([10(6),10(8),16075(8),10(6),8(8),10(4)])].
% 5.69/5.99 18580 star(addition(A,addition(B,multiplication(A,B)))) = star(addition(A,B)). [para(15647(a,1),16315(a,1,1)),rewrite([541(3),12(5),10(4),12(5,R),10(4)]),flip(a)].
% 5.69/5.99 19887 star(addition(A,B)) = star(multiplication(star(A),star(B))). [para(9305(a,1),18580(a,1,1,2,2)),rewrite([10(7),12(7),10(6),640(6),212(6),211(5),12(8,R),10(7),2107(8),16315(8),10(6),16315(7),10(5)]),flip(a)].
% 5.69/5.99 20268 $F # answer(goals). [back_rewrite(15907),rewrite([19887(4),540(2),4(4),541(3),32(5)]),xx(a)].
% 5.69/5.99
% 5.69/5.99 % SZS output end Refutation
% 5.69/5.99 ============================== end of proof ==========================
% 5.69/5.99
% 5.69/5.99 ============================== STATISTICS ============================
% 5.69/5.99
% 5.69/5.99 Given=1300. Generated=207236. Kept=20261. proofs=1.
% 5.69/5.99 Usable=1042. Sos=8817. Demods=9962. Limbo=381, Disabled=10042. Hints=0.
% 5.69/5.99 Megabytes=18.42.
% 5.69/5.99 User_CPU=4.91, System_CPU=0.13, Wall_clock=5.
% 5.69/5.99
% 5.69/5.99 ============================== end of statistics =====================
% 5.69/5.99
% 5.69/5.99 ============================== end of search =========================
% 5.69/5.99
% 5.69/5.99 THEOREM PROVED
% 5.69/5.99 % SZS status Unsatisfiable
% 5.69/5.99
% 5.69/5.99 Exiting with 1 proof.
% 5.69/5.99
% 5.69/5.99 Process 7389 exit (max_proofs) Thu Jun 16 13:43:56 2022
% 5.69/5.99 Prover9 interrupted
%------------------------------------------------------------------------------