TSTP Solution File: RNG008-7 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG008-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 : Mon Jul 18 20:39:10 EDT 2022
% Result : Unsatisfiable 1.57s 1.86s
% Output : Refutation 1.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG008-7 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n020.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 : Mon May 30 11:33:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.57/1.86 ============================== Prover9 ===============================
% 1.57/1.86 Prover9 (32) version 2009-11A, November 2009.
% 1.57/1.86 Process 8053 was started by sandbox2 on n020.cluster.edu,
% 1.57/1.86 Mon May 30 11:33:24 2022
% 1.57/1.86 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7899_n020.cluster.edu".
% 1.57/1.86 ============================== end of head ===========================
% 1.57/1.86
% 1.57/1.86 ============================== INPUT =================================
% 1.57/1.86
% 1.57/1.86 % Reading from file /tmp/Prover9_7899_n020.cluster.edu
% 1.57/1.86
% 1.57/1.86 set(prolog_style_variables).
% 1.57/1.86 set(auto2).
% 1.57/1.86 % set(auto2) -> set(auto).
% 1.57/1.86 % set(auto) -> set(auto_inference).
% 1.57/1.86 % set(auto) -> set(auto_setup).
% 1.57/1.86 % set(auto_setup) -> set(predicate_elim).
% 1.57/1.86 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.57/1.86 % set(auto) -> set(auto_limits).
% 1.57/1.86 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.57/1.86 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.57/1.86 % set(auto) -> set(auto_denials).
% 1.57/1.86 % set(auto) -> set(auto_process).
% 1.57/1.86 % set(auto2) -> assign(new_constants, 1).
% 1.57/1.86 % set(auto2) -> assign(fold_denial_max, 3).
% 1.57/1.86 % set(auto2) -> assign(max_weight, "200.000").
% 1.57/1.86 % set(auto2) -> assign(max_hours, 1).
% 1.57/1.86 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.57/1.86 % set(auto2) -> assign(max_seconds, 0).
% 1.57/1.86 % set(auto2) -> assign(max_minutes, 5).
% 1.57/1.86 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.57/1.86 % set(auto2) -> set(sort_initial_sos).
% 1.57/1.86 % set(auto2) -> assign(sos_limit, -1).
% 1.57/1.86 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.57/1.86 % set(auto2) -> assign(max_megs, 400).
% 1.57/1.86 % set(auto2) -> assign(stats, some).
% 1.57/1.86 % set(auto2) -> clear(echo_input).
% 1.57/1.86 % set(auto2) -> set(quiet).
% 1.57/1.86 % set(auto2) -> clear(print_initial_clauses).
% 1.57/1.86 % set(auto2) -> clear(print_given).
% 1.57/1.86 assign(lrs_ticks,-1).
% 1.57/1.86 assign(sos_limit,10000).
% 1.57/1.86 assign(order,kbo).
% 1.57/1.86 set(lex_order_vars).
% 1.57/1.86 clear(print_given).
% 1.57/1.86
% 1.57/1.86 % formulas(sos). % not echoed (12 formulas)
% 1.57/1.86
% 1.57/1.86 ============================== end of input ==========================
% 1.57/1.86
% 1.57/1.86 % From the command line: assign(max_seconds, 300).
% 1.57/1.86
% 1.57/1.86 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.57/1.86
% 1.57/1.86 % Formulas that are not ordinary clauses:
% 1.57/1.86
% 1.57/1.86 ============================== end of process non-clausal formulas ===
% 1.57/1.86
% 1.57/1.86 ============================== PROCESS INITIAL CLAUSES ===============
% 1.57/1.86
% 1.57/1.86 ============================== PREDICATE ELIMINATION =================
% 1.57/1.86
% 1.57/1.86 ============================== end predicate elimination =============
% 1.57/1.86
% 1.57/1.86 Auto_denials:
% 1.57/1.86 % copying label prove_commutativity to answer in negative clause
% 1.57/1.86
% 1.57/1.86 Term ordering decisions:
% 1.57/1.86
% 1.57/1.86 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (8).
% 1.57/1.86 Function symbol KB weights: additive_identity=1. a=1. b=1. c=1. add=1. multiply=1. additive_inverse=0.
% 1.57/1.86
% 1.57/1.86 ============================== end of process initial clauses ========
% 1.57/1.86
% 1.57/1.86 ============================== CLAUSES FOR SEARCH ====================
% 1.57/1.86
% 1.57/1.86 ============================== end of clauses for search =============
% 1.57/1.86
% 1.57/1.86 ============================== SEARCH ================================
% 1.57/1.86
% 1.57/1.86 % Starting search at 0.01 seconds.
% 1.57/1.86
% 1.57/1.86 ============================== PROOF =================================
% 1.57/1.86 % SZS status Unsatisfiable
% 1.57/1.86 % SZS output start Refutation
% 1.57/1.86
% 1.57/1.86 % Proof 1 at 0.84 (+ 0.03) seconds: prove_commutativity.
% 1.57/1.86 % Length of proof is 232.
% 1.57/1.86 % Level of proof is 38.
% 1.57/1.86 % Maximum clause weight is 21.000.
% 1.57/1.86 % Given clauses 264.
% 1.57/1.86
% 1.57/1.86 2 add(A,additive_identity) = A # label(right_additive_identity) # label(axiom). [assumption].
% 1.57/1.86 3 multiply(A,A) = A # label(boolean_ring) # label(hypothesis). [assumption].
% 1.57/1.86 4 multiply(a,b) = c # label(a_times_b_is_c) # label(negated_conjecture). [assumption].
% 1.57/1.86 5 c = multiply(a,b). [copy(4),flip(a)].
% 1.57/1.86 7 add(A,additive_inverse(A)) = additive_identity # label(right_additive_inverse) # label(axiom). [assumption].
% 1.57/1.86 8 add(A,B) = add(B,A) # label(commutativity_for_addition) # label(axiom). [assumption].
% 1.57/1.86 9 add(A,add(B,C)) = add(add(A,B),C) # label(associativity_for_addition) # label(axiom). [assumption].
% 1.57/1.86 10 add(A,add(B,C)) = add(C,add(A,B)). [copy(9),rewrite([8(4)])].
% 1.57/1.86 11 multiply(A,multiply(B,C)) = multiply(multiply(A,B),C) # label(associativity_for_multiplication) # label(axiom). [assumption].
% 1.57/1.86 12 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [copy(11),flip(a)].
% 1.57/1.86 13 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distribute1) # label(axiom). [assumption].
% 1.57/1.86 14 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(13),flip(a)].
% 1.57/1.86 15 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distribute2) # label(axiom). [assumption].
% 1.57/1.86 16 add(multiply(A,B),multiply(C,B)) = multiply(add(A,C),B). [copy(15),flip(a)].
% 1.57/1.86 17 multiply(b,a) != c # label(prove_commutativity) # label(negated_conjecture) # answer(prove_commutativity). [assumption].
% 1.57/1.86 18 multiply(b,a) != multiply(a,b) # answer(prove_commutativity). [copy(17),rewrite([5(4)])].
% 1.57/1.86 19 multiply(b,a) = c_0. [new_symbol(18)].
% 1.57/1.86 20 multiply(a,b) != c_0 # answer(prove_commutativity). [back_rewrite(18),rewrite([19(3)]),flip(a)].
% 1.57/1.86 21 add(A,add(B,additive_inverse(A))) = B. [para(7(a,1),10(a,2,2)),rewrite([8(2),2(5)])].
% 1.57/1.86 22 multiply(A,multiply(B,multiply(A,B))) = multiply(A,B). [para(12(a,1),3(a,1))].
% 1.57/1.86 23 multiply(A,multiply(A,B)) = multiply(A,B). [para(3(a,1),12(a,1,1)),flip(a)].
% 1.57/1.86 24 multiply(A,add(A,B)) = add(A,multiply(A,B)). [para(3(a,1),14(a,1,1)),flip(a)].
% 1.57/1.86 25 multiply(add(A,B),A) = add(A,multiply(B,A)). [para(3(a,1),16(a,1,1)),flip(a)].
% 1.57/1.86 26 multiply(add(A,B),B) = add(B,multiply(A,B)). [para(3(a,1),16(a,1,2)),rewrite([8(2)]),flip(a)].
% 1.57/1.86 28 add(multiply(A,multiply(B,C)),multiply(D,C)) = multiply(add(D,multiply(A,B)),C). [para(12(a,1),16(a,1,1)),rewrite([8(6)])].
% 1.57/1.86 29 add(multiply(A,B),multiply(C,multiply(D,B))) = multiply(add(A,multiply(C,D)),B). [para(12(a,1),16(a,1,2))].
% 1.57/1.86 30 multiply(add(A,A),B) = multiply(A,add(B,B)). [para(16(a,1),14(a,1))].
% 1.57/1.86 31 multiply(b,multiply(a,A)) = multiply(c_0,A). [para(19(a,1),12(a,1,1)),flip(a)].
% 1.57/1.86 32 multiply(b,add(A,a)) = add(c_0,multiply(b,A)). [para(19(a,1),14(a,1,1)),rewrite([8(7)]),flip(a)].
% 1.57/1.86 34 add(A,add(B,add(C,additive_inverse(A)))) = add(B,C). [para(21(a,1),10(a,2,2)),rewrite([8(3),10(3,R),8(2),8(5)])].
% 1.57/1.86 35 multiply(A,multiply(B,multiply(A,multiply(B,C)))) = multiply(A,multiply(B,C)). [para(23(a,1),12(a,1)),rewrite([12(2),12(4)]),flip(a)].
% 1.57/1.86 36 multiply(A,add(B,multiply(A,C))) = multiply(A,add(C,B)). [para(23(a,1),14(a,1,1)),rewrite([14(3),8(4)]),flip(a)].
% 1.57/1.86 37 multiply(add(A,multiply(B,A)),C) = multiply(add(A,B),multiply(A,C)). [para(23(a,1),16(a,1,1)),rewrite([29(4)])].
% 1.57/1.86 38 multiply(b,c_0) = c_0. [para(19(a,1),23(a,1,2)),rewrite([19(6)])].
% 1.57/1.86 39 multiply(b,multiply(c_0,A)) = multiply(c_0,A). [para(38(a,1),12(a,1,1)),flip(a)].
% 1.57/1.86 41 multiply(add(A,b),c_0) = add(c_0,multiply(A,c_0)). [para(38(a,1),16(a,1,1)),rewrite([8(6)]),flip(a)].
% 1.57/1.86 42 multiply(c_0,a) = c_0. [para(3(a,1),31(a,1,2)),rewrite([19(3)]),flip(a)].
% 1.57/1.86 43 multiply(b,add(A,multiply(a,B))) = add(multiply(c_0,B),multiply(b,A)). [para(31(a,1),14(a,1,1)),rewrite([8(9)]),flip(a)].
% 1.57/1.86 44 multiply(add(c_0,multiply(A,a)),B) = multiply(add(A,b),multiply(a,B)). [para(31(a,1),16(a,1,1)),rewrite([29(6),8(7)])].
% 1.57/1.86 45 multiply(c_0,multiply(a,A)) = multiply(c_0,A). [para(23(a,1),31(a,1,2)),rewrite([31(4)]),flip(a)].
% 1.57/1.86 46 multiply(c_0,add(A,a)) = add(c_0,multiply(c_0,A)). [para(42(a,1),14(a,1,1)),rewrite([8(7)]),flip(a)].
% 1.57/1.86 49 multiply(A,add(B,multiply(C,multiply(A,C)))) = multiply(A,add(C,B)). [para(22(a,1),14(a,1,1)),rewrite([14(3),8(5)]),flip(a)].
% 1.57/1.86 51 multiply(c_0,multiply(A,multiply(a,A))) = multiply(c_0,A). [para(22(a,1),31(a,1,2)),rewrite([31(4)]),flip(a)].
% 1.57/1.86 52 multiply(a,multiply(c_0,b)) = multiply(a,b). [para(31(a,1),22(a,1,2))].
% 1.57/1.86 54 multiply(add(A,c_0),multiply(c_0,B)) = multiply(add(A,b),multiply(c_0,B)). [para(39(a,1),16(a,1,1)),rewrite([29(6),37(5),8(2),8(7)])].
% 1.57/1.86 55 multiply(c_0,add(A,multiply(a,B))) = multiply(c_0,add(B,A)). [para(45(a,1),14(a,1,1)),rewrite([14(5),8(7)]),flip(a)].
% 1.57/1.86 56 multiply(add(A,c_0),multiply(a,B)) = multiply(add(A,b),multiply(a,B)). [para(45(a,1),16(a,1,1)),rewrite([29(6),44(5),8(7)]),flip(a)].
% 1.57/1.86 57 multiply(a,multiply(c_0,multiply(b,A))) = multiply(a,multiply(b,A)). [para(52(a,1),12(a,1,1)),rewrite([12(4),12(9)]),flip(a)].
% 1.57/1.86 58 multiply(a,add(A,multiply(c_0,b))) = multiply(a,add(A,b)). [para(52(a,1),14(a,1,1)),rewrite([14(6),8(3),8(9)]),flip(a)].
% 1.57/1.86 60 add(A,multiply(A,additive_identity)) = A. [para(2(a,1),24(a,1,2)),rewrite([3(1)]),flip(a)].
% 1.57/1.86 61 add(A,multiply(A,additive_inverse(A))) = multiply(A,additive_identity). [para(7(a,1),24(a,1,2)),flip(a)].
% 1.57/1.86 63 multiply(A,multiply(B,add(C,multiply(A,B)))) = multiply(A,add(B,multiply(B,C))). [para(24(a,1),12(a,1)),rewrite([12(3),14(4),8(5)]),flip(a)].
% 1.57/1.86 65 multiply(A,multiply(B,multiply(A,add(B,C)))) = multiply(A,add(B,multiply(B,multiply(A,C)))). [para(14(a,1),24(a,1,2)),rewrite([12(4),12(8),14(9)])].
% 1.57/1.86 66 add(add(A,multiply(A,B)),multiply(C,add(A,B))) = multiply(add(A,C),add(A,B)). [para(24(a,1),16(a,1,1))].
% 1.57/1.86 67 add(A,add(multiply(A,B),multiply(C,add(A,B)))) = multiply(add(C,A),add(A,B)). [para(24(a,1),16(a,1,2)),rewrite([10(5),8(4),10(5,R),8(4)])].
% 1.57/1.86 69 multiply(A,multiply(B,multiply(add(A,C),B))) = multiply(A,add(B,multiply(B,multiply(C,B)))). [para(16(a,1),24(a,1,2)),rewrite([12(4),12(8),14(9)])].
% 1.57/1.86 70 multiply(b,add(a,b)) = add(b,c_0). [para(19(a,1),24(a,2,2)),rewrite([8(4)])].
% 1.57/1.86 71 add(A,multiply(A,add(B,additive_inverse(A)))) = multiply(A,B). [para(21(a,1),24(a,1,2)),flip(a)].
% 1.57/1.86 72 multiply(c_0,add(A,c_0)) = add(c_0,multiply(c_0,A)). [para(24(a,1),31(a,2)),rewrite([8(4),31(6)])].
% 1.57/1.86 73 multiply(A,multiply(add(A,B),add(A,multiply(A,B)))) = add(A,multiply(A,B)). [para(24(a,1),22(a,1,2,2)),rewrite([24(7)])].
% 1.57/1.86 74 add(A,multiply(additive_identity,A)) = A. [para(2(a,1),25(a,1,1)),rewrite([3(1)]),flip(a)].
% 1.57/1.86 75 add(A,multiply(additive_inverse(A),A)) = multiply(additive_identity,A). [para(7(a,1),25(a,1,1)),flip(a)].
% 1.57/1.86 76 multiply(add(A,add(B,C)),B) = add(B,multiply(add(A,C),B)). [para(10(a,1),25(a,1,1)),rewrite([8(4)])].
% 1.57/1.86 78 add(add(A,multiply(B,A)),multiply(add(A,B),C)) = multiply(add(A,B),add(A,C)). [para(25(a,1),14(a,1,1))].
% 1.57/1.86 83 add(A,multiply(add(B,additive_inverse(A)),A)) = multiply(B,A). [para(21(a,1),25(a,1,1)),flip(a)].
% 1.57/1.86 85 multiply(add(A,B),add(A,multiply(A,multiply(B,A)))) = add(A,multiply(B,A)). [para(25(a,1),22(a,1,2,2)),rewrite([24(4),25(7)])].
% 1.57/1.86 87 add(A,add(B,multiply(A,additive_identity))) = add(A,B). [para(60(a,1),10(a,2,2)),rewrite([8(3),8(5)])].
% 1.57/1.86 89 add(A,add(B,multiply(additive_identity,A))) = add(A,B). [para(74(a,1),10(a,2,2)),rewrite([8(3),8(5)])].
% 1.57/1.86 90 multiply(additive_identity,add(A,A)) = multiply(additive_identity,A). [para(23(a,1),74(a,1,2)),rewrite([14(5)])].
% 1.57/1.86 91 multiply(b,multiply(add(a,b),A)) = multiply(add(b,c_0),A). [para(70(a,1),12(a,1,1)),flip(a)].
% 1.57/1.86 102 add(additive_identity,multiply(A,additive_identity)) = multiply(A,additive_identity). [para(2(a,1),26(a,1,1)),flip(a)].
% 1.57/1.86 103 add(additive_inverse(A),multiply(A,additive_inverse(A))) = multiply(additive_identity,additive_inverse(A)). [para(7(a,1),26(a,1,1)),flip(a)].
% 1.57/1.86 109 add(add(A,additive_inverse(B)),multiply(B,add(A,additive_inverse(B)))) = add(A,multiply(A,additive_inverse(B))). [para(21(a,1),26(a,1,1)),rewrite([24(3)]),flip(a)].
% 1.57/1.86 114 multiply(additive_identity,add(A,add(A,B))) = multiply(additive_identity,add(A,B)). [para(90(a,1),14(a,1,1)),rewrite([14(5),8(6),10(6),8(5)]),flip(a)].
% 1.57/1.86 118 add(additive_identity,multiply(additive_identity,A)) = multiply(additive_identity,A). [para(90(a,1),24(a,2,2)),rewrite([10(4),8(3),2(3),90(3)]),flip(a)].
% 1.57/1.86 174 multiply(add(A,A),additive_identity) = multiply(A,additive_identity). [para(2(a,1),30(a,2,2))].
% 1.57/1.86 286 multiply(add(b,additive_inverse(c_0)),c_0) = multiply(additive_identity,c_0). [para(75(a,1),41(a,2)),rewrite([8(4)])].
% 1.57/1.86 291 add(add(b,additive_inverse(c_0)),multiply(additive_identity,c_0)) = add(b,multiply(additive_inverse(c_0),b)). [para(286(a,1),24(a,2,2)),rewrite([8(10),21(10),25(6)]),flip(a)].
% 1.57/1.86 301 multiply(c_0,add(a,additive_inverse(c_0))) = multiply(c_0,additive_identity). [para(61(a,1),46(a,2)),rewrite([8(5)])].
% 1.57/1.86 324 multiply(add(A,multiply(B,C)),multiply(B,multiply(C,D))) = multiply(add(B,A),multiply(B,multiply(C,D))). [para(35(a,1),28(a,1,1)),rewrite([29(6),37(4)]),flip(a)].
% 1.57/1.86 344 multiply(c_0,multiply(add(a,additive_inverse(c_0)),A)) = multiply(c_0,multiply(additive_identity,A)). [para(301(a,1),12(a,1,1)),rewrite([12(4)]),flip(a)].
% 1.57/1.86 346 add(multiply(c_0,additive_identity),multiply(A,add(a,additive_inverse(c_0)))) = multiply(add(A,c_0),add(a,additive_inverse(c_0))). [para(301(a,1),16(a,1,1)),rewrite([8(11)])].
% 1.57/1.86 347 add(add(a,additive_inverse(c_0)),multiply(c_0,additive_identity)) = add(a,multiply(a,additive_inverse(c_0))). [para(301(a,1),25(a,2,2)),rewrite([8(6),21(6),24(6)]),flip(a)].
% 1.57/1.86 364 multiply(c_0,multiply(add(A,b),multiply(a,add(A,c_0)))) = add(c_0,multiply(c_0,A)). [para(24(a,1),51(a,2)),rewrite([8(3),8(6),56(8)])].
% 1.57/1.86 372 multiply(c_0,multiply(additive_identity,add(a,multiply(a,additive_inverse(c_0))))) = multiply(c_0,additive_identity). [para(301(a,1),51(a,2)),rewrite([24(11),344(13)])].
% 1.57/1.86 483 add(A,add(B,multiply(A,add(C,additive_inverse(A))))) = add(B,multiply(A,C)). [para(71(a,1),10(a,2,2)),rewrite([8(4)])].
% 1.57/1.86 491 add(multiply(additive_identity,A),multiply(A,B)) = multiply(A,B). [para(71(a,1),89(a,2)),rewrite([8(6),483(7)])].
% 1.57/1.86 504 multiply(add(b,c_0),additive_identity) = multiply(c_0,additive_identity). [para(102(a,1),43(a,1,2)),rewrite([31(5),8(10),16(10)]),flip(a)].
% 1.57/1.86 505 add(c_0,multiply(c_0,additive_inverse(a))) = multiply(c_0,additive_identity). [para(61(a,1),43(a,1,2)),rewrite([31(5),19(10),8(9)]),flip(a)].
% 1.57/1.86 524 multiply(add(b,c_0),multiply(additive_identity,A)) = multiply(c_0,multiply(additive_identity,A)). [para(504(a,1),12(a,1,1)),rewrite([12(4)]),flip(a)].
% 1.57/1.86 537 multiply(c_0,multiply(additive_identity,multiply(c_0,additive_inverse(a)))) = multiply(c_0,add(additive_inverse(a),additive_inverse(a))). [para(505(a,1),26(a,1,1)),rewrite([12(8),23(18),14(17)])].
% 1.57/1.86 574 add(multiply(A,B),multiply(additive_identity,A)) = multiply(A,B). [para(491(a,1),8(a,1)),flip(a)].
% 1.57/1.86 576 add(c_0,multiply(additive_identity,b)) = c_0. [para(19(a,1),491(a,1,2)),rewrite([8(5),19(8)])].
% 1.57/1.86 577 multiply(additive_identity,add(A,multiply(A,B))) = multiply(additive_identity,multiply(A,B)). [para(23(a,1),491(a,1,1)),rewrite([12(5),14(6),12(7)])].
% 1.57/1.86 578 add(multiply(additive_identity,b),multiply(c_0,A)) = multiply(c_0,A). [para(31(a,1),491(a,1,2)),rewrite([31(10)])].
% 1.57/1.86 585 multiply(additive_identity,c_0) = multiply(additive_identity,b). [para(286(a,1),491(a,1,2)),rewrite([8(10),14(10),21(7),286(9)]),flip(a)].
% 1.57/1.86 586 multiply(additive_identity,add(b,additive_inverse(c_0))) = multiply(additive_identity,b). [para(286(a,1),491(a,2)),rewrite([286(12),585(9),8(10),14(10),114(8),585(9)])].
% 1.57/1.86 590 multiply(A,add(B,multiply(additive_identity,A))) = multiply(A,B). [para(491(a,1),36(a,1,2)),rewrite([23(2)]),flip(a)].
% 1.57/1.86 598 multiply(c_0,multiply(additive_identity,multiply(a,additive_inverse(c_0)))) = multiply(c_0,additive_identity). [back_rewrite(372),rewrite([577(9)])].
% 1.57/1.86 613 add(add(b,additive_inverse(c_0)),multiply(additive_identity,b)) = add(b,multiply(additive_inverse(c_0),b)). [back_rewrite(291),rewrite([585(7)])].
% 1.57/1.86 616 multiply(add(b,additive_inverse(c_0)),c_0) = multiply(additive_identity,b). [back_rewrite(286),rewrite([585(9)])].
% 1.57/1.86 642 multiply(additive_identity,multiply(c_0,A)) = multiply(additive_identity,multiply(b,A)). [para(585(a,1),12(a,1,1)),rewrite([12(4)]),flip(a)].
% 1.57/1.86 643 multiply(additive_identity,add(A,c_0)) = multiply(additive_identity,add(A,b)). [para(585(a,1),14(a,1,1)),rewrite([14(6),8(3),8(7)]),flip(a)].
% 1.57/1.86 651 multiply(c_0,multiply(additive_identity,multiply(b,additive_inverse(a)))) = multiply(c_0,add(additive_inverse(a),additive_inverse(a))). [back_rewrite(537),rewrite([642(7)])].
% 1.57/1.86 702 multiply(additive_identity,add(A,add(b,additive_inverse(c_0)))) = multiply(additive_identity,add(A,b)). [para(586(a,1),14(a,1,1)),rewrite([14(6),8(3),8(10)]),flip(a)].
% 1.57/1.86 703 add(multiply(additive_identity,b),multiply(A,add(b,additive_inverse(c_0)))) = multiply(A,add(b,additive_inverse(c_0))). [para(586(a,1),16(a,1,1)),rewrite([8(11),2(11)])].
% 1.57/1.86 704 add(b,multiply(additive_inverse(c_0),b)) = add(b,additive_inverse(c_0)). [para(586(a,1),74(a,1,2)),rewrite([613(8)])].
% 1.57/1.86 710 add(add(b,additive_inverse(c_0)),multiply(additive_identity,b)) = add(b,additive_inverse(c_0)). [back_rewrite(613),rewrite([704(14)])].
% 1.57/1.86 738 multiply(add(additive_identity,c_0),b) = multiply(c_0,b). [para(578(a,1),16(a,1)),flip(a)].
% 1.57/1.86 744 add(multiply(c_0,b),multiply(add(additive_identity,c_0),A)) = multiply(add(additive_identity,c_0),add(A,b)). [para(738(a,1),14(a,1,1)),rewrite([8(13)])].
% 1.57/1.86 776 multiply(A,multiply(additive_identity,A)) = multiply(A,additive_identity). [para(118(a,1),590(a,1,2))].
% 1.57/1.86 788 multiply(c_0,multiply(additive_identity,b)) = multiply(c_0,additive_identity). [para(504(a,1),590(a,2)),rewrite([643(9),90(9),118(8),524(7)])].
% 1.57/1.86 806 multiply(additive_identity,multiply(A,additive_identity)) = multiply(additive_identity,A). [para(23(a,1),776(a,1,2)),rewrite([3(5),12(6)]),flip(a)].
% 1.57/1.86 807 multiply(c_0,multiply(additive_identity,a)) = multiply(c_0,additive_identity). [para(776(a,1),31(a,1,2)),rewrite([31(5)]),flip(a)].
% 1.57/1.86 823 multiply(c_0,multiply(additive_identity,multiply(b,A))) = multiply(c_0,multiply(additive_identity,A)). [para(788(a,1),12(a,1,1)),rewrite([12(4),12(9)]),flip(a)].
% 1.57/1.86 824 add(multiply(c_0,additive_identity),multiply(A,multiply(additive_identity,b))) = multiply(add(A,c_0),multiply(additive_identity,b)). [para(788(a,1),16(a,1,1)),rewrite([8(10)])].
% 1.57/1.86 829 multiply(c_0,multiply(additive_identity,additive_inverse(a))) = multiply(c_0,add(additive_inverse(a),additive_inverse(a))). [back_rewrite(651),rewrite([823(8)])].
% 1.57/1.86 854 multiply(additive_identity,multiply(A,multiply(additive_identity,B))) = multiply(additive_identity,multiply(A,B)). [para(806(a,1),12(a,1,1)),rewrite([12(3),12(7)]),flip(a)].
% 1.57/1.86 862 multiply(c_0,multiply(additive_identity,multiply(a,A))) = multiply(c_0,multiply(additive_identity,A)). [para(807(a,1),12(a,1,1)),rewrite([12(4),12(9)]),flip(a)].
% 1.57/1.86 871 multiply(c_0,multiply(additive_identity,additive_inverse(c_0))) = multiply(c_0,additive_identity). [back_rewrite(598),rewrite([862(8)])].
% 1.57/1.86 923 multiply(additive_identity,multiply(b,additive_inverse(c_0))) = multiply(additive_identity,b). [para(871(a,1),642(a,1,2)),rewrite([806(5),585(3),854(11)]),flip(a)].
% 1.57/1.86 956 multiply(a,add(A,multiply(c_0,multiply(b,B)))) = multiply(a,add(A,multiply(b,B))). [para(57(a,1),14(a,1,1)),rewrite([14(7),8(4),8(11)]),flip(a)].
% 1.57/1.86 979 add(b,multiply(add(additive_identity,additive_inverse(c_0)),b)) = add(b,additive_inverse(c_0)). [para(704(a,1),89(a,2)),rewrite([8(9),16(9)])].
% 1.57/1.86 981 multiply(c_0,add(b,additive_inverse(c_0))) = multiply(c_0,additive_identity). [para(704(a,1),55(a,2,2)),rewrite([8(9),16(9),344(8),788(5)]),flip(a)].
% 1.57/1.86 997 add(multiply(c_0,additive_identity),multiply(A,add(b,additive_inverse(c_0)))) = multiply(add(A,c_0),add(b,additive_inverse(c_0))). [para(981(a,1),16(a,1,1)),rewrite([8(11)])].
% 1.57/1.86 998 multiply(c_0,b) = c_0. [para(981(a,1),24(a,2,2)),rewrite([21(7),60(8)])].
% 1.57/1.86 999 add(add(b,additive_inverse(c_0)),multiply(c_0,additive_identity)) = add(b,multiply(b,additive_inverse(c_0))). [para(981(a,1),25(a,2,2)),rewrite([8(6),21(6),24(6)]),flip(a)].
% 1.57/1.86 1013 multiply(add(additive_identity,c_0),add(A,b)) = add(c_0,multiply(add(additive_identity,c_0),A)). [back_rewrite(744),rewrite([998(3)]),flip(a)].
% 1.57/1.86 1019 multiply(a,add(A,c_0)) = multiply(a,add(A,b)). [back_rewrite(58),rewrite([998(4)])].
% 1.57/1.86 1020 multiply(a,c_0) = multiply(a,b). [back_rewrite(52),rewrite([998(4)])].
% 1.57/1.86 1022 multiply(c_0,add(A,b)) = add(c_0,multiply(c_0,A)). [back_rewrite(364),rewrite([1019(7),51(9)])].
% 1.57/1.86 1027 multiply(c_0,multiply(b,A)) = multiply(c_0,A). [para(998(a,1),12(a,1,1)),flip(a)].
% 1.57/1.86 1037 multiply(a,add(A,multiply(c_0,B))) = multiply(a,add(A,multiply(b,B))). [back_rewrite(956),rewrite([1027(5)])].
% 1.57/1.86 1040 multiply(a,multiply(c_0,A)) = multiply(a,multiply(b,A)). [back_rewrite(57),rewrite([1027(5)])].
% 1.57/1.86 1260 add(add(c_0,multiply(c_0,A)),multiply(B,add(A,b))) = multiply(add(B,c_0),add(A,b)). [para(1022(a,1),16(a,1,1)),rewrite([8(10)])].
% 1.57/1.86 1267 multiply(c_0,add(b,additive_inverse(a))) = multiply(c_0,additive_identity). [para(505(a,1),1022(a,2)),rewrite([8(5)])].
% 1.57/1.86 1322 multiply(additive_identity,multiply(b,additive_inverse(a))) = multiply(additive_identity,b). [para(1267(a,1),642(a,1,2)),rewrite([806(5),585(3),24(10),577(11)]),flip(a)].
% 1.57/1.86 1480 multiply(a,add(b,multiply(b,additive_inverse(c_0)))) = multiply(a,multiply(b,additive_identity)). [para(981(a,1),1040(a,1,2)),rewrite([1040(5),24(12)]),flip(a)].
% 1.57/1.86 1519 add(add(A,A),multiply(B,add(A,A))) = multiply(add(A,B),add(A,A)). [para(3(a,1),66(a,1,1,2))].
% 1.57/1.86 1587 multiply(add(additive_identity,b),add(b,additive_inverse(c_0))) = add(b,multiply(b,additive_inverse(c_0))). [para(586(a,1),66(a,1,2)),rewrite([8(10),10(10,R),8(9),491(9),8(9)]),flip(a)].
% 1.57/1.86 1588 add(add(b,additive_inverse(c_0)),multiply(A,b)) = add(b,multiply(add(A,additive_inverse(c_0)),b)). [para(616(a,1),66(a,1,1,2)),rewrite([710(8),8(10),21(10),8(12),8(18),21(18),76(14)])].
% 1.57/1.86 1696 add(A,add(B,multiply(add(C,additive_inverse(A)),A))) = add(B,multiply(C,A)). [para(83(a,1),10(a,2,2)),rewrite([8(4)])].
% 1.57/1.86 1703 add(multiply(A,additive_identity),multiply(B,A)) = multiply(B,A). [para(83(a,1),87(a,2)),rewrite([8(6),1696(7)])].
% 1.57/1.86 1711 add(c_0,multiply(a,additive_identity)) = c_0. [para(19(a,1),1703(a,1,2)),rewrite([8(5),19(8)])].
% 1.57/1.86 1717 multiply(additive_identity,A) = multiply(A,additive_identity). [para(90(a,1),1703(a,1,2)),rewrite([174(3),574(5),90(5)]),flip(a)].
% 1.57/1.86 1720 multiply(additive_identity,multiply(A,B)) = multiply(A,multiply(B,additive_identity)). [para(1703(a,1),29(a,1)),rewrite([1703(7),1717(6,R)]),flip(a)].
% 1.57/1.86 1725 multiply(additive_identity,add(a,b)) = multiply(additive_identity,b). [para(301(a,1),1703(a,1,2)),rewrite([1717(6,R),1717(9,R),585(9),8(10),14(10),10(7,R),8(6),702(8),301(11),1717(8,R),585(8)])].
% 1.57/1.86 1727 add(c_0,multiply(add(additive_identity,c_0),A)) = add(c_0,multiply(c_0,A)). [para(72(a,1),1703(a,1,2)),rewrite([1717(4,R),643(4),8(9),1260(9),1013(6),72(10)])].
% 1.57/1.86 1751 add(c_0,multiply(additive_identity,a)) = c_0. [back_rewrite(1711),rewrite([1717(4,R)])].
% 1.57/1.86 1762 multiply(a,add(b,multiply(b,additive_inverse(c_0)))) = multiply(a,multiply(additive_identity,b)). [back_rewrite(1480),rewrite([1717(12,R)])].
% 1.57/1.86 1789 add(b,multiply(b,additive_inverse(c_0))) = add(b,additive_inverse(c_0)). [back_rewrite(999),rewrite([1717(7,R),585(7),1588(8),979(8)]),flip(a)].
% 1.57/1.86 1790 multiply(add(A,c_0),add(b,additive_inverse(c_0))) = multiply(A,add(b,additive_inverse(c_0))). [back_rewrite(997),rewrite([1717(3,R),585(3),703(9)]),flip(a)].
% 1.57/1.86 1792 multiply(c_0,add(b,additive_inverse(c_0))) = multiply(additive_identity,b). [back_rewrite(981),rewrite([1717(9,R),585(9)])].
% 1.57/1.86 1815 multiply(add(A,c_0),multiply(additive_identity,b)) = multiply(A,multiply(additive_identity,b)). [back_rewrite(824),rewrite([1717(3,R),585(3),29(8),102(4),12(4)]),flip(a)].
% 1.57/1.86 1844 add(c_0,multiply(c_0,additive_inverse(a))) = multiply(additive_identity,b). [back_rewrite(505),rewrite([1717(9,R),585(9)])].
% 1.57/1.86 1851 add(add(a,additive_inverse(c_0)),multiply(additive_identity,b)) = add(a,multiply(a,additive_inverse(c_0))). [back_rewrite(347),rewrite([1717(7,R),585(7)])].
% 1.57/1.86 1852 add(multiply(additive_identity,b),multiply(A,add(a,additive_inverse(c_0)))) = multiply(add(A,c_0),add(a,additive_inverse(c_0))). [back_rewrite(346),rewrite([1717(3,R),585(3)])].
% 1.57/1.86 1854 multiply(c_0,add(a,additive_inverse(c_0))) = multiply(additive_identity,b). [back_rewrite(301),rewrite([1717(9,R),585(9)])].
% 1.57/1.86 1862 multiply(additive_identity,add(A,A)) = multiply(A,additive_identity). [back_rewrite(90),rewrite([1717(5)])].
% 1.57/1.86 1872 multiply(additive_identity,add(A,multiply(A,B))) = multiply(A,multiply(B,additive_identity)). [back_rewrite(577),rewrite([1720(7)])].
% 1.57/1.86 1880 multiply(add(additive_identity,c_0),add(A,b)) = add(c_0,multiply(c_0,A)). [back_rewrite(1013),rewrite([1727(12)])].
% 1.57/1.86 1886 multiply(a,multiply(additive_identity,b)) = multiply(a,add(b,additive_inverse(c_0))). [back_rewrite(1762),rewrite([1789(7)]),flip(a)].
% 1.57/1.86 1887 multiply(add(additive_identity,b),add(b,additive_inverse(c_0))) = add(b,additive_inverse(c_0)). [back_rewrite(1587),rewrite([1789(14)])].
% 1.57/1.86 1894 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(2(a,1),67(a,2,1)),rewrite([1717(3),8(5),2(5),1703(5),8(5),2(5)])].
% 1.57/1.86 1956 add(b,add(multiply(additive_identity,b),multiply(b,additive_inverse(c_0)))) = add(b,additive_inverse(c_0)). [para(586(a,1),67(a,1,2,2)),rewrite([8(9),1887(18)])].
% 1.57/1.86 1959 add(additive_identity,c_0) = c_0. [para(578(a,1),67(a,1,2)),rewrite([1022(6),1717(5,R),585(5),576(6),8(6),1880(10),1717(7,R),585(7),576(8)])].
% 1.57/1.86 2009 multiply(b,multiply(additive_identity,a)) = multiply(additive_identity,b). [para(1717(a,2),31(a,1,2)),rewrite([1717(8,R),585(8)])].
% 1.57/1.86 2016 multiply(add(A,b),multiply(additive_identity,b)) = multiply(A,multiply(additive_identity,b)). [para(1717(a,2),54(a,1,2)),rewrite([585(5),1815(6),1717(9,R),585(9)]),flip(a)].
% 1.57/1.86 2025 multiply(a,add(b,additive_inverse(c_0))) = multiply(additive_identity,multiply(a,b)). [para(1751(a,1),63(a,1,2,2)),rewrite([1020(4),1020(10),1872(12),1717(9,R),1886(10)]),flip(a)].
% 1.57/1.86 2031 multiply(a,multiply(additive_identity,b)) = multiply(additive_identity,multiply(a,b)). [back_rewrite(1886),rewrite([2025(11)])].
% 1.57/1.86 2037 multiply(additive_identity,multiply(a,b)) = multiply(additive_identity,b). [para(1725(a,1),22(a,1,2,2)),rewrite([2016(8),2031(6),23(7),1725(10)])].
% 1.57/1.86 2048 multiply(a,add(b,additive_inverse(c_0))) = multiply(additive_identity,b). [back_rewrite(2025),rewrite([2037(11)])].
% 1.57/1.86 2106 add(additive_identity,add(b,c_0)) = add(b,c_0). [para(70(a,1),1894(a,1,2)),rewrite([70(10)])].
% 1.57/1.86 2502 multiply(c_0,add(additive_inverse(a),additive_inverse(a))) = multiply(additive_identity,b). [para(1844(a,1),26(a,1,1)),rewrite([12(8),39(7),642(6),1322(6),23(13),14(12)]),flip(a)].
% 1.57/1.86 2509 multiply(c_0,multiply(additive_identity,additive_inverse(a))) = multiply(additive_identity,b). [back_rewrite(829),rewrite([2502(13)])].
% 1.57/1.86 2569 multiply(additive_identity,b) = multiply(additive_identity,a). [para(2048(a,1),49(a,2)),rewrite([31(8),998(6),8(5),7(5),1717(3,R)]),flip(a)].
% 1.57/1.86 2573 multiply(a,multiply(additive_identity,a)) = multiply(additive_identity,a). [para(2048(a,1),65(a,1,2,2)),rewrite([2569(5),2009(6),2569(4),31(13),1037(13),1789(12),2048(11),2569(8)])].
% 1.57/1.86 2575 multiply(add(a,b),add(b,additive_inverse(c_0))) = add(add(b,additive_inverse(c_0)),multiply(additive_identity,a)). [para(2048(a,1),66(a,1,2)),rewrite([1789(6),2569(7),8(11)]),flip(a)].
% 1.57/1.86 2577 add(b,add(multiply(additive_identity,a),multiply(b,additive_inverse(c_0)))) = add(add(b,additive_inverse(c_0)),multiply(additive_identity,a)). [para(2048(a,1),67(a,1,2,2)),rewrite([2569(8),8(9),2575(18)])].
% 1.57/1.86 2583 multiply(c_0,multiply(additive_identity,additive_inverse(a))) = multiply(additive_identity,a). [back_rewrite(2509),rewrite([2569(9)])].
% 1.57/1.86 2636 multiply(a,add(b,additive_inverse(c_0))) = multiply(additive_identity,a). [back_rewrite(2048),rewrite([2569(9)])].
% 1.57/1.86 2657 add(add(b,additive_inverse(c_0)),multiply(additive_identity,a)) = add(b,additive_inverse(c_0)). [back_rewrite(1956),rewrite([2569(4),2577(10)])].
% 1.57/1.86 2659 multiply(c_0,add(a,additive_inverse(c_0))) = multiply(additive_identity,a). [back_rewrite(1854),rewrite([2569(9)])].
% 1.57/1.86 2660 add(multiply(additive_identity,a),multiply(A,add(a,additive_inverse(c_0)))) = multiply(add(A,c_0),add(a,additive_inverse(c_0))). [back_rewrite(1852),rewrite([2569(3)])].
% 1.57/1.86 2661 add(add(a,additive_inverse(c_0)),multiply(additive_identity,a)) = add(a,multiply(a,additive_inverse(c_0))). [back_rewrite(1851),rewrite([2569(7)])].
% 1.57/1.86 2678 multiply(c_0,add(b,additive_inverse(c_0))) = multiply(additive_identity,a). [back_rewrite(1792),rewrite([2569(9)])].
% 1.57/1.86 2709 multiply(additive_identity,multiply(b,additive_inverse(c_0))) = multiply(additive_identity,a). [back_rewrite(923),rewrite([2569(9)])].
% 1.57/1.86 2742 multiply(add(a,b),add(b,additive_inverse(c_0))) = add(b,additive_inverse(c_0)). [back_rewrite(2575),rewrite([2657(16)])].
% 1.57/1.86 2744 multiply(additive_identity,multiply(b,A)) = multiply(additive_identity,multiply(a,A)). [para(2569(a,1),12(a,1,1)),rewrite([12(4)]),flip(a)].
% 1.57/1.86 2756 multiply(additive_identity,multiply(a,additive_inverse(c_0))) = multiply(additive_identity,a). [back_rewrite(2709),rewrite([2744(6)])].
% 1.57/1.86 2977 multiply(A,add(a,multiply(additive_identity,a))) = multiply(A,a). [para(2573(a,1),63(a,2,2,2)),rewrite([16(7),8(3),2(3),22(5)]),flip(a)].
% 1.57/1.86 3108 multiply(c_0,multiply(additive_identity,multiply(additive_inverse(a),A))) = multiply(additive_identity,multiply(a,A)). [para(2583(a,1),12(a,1,1)),rewrite([12(4),12(10)]),flip(a)].
% 1.57/1.86 3114 multiply(additive_identity,multiply(a,A)) = multiply(A,additive_identity). [para(2583(a,1),37(a,1,1,2)),rewrite([8(8),14(8),7(5),3(3),1717(2),8(8),12(13),324(14),1959(5),3108(9)]),flip(a)].
% 1.57/1.86 3119 multiply(additive_identity,a) = additive_identity. [para(2583(a,1),1703(a,1,2)),rewrite([1717(6,R),23(6),8(8),14(8),7(5),3(3),2583(7)]),flip(a)].
% 1.57/1.86 3160 multiply(additive_identity,additive_inverse(c_0)) = additive_identity. [back_rewrite(2756),rewrite([3114(6),1717(4,R),3119(7)])].
% 1.57/1.86 3161 multiply(additive_identity,multiply(b,A)) = multiply(A,additive_identity). [back_rewrite(2744),rewrite([3114(8)])].
% 1.57/1.86 3166 multiply(A,add(additive_identity,a)) = multiply(A,a). [back_rewrite(2977),rewrite([3119(4),8(3)])].
% 1.57/1.86 3192 multiply(c_0,add(b,additive_inverse(c_0))) = additive_identity. [back_rewrite(2678),rewrite([3119(9)])].
% 1.57/1.86 3199 add(a,multiply(a,additive_inverse(c_0))) = add(additive_identity,add(a,additive_inverse(c_0))). [back_rewrite(2661),rewrite([3119(7),8(6)]),flip(a)].
% 1.57/1.86 3200 multiply(add(A,c_0),add(a,additive_inverse(c_0))) = multiply(A,add(a,additive_inverse(c_0))). [back_rewrite(2660),rewrite([3119(3),1894(7)]),flip(a)].
% 1.57/1.86 3201 multiply(c_0,add(a,additive_inverse(c_0))) = additive_identity. [back_rewrite(2659),rewrite([3119(9)])].
% 1.57/1.86 3202 add(additive_identity,add(b,additive_inverse(c_0))) = add(b,additive_inverse(c_0)). [back_rewrite(2657),rewrite([3119(7),8(6)])].
% 1.57/1.86 3207 multiply(a,add(b,additive_inverse(c_0))) = additive_identity. [back_rewrite(2636),rewrite([3119(9)])].
% 1.57/1.86 3229 multiply(additive_identity,b) = additive_identity. [back_rewrite(2569),rewrite([3119(6)])].
% 1.57/1.86 3423 multiply(additive_identity,add(A,additive_inverse(c_0))) = multiply(A,additive_identity). [para(3160(a,1),14(a,1,1)),rewrite([1717(3),1894(4),8(6)]),flip(a)].
% 1.57/1.86 3561 multiply(b,add(A,add(b,additive_inverse(c_0)))) = add(add(b,additive_inverse(c_0)),multiply(b,A)). [para(3192(a,1),78(a,1,1,2)),rewrite([8(6),3202(6),8(10),21(10),8(13),21(13),8(13)]),flip(a)].
% 1.57/1.86 3655 multiply(b,add(additive_identity,add(a,additive_inverse(c_0)))) = additive_identity. [para(3201(a,1),31(a,2)),rewrite([24(7),3199(7)])].
% 1.57/1.86 3660 multiply(A,add(additive_identity,add(a,additive_inverse(c_0)))) = multiply(A,add(a,additive_inverse(c_0))). [para(3201(a,1),69(a,2,2,2,2)),rewrite([3200(11),22(11),1717(15,R),3423(15),1717(12,R),3119(12),8(11)]),flip(a)].
% 1.57/1.86 3666 multiply(b,add(a,additive_inverse(c_0))) = additive_identity. [back_rewrite(3655),rewrite([3660(8)])].
% 1.57/1.86 3675 add(c_0,multiply(b,additive_inverse(c_0))) = additive_identity. [para(3666(a,1),14(a,2)),rewrite([19(3)])].
% 1.57/1.86 3677 add(additive_identity,b) = b. [para(3666(a,1),24(a,2,2)),rewrite([10(7,R),8(6),3561(8),19(7),8(6),21(6),8(4)]),flip(a)].
% 1.57/1.86 3770 multiply(add(b,c_0),additive_inverse(c_0)) = additive_identity. [para(3675(a,1),26(a,1,1)),rewrite([3161(6),1717(4,R),3160(4),1027(11),16(10)]),flip(a)].
% 1.57/1.86 3785 multiply(b,additive_inverse(c_0)) = add(additive_identity,additive_inverse(c_0)). [para(3770(a,1),25(a,2,2)),rewrite([10(6),8(5),21(6),8(8)])].
% 1.57/1.86 3792 add(b,additive_inverse(c_0)) = add(b,c_0). [para(3770(a,1),78(a,1,2)),rewrite([998(4),8(5),2106(5),1790(11),24(9),3785(8),10(9,R),8(8),3202(9)]),flip(a)].
% 1.57/1.86 3822 multiply(a,add(b,b)) = additive_identity. [back_rewrite(3207),rewrite([3792(5),1019(5)])].
% 1.57/1.86 3823 add(c_0,c_0) = additive_identity. [back_rewrite(3192),rewrite([3792(5),72(5),998(4)])].
% 1.57/1.86 3828 multiply(add(a,b),add(b,c_0)) = add(b,c_0). [back_rewrite(2742),rewrite([3792(7),3792(11)])].
% 1.57/1.86 3912 multiply(add(a,b),add(b,b)) = add(additive_identity,add(b,b)). [para(3822(a,1),66(a,1,2)),rewrite([3(4),8(5),8(8)]),flip(a)].
% 1.57/1.86 3914 add(additive_identity,add(b,b)) = add(b,b). [para(3822(a,1),67(a,1,2,2)),rewrite([3(4),8(4),3677(4),3912(10)]),flip(a)].
% 1.57/1.86 3915 add(additive_identity,a) = a. [para(3822(a,1),73(a,1,2,2,2)),rewrite([8(9),3166(10),25(8),30(7),32(7),19(6),3823(5),8(4),3166(5),3(3),3822(7),8(4)]),flip(a)].
% 1.57/1.86 3931 add(b,multiply(a,b)) = add(b,c_0). [para(31(a,1),85(a,1,2,2)),rewrite([8(3),998(7),3828(7)]),flip(a)].
% 1.57/1.86 4220 multiply(add(a,add(b,b)),add(b,add(b,c_0))) = add(b,add(b,c_0)). [para(91(a,1),85(a,1,2,2)),rewrite([10(5,R),25(11),998(10),26(17),3931(17)])].
% 1.57/1.86 4648 multiply(additive_inverse(A),additive_identity) = multiply(additive_identity,additive_inverse(A)). [para(1717(a,1),103(a,2)),rewrite([103(4)]),flip(a)].
% 1.57/1.86 4683 add(additive_inverse(A),multiply(additive_identity,additive_inverse(A))) = additive_inverse(A). [para(4648(a,1),24(a,2,2)),rewrite([2(4),3(3)]),flip(a)].
% 1.57/1.86 5001 add(A,add(additive_inverse(A),additive_inverse(B))) = additive_inverse(B). [para(4683(a,1),34(a,2)),rewrite([10(7),4683(6)])].
% 1.57/1.86 5120 additive_inverse(additive_inverse(A)) = A. [para(7(a,1),5001(a,1,2)),rewrite([2(2)]),flip(a)].
% 1.57/1.86 5432 multiply(additive_inverse(A),additive_identity) = add(additive_inverse(A),additive_inverse(A)). [para(3(a,1),109(a,2,2)),rewrite([1519(8),8(2),7(2),1862(5)])].
% 1.57/1.86 5509 multiply(A,additive_identity) = add(A,A). [para(5120(a,1),5432(a,1,1)),rewrite([5120(4),5120(4)])].
% 1.57/1.86 5539 add(b,add(b,c_0)) = c_0. [para(5509(a,1),32(a,2,2)),rewrite([3915(4),19(3),10(6),8(5)]),flip(a)].
% 1.57/1.86 5555 add(b,b) = additive_identity. [para(5509(a,2),3914(a,1,2)),rewrite([1717(4,R),3229(4),2(3)]),flip(a)].
% 1.57/1.86 5674 multiply(a,b) = c_0. [back_rewrite(4220),rewrite([5555(4),8(3),3915(3),5539(6),1020(3),5539(8)])].
% 1.57/1.86 5675 $F # answer(prove_commutativity). [resolve(5674,a,20,a)].
% 1.57/1.86
% 1.57/1.86 % SZS output end Refutation
% 1.57/1.86 ============================== end of proof ==========================
% 1.57/1.86
% 1.57/1.86 ============================== STATISTICS ============================
% 1.57/1.86
% 1.57/1.86 Given=264. Generated=25791. Kept=5668. proofs=1.
% 1.57/1.86 Usable=138. Sos=2871. Demods=2931. Limbo=135, Disabled=2535. Hints=0.
% 1.57/1.86 Megabytes=6.47.
% 1.57/1.86 User_CPU=0.84, System_CPU=0.03, Wall_clock=1.
% 1.57/1.86
% 1.57/1.86 ============================== end of statistics =====================
% 1.57/1.86
% 1.57/1.86 ============================== end of search =========================
% 1.57/1.86
% 1.57/1.86 THEOREM PROVED
% 1.57/1.86 % SZS status Unsatisfiable
% 1.57/1.86
% 1.57/1.86 Exiting with 1 proof.
% 1.57/1.86
% 1.57/1.86 Process 8053 exit (max_proofs) Mon May 30 11:33:25 2022
% 1.57/1.86 Prover9 interrupted
%------------------------------------------------------------------------------