TSTP Solution File: BOO014-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO014-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 : Thu Jul 14 23:48:01 EDT 2022
% Result : Unsatisfiable 4.94s 5.21s
% Output : Refutation 4.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO014-4 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 1 21:55:46 EDT 2022
% 0.13/0.33 % CPUTime :
% 4.94/5.21 ============================== Prover9 ===============================
% 4.94/5.21 Prover9 (32) version 2009-11A, November 2009.
% 4.94/5.21 Process 10526 was started by sandbox on n021.cluster.edu,
% 4.94/5.21 Wed Jun 1 21:55:46 2022
% 4.94/5.21 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10373_n021.cluster.edu".
% 4.94/5.21 ============================== end of head ===========================
% 4.94/5.21
% 4.94/5.21 ============================== INPUT =================================
% 4.94/5.21
% 4.94/5.21 % Reading from file /tmp/Prover9_10373_n021.cluster.edu
% 4.94/5.21
% 4.94/5.21 set(prolog_style_variables).
% 4.94/5.21 set(auto2).
% 4.94/5.21 % set(auto2) -> set(auto).
% 4.94/5.21 % set(auto) -> set(auto_inference).
% 4.94/5.21 % set(auto) -> set(auto_setup).
% 4.94/5.21 % set(auto_setup) -> set(predicate_elim).
% 4.94/5.21 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.94/5.21 % set(auto) -> set(auto_limits).
% 4.94/5.21 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.94/5.21 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.94/5.21 % set(auto) -> set(auto_denials).
% 4.94/5.21 % set(auto) -> set(auto_process).
% 4.94/5.21 % set(auto2) -> assign(new_constants, 1).
% 4.94/5.21 % set(auto2) -> assign(fold_denial_max, 3).
% 4.94/5.21 % set(auto2) -> assign(max_weight, "200.000").
% 4.94/5.21 % set(auto2) -> assign(max_hours, 1).
% 4.94/5.21 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.94/5.21 % set(auto2) -> assign(max_seconds, 0).
% 4.94/5.21 % set(auto2) -> assign(max_minutes, 5).
% 4.94/5.21 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.94/5.21 % set(auto2) -> set(sort_initial_sos).
% 4.94/5.21 % set(auto2) -> assign(sos_limit, -1).
% 4.94/5.21 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.94/5.21 % set(auto2) -> assign(max_megs, 400).
% 4.94/5.21 % set(auto2) -> assign(stats, some).
% 4.94/5.21 % set(auto2) -> clear(echo_input).
% 4.94/5.21 % set(auto2) -> set(quiet).
% 4.94/5.21 % set(auto2) -> clear(print_initial_clauses).
% 4.94/5.21 % set(auto2) -> clear(print_given).
% 4.94/5.21 assign(lrs_ticks,-1).
% 4.94/5.21 assign(sos_limit,10000).
% 4.94/5.21 assign(order,kbo).
% 4.94/5.21 set(lex_order_vars).
% 4.94/5.21 clear(print_given).
% 4.94/5.21
% 4.94/5.21 % formulas(sos). % not echoed (9 formulas)
% 4.94/5.21
% 4.94/5.21 ============================== end of input ==========================
% 4.94/5.21
% 4.94/5.21 % From the command line: assign(max_seconds, 300).
% 4.94/5.21
% 4.94/5.21 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.94/5.21
% 4.94/5.21 % Formulas that are not ordinary clauses:
% 4.94/5.21
% 4.94/5.21 ============================== end of process non-clausal formulas ===
% 4.94/5.21
% 4.94/5.21 ============================== PROCESS INITIAL CLAUSES ===============
% 4.94/5.21
% 4.94/5.21 ============================== PREDICATE ELIMINATION =================
% 4.94/5.21
% 4.94/5.21 ============================== end predicate elimination =============
% 4.94/5.21
% 4.94/5.21 Auto_denials:
% 4.94/5.21 % copying label prove_c_inverse_is_d to answer in negative clause
% 4.94/5.21
% 4.94/5.21 Term ordering decisions:
% 4.94/5.21
% 4.94/5.21 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 4.94/5.21 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. a=1. b=1. add=1. multiply=1. inverse=0.
% 4.94/5.21
% 4.94/5.21 ============================== end of process initial clauses ========
% 4.94/5.21
% 4.94/5.21 ============================== CLAUSES FOR SEARCH ====================
% 4.94/5.21
% 4.94/5.21 ============================== end of clauses for search =============
% 4.94/5.21
% 4.94/5.21 ============================== SEARCH ================================
% 4.94/5.21
% 4.94/5.21 % Starting search at 0.01 seconds.
% 4.94/5.21
% 4.94/5.21 ============================== PROOF =================================
% 4.94/5.21 % SZS status Unsatisfiable
% 4.94/5.21 % SZS output start Refutation
% 4.94/5.21
% 4.94/5.21 % Proof 1 at 4.20 (+ 0.05) seconds: prove_c_inverse_is_d.
% 4.94/5.21 % Length of proof is 280.
% 4.94/5.21 % Level of proof is 42.
% 4.94/5.21 % Maximum clause weight is 45.000.
% 4.94/5.21 % Given clauses 289.
% 4.94/5.21
% 4.94/5.21 1 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 4.94/5.21 2 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 4.94/5.21 3 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 4.94/5.21 4 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 4.94/5.21 5 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 4.94/5.21 6 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 4.94/5.21 7 add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)) # label(distributivity1) # label(axiom). [assumption].
% 4.94/5.21 8 multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)). [copy(7),flip(a)].
% 4.94/5.21 9 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distributivity2) # label(axiom). [assumption].
% 4.94/5.21 10 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(9),flip(a)].
% 4.94/5.21 11 inverse(add(a,b)) != multiply(inverse(a),inverse(b)) # label(prove_c_inverse_is_d) # label(negated_conjecture) # answer(prove_c_inverse_is_d). [assumption].
% 4.94/5.21 12 multiply(A,add(A,B)) = add(A,multiply(B,additive_identity)). [para(1(a,1),8(a,1,1)),rewrite([6(4)])].
% 4.94/5.21 13 multiply(multiplicative_identity,add(A,B)) = add(A,multiply(B,inverse(A))). [para(3(a,1),8(a,1,1)),rewrite([6(5)])].
% 4.94/5.21 14 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [para(5(a,1),8(a,1,1))].
% 4.94/5.21 15 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(A,B)). [para(2(a,1),10(a,1,1)),rewrite([5(4)]),flip(a)].
% 4.94/5.21 16 multiply(A,add(B,inverse(A))) = add(additive_identity,multiply(A,B)). [para(4(a,1),10(a,1,1)),rewrite([5(5)]),flip(a)].
% 4.94/5.21 17 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [para(6(a,1),10(a,1,1))].
% 4.94/5.21 18 multiply(multiply(A,add(B,C)),add(D,multiply(A,B))) = add(multiply(A,B),multiply(D,multiply(A,C))). [para(10(a,1),8(a,1,1)),rewrite([5(4),6(8)])].
% 4.94/5.21 19 multiply(add(A,multiply(B,C)),multiply(B,add(C,D))) = add(multiply(B,C),multiply(A,multiply(B,D))). [para(10(a,1),8(a,1,2)),rewrite([5(2)])].
% 4.94/5.21 21 add(add(A,multiply(B,C)),multiply(D,add(A,B))) = multiply(add(A,B),add(D,add(A,C))). [para(8(a,1),10(a,1,1)),rewrite([6(4),5(8)])].
% 4.94/5.21 22 add(multiply(A,add(B,C)),add(B,multiply(C,D))) = multiply(add(B,C),add(A,add(B,D))). [para(8(a,1),10(a,1,2)),rewrite([6(2)])].
% 4.94/5.21 24 multiply(A,A) = add(A,multiply(additive_identity,additive_identity)). [para(1(a,1),12(a,1,2))].
% 4.94/5.21 25 add(A,multiply(inverse(A),additive_identity)) = A. [para(3(a,1),12(a,1,2)),rewrite([2(2)]),flip(a)].
% 4.94/5.21 36 add(A,multiply(B,multiply(inverse(A),additive_identity))) = multiply(A,add(A,B)). [para(25(a,1),8(a,1,1)),rewrite([6(6)]),flip(a)].
% 4.94/5.21 39 add(multiplicative_identity,multiply(additive_identity,additive_identity)) = multiplicative_identity. [para(24(a,1),2(a,1))].
% 4.94/5.21 40 add(add(A,B),multiply(additive_identity,additive_identity)) = add(A,multiply(B,B)). [para(24(a,1),8(a,1))].
% 4.94/5.21 46 multiply(A,A) = add(A,add(additive_identity,multiply(additive_identity,additive_identity))). [para(24(a,1),12(a,2,2)),rewrite([1(2)])].
% 4.94/5.21 49 add(additive_identity,multiplicative_identity) = multiplicative_identity. [para(39(a,1),8(a,2)),rewrite([5(3),5(6),8(7),2(4)])].
% 4.94/5.21 53 multiply(multiplicative_identity,add(A,A)) = A. [para(4(a,1),13(a,2,2)),rewrite([1(5)])].
% 4.94/5.21 54 multiply(multiplicative_identity,add(A,B)) = add(B,multiply(A,inverse(B))). [para(13(a,2),5(a,2)),rewrite([5(3),5(5)]),flip(a)].
% 4.94/5.21 57 multiply(add(A,B),multiply(multiplicative_identity,add(A,C))) = add(A,multiply(B,multiply(C,inverse(A)))). [para(13(a,2),8(a,1,2))].
% 4.94/5.21 59 add(A,multiply(B,inverse(A))) = add(A,B). [para(13(a,1),10(a,2)),rewrite([6(2),2(2),6(2),2(2)]),flip(a)].
% 4.94/5.21 63 add(multiplicative_identity,multiply(A,additive_identity)) = add(A,multiplicative_identity). [para(13(a,1),12(a,1)),rewrite([59(5),5(2)]),flip(a)].
% 4.94/5.21 70 multiply(multiplicative_identity,add(A,B)) = add(A,B). [back_rewrite(54),rewrite([59(6),5(4)])].
% 4.94/5.21 71 add(A,multiply(B,multiply(C,inverse(A)))) = add(A,multiply(B,C)). [back_rewrite(57),rewrite([70(4),8(3)]),flip(a)].
% 4.94/5.21 74 add(A,A) = A. [back_rewrite(53),rewrite([70(3)])].
% 4.94/5.21 75 add(A,multiply(A,additive_identity)) = A. [para(49(a,1),10(a,2,2)),rewrite([2(4),5(3),2(5)])].
% 4.94/5.21 76 multiply(A,A) = A. [back_rewrite(46),rewrite([75(6),1(3)])].
% 4.94/5.21 77 add(additive_identity,add(A,B)) = add(A,B). [back_rewrite(40),rewrite([76(4),5(3),76(4)])].
% 4.94/5.21 78 multiply(A,add(A,B)) = add(A,multiply(A,B)). [para(74(a,1),8(a,1,1))].
% 4.94/5.21 79 multiply(A,multiply(A,additive_identity)) = multiply(A,additive_identity). [para(74(a,1),12(a,2)),rewrite([5(5),75(5),6(3)])].
% 4.94/5.21 80 add(A,multiply(B,multiply(inverse(A),additive_identity))) = add(A,multiply(A,B)). [back_rewrite(36),rewrite([78(7)])].
% 4.94/5.21 86 add(A,multiply(B,additive_identity)) = add(A,multiply(A,B)). [back_rewrite(12),rewrite([78(2)]),flip(a)].
% 4.94/5.21 88 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(1(a,1),14(a,1,1)),rewrite([5(2),1(2)]),flip(a)].
% 4.94/5.21 89 add(inverse(A),multiply(A,B)) = add(B,inverse(A)). [para(3(a,1),14(a,1,1)),rewrite([5(3),70(4)]),flip(a)].
% 4.94/5.21 90 add(multiply(A,add(B,C)),add(C,multiply(B,D))) = multiply(add(B,C),add(A,add(C,D))). [para(14(a,1),10(a,1,2)),rewrite([6(2)])].
% 4.94/5.21 92 multiply(multiply(A,add(B,C)),add(D,multiply(A,C))) = add(multiply(A,C),multiply(D,multiply(A,B))). [para(10(a,1),14(a,1,1)),rewrite([5(4),6(8)])].
% 4.94/5.21 94 multiply(A,add(B,A)) = add(A,multiply(B,A)). [para(25(a,1),14(a,1,2)),rewrite([6(2),80(7),6(3)])].
% 4.94/5.21 96 multiply(A,add(B,inverse(A))) = multiply(A,B). [back_rewrite(16),rewrite([88(6)])].
% 4.94/5.21 97 multiply(add(A,multiplicative_identity),add(B,multiplicative_identity)) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [para(63(a,1),8(a,1,1)),rewrite([5(4),6(9)])].
% 4.94/5.21 99 add(A,multiply(A,multiply(B,additive_identity))) = multiply(A,add(B,multiplicative_identity)). [para(63(a,1),10(a,2,2)),rewrite([2(2)])].
% 4.94/5.21 101 add(add(A,B),multiply(C,add(A,B))) = add(add(A,B),multiply(C,additive_identity)). [para(77(a,1),14(a,1,1)),rewrite([5(3),94(4),6(7)])].
% 4.94/5.21 103 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,A)). [para(15(a,1),6(a,2)),rewrite([6(3),6(4)])].
% 4.94/5.21 104 add(add(A,B),add(A,multiply(A,B))) = add(A,B). [para(15(a,1),8(a,1)),rewrite([6(3),78(3),2(6)])].
% 4.94/5.21 110 add(multiply(A,B),add(A,multiply(A,C))) = multiply(A,add(B,add(C,multiplicative_identity))). [para(15(a,1),10(a,1,2))].
% 4.94/5.21 112 add(A,add(A,multiplicative_identity)) = add(A,multiplicative_identity). [para(15(a,1),76(a,1)),rewrite([6(5),78(5),2(4),74(3),5(3)])].
% 4.94/5.21 113 add(add(A,B),add(B,multiply(A,B))) = add(A,B). [para(15(a,1),14(a,1)),rewrite([6(3),94(3),2(6),5(5)])].
% 4.94/5.21 117 multiply(add(A,B),add(C,multiplicative_identity)) = add(add(A,B),multiply(C,additive_identity)). [back_rewrite(101),rewrite([103(4,R)])].
% 4.94/5.21 118 add(add(A,multiplicative_identity),multiply(B,additive_identity)) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [back_rewrite(97),rewrite([117(5)])].
% 4.94/5.21 120 multiply(multiply(A,B),add(C,multiplicative_identity)) = add(multiply(A,B),multiply(C,additive_identity)). [para(88(a,1),14(a,1,1)),rewrite([5(3),94(4),103(4,R),6(7)])].
% 4.94/5.21 121 multiply(multiplicative_identity,multiply(A,B)) = multiply(A,B). [para(88(a,1),70(a,1,2)),rewrite([88(6)])].
% 4.94/5.21 124 multiply(inverse(A),add(A,B)) = multiply(B,inverse(A)). [para(4(a,1),17(a,1,1)),rewrite([6(3),88(4)]),flip(a)].
% 4.94/5.21 125 multiply(add(A,multiply(B,C)),multiply(C,add(B,D))) = add(multiply(B,C),multiply(A,multiply(C,D))). [para(17(a,1),8(a,1,2)),rewrite([5(2)])].
% 4.94/5.21 127 add(add(A,multiply(B,C)),multiply(D,add(A,C))) = multiply(add(A,C),add(D,add(A,B))). [para(8(a,1),17(a,1,1)),rewrite([6(4),5(8)])].
% 4.94/5.21 129 multiply(multiply(A,additive_identity),add(A,B)) = add(multiply(A,additive_identity),multiply(B,additive_identity)). [para(79(a,1),17(a,1,1)),rewrite([6(5),103(6,R),120(5)]),flip(a)].
% 4.94/5.21 131 add(multiply(A,B),add(B,multiply(B,C))) = multiply(B,add(A,add(C,multiplicative_identity))). [para(15(a,1),17(a,1,2))].
% 4.94/5.21 150 add(add(multiply(A,B),multiply(C,multiply(A,D))),multiply(E,multiply(A,add(B,D)))) = multiply(multiply(A,add(B,D)),add(E,add(C,multiply(A,B)))). [para(18(a,1),10(a,1,1)),rewrite([6(7),5(13)])].
% 4.94/5.21 151 add(multiply(A,multiply(B,add(C,D))),add(multiply(B,C),multiply(E,multiply(B,D)))) = multiply(multiply(B,add(C,D)),add(A,add(E,multiply(B,C)))). [para(18(a,1),10(a,1,2)),rewrite([6(3)])].
% 4.94/5.21 153 multiply(multiply(A,multiply(B,add(C,D))),add(E,multiply(A,multiply(B,C)))) = add(multiply(A,multiply(B,C)),multiply(E,multiply(A,multiply(B,D)))). [para(10(a,1),18(a,1,1,2))].
% 4.94/5.21 154 multiply(multiply(A,add(B,C)),multiply(A,add(B,D))) = add(multiply(A,B),multiply(multiply(A,D),multiply(A,C))). [para(10(a,1),18(a,1,2)),rewrite([5(3)])].
% 4.94/5.21 160 multiply(multiply(add(A,B),add(C,add(B,D))),add(E,add(B,multiply(A,D)))) = add(add(B,multiply(A,D)),multiply(E,multiply(C,add(A,B)))). [para(14(a,1),18(a,1,2,2)),rewrite([5(3),14(11),6(12)])].
% 4.94/5.21 166 add(multiply(A,add(B,C)),add(multiply(A,B),multiply(D,multiply(A,C)))) = multiply(multiply(A,add(B,C)),add(multiplicative_identity,add(D,multiply(A,B)))). [para(18(a,1),15(a,2,2)),rewrite([5(6)]),flip(a)].
% 4.94/5.21 167 multiply(multiply(A,add(B,add(C,multiplicative_identity))),add(D,add(A,multiply(A,C)))) = add(multiply(A,add(C,multiplicative_identity)),multiply(D,multiply(A,B))). [para(15(a,1),18(a,1,2,2)),rewrite([5(3)])].
% 4.94/5.21 172 add(multiply(A,B),multiply(C,multiply(A,add(B,multiplicative_identity)))) = multiply(A,add(B,C)). [para(112(a,1),18(a,1,1,2)),rewrite([18(6),2(3),6(2),10(3)]),flip(a)].
% 4.94/5.21 176 multiply(add(A,B),multiply(A,add(C,inverse(B)))) = add(multiply(A,inverse(B)),multiply(B,multiply(A,C))). [para(59(a,1),18(a,1,2)),rewrite([5(2),5(4),6(5)])].
% 4.94/5.21 179 multiply(multiply(multiply(A,add(B,C)),add(D,add(E,multiply(A,B)))),add(F,add(multiply(A,B),multiply(E,multiply(A,C))))) = add(add(multiply(A,B),multiply(E,multiply(A,C))),multiply(F,multiply(D,multiply(A,add(B,C))))). [para(18(a,1),18(a,1,2,2)),rewrite([5(5),18(17),6(19)])].
% 4.94/5.21 196 multiply(multiply(A,add(B,C)),multiply(A,add(C,D))) = add(multiply(A,C),multiply(multiply(A,B),multiply(A,D))). [para(10(a,1),19(a,1,1))].
% 4.94/5.21 199 multiply(add(A,multiply(A,multiply(A,B))),multiply(A,add(B,multiply(A,B)))) = multiply(A,multiply(A,B)). [para(74(a,1),19(a,2)),rewrite([5(5)])].
% 4.94/5.21 201 multiply(add(A,add(B,multiply(C,D))),multiply(add(C,B),add(E,add(B,D)))) = add(add(B,multiply(C,D)),multiply(A,multiply(E,add(C,B)))). [para(14(a,1),19(a,2,1)),rewrite([14(3),5(6),6(12)])].
% 4.94/5.21 210 add(multiply(A,B),multiply(C,A)) = multiply(A,add(C,B)). [para(112(a,1),19(a,1,2,2)),rewrite([19(6),2(3),172(9),5(4)])].
% 4.94/5.21 216 multiply(add(A,add(multiply(B,C),multiply(D,multiply(B,E)))),multiply(add(D,multiply(B,C)),add(F,multiply(B,add(C,E))))) = add(add(multiply(B,C),multiply(D,multiply(B,E))),multiply(A,multiply(F,add(D,multiply(B,C))))). [para(19(a,1),19(a,1,1,2)),rewrite([5(10),19(17),6(19)])].
% 4.94/5.21 237 add(add(A,multiply(B,C)),multiply(D,add(B,A))) = multiply(add(B,A),add(D,add(C,A))). [para(5(a,1),21(a,1,1)),rewrite([5(2),5(3),5(6),5(7)])].
% 4.94/5.21 241 multiply(add(A,multiply(A,B)),add(C,add(D,multiply(A,B)))) = add(multiply(A,add(B,D)),multiply(C,add(A,multiply(A,B)))). [para(10(a,1),21(a,1,1)),rewrite([5(4),5(8),5(10)]),flip(a)].
% 4.94/5.21 244 add(add(A,multiply(B,C)),add(B,multiply(A,B))) = add(B,add(A,multiply(A,C))). [para(14(a,1),21(a,2)),rewrite([94(4),78(7)])].
% 4.94/5.21 248 multiply(add(A,B),add(C,add(A,multiply(B,additive_identity)))) = add(A,multiply(B,C)). [para(79(a,1),21(a,1,1,2)),rewrite([21(6),1(3),5(2),8(3)]),flip(a)].
% 4.94/5.21 284 multiply(add(A,multiply(B,additive_identity)),add(C,multiply(A,B))) = multiply(A,add(B,C)). [para(86(a,2),14(a,1,1)),rewrite([5(5),10(9)])].
% 4.94/5.21 287 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,additive_identity)). [para(86(a,2),15(a,2))].
% 4.94/5.21 293 multiply(multiply(A,add(B,C)),add(multiplicative_identity,add(D,multiply(A,B)))) = add(multiply(A,add(B,C)),multiply(additive_identity,add(D,multiply(A,B)))). [para(18(a,1),86(a,2,2)),rewrite([6(6),166(14)]),flip(a)].
% 4.94/5.21 296 multiply(add(A,multiply(B,additive_identity)),multiply(A,add(B,C))) = multiply(A,add(B,multiply(A,C))). [para(86(a,2),19(a,1,1)),rewrite([10(10)])].
% 4.94/5.21 299 multiply(add(A,multiply(B,additive_identity)),add(C,add(A,D))) = multiply(add(A,multiply(A,B)),add(C,add(A,D))). [para(86(a,1),21(a,2,1)),rewrite([6(3),127(9)])].
% 4.94/5.21 303 add(A,multiply(A,multiply(A,B))) = add(A,multiply(B,additive_identity)). [para(86(a,1),78(a,1,2)),rewrite([78(3),99(7),287(6)])].
% 4.94/5.21 313 multiply(multiply(A,add(B,add(C,multiplicative_identity))),add(D,add(A,multiply(A,C)))) = add(add(A,multiply(C,additive_identity)),multiply(D,multiply(A,B))). [back_rewrite(167),rewrite([287(11)])].
% 4.94/5.21 322 add(multiply(A,add(B,C)),add(multiply(A,B),multiply(D,multiply(A,C)))) = add(multiply(A,add(B,C)),multiply(additive_identity,add(D,multiply(A,B)))). [back_rewrite(166),rewrite([293(14)])].
% 4.94/5.21 326 multiply(A,add(B,multiply(A,multiply(A,B)))) = multiply(A,multiply(A,B)). [back_rewrite(199),rewrite([303(3),296(7)])].
% 4.94/5.21 328 add(multiplicative_identity,inverse(A)) = multiplicative_identity. [para(2(a,1),89(a,1,2)),rewrite([5(2),3(2)]),flip(a)].
% 4.94/5.21 329 add(inverse(A),multiply(B,A)) = add(B,inverse(A)). [para(89(a,1),5(a,1)),rewrite([6(3),5(5)]),flip(a)].
% 4.94/5.21 330 multiply(add(A,inverse(B)),add(C,inverse(B))) = add(inverse(B),multiply(C,multiply(A,B))). [para(89(a,1),8(a,1,1)),rewrite([5(4),6(7),6(8)])].
% 4.94/5.21 345 add(inverse(A),add(A,multiply(A,B))) = add(inverse(A),add(A,B)). [para(78(a,1),89(a,1,2)),rewrite([5(7)])].
% 4.94/5.21 346 add(additive_identity,inverse(A)) = inverse(A). [para(89(a,1),86(a,1)),rewrite([6(6),4(6),1(6)])].
% 4.94/5.21 348 add(multiplicative_identity,multiply(A,inverse(B))) = add(A,multiplicative_identity). [para(328(a,1),8(a,1,1)),rewrite([5(3),94(4),2(3),5(2),6(5)]),flip(a)].
% 4.94/5.21 351 add(add(A,multiplicative_identity),add(B,multiply(A,additive_identity))) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [para(328(a,1),21(a,2,2,2)),rewrite([348(4),5(4),287(5),5(8),287(11),118(11)])].
% 4.94/5.21 353 add(multiply(A,B),add(B,multiply(C,additive_identity))) = multiply(B,add(A,add(B,C))). [para(1(a,1),22(a,1,1,2)),rewrite([6(3),1(7)])].
% 4.94/5.21 357 add(multiply(A,add(B,C)),add(B,multiply(B,C))) = multiply(add(B,C),add(A,B)). [para(25(a,1),22(a,2,2,2)),rewrite([80(7)])].
% 4.94/5.21 362 multiply(add(A,B),add(C,A)) = add(A,multiply(C,B)). [para(79(a,1),22(a,1,2,2)),rewrite([22(6),1(3),248(9),6(4)])].
% 4.94/5.21 376 add(multiply(A,add(B,multiply(C,additive_identity))),add(B,multiply(D,multiply(B,C)))) = multiply(add(B,multiply(B,C)),add(A,add(B,D))). [para(86(a,2),22(a,1,1,2)),rewrite([6(6)])].
% 4.94/5.21 381 add(multiply(A,add(B,C)),add(B,multiply(B,C))) = add(B,multiply(A,C)). [back_rewrite(357),rewrite([362(8)])].
% 4.94/5.21 384 multiply(multiplicative_identity,inverse(A)) = inverse(A). [para(346(a,1),70(a,1,2)),rewrite([346(6)])].
% 4.94/5.21 385 multiply(A,additive_identity) = additive_identity. [para(346(a,1),96(a,1,2)),rewrite([4(2)]),flip(a)].
% 4.94/5.21 386 add(multiply(A,inverse(B)),multiply(C,inverse(B))) = multiply(inverse(B),add(A,C)). [para(346(a,1),21(a,1,2,2)),rewrite([6(3),88(4),346(8),5(8),1(8),5(7)])].
% 4.94/5.21 390 multiply(add(A,multiply(A,B)),add(C,add(A,D))) = add(multiply(C,A),add(A,multiply(D,multiply(A,B)))). [back_rewrite(376),rewrite([385(2),1(2)]),flip(a)].
% 4.94/5.21 394 multiply(A,add(B,add(A,C))) = add(A,multiply(B,A)). [back_rewrite(353),rewrite([385(3),1(3),5(2)]),flip(a)].
% 4.94/5.21 395 add(A,add(B,multiplicative_identity)) = multiplicative_identity. [back_rewrite(351),rewrite([385(4),1(4),5(3),385(6),385(6),5(6),49(6)])].
% 4.94/5.21 399 add(A,multiply(B,multiply(A,C))) = add(A,multiply(A,B)). [back_rewrite(313),rewrite([395(3),2(2),394(4),6(1),385(4),1(4)]),flip(a)].
% 4.94/5.21 407 add(A,multiply(A,B)) = A. [back_rewrite(299),rewrite([385(2),1(2),394(3),6(1),390(7),6(3),399(6),110(6),395(5),2(4)])].
% 4.94/5.21 412 multiply(A,add(B,multiply(A,C))) = multiply(A,add(C,B)). [back_rewrite(284),rewrite([385(2),1(2)])].
% 4.94/5.21 413 multiply(additive_identity,add(A,B)) = additive_identity. [back_rewrite(129),rewrite([385(2),385(5),385(6),74(6)])].
% 4.94/5.21 415 add(A,multiplicative_identity) = multiplicative_identity. [back_rewrite(63),rewrite([385(3),5(3),49(3)]),flip(a)].
% 4.94/5.21 418 add(A,multiply(B,A)) = A. [back_rewrite(131),rewrite([407(3),5(2),415(4),415(4),2(4)])].
% 4.94/5.21 419 multiply(A,add(B,add(C,multiply(A,D)))) = multiply(A,add(B,add(D,C))). [back_rewrite(241),rewrite([407(2),407(8),6(7),10(8),5(6)])].
% 4.94/5.21 421 add(A,add(B,multiply(A,C))) = add(B,A). [back_rewrite(244),rewrite([418(4),5(3),407(5),5(4)])].
% 4.94/5.21 422 add(A,add(B,A)) = add(B,A). [back_rewrite(113),rewrite([418(3),5(2)])].
% 4.94/5.21 424 add(A,multiply(B,multiply(A,C))) = A. [back_rewrite(399),rewrite([407(5)])].
% 4.94/5.21 425 add(A,multiply(B,add(A,C))) = add(A,multiply(B,C)). [back_rewrite(381),rewrite([407(4),5(3)])].
% 4.94/5.21 427 add(inverse(A),add(A,B)) = multiplicative_identity. [back_rewrite(345),rewrite([407(3),5(2),3(2)]),flip(a)].
% 4.94/5.21 429 add(A,add(A,B)) = add(A,B). [back_rewrite(104),rewrite([407(3),5(2)])].
% 4.94/5.21 430 multiply(A,add(A,B)) = A. [back_rewrite(78),rewrite([407(4)])].
% 4.94/5.21 433 multiply(A,multiply(A,B)) = multiply(A,B). [back_rewrite(326),rewrite([412(4),5(2),418(2)]),flip(a)].
% 4.94/5.21 436 add(multiply(A,add(B,C)),add(multiply(A,B),multiply(D,multiply(A,C)))) = multiply(A,add(B,C)). [back_rewrite(322),rewrite([413(13),5(11),88(11)])].
% 4.94/5.21 442 multiply(A,add(B,add(A,C))) = A. [back_rewrite(394),rewrite([6(4),407(5)])].
% 4.94/5.21 453 multiply(A,add(B,A)) = A. [para(385(a,1),14(a,2,2)),rewrite([1(3),6(2),1(4)])].
% 4.94/5.21 455 add(A,multiply(B,multiply(C,multiply(D,inverse(A))))) = add(A,multiply(B,multiply(C,D))). [para(71(a,1),8(a,1,1)),rewrite([8(4),6(2),6(7)]),flip(a)].
% 4.94/5.21 459 add(A,multiply(inverse(A),multiply(B,C))) = add(A,multiply(B,C)). [para(71(a,1),59(a,2)),rewrite([6(5),455(6)])].
% 4.94/5.21 461 multiply(add(A,multiply(B,C)),multiply(B,add(D,multiply(C,inverse(A))))) = add(multiply(B,multiply(C,inverse(A))),multiply(A,multiply(B,D))). [para(71(a,1),18(a,1,2)),rewrite([5(3),6(7)])].
% 4.94/5.21 464 add(inverse(A),multiply(B,multiply(A,C))) = add(inverse(A),multiply(C,B)). [para(384(a,1),18(a,1,2,2)),rewrite([5(3),70(4),330(5),6(2),384(7),6(7),2(7),6(6)])].
% 4.94/5.21 466 add(A,multiply(inverse(A),inverse(B))) = add(A,inverse(B)). [para(384(a,1),71(a,2,2)),rewrite([6(4),121(5)])].
% 4.94/5.21 493 multiply(A,multiply(B,add(A,C))) = multiply(B,A). [para(418(a,1),18(a,1,2)),rewrite([6(3),17(7),407(5),6(4)])].
% 4.94/5.21 501 multiply(multiply(A,B),multiply(A,add(C,B))) = multiply(A,B). [para(74(a,1),92(a,1,2)),rewrite([6(4),407(9)])].
% 4.94/5.21 502 add(multiply(A,B),multiply(C,multiply(A,add(D,B)))) = add(multiply(A,B),multiply(C,multiply(A,D))). [para(92(a,1),17(a,2)),rewrite([6(7),501(7),5(5)])].
% 4.94/5.21 503 multiply(A,multiply(B,add(C,A))) = multiply(B,A). [para(17(a,1),92(a,2)),rewrite([418(4),6(3),407(5),6(4)])].
% 4.94/5.21 516 multiply(multiply(A,B),add(C,multiply(A,multiply(B,D)))) = add(multiply(A,multiply(B,D)),multiply(C,multiply(A,B))). [para(407(a,1),92(a,1,1,2))].
% 4.94/5.21 521 multiply(A,multiply(B,A)) = multiply(B,A). [para(418(a,1),453(a,1,2)),rewrite([6(2)])].
% 4.94/5.21 523 add(inverse(multiply(A,B)),multiply(A,add(B,C))) = multiplicative_identity. [para(10(a,1),427(a,1,2))].
% 4.94/5.21 525 add(inverse(multiply(A,B)),multiply(B,add(A,C))) = multiplicative_identity. [para(17(a,1),427(a,1,2))].
% 4.94/5.21 529 add(inverse(inverse(A)),add(B,inverse(A))) = multiplicative_identity. [para(89(a,1),427(a,1,2))].
% 4.94/5.21 531 multiply(inverse(A),add(B,A)) = multiply(B,inverse(A)). [para(124(a,1),6(a,1)),rewrite([5(3),6(5)]),flip(a)].
% 4.94/5.21 533 multiply(inverse(A),add(B,add(A,C))) = multiply(inverse(A),add(B,C)). [para(124(a,1),10(a,1,2)),rewrite([6(2),386(5)]),flip(a)].
% 4.94/5.21 543 multiply(inverse(A),multiply(A,B)) = additive_identity. [para(407(a,1),124(a,1,2)),rewrite([6(2),4(2),6(4)]),flip(a)].
% 4.94/5.21 547 multiply(inverse(add(A,B)),add(A,multiply(B,C))) = additive_identity. [para(8(a,1),543(a,1,2))].
% 4.94/5.21 550 multiply(multiply(A,B),add(C,inverse(A))) = multiply(C,multiply(A,B)). [para(543(a,1),17(a,1,1)),rewrite([6(3),88(4),5(5)]),flip(a)].
% 4.94/5.21 556 multiply(inverse(inverse(A)),multiply(B,inverse(A))) = additive_identity. [para(124(a,1),543(a,1,2))].
% 4.94/5.21 557 add(A,multiply(B,add(C,A))) = add(A,multiply(C,B)). [para(422(a,1),8(a,1,1)),rewrite([14(3),6(4)]),flip(a)].
% 4.94/5.21 578 multiply(add(A,B),add(C,B)) = add(B,multiply(C,A)). [para(424(a,1),90(a,1,2)),rewrite([5(3),557(3),6(1),407(5)]),flip(a)].
% 4.94/5.21 581 multiply(A,multiply(B,multiply(A,C))) = multiply(B,multiply(A,C)). [para(424(a,1),453(a,1,2)),rewrite([6(3)])].
% 4.94/5.21 582 multiply(inverse(A),multiply(B,multiply(A,C))) = additive_identity. [para(424(a,1),124(a,1,2)),rewrite([6(2),4(2),6(5)]),flip(a)].
% 4.94/5.21 586 multiply(A,add(B,multiply(C,A))) = add(multiply(C,A),multiply(B,A)). [para(2(a,1),125(a,2,2,2)),rewrite([415(4),2(4),6(3)])].
% 4.94/5.21 611 multiply(multiply(A,B),add(A,C)) = multiply(A,B). [para(433(a,1),17(a,1,1)),rewrite([6(3),418(4)]),flip(a)].
% 4.94/5.21 619 multiply(add(A,add(B,C)),add(B,D)) = add(B,multiply(D,add(A,add(B,C)))). [para(442(a,1),17(a,1,1)),rewrite([6(3)]),flip(a)].
% 4.94/5.21 656 multiply(add(A,B),add(C,add(A,D))) = add(A,multiply(B,add(C,add(A,D)))). [para(6(a,1),127(a,2)),rewrite([127(5),619(8)])].
% 4.94/5.21 657 add(A,multiply(multiply(B,add(C,add(A,D))),add(E,add(A,multiply(B,D))))) = add(add(A,multiply(B,D)),multiply(E,multiply(C,add(A,B)))). [para(127(a,1),8(a,1,1)),rewrite([656(4),6(5),5(7),656(8),6(9),6(13)])].
% 4.94/5.21 660 add(add(A,multiply(B,C)),add(A,multiply(C,D))) = add(A,multiply(C,add(add(A,D),add(A,B)))). [para(8(a,1),127(a,1,2)),rewrite([6(3),656(10)])].
% 4.94/5.21 665 add(A,add(B,multiply(C,A))) = add(B,A). [para(14(a,1),127(a,2)),rewrite([453(4),5(3),430(5),5(4)])].
% 4.94/5.21 748 add(inverse(inverse(A)),multiply(B,add(C,inverse(A)))) = add(B,inverse(inverse(A))). [para(529(a,1),8(a,1,1)),rewrite([5(4),70(5),6(8)]),flip(a)].
% 4.94/5.21 753 multiply(inverse(inverse(A)),add(B,multiply(C,inverse(A)))) = multiply(B,inverse(inverse(A))). [para(556(a,1),10(a,1,1)),rewrite([6(4),88(5),5(8)]),flip(a)].
% 4.94/5.21 756 add(A,multiply(B,inverse(inverse(A)))) = A. [para(556(a,1),71(a,1,2)),rewrite([1(2),6(3)]),flip(a)].
% 4.94/5.21 760 add(A,inverse(inverse(A))) = A. [para(76(a,1),756(a,1,2))].
% 4.94/5.21 800 inverse(inverse(A)) = A. [para(760(a,1),89(a,2)),rewrite([6(4),4(4),1(4)])].
% 4.94/5.21 803 multiply(A,add(B,multiply(C,inverse(A)))) = multiply(A,B). [back_rewrite(753),rewrite([800(2),800(6),6(5)])].
% 4.94/5.21 807 add(A,multiply(B,add(C,inverse(A)))) = add(A,B). [back_rewrite(748),rewrite([800(2),800(6),5(5)])].
% 4.94/5.21 809 add(A,add(B,inverse(A))) = multiplicative_identity. [back_rewrite(529),rewrite([800(2)])].
% 4.94/5.21 834 multiply(A,multiply(B,multiply(C,inverse(A)))) = additive_identity. [para(124(a,1),582(a,1,2,2)),rewrite([800(2)])].
% 4.94/5.21 854 multiply(multiply(A,add(B,C)),add(D,add(multiply(A,B),multiply(E,multiply(A,C))))) = multiply(multiply(A,add(B,C)),add(D,add(E,multiply(A,B)))). [para(150(a,1),8(a,2)),rewrite([5(5),5(12),436(12),6(8)])].
% 4.94/5.21 915 add(multiply(A,B),inverse(add(A,inverse(B)))) = add(B,inverse(add(A,inverse(B)))). [para(96(a,1),329(a,1,2)),rewrite([6(4),5(5)])].
% 4.94/5.21 919 add(A,inverse(multiply(A,B))) = multiplicative_identity. [para(433(a,1),329(a,1,2)),rewrite([5(4),3(4)]),flip(a)].
% 4.94/5.21 920 add(A,inverse(multiply(B,A))) = multiplicative_identity. [para(521(a,1),329(a,1,2)),rewrite([5(4),3(4)]),flip(a)].
% 4.94/5.21 927 add(inverse(multiply(A,B)),multiply(A,C)) = add(C,inverse(multiply(A,B))). [para(919(a,1),14(a,1,1)),rewrite([5(4),70(5)]),flip(a)].
% 4.94/5.21 933 multiply(inverse(A),inverse(multiply(A,B))) = inverse(A). [para(919(a,1),124(a,1,2)),rewrite([2(3),6(5)]),flip(a)].
% 4.94/5.21 936 add(add(A,B),inverse(multiply(C,A))) = multiplicative_identity. [back_rewrite(523),rewrite([927(5)])].
% 4.94/5.21 941 multiply(multiply(A,B),add(C,A)) = multiply(A,B). [para(74(a,1),151(a,1,2)),rewrite([5(2),418(2),433(4),5(4),418(4),5(3),418(3),433(4),407(4)]),flip(a)].
% 4.94/5.21 971 add(inverse(multiply(A,B)),multiply(B,C)) = add(C,inverse(multiply(A,B))). [para(920(a,1),14(a,1,1)),rewrite([5(4),70(5)]),flip(a)].
% 4.94/5.21 974 add(inverse(A),add(B,A)) = multiplicative_identity. [para(453(a,1),920(a,1,2,1)),rewrite([5(3)])].
% 4.94/5.21 977 add(add(A,B),inverse(multiply(A,C))) = multiplicative_identity. [back_rewrite(525),rewrite([971(5)])].
% 4.94/5.21 981 add(A,inverse(multiply(B,multiply(A,C)))) = multiplicative_identity. [para(424(a,1),974(a,1,2)),rewrite([5(4)])].
% 4.94/5.21 992 multiply(A,inverse(multiply(B,inverse(A)))) = A. [para(124(a,1),933(a,1,2,1)),rewrite([800(2),800(6)])].
% 4.94/5.21 1000 multiply(add(A,B),inverse(multiply(A,inverse(B)))) = B. [para(992(a,1),124(a,2)),rewrite([5(6),59(6),5(4),6(5)])].
% 4.94/5.21 1001 multiply(multiply(A,inverse(B)),multiply(B,C)) = additive_identity. [para(992(a,1),834(a,1,2,2)),rewrite([6(3)])].
% 4.94/5.21 1079 add(multiply(A,add(B,C)),multiply(D,multiply(A,inverse(multiply(B,E))))) = multiply(A,add(D,add(B,C))). [para(936(a,1),18(a,1,1,2)),rewrite([2(2),412(4),5(2),6(6)]),flip(a)].
% 4.94/5.21 1099 add(inverse(multiply(A,B)),add(A,C)) = multiplicative_identity. [para(977(a,1),5(a,1)),flip(a)].
% 4.94/5.21 1115 multiply(inverse(A),inverse(multiply(B,multiply(A,C)))) = inverse(A). [para(981(a,1),124(a,1,2)),rewrite([2(3),6(6)]),flip(a)].
% 4.94/5.21 1137 multiply(multiply(A,add(B,C)),multiply(A,add(B,D))) = add(multiply(multiply(A,D),multiply(A,C)),multiply(A,B)). [para(154(a,2),5(a,1))].
% 4.94/5.21 1155 add(add(multiply(A,B),multiply(multiply(A,C),multiply(A,D))),multiply(E,multiply(A,add(B,C)))) = multiply(multiply(A,add(B,C)),add(E,multiply(A,add(B,D)))). [para(154(a,1),17(a,1,1)),rewrite([6(8),5(14)])].
% 4.94/5.21 1270 multiply(A,add(multiply(A,B),add(C,D))) = multiply(A,add(B,add(C,D))). [para(936(a,1),154(a,1,1,2)),rewrite([2(2),5(2),433(4),6(7),1079(11)]),flip(a)].
% 4.94/5.21 1287 multiply(inverse(A),multiply(B,A)) = additive_identity. [para(933(a,1),1001(a,1,2)),rewrite([800(2),6(3)])].
% 4.94/5.21 1292 multiply(A,inverse(add(A,B))) = additive_identity. [para(430(a,1),1287(a,1,2)),rewrite([6(3)])].
% 4.94/5.21 1296 multiply(A,inverse(add(B,add(A,C)))) = additive_identity. [para(442(a,1),1287(a,1,2)),rewrite([6(4)])].
% 4.94/5.21 1305 multiply(A,add(B,inverse(add(A,C)))) = multiply(A,B). [para(1292(a,1),10(a,1,1)),rewrite([88(3),5(4)]),flip(a)].
% 4.94/5.21 1307 multiply(inverse(add(A,B)),add(A,C)) = multiply(C,inverse(add(A,B))). [para(1292(a,1),17(a,1,1)),rewrite([6(4),88(5)]),flip(a)].
% 4.94/5.21 1309 add(inverse(A),inverse(add(A,B))) = inverse(A). [para(1292(a,1),89(a,1,2)),rewrite([1(3),5(5)]),flip(a)].
% 4.94/5.21 1318 multiply(multiply(A,B),inverse(add(C,A))) = additive_identity. [back_rewrite(547),rewrite([1307(5)])].
% 4.94/5.21 1532 multiply(add(A,B),multiply(A,C)) = multiply(A,C). [para(1099(a,1),124(a,1,2)),rewrite([800(3),6(3),121(3),800(5)]),flip(a)].
% 4.94/5.21 1541 add(multiply(A,inverse(B)),multiply(B,multiply(A,C))) = multiply(A,add(C,inverse(B))). [back_rewrite(176),rewrite([1532(5)]),flip(a)].
% 4.94/5.21 1563 add(inverse(A),inverse(add(B,add(A,C)))) = inverse(A). [para(1296(a,1),89(a,1,2)),rewrite([1(3),5(6)]),flip(a)].
% 4.94/5.21 1578 add(A,inverse(add(B,inverse(A)))) = A. [para(89(a,1),1309(a,1,2,1)),rewrite([800(2),800(6)])].
% 4.94/5.21 1589 add(multiply(A,B),inverse(add(A,inverse(B)))) = B. [back_rewrite(915),rewrite([1578(9)])].
% 4.94/5.21 1714 add(inverse(add(A,B)),inverse(multiply(A,C))) = inverse(multiply(A,C)). [para(1318(a,1),89(a,1,2)),rewrite([5(4),346(4),5(3)]),flip(a)].
% 4.94/5.21 1728 add(multiply(A,B),add(C,A)) = add(C,A). [para(1318(a,1),329(a,1,2)),rewrite([800(3),5(3),77(3),800(5)]),flip(a)].
% 4.94/5.21 2013 add(multiply(A,multiply(B,C)),multiply(multiply(A,B),multiply(A,D))) = multiply(multiply(A,B),multiply(A,add(D,multiply(B,C)))). [para(407(a,1),196(a,1,1,2)),rewrite([5(3)]),flip(a)].
% 4.94/5.21 2193 multiply(multiply(A,B),multiply(A,C)) = multiply(C,multiply(A,B)). [para(407(a,1),503(a,1,2,2)),rewrite([6(2)])].
% 4.94/5.21 2200 multiply(multiply(A,add(B,C)),add(C,add(D,multiply(A,B)))) = multiply(A,add(B,C)). [para(503(a,1),150(a,1,2)),rewrite([5(6),665(6),10(3)]),flip(a)].
% 4.94/5.21 2206 multiply(multiply(A,B),add(C,multiply(B,multiply(A,D)))) = add(multiply(B,multiply(A,D)),multiply(C,multiply(A,B))). [para(503(a,1),153(a,1,1)),rewrite([521(9)])].
% 4.94/5.21 2216 multiply(multiply(A,add(B,C)),add(D,add(E,multiply(A,B)))) = add(add(multiply(A,B),multiply(E,multiply(A,C))),multiply(D,multiply(A,C))). [para(503(a,1),179(a,2,2,2)),rewrite([2200(6),854(8)])].
% 4.94/5.21 2336 add(multiply(A,multiply(B,C)),multiply(D,multiply(A,B))) = multiply(add(D,multiply(B,C)),multiply(A,B)). [back_rewrite(2013),rewrite([2193(5),2193(10)])].
% 4.94/5.21 2504 multiply(multiply(A,add(B,C)),add(D,multiply(A,add(B,E)))) = multiply(multiply(A,add(B,C)),add(D,add(E,multiply(A,B)))). [back_rewrite(1155),rewrite([2193(4),150(8)]),flip(a)].
% 4.94/5.21 2517 multiply(add(A,B),multiply(C,add(A,D))) = add(multiply(D,multiply(C,B)),multiply(C,A)). [back_rewrite(1137),rewrite([2193(5),2193(7)])].
% 4.94/5.21 2545 multiply(multiply(A,B),add(C,multiply(A,multiply(B,D)))) = multiply(add(C,multiply(B,D)),multiply(A,B)). [back_rewrite(516),rewrite([2336(10)])].
% 4.94/5.21 2735 multiply(add(A,add(B,multiply(C,D))),multiply(add(C,B),add(E,add(D,B)))) = add(add(B,multiply(C,D)),multiply(A,multiply(E,add(C,B)))). [para(5(a,1),201(a,1,1,2)),rewrite([5(2),5(5)])].
% 4.94/5.21 2807 add(add(A,multiply(B,C)),multiply(D,multiply(E,add(A,B)))) = add(add(A,multiply(B,C)),multiply(D,multiply(B,E))). [para(611(a,1),201(a,2,2,2)),rewrite([5(4),656(8),1270(7),619(8),657(8)])].
% 4.94/5.21 2890 add(add(A,B),add(A,C)) = add(C,add(A,B)). [para(430(a,1),665(a,1,2,2)),rewrite([5(2)])].
% 4.94/5.21 2912 multiply(add(A,add(add(B,multiply(C,D)),multiply(D,E))),multiply(add(B,D),add(F,add(E,add(B,multiply(C,D)))))) = add(add(add(B,multiply(C,D)),multiply(D,E)),multiply(A,multiply(F,add(B,D)))). [para(665(a,1),201(a,1,2,1)),rewrite([5(9),665(19)])].
% 4.94/5.21 2931 add(multiply(A,B),add(C,multiply(D,A))) = add(C,multiply(A,add(D,add(C,B)))). [back_rewrite(660),rewrite([2890(5),2890(7)])].
% 4.94/5.21 2951 multiply(add(A,B),multiply(B,C)) = multiply(B,C). [para(941(a,1),6(a,2))].
% 4.94/5.21 3014 multiply(add(A,B),inverse(multiply(B,inverse(A)))) = A. [para(5(a,1),1000(a,1,1))].
% 4.94/5.21 3019 add(A,inverse(add(B,A))) = inverse(multiply(B,inverse(A))). [para(1000(a,1),89(a,1,2)),rewrite([5(3),5(9),1714(9)])].
% 4.94/5.21 3043 multiply(A,inverse(multiply(A,B))) = inverse(add(B,inverse(A))). [para(1578(a,1),1000(a,1,1)),rewrite([800(4),96(3)])].
% 4.94/5.21 3385 add(multiply(A,B),inverse(add(B,inverse(A)))) = A. [para(1589(a,1),5(a,1)),rewrite([6(4),5(5)]),flip(a)].
% 4.94/5.21 3387 add(multiply(A,B),multiply(C,inverse(add(A,inverse(B))))) = multiply(B,add(A,C)). [para(1589(a,1),8(a,1,2)),rewrite([5(2),6(3),586(3),6(2),17(3)]),flip(a)].
% 4.94/5.21 3390 add(multiply(A,B),multiply(C,B)) = multiply(B,add(C,A)). [para(1589(a,1),14(a,1,2)),rewrite([6(3),586(3),3387(9),5(4)])].
% 4.94/5.21 3391 add(multiply(A,multiply(B,C)),multiply(D,multiply(A,inverse(add(C,inverse(B)))))) = multiply(add(D,multiply(B,C)),multiply(A,B)). [para(1589(a,1),18(a,1,1,2)),rewrite([6(2),2545(5),6(5)]),flip(a)].
% 4.94/5.21 3602 multiply(add(A,multiply(B,C)),add(B,D)) = add(multiply(B,C),multiply(A,add(B,D))). [para(1728(a,1),8(a,1,2)),rewrite([5(2),5(3),5(6)])].
% 4.94/5.21 3663 multiply(multiply(A,add(B,C)),add(D,add(multiply(A,B),multiply(C,multiply(A,E))))) = add(add(multiply(A,B),multiply(C,multiply(A,E))),multiply(D,multiply(A,add(B,C)))). [para(407(a,1),216(a,1,2,2)),rewrite([6(8),412(8),6(8),412(15)])].
% 4.94/5.21 3812 multiply(A,add(B,add(C,multiply(D,A)))) = multiply(A,add(B,add(D,C))). [para(418(a,1),237(a,1,2,2)),rewrite([17(3),6(3),10(4),5(2),418(5)]),flip(a)].
% 4.94/5.21 3943 add(multiply(A,multiply(B,C)),multiply(D,multiply(B,A))) = multiply(add(D,multiply(B,C)),multiply(B,A)). [para(3385(a,1),125(a,1,2,2)),rewrite([6(2),6(4),6(5),2206(5),6(7),3391(13),6(8)])].
% 4.94/5.21 4112 multiply(add(A,inverse(B)),inverse(multiply(inverse(A),inverse(B)))) = multiply(A,inverse(multiply(inverse(A),inverse(B)))). [para(466(a,1),531(a,1,2)),rewrite([6(7)])].
% 4.94/5.21 4124 multiply(A,inverse(multiply(inverse(A),inverse(B)))) = A. [para(466(a,1),3014(a,1,1)),rewrite([6(7),433(7),4112(7)])].
% 4.94/5.21 4231 multiply(multiply(inverse(A),inverse(B)),multiply(A,C)) = additive_identity. [para(4124(a,1),834(a,1,2,2)),rewrite([6(4)])].
% 4.94/5.21 4277 multiply(multiply(A,B),multiply(inverse(A),inverse(C))) = additive_identity. [para(4231(a,1),6(a,1)),flip(a)].
% 4.94/5.21 4335 multiply(multiply(A,B),multiply(inverse(B),inverse(C))) = additive_identity. [para(6(a,1),4277(a,1,1))].
% 4.94/5.21 4364 inverse(add(multiply(A,B),inverse(multiply(inverse(B),inverse(C))))) = multiply(inverse(B),inverse(C)). [para(4335(a,1),1589(a,1,1)),rewrite([346(9)])].
% 4.94/5.21 4469 multiply(A,multiply(B,add(C,inverse(A)))) = multiply(A,multiply(B,C)). [para(10(a,1),803(a,1,2))].
% 4.94/5.21 4599 add(A,add(inverse(A),multiply(B,C))) = multiplicative_identity. [para(809(a,1),807(a,2)),rewrite([578(5),6(2)])].
% 4.94/5.21 4618 add(A,add(inverse(A),inverse(B))) = multiplicative_identity. [para(384(a,1),4599(a,1,2,2))].
% 4.94/5.21 4627 add(A,multiply(B,add(inverse(A),inverse(C)))) = add(A,B). [para(4618(a,1),8(a,1,1)),rewrite([70(3),6(5)]),flip(a)].
% 4.94/5.21 4633 add(add(inverse(A),inverse(B)),add(A,C)) = multiplicative_identity. [para(4618(a,1),421(a,2)),rewrite([6(7),4627(8)])].
% 4.94/5.21 4643 add(multiply(A,B),multiply(multiply(C,add(A,D)),add(E,add(multiply(A,B),multiply(C,D))))) = add(add(multiply(A,B),multiply(C,D)),multiply(E,multiply(A,add(C,B)))). [para(412(a,1),160(a,2,2,2)),rewrite([5(4),421(5),5(3),3602(4),656(9),5(13)])].
% 4.94/5.21 4651 multiply(add(A,multiply(B,C)),multiply(B,add(D,add(A,C)))) = multiply(B,add(A,C)). [para(412(a,1),493(a,2)),rewrite([5(5),419(6),5(3),5(7)])].
% 4.94/5.21 4685 add(add(A,B),add(inverse(A),inverse(C))) = multiplicative_identity. [para(4633(a,1),5(a,1)),flip(a)].
% 4.94/5.21 4700 add(add(A,B),add(inverse(B),inverse(C))) = multiplicative_identity. [para(5(a,1),4685(a,1,1))].
% 4.94/5.21 4713 inverse(multiply(add(A,B),inverse(add(inverse(B),inverse(C))))) = add(inverse(B),inverse(C)). [para(4700(a,1),1000(a,1,1)),rewrite([384(9)])].
% 4.94/5.21 5040 multiply(A,add(inverse(A),multiply(B,C))) = multiply(B,multiply(A,C)). [para(1115(a,1),1000(a,1,2,1)),rewrite([464(4),6(2),800(5),6(4)])].
% 4.94/5.21 5095 add(multiply(A,add(B,C)),multiply(B,multiply(A,D))) = multiply(A,add(B,C)). [para(425(a,1),18(a,1,2)),rewrite([5(2),6(6),4651(6)]),flip(a)].
% 4.94/5.21 5099 multiply(multiply(A,add(B,add(C,D))),add(E,add(C,multiply(A,D)))) = add(multiply(A,add(C,D)),multiply(E,multiply(A,B))). [para(425(a,1),150(a,2,2,2)),rewrite([5095(5),5(4),502(7),5(7)]),flip(a)].
% 4.94/5.21 5104 add(A,add(multiply(B,add(A,C)),multiply(D,multiply(B,E)))) = add(add(A,multiply(B,C)),multiply(D,multiply(B,E))). [para(425(a,1),201(a,1,1,2)),rewrite([5(4),429(6),656(7),619(8),5099(7),425(9),5(9),2807(12)])].
% 4.94/5.21 5386 add(A,multiply(inverse(A),add(B,C))) = add(B,add(A,C)). [para(1563(a,1),1589(a,1,2,1)),rewrite([533(4),800(5),5(4)])].
% 4.94/5.21 6703 add(A,add(B,C)) = add(B,add(A,C)). [para(70(a,1),459(a,1,2,2)),rewrite([5386(4),70(5)])].
% 4.94/5.21 6709 add(multiply(inverse(A),multiply(B,C)),multiply(A,multiply(D,multiply(B,C)))) = multiply(multiply(B,C),add(D,inverse(A))). [para(459(a,1),125(a,1,1)),rewrite([5(5),2951(7),6(9)]),flip(a)].
% 4.94/5.21 6718 add(add(A,multiply(B,C)),multiply(D,E)) = add(A,add(multiply(B,C),multiply(D,E))). [para(459(a,1),160(a,1,2,2)),rewrite([5(2),3(2),6703(4),70(5),6703(6),8(7),578(5),6(2),459(8),5(8),3(8),2(8),6(7)]),flip(a)].
% 4.94/5.21 7628 add(A,multiply(B,add(C,add(A,D)))) = add(A,multiply(B,add(C,D))). [back_rewrite(2931),rewrite([6(2),6703(4),10(3),5(4),6703(5),5(4)]),flip(a)].
% 4.94/5.21 7634 add(A,multiply(multiply(B,add(C,add(D,E))),add(F,add(D,multiply(C,B))))) = add(A,add(multiply(B,add(C,D)),multiply(F,multiply(E,add(A,B))))). [back_rewrite(2912),rewrite([6718(4),17(3),6703(8),6703(9),6703(8),8(10),3812(8),6703(6),619(9),7628(9),2504(7),6(4),6718(12),17(11),6718(15)])].
% 4.94/5.21 7688 add(A,add(multiply(B,C),multiply(D,multiply(E,add(A,B))))) = add(A,add(multiply(B,C),multiply(D,multiply(B,E)))). [back_rewrite(2735),rewrite([5(4),5(5),6703(6),5(5),8(7),619(7),7628(7),18(5),5(8),6718(11)]),flip(a)].
% 4.94/5.21 8244 add(A,add(multiply(B,add(A,C)),multiply(D,multiply(B,E)))) = add(A,add(multiply(B,C),multiply(D,multiply(B,E)))). [back_rewrite(5104),rewrite([6718(11)])].
% 4.94/5.21 8274 add(multiply(A,B),add(multiply(C,D),multiply(E,multiply(A,add(B,C))))) = add(multiply(A,B),add(multiply(C,D),multiply(E,multiply(A,C)))). [back_rewrite(4643),rewrite([7628(9),92(6),6(3),5(10),6718(13)]),flip(a)].
% 4.94/5.21 8335 multiply(multiply(A,add(B,C)),add(D,add(multiply(A,B),multiply(C,multiply(A,E))))) = add(multiply(A,B),multiply(add(D,multiply(A,E)),multiply(A,C))). [back_rewrite(3663),rewrite([6718(16),8274(16),3943(14)])].
% 4.94/5.21 8449 multiply(multiply(A,add(B,C)),add(D,add(E,multiply(A,B)))) = add(multiply(A,B),multiply(multiply(A,C),add(D,E))). [back_rewrite(2216),rewrite([6718(13),3390(12)])].
% 4.94/5.21 8628 add(A,add(multiply(B,C),multiply(multiply(B,add(D,E)),add(D,F)))) = add(A,add(multiply(B,add(C,D)),multiply(F,multiply(B,E)))). [back_rewrite(7634),rewrite([6(4),6703(6),8449(7),7688(14)])].
% 4.94/5.21 9033 multiply(multiply(A,add(B,C)),add(D,add(multiply(A,B),multiply(E,multiply(A,C))))) = add(multiply(A,B),multiply(multiply(A,C),add(D,E))). [back_rewrite(854),rewrite([8449(14)])].
% 4.94/5.21 9749 add(additive_identity,add(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(A,D)))) = add(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(A,D))). [para(461(a,1),88(a,1,2)),rewrite([461(15)])].
% 4.94/5.21 10007 multiply(A,multiply(B,C)) = multiply(C,multiply(B,A)). [para(464(a,1),124(a,1,2)),rewrite([800(2),5040(4),800(6),6(5),581(5)])].
% 4.94/5.21 10404 add(multiply(A,B),multiply(multiply(A,C),add(D,E))) = add(multiply(A,B),multiply(C,multiply(A,add(D,E)))). [back_rewrite(9033),rewrite([10007(5),8335(8),10007(5),412(4),5(2)]),flip(a)].
% 4.94/5.21 10569 add(A,add(multiply(B,C),multiply(add(D,E),multiply(B,add(D,F))))) = add(A,add(multiply(B,add(C,D)),multiply(E,multiply(B,F)))). [back_rewrite(8628),rewrite([10404(6),10007(11)])].
% 4.94/5.21 10838 add(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(A,multiply(B,D)))) = multiply(multiply(B,A),add(D,inverse(C))). [back_rewrite(6709),rewrite([10007(3),10007(5)])].
% 4.94/5.21 11163 multiply(add(A,B),multiply(C,add(A,D))) = multiply(C,add(A,multiply(B,D))). [back_rewrite(2517),rewrite([6(5),10007(6),6(7),210(8)])].
% 4.94/5.21 11278 multiply(multiply(A,B),add(C,inverse(A))) = multiply(B,multiply(A,C)). [back_rewrite(550),rewrite([10007(6)])].
% 4.94/5.21 11544 add(A,add(multiply(B,add(C,D)),multiply(E,multiply(B,F)))) = add(A,multiply(B,add(C,add(D,multiply(E,F))))). [back_rewrite(10569),rewrite([11163(5),10(5)]),flip(a)].
% 4.94/5.21 11785 add(A,add(multiply(B,C),multiply(D,multiply(B,E)))) = add(A,multiply(B,add(C,multiply(D,E)))). [back_rewrite(8244),rewrite([11544(6),425(5)]),flip(a)].
% 4.96/5.21 12295 add(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(A,D))) = multiply(A,add(multiply(B,inverse(C)),multiply(C,D))). [back_rewrite(9749),rewrite([11785(8),88(7)]),flip(a)].
% 4.96/5.21 12544 multiply(multiply(A,B),add(C,inverse(D))) = multiply(A,multiply(B,add(C,inverse(D)))). [back_rewrite(10838),rewrite([12295(7),1541(5),6(5)]),flip(a)].
% 4.96/5.21 12582 multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)). [back_rewrite(11278),rewrite([12544(4),4469(4)])].
% 4.96/5.21 15311 inverse(add(inverse(A),inverse(B))) = multiply(A,B). [para(3019(a,1),1305(a,1,2)),rewrite([3043(4),5(3)])].
% 4.96/5.21 15321 inverse(multiply(A,B)) = add(inverse(A),inverse(B)). [back_rewrite(4713),rewrite([15311(5),12582(3),6(2),503(3),6(1)])].
% 4.96/5.21 15681 inverse(add(A,B)) = multiply(inverse(A),inverse(B)). [back_rewrite(4364),rewrite([15321(5),800(3),800(3),6703(3),5(2),665(3),5(1)])].
% 4.96/5.21 15682 $F # answer(prove_c_inverse_is_d). [resolve(15681,a,11,a)].
% 4.96/5.21
% 4.96/5.21 % SZS output end Refutation
% 4.96/5.21 ============================== end of proof ==========================
% 4.96/5.21
% 4.96/5.21 ============================== STATISTICS ============================
% 4.96/5.21
% 4.96/5.21 Given=289. Generated=76526. Kept=15679. proofs=1.
% 4.96/5.21 Usable=117. Sos=1994. Demods=2372. Limbo=360, Disabled=13216. Hints=0.
% 4.96/5.21 Megabytes=18.35.
% 4.96/5.21 User_CPU=4.20, System_CPU=0.05, Wall_clock=5.
% 4.96/5.21
% 4.96/5.21 ============================== end of statistics =====================
% 4.96/5.21
% 4.96/5.21 ============================== end of search =========================
% 4.96/5.21
% 4.96/5.21 THEOREM PROVED
% 4.96/5.21 % SZS status Unsatisfiable
% 4.96/5.21
% 4.96/5.21 Exiting with 1 proof.
% 4.96/5.21
% 4.96/5.21 Process 10526 exit (max_proofs) Wed Jun 1 21:55:51 2022
% 4.96/5.21 Prover9 interrupted
%------------------------------------------------------------------------------