TSTP Solution File: BOO007-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO007-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 23:47:58 EDT 2022
% Result : Unsatisfiable 4.33s 4.57s
% Output : Refutation 4.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO007-4 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 1 17:50:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 4.33/4.57 ============================== Prover9 ===============================
% 4.33/4.57 Prover9 (32) version 2009-11A, November 2009.
% 4.33/4.57 Process 12216 was started by sandbox2 on n018.cluster.edu,
% 4.33/4.57 Wed Jun 1 17:51:00 2022
% 4.33/4.57 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12063_n018.cluster.edu".
% 4.33/4.57 ============================== end of head ===========================
% 4.33/4.57
% 4.33/4.57 ============================== INPUT =================================
% 4.33/4.57
% 4.33/4.57 % Reading from file /tmp/Prover9_12063_n018.cluster.edu
% 4.33/4.57
% 4.33/4.57 set(prolog_style_variables).
% 4.33/4.57 set(auto2).
% 4.33/4.57 % set(auto2) -> set(auto).
% 4.33/4.57 % set(auto) -> set(auto_inference).
% 4.33/4.57 % set(auto) -> set(auto_setup).
% 4.33/4.57 % set(auto_setup) -> set(predicate_elim).
% 4.33/4.57 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.33/4.57 % set(auto) -> set(auto_limits).
% 4.33/4.57 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.33/4.57 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.33/4.57 % set(auto) -> set(auto_denials).
% 4.33/4.57 % set(auto) -> set(auto_process).
% 4.33/4.57 % set(auto2) -> assign(new_constants, 1).
% 4.33/4.57 % set(auto2) -> assign(fold_denial_max, 3).
% 4.33/4.57 % set(auto2) -> assign(max_weight, "200.000").
% 4.33/4.57 % set(auto2) -> assign(max_hours, 1).
% 4.33/4.57 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.33/4.57 % set(auto2) -> assign(max_seconds, 0).
% 4.33/4.57 % set(auto2) -> assign(max_minutes, 5).
% 4.33/4.57 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.33/4.57 % set(auto2) -> set(sort_initial_sos).
% 4.33/4.57 % set(auto2) -> assign(sos_limit, -1).
% 4.33/4.57 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.33/4.57 % set(auto2) -> assign(max_megs, 400).
% 4.33/4.57 % set(auto2) -> assign(stats, some).
% 4.33/4.57 % set(auto2) -> clear(echo_input).
% 4.33/4.57 % set(auto2) -> set(quiet).
% 4.33/4.57 % set(auto2) -> clear(print_initial_clauses).
% 4.33/4.57 % set(auto2) -> clear(print_given).
% 4.33/4.57 assign(lrs_ticks,-1).
% 4.33/4.57 assign(sos_limit,10000).
% 4.33/4.57 assign(order,kbo).
% 4.33/4.57 set(lex_order_vars).
% 4.33/4.57 clear(print_given).
% 4.33/4.57
% 4.33/4.57 % formulas(sos). % not echoed (9 formulas)
% 4.33/4.57
% 4.33/4.57 ============================== end of input ==========================
% 4.33/4.57
% 4.33/4.57 % From the command line: assign(max_seconds, 300).
% 4.33/4.57
% 4.33/4.57 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.33/4.57
% 4.33/4.57 % Formulas that are not ordinary clauses:
% 4.33/4.57
% 4.33/4.57 ============================== end of process non-clausal formulas ===
% 4.33/4.57
% 4.33/4.57 ============================== PROCESS INITIAL CLAUSES ===============
% 4.33/4.57
% 4.33/4.57 ============================== PREDICATE ELIMINATION =================
% 4.33/4.57
% 4.33/4.57 ============================== end predicate elimination =============
% 4.33/4.57
% 4.33/4.57 Auto_denials:
% 4.33/4.57 % copying label prove_associativity to answer in negative clause
% 4.33/4.57
% 4.33/4.57 Term ordering decisions:
% 4.33/4.57
% 4.33/4.57 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 4.33/4.57 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. a=1. b=1. c=1. add=1. multiply=1. inverse=0.
% 4.33/4.57
% 4.33/4.57 ============================== end of process initial clauses ========
% 4.33/4.57
% 4.33/4.57 ============================== CLAUSES FOR SEARCH ====================
% 4.33/4.57
% 4.33/4.57 ============================== end of clauses for search =============
% 4.33/4.57
% 4.33/4.57 ============================== SEARCH ================================
% 4.33/4.57
% 4.33/4.57 % Starting search at 0.01 seconds.
% 4.33/4.57
% 4.33/4.57 Low Water (keep): wt=49.000, iters=3408
% 4.33/4.57
% 4.33/4.57 Low Water (keep): wt=45.000, iters=3389
% 4.33/4.57
% 4.33/4.57 ============================== PROOF =================================
% 4.33/4.57 % SZS status Unsatisfiable
% 4.33/4.57 % SZS output start Refutation
% 4.33/4.57
% 4.33/4.57 % Proof 1 at 3.54 (+ 0.05) seconds: prove_associativity.
% 4.33/4.57 % Length of proof is 255.
% 4.33/4.57 % Level of proof is 40.
% 4.33/4.57 % Maximum clause weight is 45.000.
% 4.33/4.57 % Given clauses 280.
% 4.33/4.57
% 4.33/4.57 1 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 4.33/4.57 2 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 4.33/4.57 3 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 4.33/4.57 4 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 4.33/4.57 5 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 4.33/4.57 6 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 4.33/4.57 7 add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)) # label(distributivity1) # label(axiom). [assumption].
% 4.33/4.57 8 multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)). [copy(7),flip(a)].
% 4.33/4.57 9 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distributivity2) # label(axiom). [assumption].
% 4.33/4.57 10 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(9),flip(a)].
% 4.33/4.57 11 multiply(a,multiply(b,c)) != multiply(multiply(a,b),c) # label(prove_associativity) # label(negated_conjecture) # answer(prove_associativity). [assumption].
% 4.33/4.57 12 multiply(c,multiply(a,b)) != multiply(a,multiply(b,c)) # answer(prove_associativity). [copy(11),rewrite([6(10)]),flip(a)].
% 4.33/4.57 13 multiply(A,add(A,B)) = add(A,multiply(B,additive_identity)). [para(1(a,1),8(a,1,1)),rewrite([6(4)])].
% 4.33/4.57 14 multiply(multiplicative_identity,add(A,B)) = add(A,multiply(B,inverse(A))). [para(3(a,1),8(a,1,1)),rewrite([6(5)])].
% 4.33/4.57 15 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [para(5(a,1),8(a,1,1))].
% 4.33/4.57 16 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(A,B)). [para(2(a,1),10(a,1,1)),rewrite([5(4)]),flip(a)].
% 4.33/4.57 17 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)].
% 4.33/4.57 18 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [para(6(a,1),10(a,1,1))].
% 4.33/4.57 19 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)])].
% 4.33/4.57 20 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)])].
% 4.33/4.57 22 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)])].
% 4.33/4.57 23 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)])].
% 4.33/4.57 25 multiply(A,A) = add(A,multiply(additive_identity,additive_identity)). [para(1(a,1),13(a,1,2))].
% 4.33/4.57 26 add(A,multiply(inverse(A),additive_identity)) = A. [para(3(a,1),13(a,1,2)),rewrite([2(2)]),flip(a)].
% 4.33/4.57 37 add(A,multiply(B,multiply(inverse(A),additive_identity))) = multiply(A,add(A,B)). [para(26(a,1),8(a,1,1)),rewrite([6(6)]),flip(a)].
% 4.33/4.57 40 add(multiplicative_identity,multiply(additive_identity,additive_identity)) = multiplicative_identity. [para(25(a,1),2(a,1))].
% 4.33/4.57 41 add(add(A,B),multiply(additive_identity,additive_identity)) = add(A,multiply(B,B)). [para(25(a,1),8(a,1))].
% 4.33/4.57 47 multiply(A,A) = add(A,add(additive_identity,multiply(additive_identity,additive_identity))). [para(25(a,1),13(a,2,2)),rewrite([1(2)])].
% 4.33/4.57 50 add(additive_identity,multiplicative_identity) = multiplicative_identity. [para(40(a,1),8(a,2)),rewrite([5(3),5(6),8(7),2(4)])].
% 4.33/4.57 54 multiply(multiplicative_identity,add(A,A)) = A. [para(4(a,1),14(a,2,2)),rewrite([1(5)])].
% 4.33/4.57 55 multiply(multiplicative_identity,add(A,B)) = add(B,multiply(A,inverse(B))). [para(14(a,2),5(a,2)),rewrite([5(3),5(5)]),flip(a)].
% 4.33/4.57 58 multiply(add(A,B),multiply(multiplicative_identity,add(A,C))) = add(A,multiply(B,multiply(C,inverse(A)))). [para(14(a,2),8(a,1,2))].
% 4.33/4.57 60 add(A,multiply(B,inverse(A))) = add(A,B). [para(14(a,1),10(a,2)),rewrite([6(2),2(2),6(2),2(2)]),flip(a)].
% 4.33/4.57 64 add(multiplicative_identity,multiply(A,additive_identity)) = add(A,multiplicative_identity). [para(14(a,1),13(a,1)),rewrite([60(5),5(2)]),flip(a)].
% 4.33/4.57 71 multiply(multiplicative_identity,add(A,B)) = add(A,B). [back_rewrite(55),rewrite([60(6),5(4)])].
% 4.33/4.57 72 add(A,multiply(B,multiply(C,inverse(A)))) = add(A,multiply(B,C)). [back_rewrite(58),rewrite([71(4),8(3)]),flip(a)].
% 4.33/4.57 75 add(A,A) = A. [back_rewrite(54),rewrite([71(3)])].
% 4.33/4.57 76 add(A,multiply(A,additive_identity)) = A. [para(50(a,1),10(a,2,2)),rewrite([2(4),5(3),2(5)])].
% 4.33/4.57 77 multiply(A,A) = A. [back_rewrite(47),rewrite([76(6),1(3)])].
% 4.33/4.57 78 add(additive_identity,add(A,B)) = add(A,B). [back_rewrite(41),rewrite([77(4),5(3),77(4)])].
% 4.33/4.57 79 multiply(A,add(A,B)) = add(A,multiply(A,B)). [para(75(a,1),8(a,1,1))].
% 4.33/4.57 80 multiply(A,multiply(A,additive_identity)) = multiply(A,additive_identity). [para(75(a,1),13(a,2)),rewrite([5(5),76(5),6(3)])].
% 4.33/4.57 81 add(A,multiply(B,multiply(inverse(A),additive_identity))) = add(A,multiply(A,B)). [back_rewrite(37),rewrite([79(7)])].
% 4.33/4.57 87 add(A,multiply(B,additive_identity)) = add(A,multiply(A,B)). [back_rewrite(13),rewrite([79(2)]),flip(a)].
% 4.33/4.57 89 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(1(a,1),15(a,1,1)),rewrite([5(2),1(2)]),flip(a)].
% 4.33/4.57 90 add(inverse(A),multiply(A,B)) = add(B,inverse(A)). [para(3(a,1),15(a,1,1)),rewrite([5(3),71(4)]),flip(a)].
% 4.33/4.57 91 add(multiply(A,add(B,C)),add(C,multiply(B,D))) = multiply(add(B,C),add(A,add(C,D))). [para(15(a,1),10(a,1,2)),rewrite([6(2)])].
% 4.33/4.57 93 multiply(multiply(A,add(B,C)),add(D,multiply(A,C))) = add(multiply(A,C),multiply(D,multiply(A,B))). [para(10(a,1),15(a,1,1)),rewrite([5(4),6(8)])].
% 4.33/4.57 95 multiply(A,add(B,A)) = add(A,multiply(B,A)). [para(26(a,1),15(a,1,2)),rewrite([6(2),81(7),6(3)])].
% 4.33/4.57 97 multiply(A,add(B,inverse(A))) = multiply(A,B). [back_rewrite(17),rewrite([89(6)])].
% 4.33/4.57 98 multiply(add(A,multiplicative_identity),add(B,multiplicative_identity)) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [para(64(a,1),8(a,1,1)),rewrite([5(4),6(9)])].
% 4.33/4.57 100 add(A,multiply(A,multiply(B,additive_identity))) = multiply(A,add(B,multiplicative_identity)). [para(64(a,1),10(a,2,2)),rewrite([2(2)])].
% 4.33/4.57 102 add(add(A,B),multiply(C,add(A,B))) = add(add(A,B),multiply(C,additive_identity)). [para(78(a,1),15(a,1,1)),rewrite([5(3),95(4),6(7)])].
% 4.33/4.57 104 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,A)). [para(16(a,1),6(a,2)),rewrite([6(3),6(4)])].
% 4.33/4.57 105 add(add(A,B),add(A,multiply(A,B))) = add(A,B). [para(16(a,1),8(a,1)),rewrite([6(3),79(3),2(6)])].
% 4.33/4.57 111 add(multiply(A,B),add(A,multiply(A,C))) = multiply(A,add(B,add(C,multiplicative_identity))). [para(16(a,1),10(a,1,2))].
% 4.33/4.57 113 add(A,add(A,multiplicative_identity)) = add(A,multiplicative_identity). [para(16(a,1),77(a,1)),rewrite([6(5),79(5),2(4),75(3),5(3)])].
% 4.33/4.57 114 add(add(A,B),add(B,multiply(A,B))) = add(A,B). [para(16(a,1),15(a,1)),rewrite([6(3),95(3),2(6),5(5)])].
% 4.33/4.57 118 multiply(add(A,B),add(C,multiplicative_identity)) = add(add(A,B),multiply(C,additive_identity)). [back_rewrite(102),rewrite([104(4,R)])].
% 4.33/4.57 119 add(add(A,multiplicative_identity),multiply(B,additive_identity)) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [back_rewrite(98),rewrite([118(5)])].
% 4.33/4.57 121 multiply(multiply(A,B),add(C,multiplicative_identity)) = add(multiply(A,B),multiply(C,additive_identity)). [para(89(a,1),15(a,1,1)),rewrite([5(3),95(4),104(4,R),6(7)])].
% 4.33/4.57 122 multiply(multiplicative_identity,multiply(A,B)) = multiply(A,B). [para(89(a,1),71(a,1,2)),rewrite([89(6)])].
% 4.33/4.57 125 multiply(inverse(A),add(A,B)) = multiply(B,inverse(A)). [para(4(a,1),18(a,1,1)),rewrite([6(3),89(4)]),flip(a)].
% 4.33/4.57 126 multiply(add(A,multiply(B,C)),multiply(C,add(B,D))) = add(multiply(B,C),multiply(A,multiply(C,D))). [para(18(a,1),8(a,1,2)),rewrite([5(2)])].
% 4.33/4.57 128 add(add(A,multiply(B,C)),multiply(D,add(A,C))) = multiply(add(A,C),add(D,add(A,B))). [para(8(a,1),18(a,1,1)),rewrite([6(4),5(8)])].
% 4.33/4.57 130 multiply(multiply(A,additive_identity),add(A,B)) = add(multiply(A,additive_identity),multiply(B,additive_identity)). [para(80(a,1),18(a,1,1)),rewrite([6(5),104(6,R),121(5)]),flip(a)].
% 4.33/4.57 132 add(multiply(A,B),add(B,multiply(B,C))) = multiply(B,add(A,add(C,multiplicative_identity))). [para(16(a,1),18(a,1,2))].
% 4.33/4.57 151 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(19(a,1),10(a,1,1)),rewrite([6(7),5(13)])].
% 4.33/4.57 152 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(19(a,1),10(a,1,2)),rewrite([6(3)])].
% 4.33/4.57 154 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),19(a,1,1,2))].
% 4.33/4.57 155 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),19(a,1,2)),rewrite([5(3)])].
% 4.33/4.57 161 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(15(a,1),19(a,1,2,2)),rewrite([5(3),15(11),6(12)])].
% 4.33/4.57 167 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(19(a,1),16(a,2,2)),rewrite([5(6)]),flip(a)].
% 4.33/4.57 168 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(16(a,1),19(a,1,2,2)),rewrite([5(3)])].
% 4.33/4.57 173 add(multiply(A,B),multiply(C,multiply(A,add(B,multiplicative_identity)))) = multiply(A,add(B,C)). [para(113(a,1),19(a,1,1,2)),rewrite([19(6),2(3),6(2),10(3)]),flip(a)].
% 4.33/4.57 177 multiply(add(A,B),multiply(A,add(C,inverse(B)))) = add(multiply(A,inverse(B)),multiply(B,multiply(A,C))). [para(60(a,1),19(a,1,2)),rewrite([5(2),5(4),6(5)])].
% 4.33/4.57 180 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(19(a,1),19(a,1,2,2)),rewrite([5(5),19(17),6(19)])].
% 4.33/4.57 197 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),20(a,1,1))].
% 4.33/4.57 200 multiply(add(A,multiply(A,multiply(A,B))),multiply(A,add(B,multiply(A,B)))) = multiply(A,multiply(A,B)). [para(75(a,1),20(a,2)),rewrite([5(5)])].
% 4.33/4.57 202 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(15(a,1),20(a,2,1)),rewrite([15(3),5(6),6(12)])].
% 4.33/4.57 211 add(multiply(A,B),multiply(C,A)) = multiply(A,add(C,B)). [para(113(a,1),20(a,1,2,2)),rewrite([20(6),2(3),173(9),5(4)])].
% 4.33/4.57 217 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(20(a,1),20(a,1,1,2)),rewrite([5(10),20(17),6(19)])].
% 4.33/4.57 238 add(add(A,multiply(B,C)),multiply(D,add(B,A))) = multiply(add(B,A),add(D,add(C,A))). [para(5(a,1),22(a,1,1)),rewrite([5(2),5(3),5(6),5(7)])].
% 4.33/4.57 242 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),22(a,1,1)),rewrite([5(4),5(8),5(10)]),flip(a)].
% 4.33/4.57 245 add(add(A,multiply(B,C)),add(B,multiply(A,B))) = add(B,add(A,multiply(A,C))). [para(15(a,1),22(a,2)),rewrite([95(4),79(7)])].
% 4.33/4.57 249 multiply(add(A,B),add(C,add(A,multiply(B,additive_identity)))) = add(A,multiply(B,C)). [para(80(a,1),22(a,1,1,2)),rewrite([22(6),1(3),5(2),8(3)]),flip(a)].
% 4.33/4.57 285 multiply(add(A,multiply(B,additive_identity)),add(C,multiply(A,B))) = multiply(A,add(B,C)). [para(87(a,2),15(a,1,1)),rewrite([5(5),10(9)])].
% 4.33/4.57 288 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,additive_identity)). [para(87(a,2),16(a,2))].
% 4.33/4.57 294 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(19(a,1),87(a,2,2)),rewrite([6(6),167(14)]),flip(a)].
% 4.33/4.57 297 multiply(add(A,multiply(B,additive_identity)),multiply(A,add(B,C))) = multiply(A,add(B,multiply(A,C))). [para(87(a,2),20(a,1,1)),rewrite([10(10)])].
% 4.33/4.57 300 multiply(add(A,multiply(B,additive_identity)),add(C,add(A,D))) = multiply(add(A,multiply(A,B)),add(C,add(A,D))). [para(87(a,1),22(a,2,1)),rewrite([6(3),128(9)])].
% 4.33/4.57 304 add(A,multiply(A,multiply(A,B))) = add(A,multiply(B,additive_identity)). [para(87(a,1),79(a,1,2)),rewrite([79(3),100(7),288(6)])].
% 4.33/4.57 314 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(168),rewrite([288(11)])].
% 4.33/4.57 323 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(167),rewrite([294(14)])].
% 4.33/4.57 327 multiply(A,add(B,multiply(A,multiply(A,B)))) = multiply(A,multiply(A,B)). [back_rewrite(200),rewrite([304(3),297(7)])].
% 4.33/4.57 329 add(multiplicative_identity,inverse(A)) = multiplicative_identity. [para(2(a,1),90(a,1,2)),rewrite([5(2),3(2)]),flip(a)].
% 4.33/4.57 330 add(inverse(A),multiply(B,A)) = add(B,inverse(A)). [para(90(a,1),5(a,1)),rewrite([6(3),5(5)]),flip(a)].
% 4.33/4.57 331 multiply(add(A,inverse(B)),add(C,inverse(B))) = add(inverse(B),multiply(C,multiply(A,B))). [para(90(a,1),8(a,1,1)),rewrite([5(4),6(7),6(8)])].
% 4.33/4.57 346 add(inverse(A),add(A,multiply(A,B))) = add(inverse(A),add(A,B)). [para(79(a,1),90(a,1,2)),rewrite([5(7)])].
% 4.33/4.57 347 add(additive_identity,inverse(A)) = inverse(A). [para(90(a,1),87(a,1)),rewrite([6(6),4(6),1(6)])].
% 4.33/4.57 349 add(multiplicative_identity,multiply(A,inverse(B))) = add(A,multiplicative_identity). [para(329(a,1),8(a,1,1)),rewrite([5(3),95(4),2(3),5(2),6(5)]),flip(a)].
% 4.33/4.57 352 add(add(A,multiplicative_identity),add(B,multiply(A,additive_identity))) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [para(329(a,1),22(a,2,2,2)),rewrite([349(4),5(4),288(5),5(8),288(11),119(11)])].
% 4.33/4.57 354 add(multiply(A,B),add(B,multiply(C,additive_identity))) = multiply(B,add(A,add(B,C))). [para(1(a,1),23(a,1,1,2)),rewrite([6(3),1(7)])].
% 4.33/4.57 358 add(multiply(A,add(B,C)),add(B,multiply(B,C))) = multiply(add(B,C),add(A,B)). [para(26(a,1),23(a,2,2,2)),rewrite([81(7)])].
% 4.33/4.57 363 multiply(add(A,B),add(C,A)) = add(A,multiply(C,B)). [para(80(a,1),23(a,1,2,2)),rewrite([23(6),1(3),249(9),6(4)])].
% 4.33/4.57 377 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(87(a,2),23(a,1,1,2)),rewrite([6(6)])].
% 4.33/4.57 382 add(multiply(A,add(B,C)),add(B,multiply(B,C))) = add(B,multiply(A,C)). [back_rewrite(358),rewrite([363(8)])].
% 4.33/4.57 385 multiply(multiplicative_identity,inverse(A)) = inverse(A). [para(347(a,1),71(a,1,2)),rewrite([347(6)])].
% 4.33/4.57 386 multiply(A,additive_identity) = additive_identity. [para(347(a,1),97(a,1,2)),rewrite([4(2)]),flip(a)].
% 4.33/4.57 387 add(multiply(A,inverse(B)),multiply(C,inverse(B))) = multiply(inverse(B),add(A,C)). [para(347(a,1),22(a,1,2,2)),rewrite([6(3),89(4),347(8),5(8),1(8),5(7)])].
% 4.33/4.57 391 multiply(add(A,multiply(A,B)),add(C,add(A,D))) = add(multiply(C,A),add(A,multiply(D,multiply(A,B)))). [back_rewrite(377),rewrite([386(2),1(2)]),flip(a)].
% 4.33/4.57 395 multiply(A,add(B,add(A,C))) = add(A,multiply(B,A)). [back_rewrite(354),rewrite([386(3),1(3),5(2)]),flip(a)].
% 4.33/4.57 396 add(A,add(B,multiplicative_identity)) = multiplicative_identity. [back_rewrite(352),rewrite([386(4),1(4),5(3),386(6),386(6),5(6),50(6)])].
% 4.33/4.57 400 add(A,multiply(B,multiply(A,C))) = add(A,multiply(A,B)). [back_rewrite(314),rewrite([396(3),2(2),395(4),6(1),386(4),1(4)]),flip(a)].
% 4.33/4.57 408 add(A,multiply(A,B)) = A. [back_rewrite(300),rewrite([386(2),1(2),395(3),6(1),391(7),6(3),400(6),111(6),396(5),2(4)])].
% 4.33/4.57 413 multiply(A,add(B,multiply(A,C))) = multiply(A,add(C,B)). [back_rewrite(285),rewrite([386(2),1(2)])].
% 4.33/4.57 414 multiply(additive_identity,add(A,B)) = additive_identity. [back_rewrite(130),rewrite([386(2),386(5),386(6),75(6)])].
% 4.33/4.57 416 add(A,multiplicative_identity) = multiplicative_identity. [back_rewrite(64),rewrite([386(3),5(3),50(3)]),flip(a)].
% 4.33/4.57 419 add(A,multiply(B,A)) = A. [back_rewrite(132),rewrite([408(3),5(2),416(4),416(4),2(4)])].
% 4.33/4.57 420 multiply(A,add(B,add(C,multiply(A,D)))) = multiply(A,add(B,add(D,C))). [back_rewrite(242),rewrite([408(2),408(8),6(7),10(8),5(6)])].
% 4.33/4.57 422 add(A,add(B,multiply(A,C))) = add(B,A). [back_rewrite(245),rewrite([419(4),5(3),408(5),5(4)])].
% 4.33/4.57 423 add(A,add(B,A)) = add(B,A). [back_rewrite(114),rewrite([419(3),5(2)])].
% 4.33/4.57 425 add(A,multiply(B,multiply(A,C))) = A. [back_rewrite(400),rewrite([408(5)])].
% 4.33/4.57 426 add(A,multiply(B,add(A,C))) = add(A,multiply(B,C)). [back_rewrite(382),rewrite([408(4),5(3)])].
% 4.33/4.57 428 add(inverse(A),add(A,B)) = multiplicative_identity. [back_rewrite(346),rewrite([408(3),5(2),3(2)]),flip(a)].
% 4.33/4.57 430 add(A,add(A,B)) = add(A,B). [back_rewrite(105),rewrite([408(3),5(2)])].
% 4.33/4.57 431 multiply(A,add(A,B)) = A. [back_rewrite(79),rewrite([408(4)])].
% 4.33/4.57 434 multiply(A,multiply(A,B)) = multiply(A,B). [back_rewrite(327),rewrite([413(4),5(2),419(2)]),flip(a)].
% 4.33/4.57 437 add(multiply(A,add(B,C)),add(multiply(A,B),multiply(D,multiply(A,C)))) = multiply(A,add(B,C)). [back_rewrite(323),rewrite([414(13),5(11),89(11)])].
% 4.33/4.57 443 multiply(A,add(B,add(A,C))) = A. [back_rewrite(395),rewrite([6(4),408(5)])].
% 4.33/4.57 454 multiply(A,add(B,A)) = A. [para(386(a,1),15(a,2,2)),rewrite([1(3),6(2),1(4)])].
% 4.33/4.57 456 add(A,multiply(B,multiply(C,multiply(D,inverse(A))))) = add(A,multiply(B,multiply(C,D))). [para(72(a,1),8(a,1,1)),rewrite([8(4),6(2),6(7)]),flip(a)].
% 4.33/4.57 460 add(A,multiply(inverse(A),multiply(B,C))) = add(A,multiply(B,C)). [para(72(a,1),60(a,2)),rewrite([6(5),456(6)])].
% 4.33/4.57 462 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(72(a,1),19(a,1,2)),rewrite([5(3),6(7)])].
% 4.33/4.57 465 add(inverse(A),multiply(B,multiply(A,C))) = add(inverse(A),multiply(C,B)). [para(385(a,1),19(a,1,2,2)),rewrite([5(3),71(4),331(5),6(2),385(7),6(7),2(7),6(6)])].
% 4.33/4.57 494 multiply(A,multiply(B,add(A,C))) = multiply(B,A). [para(419(a,1),19(a,1,2)),rewrite([6(3),18(7),408(5),6(4)])].
% 4.33/4.57 502 multiply(multiply(A,B),multiply(A,add(C,B))) = multiply(A,B). [para(75(a,1),93(a,1,2)),rewrite([6(4),408(9)])].
% 4.33/4.57 503 add(multiply(A,B),multiply(C,multiply(A,add(D,B)))) = add(multiply(A,B),multiply(C,multiply(A,D))). [para(93(a,1),18(a,2)),rewrite([6(7),502(7),5(5)])].
% 4.33/4.57 504 multiply(A,multiply(B,add(C,A))) = multiply(B,A). [para(18(a,1),93(a,2)),rewrite([419(4),6(3),408(5),6(4)])].
% 4.33/4.57 517 multiply(multiply(A,B),add(C,multiply(A,multiply(B,D)))) = add(multiply(A,multiply(B,D)),multiply(C,multiply(A,B))). [para(408(a,1),93(a,1,1,2))].
% 4.33/4.57 522 multiply(A,multiply(B,A)) = multiply(B,A). [para(419(a,1),454(a,1,2)),rewrite([6(2)])].
% 4.33/4.57 524 add(inverse(multiply(A,B)),multiply(A,add(B,C))) = multiplicative_identity. [para(10(a,1),428(a,1,2))].
% 4.33/4.57 526 add(inverse(multiply(A,B)),multiply(B,add(A,C))) = multiplicative_identity. [para(18(a,1),428(a,1,2))].
% 4.33/4.57 534 multiply(inverse(A),add(B,add(A,C))) = multiply(inverse(A),add(B,C)). [para(125(a,1),10(a,1,2)),rewrite([6(2),387(5)]),flip(a)].
% 4.33/4.57 544 multiply(inverse(A),multiply(A,B)) = additive_identity. [para(408(a,1),125(a,1,2)),rewrite([6(2),4(2),6(4)]),flip(a)].
% 4.33/4.57 548 multiply(inverse(add(A,B)),add(A,multiply(B,C))) = additive_identity. [para(8(a,1),544(a,1,2))].
% 4.33/4.57 551 multiply(multiply(A,B),add(C,inverse(A))) = multiply(C,multiply(A,B)). [para(544(a,1),18(a,1,1)),rewrite([6(3),89(4),5(5)]),flip(a)].
% 4.33/4.57 557 multiply(inverse(inverse(A)),multiply(B,inverse(A))) = additive_identity. [para(125(a,1),544(a,1,2))].
% 4.33/4.57 558 add(A,multiply(B,add(C,A))) = add(A,multiply(C,B)). [para(423(a,1),8(a,1,1)),rewrite([15(3),6(4)]),flip(a)].
% 4.33/4.57 579 multiply(add(A,B),add(C,B)) = add(B,multiply(C,A)). [para(425(a,1),91(a,1,2)),rewrite([5(3),558(3),6(1),408(5)]),flip(a)].
% 4.33/4.57 582 multiply(A,multiply(B,multiply(A,C))) = multiply(B,multiply(A,C)). [para(425(a,1),454(a,1,2)),rewrite([6(3)])].
% 4.33/4.57 583 multiply(inverse(A),multiply(B,multiply(A,C))) = additive_identity. [para(425(a,1),125(a,1,2)),rewrite([6(2),4(2),6(5)]),flip(a)].
% 4.33/4.57 587 multiply(A,add(B,multiply(C,A))) = add(multiply(C,A),multiply(B,A)). [para(2(a,1),126(a,2,2,2)),rewrite([416(4),2(4),6(3)])].
% 4.33/4.57 612 multiply(multiply(A,B),add(A,C)) = multiply(A,B). [para(434(a,1),18(a,1,1)),rewrite([6(3),419(4)]),flip(a)].
% 4.33/4.57 620 multiply(add(A,add(B,C)),add(B,D)) = add(B,multiply(D,add(A,add(B,C)))). [para(443(a,1),18(a,1,1)),rewrite([6(3)]),flip(a)].
% 4.33/4.57 657 multiply(add(A,B),add(C,add(A,D))) = add(A,multiply(B,add(C,add(A,D)))). [para(6(a,1),128(a,2)),rewrite([128(5),620(8)])].
% 4.33/4.57 658 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(128(a,1),8(a,1,1)),rewrite([657(4),6(5),5(7),657(8),6(9),6(13)])].
% 4.33/4.57 661 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),128(a,1,2)),rewrite([6(3),657(10)])].
% 4.33/4.57 666 add(A,add(B,multiply(C,A))) = add(B,A). [para(15(a,1),128(a,2)),rewrite([454(4),5(3),431(5),5(4)])].
% 4.33/4.57 754 multiply(inverse(inverse(A)),add(B,multiply(C,inverse(A)))) = multiply(B,inverse(inverse(A))). [para(557(a,1),10(a,1,1)),rewrite([6(4),89(5),5(8)]),flip(a)].
% 4.33/4.57 757 add(A,multiply(B,inverse(inverse(A)))) = A. [para(557(a,1),72(a,1,2)),rewrite([1(2),6(3)]),flip(a)].
% 4.33/4.57 761 add(A,inverse(inverse(A))) = A. [para(77(a,1),757(a,1,2))].
% 4.33/4.57 801 inverse(inverse(A)) = A. [para(761(a,1),90(a,2)),rewrite([6(4),4(4),1(4)])].
% 4.33/4.57 804 multiply(A,add(B,multiply(C,inverse(A)))) = multiply(A,B). [back_rewrite(754),rewrite([801(2),801(6),6(5)])].
% 4.33/4.57 835 multiply(A,multiply(B,multiply(C,inverse(A)))) = additive_identity. [para(125(a,1),583(a,1,2,2)),rewrite([801(2)])].
% 4.33/4.57 855 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(151(a,1),8(a,2)),rewrite([5(5),5(12),437(12),6(8)])].
% 4.33/4.57 916 add(multiply(A,B),inverse(add(A,inverse(B)))) = add(B,inverse(add(A,inverse(B)))). [para(97(a,1),330(a,1,2)),rewrite([6(4),5(5)])].
% 4.33/4.57 920 add(A,inverse(multiply(A,B))) = multiplicative_identity. [para(434(a,1),330(a,1,2)),rewrite([5(4),3(4)]),flip(a)].
% 4.33/4.57 921 add(A,inverse(multiply(B,A))) = multiplicative_identity. [para(522(a,1),330(a,1,2)),rewrite([5(4),3(4)]),flip(a)].
% 4.33/4.57 928 add(inverse(multiply(A,B)),multiply(A,C)) = add(C,inverse(multiply(A,B))). [para(920(a,1),15(a,1,1)),rewrite([5(4),71(5)]),flip(a)].
% 4.33/4.57 934 multiply(inverse(A),inverse(multiply(A,B))) = inverse(A). [para(920(a,1),125(a,1,2)),rewrite([2(3),6(5)]),flip(a)].
% 4.33/4.57 937 add(add(A,B),inverse(multiply(C,A))) = multiplicative_identity. [back_rewrite(524),rewrite([928(5)])].
% 4.33/4.57 942 multiply(multiply(A,B),add(C,A)) = multiply(A,B). [para(75(a,1),152(a,1,2)),rewrite([5(2),419(2),434(4),5(4),419(4),5(3),419(3),434(4),408(4)]),flip(a)].
% 4.33/4.57 972 add(inverse(multiply(A,B)),multiply(B,C)) = add(C,inverse(multiply(A,B))). [para(921(a,1),15(a,1,1)),rewrite([5(4),71(5)]),flip(a)].
% 4.33/4.57 975 add(inverse(A),add(B,A)) = multiplicative_identity. [para(454(a,1),921(a,1,2,1)),rewrite([5(3)])].
% 4.33/4.57 978 add(add(A,B),inverse(multiply(A,C))) = multiplicative_identity. [back_rewrite(526),rewrite([972(5)])].
% 4.33/4.57 982 add(A,inverse(multiply(B,multiply(A,C)))) = multiplicative_identity. [para(425(a,1),975(a,1,2)),rewrite([5(4)])].
% 4.33/4.57 993 multiply(A,inverse(multiply(B,inverse(A)))) = A. [para(125(a,1),934(a,1,2,1)),rewrite([801(2),801(6)])].
% 4.33/4.57 1001 multiply(add(A,B),inverse(multiply(A,inverse(B)))) = B. [para(993(a,1),125(a,2)),rewrite([5(6),60(6),5(4),6(5)])].
% 4.33/4.57 1002 multiply(multiply(A,inverse(B)),multiply(B,C)) = additive_identity. [para(993(a,1),835(a,1,2,2)),rewrite([6(3)])].
% 4.33/4.57 1080 add(multiply(A,add(B,C)),multiply(D,multiply(A,inverse(multiply(B,E))))) = multiply(A,add(D,add(B,C))). [para(937(a,1),19(a,1,1,2)),rewrite([2(2),413(4),5(2),6(6)]),flip(a)].
% 4.33/4.57 1100 add(inverse(multiply(A,B)),add(A,C)) = multiplicative_identity. [para(978(a,1),5(a,1)),flip(a)].
% 4.33/4.57 1116 multiply(inverse(A),inverse(multiply(B,multiply(A,C)))) = inverse(A). [para(982(a,1),125(a,1,2)),rewrite([2(3),6(6)]),flip(a)].
% 4.33/4.57 1138 multiply(multiply(A,add(B,C)),multiply(A,add(B,D))) = add(multiply(multiply(A,D),multiply(A,C)),multiply(A,B)). [para(155(a,2),5(a,1))].
% 4.33/4.57 1156 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(155(a,1),18(a,1,1)),rewrite([6(8),5(14)])].
% 4.33/4.57 1271 multiply(A,add(multiply(A,B),add(C,D))) = multiply(A,add(B,add(C,D))). [para(937(a,1),155(a,1,1,2)),rewrite([2(2),5(2),434(4),6(7),1080(11)]),flip(a)].
% 4.33/4.57 1288 multiply(inverse(A),multiply(B,A)) = additive_identity. [para(934(a,1),1002(a,1,2)),rewrite([801(2),6(3)])].
% 4.33/4.57 1293 multiply(A,inverse(add(A,B))) = additive_identity. [para(431(a,1),1288(a,1,2)),rewrite([6(3)])].
% 4.33/4.57 1297 multiply(A,inverse(add(B,add(A,C)))) = additive_identity. [para(443(a,1),1288(a,1,2)),rewrite([6(4)])].
% 4.33/4.57 1308 multiply(inverse(add(A,B)),add(A,C)) = multiply(C,inverse(add(A,B))). [para(1293(a,1),18(a,1,1)),rewrite([6(4),89(5)]),flip(a)].
% 4.33/4.57 1310 add(inverse(A),inverse(add(A,B))) = inverse(A). [para(1293(a,1),90(a,1,2)),rewrite([1(3),5(5)]),flip(a)].
% 4.33/4.57 1319 multiply(multiply(A,B),inverse(add(C,A))) = additive_identity. [back_rewrite(548),rewrite([1308(5)])].
% 4.33/4.57 1533 multiply(add(A,B),multiply(A,C)) = multiply(A,C). [para(1100(a,1),125(a,1,2)),rewrite([801(3),6(3),122(3),801(5)]),flip(a)].
% 4.33/4.57 1542 add(multiply(A,inverse(B)),multiply(B,multiply(A,C))) = multiply(A,add(C,inverse(B))). [back_rewrite(177),rewrite([1533(5)]),flip(a)].
% 4.33/4.57 1564 add(inverse(A),inverse(add(B,add(A,C)))) = inverse(A). [para(1297(a,1),90(a,1,2)),rewrite([1(3),5(6)]),flip(a)].
% 4.33/4.57 1579 add(A,inverse(add(B,inverse(A)))) = A. [para(90(a,1),1310(a,1,2,1)),rewrite([801(2),801(6)])].
% 4.33/4.57 1590 add(multiply(A,B),inverse(add(A,inverse(B)))) = B. [back_rewrite(916),rewrite([1579(9)])].
% 4.33/4.57 1729 add(multiply(A,B),add(C,A)) = add(C,A). [para(1319(a,1),330(a,1,2)),rewrite([801(3),5(3),78(3),801(5)]),flip(a)].
% 4.33/4.57 2014 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(408(a,1),197(a,1,1,2)),rewrite([5(3)]),flip(a)].
% 4.33/4.57 2194 multiply(multiply(A,B),multiply(A,C)) = multiply(C,multiply(A,B)). [para(408(a,1),504(a,1,2,2)),rewrite([6(2)])].
% 4.33/4.57 2201 multiply(multiply(A,add(B,C)),add(C,add(D,multiply(A,B)))) = multiply(A,add(B,C)). [para(504(a,1),151(a,1,2)),rewrite([5(6),666(6),10(3)]),flip(a)].
% 4.33/4.57 2207 multiply(multiply(A,B),add(C,multiply(B,multiply(A,D)))) = add(multiply(B,multiply(A,D)),multiply(C,multiply(A,B))). [para(504(a,1),154(a,1,1)),rewrite([522(9)])].
% 4.33/4.57 2217 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(504(a,1),180(a,2,2,2)),rewrite([2201(6),855(8)])].
% 4.33/4.57 2337 add(multiply(A,multiply(B,C)),multiply(D,multiply(A,B))) = multiply(add(D,multiply(B,C)),multiply(A,B)). [back_rewrite(2014),rewrite([2194(5),2194(10)])].
% 4.33/4.57 2505 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(1156),rewrite([2194(4),151(8)]),flip(a)].
% 4.33/4.57 2518 multiply(add(A,B),multiply(C,add(A,D))) = add(multiply(D,multiply(C,B)),multiply(C,A)). [back_rewrite(1138),rewrite([2194(5),2194(7)])].
% 4.33/4.57 2546 multiply(multiply(A,B),add(C,multiply(A,multiply(B,D)))) = multiply(add(C,multiply(B,D)),multiply(A,B)). [back_rewrite(517),rewrite([2337(10)])].
% 4.33/4.57 2736 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),202(a,1,1,2)),rewrite([5(2),5(5)])].
% 4.33/4.57 2808 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(612(a,1),202(a,2,2,2)),rewrite([5(4),657(8),1271(7),620(8),658(8)])].
% 4.33/4.57 2891 add(add(A,B),add(A,C)) = add(C,add(A,B)). [para(431(a,1),666(a,1,2,2)),rewrite([5(2)])].
% 4.33/4.57 2913 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(666(a,1),202(a,1,2,1)),rewrite([5(9),666(19)])].
% 4.33/4.57 2932 add(multiply(A,B),add(C,multiply(D,A))) = add(C,multiply(A,add(D,add(C,B)))). [back_rewrite(661),rewrite([2891(5),2891(7)])].
% 4.33/4.57 2952 multiply(add(A,B),multiply(B,C)) = multiply(B,C). [para(942(a,1),6(a,2))].
% 4.33/4.57 3386 add(multiply(A,B),inverse(add(B,inverse(A)))) = A. [para(1590(a,1),5(a,1)),rewrite([6(4),5(5)]),flip(a)].
% 4.33/4.57 3388 add(multiply(A,B),multiply(C,inverse(add(A,inverse(B))))) = multiply(B,add(A,C)). [para(1590(a,1),8(a,1,2)),rewrite([5(2),6(3),587(3),6(2),18(3)]),flip(a)].
% 4.33/4.57 3391 add(multiply(A,B),multiply(C,B)) = multiply(B,add(C,A)). [para(1590(a,1),15(a,1,2)),rewrite([6(3),587(3),3388(9),5(4)])].
% 4.33/4.57 3392 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(1590(a,1),19(a,1,1,2)),rewrite([6(2),2546(5),6(5)]),flip(a)].
% 4.33/4.57 3603 multiply(add(A,multiply(B,C)),add(B,D)) = add(multiply(B,C),multiply(A,add(B,D))). [para(1729(a,1),8(a,1,2)),rewrite([5(2),5(3),5(6)])].
% 4.33/4.57 3664 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(408(a,1),217(a,1,2,2)),rewrite([6(8),413(8),6(8),413(15)])].
% 4.33/4.57 3813 multiply(A,add(B,add(C,multiply(D,A)))) = multiply(A,add(B,add(D,C))). [para(419(a,1),238(a,1,2,2)),rewrite([18(3),6(3),10(4),5(2),419(5)]),flip(a)].
% 4.33/4.57 3944 add(multiply(A,multiply(B,C)),multiply(D,multiply(B,A))) = multiply(add(D,multiply(B,C)),multiply(B,A)). [para(3386(a,1),126(a,1,2,2)),rewrite([6(2),6(4),6(5),2207(5),6(7),3392(13),6(8)])].
% 4.33/4.57 4470 multiply(A,multiply(B,add(C,inverse(A)))) = multiply(A,multiply(B,C)). [para(10(a,1),804(a,1,2))].
% 4.33/4.57 4644 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(413(a,1),161(a,2,2,2)),rewrite([5(4),422(5),5(3),3603(4),657(9),5(13)])].
% 4.33/4.57 4652 multiply(add(A,multiply(B,C)),multiply(B,add(D,add(A,C)))) = multiply(B,add(A,C)). [para(413(a,1),494(a,2)),rewrite([5(5),420(6),5(3),5(7)])].
% 4.33/4.57 5041 multiply(A,add(inverse(A),multiply(B,C))) = multiply(B,multiply(A,C)). [para(1116(a,1),1001(a,1,2,1)),rewrite([465(4),6(2),801(5),6(4)])].
% 4.33/4.57 5096 add(multiply(A,add(B,C)),multiply(B,multiply(A,D))) = multiply(A,add(B,C)). [para(426(a,1),19(a,1,2)),rewrite([5(2),6(6),4652(6)]),flip(a)].
% 4.33/4.57 5100 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(426(a,1),151(a,2,2,2)),rewrite([5096(5),5(4),503(7),5(7)]),flip(a)].
% 4.33/4.57 5105 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(426(a,1),202(a,1,1,2)),rewrite([5(4),430(6),657(7),620(8),5100(7),426(9),5(9),2808(12)])].
% 4.33/4.57 5387 add(A,multiply(inverse(A),add(B,C))) = add(B,add(A,C)). [para(1564(a,1),1590(a,1,2,1)),rewrite([534(4),801(5),5(4)])].
% 4.33/4.57 6704 add(A,add(B,C)) = add(B,add(A,C)). [para(71(a,1),460(a,1,2,2)),rewrite([5387(4),71(5)])].
% 4.33/4.57 6710 add(multiply(inverse(A),multiply(B,C)),multiply(A,multiply(D,multiply(B,C)))) = multiply(multiply(B,C),add(D,inverse(A))). [para(460(a,1),126(a,1,1)),rewrite([5(5),2952(7),6(9)]),flip(a)].
% 4.33/4.57 6719 add(add(A,multiply(B,C)),multiply(D,E)) = add(A,add(multiply(B,C),multiply(D,E))). [para(460(a,1),161(a,1,2,2)),rewrite([5(2),3(2),6704(4),71(5),6704(6),8(7),579(5),6(2),460(8),5(8),3(8),2(8),6(7)]),flip(a)].
% 4.33/4.57 7629 add(A,multiply(B,add(C,add(A,D)))) = add(A,multiply(B,add(C,D))). [back_rewrite(2932),rewrite([6(2),6704(4),10(3),5(4),6704(5),5(4)]),flip(a)].
% 4.33/4.57 7635 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(2913),rewrite([6719(4),18(3),6704(8),6704(9),6704(8),8(10),3813(8),6704(6),620(9),7629(9),2505(7),6(4),6719(12),18(11),6719(15)])].
% 4.33/4.57 7689 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(2736),rewrite([5(4),5(5),6704(6),5(5),8(7),620(7),7629(7),19(5),5(8),6719(11)]),flip(a)].
% 4.33/4.57 8245 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(5105),rewrite([6719(11)])].
% 4.33/4.57 8275 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(4644),rewrite([7629(9),93(6),6(3),5(10),6719(13)]),flip(a)].
% 4.33/4.57 8336 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(3664),rewrite([6719(16),8275(16),3944(14)])].
% 4.33/4.57 8450 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(2217),rewrite([6719(13),3391(12)])].
% 4.33/4.57 8629 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(7635),rewrite([6(4),6704(6),8450(7),7689(14)])].
% 4.33/4.57 9034 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(855),rewrite([8450(14)])].
% 4.33/4.57 9750 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(462(a,1),89(a,1,2)),rewrite([462(15)])].
% 4.33/4.58 10008 multiply(A,multiply(B,C)) = multiply(C,multiply(B,A)). [para(465(a,1),125(a,1,2)),rewrite([801(2),5041(4),801(6),6(5),582(5)])].
% 4.33/4.58 10405 add(multiply(A,B),multiply(multiply(A,C),add(D,E))) = add(multiply(A,B),multiply(C,multiply(A,add(D,E)))). [back_rewrite(9034),rewrite([10008(5),8336(8),10008(5),413(4),5(2)]),flip(a)].
% 4.33/4.58 10570 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(8629),rewrite([10405(6),10008(11)])].
% 4.33/4.58 10839 add(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(A,multiply(B,D)))) = multiply(multiply(B,A),add(D,inverse(C))). [back_rewrite(6710),rewrite([10008(3),10008(5)])].
% 4.33/4.58 11164 multiply(add(A,B),multiply(C,add(A,D))) = multiply(C,add(A,multiply(B,D))). [back_rewrite(2518),rewrite([6(5),10008(6),6(7),211(8)])].
% 4.33/4.58 11279 multiply(multiply(A,B),add(C,inverse(A))) = multiply(B,multiply(A,C)). [back_rewrite(551),rewrite([10008(6)])].
% 4.33/4.58 11285 multiply(b,multiply(a,c)) != multiply(a,multiply(b,c)) # answer(prove_associativity). [back_rewrite(12),rewrite([10008(5)])].
% 4.33/4.58 11546 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(10570),rewrite([11164(5),10(5)]),flip(a)].
% 4.33/4.58 11687 add(A,add(multiply(B,C),multiply(D,multiply(B,E)))) = add(A,multiply(B,add(C,multiply(D,E)))). [back_rewrite(8245),rewrite([11546(6),426(5)]),flip(a)].
% 4.33/4.58 11990 add(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(A,D))) = multiply(A,add(multiply(B,inverse(C)),multiply(C,D))). [back_rewrite(9750),rewrite([11687(8),89(7)]),flip(a)].
% 4.33/4.58 12237 multiply(multiply(A,B),add(C,inverse(D))) = multiply(A,multiply(B,add(C,inverse(D)))). [back_rewrite(10839),rewrite([11990(7),1542(5),6(5)]),flip(a)].
% 4.33/4.58 12274 multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)). [back_rewrite(11279),rewrite([12237(4),4470(4)])].
% 4.33/4.58 12275 $F # answer(prove_associativity). [resolve(12274,a,11285,a)].
% 4.33/4.58
% 4.33/4.58 % SZS output end Refutation
% 4.33/4.58 ============================== end of proof ==========================
% 4.33/4.58
% 4.33/4.58 ============================== STATISTICS ============================
% 4.33/4.58
% 4.33/4.58 Given=280. Generated=70239. Kept=12271. proofs=1.
% 4.33/4.58 Usable=141. Sos=3501. Demods=3536. Limbo=37, Disabled=8600. Hints=0.
% 4.33/4.58 Megabytes=15.57.
% 4.33/4.58 User_CPU=3.54, System_CPU=0.05, Wall_clock=3.
% 4.33/4.58
% 4.33/4.58 ============================== end of statistics =====================
% 4.33/4.58
% 4.33/4.58 ============================== end of search =========================
% 4.33/4.58
% 4.33/4.58 THEOREM PROVED
% 4.33/4.58 % SZS status Unsatisfiable
% 4.33/4.58
% 4.33/4.58 Exiting with 1 proof.
% 4.33/4.58
% 4.33/4.58 Process 12216 exit (max_proofs) Wed Jun 1 17:51:03 2022
% 4.33/4.58 Prover9 interrupted
%------------------------------------------------------------------------------