TSTP Solution File: BOO031-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO031-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 23:48:04 EDT 2022
% Result : Unsatisfiable 1.20s 1.46s
% Output : Refutation 1.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : BOO031-1 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n020.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 22:53:08 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.20/1.46 ============================== Prover9 ===============================
% 1.20/1.46 Prover9 (32) version 2009-11A, November 2009.
% 1.20/1.46 Process 3136 was started by sandbox on n020.cluster.edu,
% 1.20/1.46 Wed Jun 1 22:53:09 2022
% 1.20/1.46 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2983_n020.cluster.edu".
% 1.20/1.46 ============================== end of head ===========================
% 1.20/1.46
% 1.20/1.46 ============================== INPUT =================================
% 1.20/1.46
% 1.20/1.46 % Reading from file /tmp/Prover9_2983_n020.cluster.edu
% 1.20/1.46
% 1.20/1.46 set(prolog_style_variables).
% 1.20/1.46 set(auto2).
% 1.20/1.46 % set(auto2) -> set(auto).
% 1.20/1.46 % set(auto) -> set(auto_inference).
% 1.20/1.46 % set(auto) -> set(auto_setup).
% 1.20/1.46 % set(auto_setup) -> set(predicate_elim).
% 1.20/1.46 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.20/1.46 % set(auto) -> set(auto_limits).
% 1.20/1.46 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.20/1.46 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.20/1.46 % set(auto) -> set(auto_denials).
% 1.20/1.46 % set(auto) -> set(auto_process).
% 1.20/1.46 % set(auto2) -> assign(new_constants, 1).
% 1.20/1.46 % set(auto2) -> assign(fold_denial_max, 3).
% 1.20/1.46 % set(auto2) -> assign(max_weight, "200.000").
% 1.20/1.46 % set(auto2) -> assign(max_hours, 1).
% 1.20/1.46 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.20/1.46 % set(auto2) -> assign(max_seconds, 0).
% 1.20/1.46 % set(auto2) -> assign(max_minutes, 5).
% 1.20/1.46 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.20/1.46 % set(auto2) -> set(sort_initial_sos).
% 1.20/1.46 % set(auto2) -> assign(sos_limit, -1).
% 1.20/1.46 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.20/1.46 % set(auto2) -> assign(max_megs, 400).
% 1.20/1.46 % set(auto2) -> assign(stats, some).
% 1.20/1.46 % set(auto2) -> clear(echo_input).
% 1.20/1.46 % set(auto2) -> set(quiet).
% 1.20/1.46 % set(auto2) -> clear(print_initial_clauses).
% 1.20/1.46 % set(auto2) -> clear(print_given).
% 1.20/1.46 assign(lrs_ticks,-1).
% 1.20/1.46 assign(sos_limit,10000).
% 1.20/1.46 assign(order,kbo).
% 1.20/1.46 set(lex_order_vars).
% 1.20/1.46 clear(print_given).
% 1.20/1.46
% 1.20/1.46 % formulas(sos). % not echoed (12 formulas)
% 1.20/1.46
% 1.20/1.46 ============================== end of input ==========================
% 1.20/1.46
% 1.20/1.46 % From the command line: assign(max_seconds, 300).
% 1.20/1.46
% 1.20/1.46 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.20/1.46
% 1.20/1.46 % Formulas that are not ordinary clauses:
% 1.20/1.46
% 1.20/1.46 ============================== end of process non-clausal formulas ===
% 1.20/1.46
% 1.20/1.46 ============================== PROCESS INITIAL CLAUSES ===============
% 1.20/1.46
% 1.20/1.46 ============================== PREDICATE ELIMINATION =================
% 1.20/1.46
% 1.20/1.46 ============================== end predicate elimination =============
% 1.20/1.46
% 1.20/1.46 Auto_denials:
% 1.20/1.46 % copying label prove_multiply_add_property to answer in negative clause
% 1.20/1.46
% 1.20/1.46 Term ordering decisions:
% 1.20/1.46
% 1.20/1.46 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 1.20/1.46 Function symbol KB weights: n0=1. n1=1. a=1. b=1. c=1. add=1. multiply=1. inverse=0.
% 1.20/1.46
% 1.20/1.46 ============================== end of process initial clauses ========
% 1.20/1.46
% 1.20/1.46 ============================== CLAUSES FOR SEARCH ====================
% 1.20/1.46
% 1.20/1.46 ============================== end of clauses for search =============
% 1.20/1.46
% 1.20/1.46 ============================== SEARCH ================================
% 1.20/1.46
% 1.20/1.46 % Starting search at 0.01 seconds.
% 1.20/1.46
% 1.20/1.46 ============================== PROOF =================================
% 1.20/1.46 % SZS status Unsatisfiable
% 1.20/1.46 % SZS output start Refutation
% 1.20/1.46
% 1.20/1.46 % Proof 1 at 0.45 (+ 0.01) seconds: prove_multiply_add_property.
% 1.20/1.46 % Length of proof is 132.
% 1.20/1.46 % Level of proof is 17.
% 1.20/1.46 % Maximum clause weight is 33.000.
% 1.20/1.46 % Given clauses 109.
% 1.20/1.46
% 1.20/1.46 1 add(A,inverse(A)) = n1 # label(additive_inverse) # label(axiom). [assumption].
% 1.20/1.46 2 multiply(A,inverse(A)) = n0 # label(multiplicative_inverse) # label(axiom). [assumption].
% 1.20/1.46 3 multiply(add(A,inverse(A)),B) = B # label(property3) # label(axiom). [assumption].
% 1.20/1.46 4 multiply(n1,A) = A. [copy(3),rewrite([1(2)])].
% 1.20/1.46 5 add(multiply(A,inverse(A)),B) = B # label(property3_dual) # label(axiom). [assumption].
% 1.20/1.46 6 add(n0,A) = A. [copy(5),rewrite([2(2)])].
% 1.20/1.46 7 add(A,multiply(B,multiply(A,C))) = A # label(l1) # label(axiom). [assumption].
% 1.20/1.46 8 multiply(A,add(B,add(A,C))) = A # label(l2) # label(axiom). [assumption].
% 1.20/1.46 9 add(add(multiply(A,B),multiply(B,C)),B) = B # label(l3) # label(axiom). [assumption].
% 1.20/1.46 10 multiply(multiply(add(A,B),add(B,C)),B) = B # label(l4) # label(axiom). [assumption].
% 1.20/1.46 11 add(add(A,B),C) = add(A,add(B,C)) # label(associativity_of_add) # label(axiom). [assumption].
% 1.20/1.46 12 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity_of_multiply) # label(axiom). [assumption].
% 1.20/1.46 13 add(multiply(A,B),add(multiply(B,C),multiply(C,A))) = multiply(add(A,B),multiply(add(B,C),add(C,A))) # label(distributivity) # label(axiom). [assumption].
% 1.20/1.46 14 multiply(add(A,B),multiply(add(B,C),add(C,A))) = add(multiply(A,B),add(multiply(B,C),multiply(C,A))). [copy(13),flip(a)].
% 1.20/1.46 15 multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)) # label(prove_multiply_add_property) # label(negated_conjecture) # answer(prove_multiply_add_property). [assumption].
% 1.20/1.46 16 add(multiply(b,a),multiply(c,a)) != multiply(a,add(b,c)) # answer(prove_multiply_add_property). [copy(15),flip(a)].
% 1.20/1.46 17 add(multiply(A,B),add(multiply(B,C),B)) = B. [back_rewrite(9),rewrite([11(4)])].
% 1.20/1.46 18 multiply(add(A,B),multiply(add(B,C),B)) = B. [back_rewrite(10),rewrite([12(4)])].
% 1.20/1.46 21 add(A,multiply(B,n0)) = A. [para(2(a,1),7(a,1,2,2))].
% 1.20/1.46 22 add(n1,multiply(A,B)) = n1. [para(4(a,1),7(a,1,2,2))].
% 1.20/1.46 23 add(A,multiply(A,B)) = A. [para(4(a,1),7(a,1,2))].
% 1.20/1.46 25 multiply(A,add(B,n1)) = A. [para(1(a,1),8(a,1,2,2))].
% 1.20/1.46 27 multiply(n0,add(A,B)) = n0. [para(6(a,1),8(a,1,2,2))].
% 1.20/1.46 28 multiply(A,add(A,B)) = A. [para(6(a,1),8(a,1,2))].
% 1.20/1.46 29 add(A,multiply(B,A)) = A. [para(8(a,1),7(a,1,2,2))].
% 1.20/1.46 30 multiply(A,add(B,A)) = A. [para(7(a,1),8(a,1,2,2))].
% 1.20/1.46 34 add(A,add(multiply(B,multiply(A,C)),D)) = add(A,D). [para(7(a,1),11(a,1,1)),flip(a)].
% 1.20/1.46 42 multiply(A,multiply(add(B,add(A,C)),D)) = multiply(A,D). [para(8(a,1),12(a,1,1)),flip(a)].
% 1.20/1.46 44 multiply(add(A,B),add(inverse(B),A)) = add(multiply(A,B),multiply(inverse(B),A)). [para(1(a,1),14(a,1,2,1)),rewrite([4(5),2(7),6(9)])].
% 1.20/1.46 45 multiply(add(inverse(A),B),multiply(add(B,A),n1)) = add(multiply(inverse(A),B),add(multiply(B,A),n0)). [para(1(a,1),14(a,1,2,2)),rewrite([2(11)])].
% 1.20/1.46 46 add(A,add(multiply(A,B),multiply(B,n1))) = multiply(add(n1,A),add(A,B)). [para(4(a,1),14(a,2,1)),rewrite([25(6)]),flip(a)].
% 1.20/1.46 47 multiply(A,multiply(add(A,B),add(B,n0))) = add(multiply(n0,A),multiply(A,B)). [para(6(a,1),14(a,1,1)),rewrite([21(11)])].
% 1.20/1.46 56 add(multiply(add(A,add(B,C)),A),add(multiply(A,B),B)) = multiply(add(A,add(B,add(C,A))),add(A,B)). [para(8(a,1),14(a,1,2)),rewrite([11(2),11(3),11(2),11(7),11(11),8(12)]),flip(a)].
% 1.20/1.46 60 multiply(add(A,add(B,C)),multiply(add(C,D),add(D,add(A,B)))) = add(multiply(add(A,B),C),add(multiply(C,D),multiply(D,add(A,B)))). [para(11(a,1),14(a,1,1))].
% 1.20/1.46 61 multiply(add(A,add(B,C)),multiply(add(B,add(C,D)),add(D,A))) = add(multiply(A,add(B,C)),add(multiply(add(B,C),D),multiply(D,A))). [para(11(a,1),14(a,1,2,1))].
% 1.20/1.46 65 add(multiply(A,B),B) = B. [para(2(a,1),17(a,1,2,1)),rewrite([6(3)])].
% 1.20/1.46 66 add(A,add(multiply(A,B),A)) = A. [para(4(a,1),17(a,1,1))].
% 1.20/1.46 68 multiply(A,multiply(B,A)) = multiply(A,B). [para(17(a,1),8(a,1,2)),rewrite([12(2)])].
% 1.20/1.46 71 add(multiply(A,B),add(multiply(B,C),add(B,D))) = add(B,D). [para(17(a,1),11(a,1,1)),rewrite([11(5)]),flip(a)].
% 1.20/1.46 76 multiply(add(multiply(A,B),add(A,C)),multiply(add(C,multiply(D,A)),A)) = add(multiply(add(multiply(A,B),A),C),multiply(D,A)). [para(17(a,1),14(a,1,2,2)),rewrite([11(3),12(16),30(15),65(14)])].
% 1.20/1.46 77 multiply(A,multiply(add(multiply(B,A),B),add(B,A))) = multiply(B,A). [para(17(a,1),14(a,2)),rewrite([29(2)])].
% 1.20/1.46 82 multiply(add(A,add(B,add(C,A))),add(A,B)) = add(multiply(add(A,add(B,C)),A),B). [back_rewrite(56),rewrite([65(5)]),flip(a)].
% 1.20/1.46 84 multiply(add(A,B),B) = B. [para(1(a,1),18(a,1,2,1)),rewrite([4(3)])].
% 1.20/1.46 86 add(A,add(B,A)) = add(A,B). [para(18(a,1),7(a,1,2)),rewrite([11(2)])].
% 1.20/1.46 88 multiply(add(A,B),multiply(B,B)) = B. [para(7(a,1),18(a,1,2,1))].
% 1.20/1.46 89 multiply(add(A,add(B,C)),multiply(add(C,D),C)) = C. [para(11(a,1),18(a,1,1))].
% 1.20/1.46 92 add(A,add(multiply(add(B,A),B),multiply(B,A))) = add(B,A). [para(18(a,1),14(a,1)),rewrite([30(3)]),flip(a)].
% 1.20/1.46 93 multiply(add(A,B),multiply(add(multiply(add(B,C),B),D),add(D,add(A,B)))) = add(B,multiply(D,add(A,B))). [para(18(a,1),14(a,2,1)),rewrite([11(4),29(3),12(11),34(15)])].
% 1.20/1.46 94 multiply(add(A,add(B,C)),multiply(add(B,C),add(multiply(add(C,D),C),A))) = add(multiply(A,add(B,C)),C). [para(18(a,1),14(a,2,2,1)),rewrite([11(6),29(5),12(13),7(14)])].
% 1.20/1.46 95 add(multiply(add(A,B),multiply(A,C)),add(multiply(C,add(D,A)),A)) = multiply(add(multiply(add(A,B),A),C),add(D,A)). [para(18(a,1),14(a,2,2,2)),rewrite([11(9),29(8),84(7),12(8)]),flip(a)].
% 1.20/1.46 96 multiply(add(A,B),A) = A. [para(18(a,1),17(a,1,1)),rewrite([12(3),34(7),29(3)]),flip(a)].
% 1.20/1.46 98 add(multiply(A,B),A) = A. [para(17(a,1),18(a,1,1)),rewrite([11(3),42(7),30(3)]),flip(a)].
% 1.20/1.46 102 add(A,A) = A. [back_rewrite(66),rewrite([98(2)])].
% 1.20/1.46 103 add(multiply(add(A,B),multiply(A,C)),add(multiply(C,add(D,A)),A)) = multiply(add(A,C),add(D,A)). [back_rewrite(95),rewrite([96(9)])].
% 1.20/1.46 104 multiply(add(A,add(B,C)),multiply(add(B,C),add(C,A))) = add(multiply(A,add(B,C)),C). [back_rewrite(94),rewrite([96(5)])].
% 1.20/1.46 105 multiply(add(A,B),multiply(add(B,C),add(C,add(A,B)))) = add(B,multiply(C,add(A,B))). [back_rewrite(93),rewrite([96(3)])].
% 1.20/1.46 106 add(A,B) = add(B,A). [back_rewrite(92),rewrite([96(2),23(2)])].
% 1.20/1.46 107 multiply(add(A,add(B,C)),C) = C. [back_rewrite(89),rewrite([96(4)])].
% 1.20/1.46 109 multiply(add(A,add(B,add(A,C))),add(A,B)) = add(A,B). [back_rewrite(82),rewrite([106(1),96(8)])].
% 1.20/1.46 110 multiply(A,B) = multiply(B,A). [back_rewrite(77),rewrite([106(2),23(2),106(1),30(2)])].
% 1.20/1.46 111 multiply(add(multiply(A,B),add(A,C)),multiply(A,add(C,multiply(A,D)))) = add(multiply(A,C),multiply(A,D)). [back_rewrite(76),rewrite([110(4),110(6),106(9),23(9),110(9)])].
% 1.20/1.46 116 multiply(add(A,add(B,C)),multiply(add(B,C),add(A,C))) = add(C,multiply(A,add(B,C))). [back_rewrite(104),rewrite([106(4),106(9)])].
% 1.20/1.46 117 add(multiply(add(A,B),multiply(A,C)),add(A,multiply(C,add(A,D)))) = multiply(add(A,C),add(A,D)). [back_rewrite(103),rewrite([106(4),106(6),106(9)])].
% 1.20/1.46 120 add(A,add(A,B)) = add(A,B). [back_rewrite(86),rewrite([106(1)])].
% 1.20/1.46 126 multiply(add(A,add(B,C)),multiply(add(B,add(C,D)),add(A,D))) = add(multiply(A,add(B,C)),add(multiply(D,add(B,C)),multiply(A,D))). [back_rewrite(61),rewrite([106(5),110(11),110(12)])].
% 1.20/1.46 131 add(A,add(multiply(A,B),multiply(B,n1))) = multiply(add(A,n1),add(A,B)). [back_rewrite(46),rewrite([106(7)])].
% 1.20/1.46 132 multiply(add(A,B),add(B,inverse(A))) = add(multiply(A,B),multiply(B,inverse(A))). [back_rewrite(45),rewrite([106(2),106(3),110(5),4(5),110(4),110(6),110(7),106(9),6(9),106(8)])].
% 1.20/1.46 133 multiply(add(A,B),add(A,inverse(B))) = add(multiply(A,B),multiply(A,inverse(B))). [back_rewrite(44),rewrite([106(3),110(7)])].
% 1.20/1.46 138 multiply(add(A,B),multiply(add(B,C),add(A,C))) = add(multiply(A,B),add(multiply(B,C),multiply(A,C))). [back_rewrite(14),rewrite([106(3),110(8)])].
% 1.20/1.46 139 add(A,add(B,C)) = add(C,add(A,B)). [back_rewrite(11),rewrite([106(2)]),flip(a)].
% 1.20/1.46 140 add(A,n0) = A. [back_rewrite(6),rewrite([106(2)])].
% 1.20/1.46 141 multiply(add(A,B),add(A,add(B,C))) = add(A,B). [back_rewrite(109),rewrite([139(2,R),106(1),120(3),110(4)])].
% 1.20/1.46 142 multiply(A,add(B,add(C,A))) = A. [back_rewrite(107),rewrite([110(3)])].
% 1.20/1.46 145 multiply(A,add(B,A)) = A. [back_rewrite(84),rewrite([110(2)])].
% 1.20/1.46 147 multiply(A,multiply(A,B)) = multiply(A,B). [back_rewrite(68),rewrite([110(1)])].
% 1.20/1.46 148 multiply(add(A,add(B,C)),multiply(add(C,D),add(A,add(B,D)))) = add(multiply(C,add(A,B)),add(multiply(C,D),multiply(D,add(A,B)))). [back_rewrite(60),rewrite([139(5),106(4),139(5,R),106(4),110(9)])].
% 1.20/1.46 153 add(multiply(A,n0),multiply(A,B)) = multiply(A,B). [back_rewrite(47),rewrite([140(3),110(2),145(2),110(3)]),flip(a)].
% 1.20/1.46 158 add(multiply(a,b),multiply(a,c)) != multiply(a,add(b,c)) # answer(prove_multiply_add_property). [back_rewrite(16),rewrite([110(3),110(6)])].
% 1.20/1.46 159 multiply(A,multiply(B,C)) = multiply(C,multiply(A,B)). [back_rewrite(12),rewrite([110(2)]),flip(a)].
% 1.20/1.46 160 multiply(A,n1) = A. [back_rewrite(4),rewrite([110(2)])].
% 1.20/1.46 164 add(A,add(multiply(A,B),multiply(B,add(A,C)))) = multiply(add(A,B),add(A,C)). [back_rewrite(117),rewrite([159(3),110(2),28(2),110(1),139(5,R),106(4)])].
% 1.20/1.46 166 multiply(A,multiply(add(A,B),add(B,multiply(A,C)))) = add(multiply(A,B),multiply(A,C)). [back_rewrite(111),rewrite([139(3),106(2),23(2),106(1),159(5,R),110(4)])].
% 1.20/1.46 167 multiply(add(A,B),add(B,C)) = add(B,multiply(C,add(A,B))). [back_rewrite(105),rewrite([139(4),106(3),139(4,R),106(3),145(5)])].
% 1.20/1.46 168 add(A,add(B,multiply(C,A))) = add(A,B). [back_rewrite(71),rewrite([139(4),106(3),23(3),106(2),139(3),106(2),139(3,R),106(2)])].
% 1.20/1.46 175 multiply(add(A,B),add(C,B)) = add(B,multiply(A,add(C,B))). [back_rewrite(116),rewrite([159(6),110(5),145(5)])].
% 1.20/1.46 177 multiply(A,A) = A. [back_rewrite(88),rewrite([159(3),110(2),145(2)])].
% 1.20/1.46 178 add(A,add(B,multiply(A,B))) = multiply(add(A,n1),add(A,B)). [back_rewrite(131),rewrite([160(3),106(2)])].
% 1.20/1.46 180 multiply(A,add(B,multiply(multiply(A,C),add(A,B)))) = add(multiply(A,B),multiply(A,C)). [back_rewrite(166),rewrite([167(4)])].
% 1.20/1.46 182 add(multiply(A,B),multiply(B,inverse(A))) = add(B,multiply(inverse(A),add(A,B))). [back_rewrite(132),rewrite([167(4)]),flip(a)].
% 1.20/1.46 187 multiply(add(A,B),add(C,multiply(B,add(A,C)))) = add(multiply(A,B),add(multiply(B,C),multiply(A,C))). [back_rewrite(138),rewrite([175(4)])].
% 1.20/1.46 190 add(A,n1) = n1. [para(160(a,1),22(a,1,2)),rewrite([106(2)])].
% 1.20/1.46 191 add(A,add(B,multiply(A,B))) = multiply(n1,add(A,B)). [back_rewrite(178),rewrite([190(5)])].
% 1.20/1.46 193 multiply(A,n0) = n0. [para(102(a,1),27(a,1,2)),rewrite([110(2)])].
% 1.20/1.46 195 add(n0,multiply(A,B)) = multiply(A,B). [back_rewrite(153),rewrite([193(2)])].
% 1.20/1.46 203 multiply(multiply(A,B),add(A,C)) = multiply(A,B). [para(23(a,1),142(a,1,2,2)),rewrite([106(2)])].
% 1.20/1.46 205 multiply(A,add(B,multiply(A,C))) = add(multiply(A,B),multiply(A,C)). [back_rewrite(180),rewrite([203(3)])].
% 1.20/1.46 208 add(add(A,B),multiply(C,add(A,B))) = add(A,B). [para(102(a,1),126(a,1,1)),rewrite([106(5),139(5),106(4),139(5,R),106(4),177(6),141(4),177(4),110(6),102(7)]),flip(a)].
% 1.20/1.46 209 multiply(add(A,add(B,C)),add(C,multiply(B,add(A,C)))) = add(C,add(multiply(A,C),multiply(A,add(B,C)))). [para(102(a,1),126(a,1,2,1,2)),rewrite([175(5),145(10),139(11),106(10),139(11,R),106(10)])].
% 1.20/1.46 212 multiply(n1,add(A,add(B,multiply(C,D)))) = add(multiply(n1,add(A,B)),multiply(C,D)). [para(22(a,1),126(a,1,2,2)),rewrite([139(3),106(2),190(2),190(2),110(6),147(7),159(14),110(13),160(13),110(12),106(13),23(13)])].
% 1.20/1.46 216 multiply(A,multiply(add(A,add(B,C)),add(B,add(C,multiply(A,D))))) = add(multiply(A,add(B,C)),multiply(A,D)). [para(23(a,1),126(a,1,2,2)),rewrite([110(6),159(7,R),110(6),147(14),106(14),23(14)])].
% 1.20/1.46 218 add(A,add(multiply(B,A),multiply(B,add(A,C)))) = add(A,multiply(C,add(B,A))). [para(28(a,1),126(a,2,2,1)),rewrite([106(3),120(4),159(6),110(5),145(5),167(3),139(8),106(7),139(8,R),106(7)]),flip(a)].
% 1.20/1.46 219 multiply(add(A,add(B,C)),multiply(add(A,D),add(A,add(B,add(C,D))))) = add(A,add(multiply(A,add(B,C)),multiply(add(A,D),add(B,C)))). [para(28(a,1),126(a,2,2,2)),rewrite([139(4,R),106(3),139(5,R),106(4),120(7),110(7),106(14),139(15,R),106(14)])].
% 1.20/1.46 234 add(A,add(multiply(A,add(B,C)),multiply(add(A,D),add(B,C)))) = multiply(add(A,D),add(A,add(B,C))). [para(142(a,1),126(a,2,1)),rewrite([106(1),139(2,R),106(1),120(3),106(3),106(4),139(4),106(3),139(4,R),106(3),139(5,R),106(4),110(7),219(8),106(8),139(9,R),106(8),106(12),164(13)])].
% 1.20/1.46 239 multiply(multiply(A,B),add(C,D)) = multiply(A,multiply(B,add(C,D))). [para(195(a,1),126(a,1,2,2)),rewrite([139(3),106(2),140(2),106(1),110(6),142(6),159(3),110(2),159(3,R),110(2),27(6),159(10),110(9),193(9),193(9),106(9),195(9),195(8)]),flip(a)].
% 1.20/1.46 241 multiply(add(A,add(B,C)),multiply(add(A,D),add(A,add(B,add(C,D))))) = multiply(add(A,D),add(A,add(B,C))). [back_rewrite(219),rewrite([234(15)])].
% 1.20/1.46 243 multiply(A,multiply(B,add(A,C))) = multiply(A,B). [back_rewrite(203),rewrite([239(3)])].
% 1.20/1.46 252 add(A,add(B,multiply(A,C))) = add(A,B). [para(23(a,1),139(a,2,2)),rewrite([106(2),106(4)])].
% 1.20/1.46 260 multiply(n1,add(A,B)) = add(A,B). [back_rewrite(191),rewrite([252(3)]),flip(a)].
% 1.20/1.46 261 add(add(A,B),multiply(C,D)) = add(A,add(B,multiply(C,D))). [back_rewrite(212),rewrite([260(5),260(6)]),flip(a)].
% 1.20/1.46 266 add(A,add(B,multiply(C,add(A,B)))) = add(A,B). [back_rewrite(208),rewrite([261(4)])].
% 1.20/1.46 320 multiply(add(A,add(B,C)),add(B,add(C,D))) = add(B,add(C,multiply(A,add(B,add(C,D))))). [para(141(a,1),126(a,2,2,1)),rewrite([139(6),106(5),139(6,R),106(5),120(5),120(6),159(9),110(8),145(8),261(12),266(12),106(10),261(10)])].
% 1.20/1.46 329 multiply(A,add(B,add(C,multiply(A,add(B,add(C,multiply(A,D))))))) = add(multiply(A,add(B,C)),multiply(A,D)). [back_rewrite(216),rewrite([320(6)])].
% 1.20/1.46 369 add(A,add(B,add(C,multiply(A,D)))) = add(A,add(B,C)). [para(168(a,1),139(a,2,2)),rewrite([110(1),106(3),139(3,R),106(2),139(6),106(5),139(6,R),106(5)])].
% 1.20/1.46 381 add(multiply(A,B),multiply(A,inverse(B))) = A. [para(133(a,1),243(a,1,2)),rewrite([205(5),147(2),28(6)])].
% 1.20/1.46 394 multiply(add(A,B),add(A,C)) = add(A,multiply(C,add(A,B))). [back_rewrite(218),rewrite([110(1),164(5),106(4)])].
% 1.20/1.46 414 add(A,add(multiply(A,add(B,C)),multiply(D,add(B,C)))) = add(A,multiply(add(B,C),add(A,D))). [back_rewrite(241),rewrite([394(7),394(8),110(7),126(7),369(8),394(10)])].
% 1.20/1.46 419 add(A,add(multiply(A,B),multiply(B,add(A,C)))) = add(A,multiply(C,add(A,B))). [back_rewrite(164),rewrite([394(8)])].
% 1.20/1.46 430 multiply(add(A,add(B,C)),add(C,D)) = add(C,multiply(add(A,B),add(C,D))). [para(28(a,1),148(a,2,2,1)),rewrite([120(4),142(7),139(11,R),106(10),414(11),120(7)])].
% 1.20/1.46 475 add(A,add(multiply(B,C),add(multiply(C,A),multiply(B,A)))) = add(A,add(multiply(B,A),multiply(B,add(C,A)))). [back_rewrite(209),rewrite([430(6),187(5)])].
% 1.20/1.46 490 add(A,multiply(inverse(B),add(B,A))) = A. [para(110(a,1),381(a,1,1)),rewrite([182(4)])].
% 1.20/1.46 508 add(multiply(A,B),multiply(B,inverse(A))) = B. [back_rewrite(182),rewrite([490(8)])].
% 1.20/1.46 645 add(A,multiply(B,A)) = A. [para(508(a,1),120(a,1,2)),rewrite([106(2),508(6)])].
% 1.20/1.46 697 add(A,multiply(add(B,C),add(A,add(B,D)))) = add(A,add(B,multiply(C,add(A,add(B,D))))). [para(139(a,2),167(a,1,1)),rewrite([106(4),139(4),106(3),139(4,R),106(3),394(5),139(8),106(7),139(8,R),106(7),261(10)])].
% 1.20/1.46 905 add(A,multiply(add(B,C),add(A,multiply(B,D)))) = add(A,multiply(B,D)). [para(252(a,1),142(a,1,2,2)),rewrite([106(3),139(4),106(3),139(4,R),106(3),394(5)])].
% 1.20/1.46 906 multiply(add(A,B),add(C,multiply(A,D))) = add(multiply(C,add(A,B)),multiply(A,D)). [para(252(a,1),126(a,1,2,1)),rewrite([159(7,R),394(6),905(6),239(9),243(9),645(10)])].
% 1.20/1.46 1286 add(multiply(A,B),add(multiply(A,C),multiply(A,multiply(B,C)))) = add(multiply(A,C),multiply(A,B)). [para(23(a,1),187(a,1,2,2,2)),rewrite([110(3),906(5),239(3),243(3),159(6,R),110(5),147(8),106(8)]),flip(a)].
% 1.20/1.46 1315 multiply(A,add(multiply(B,C),add(multiply(A,C),multiply(A,B)))) = multiply(A,add(B,C)). [para(187(a,1),243(a,1,2)),rewrite([110(2),110(3)])].
% 1.20/1.46 1400 add(A,multiply(B,add(A,C))) = add(A,multiply(C,B)). [back_rewrite(475),rewrite([110(2),110(3),369(6),252(4),110(3),106(4),419(7)]),flip(a)].
% 1.20/1.46 1476 add(A,add(B,multiply(C,add(A,add(B,D))))) = add(A,add(B,multiply(C,D))). [back_rewrite(697),rewrite([1400(5),394(3),1400(3),110(1)]),flip(a)].
% 1.20/1.46 1543 multiply(A,add(B,add(C,multiply(A,D)))) = add(multiply(A,add(B,C)),multiply(A,D)). [back_rewrite(329),rewrite([1476(6),147(2)])].
% 1.20/1.46 1549 add(multiply(A,B),multiply(A,C)) = multiply(A,add(C,B)). [back_rewrite(1315),rewrite([1543(6),205(4),106(4),106(6),1286(6)])].
% 1.20/1.46 1626 $F # answer(prove_multiply_add_property). [back_rewrite(158),rewrite([1549(7),106(4)]),xx(a)].
% 1.20/1.46
% 1.20/1.46 % SZS output end Refutation
% 1.20/1.46 ============================== end of proof ==========================
% 1.20/1.46
% 1.20/1.46 ============================== STATISTICS ============================
% 1.20/1.46
% 1.20/1.46 Given=109. Generated=7350. Kept=1621. proofs=1.
% 1.20/1.46 Usable=83. Sos=647. Demods=785. Limbo=77, Disabled=826. Hints=0.
% 1.20/1.46 Megabytes=2.39.
% 1.20/1.46 User_CPU=0.45, System_CPU=0.01, Wall_clock=0.
% 1.20/1.46
% 1.20/1.46 ============================== end of statistics =====================
% 1.20/1.46
% 1.20/1.46 ============================== end of search =========================
% 1.20/1.46
% 1.20/1.46 THEOREM PROVED
% 1.20/1.46 % SZS status Unsatisfiable
% 1.20/1.46
% 1.20/1.46 Exiting with 1 proof.
% 1.20/1.46
% 1.20/1.46 Process 3136 exit (max_proofs) Wed Jun 1 22:53:09 2022
% 1.20/1.46 Prover9 interrupted
%------------------------------------------------------------------------------