TSTP Solution File: RNG009-7 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG009-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 20:39:11 EDT 2022
% Result : Unsatisfiable 4.67s 4.95s
% Output : Refutation 4.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG009-7 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 20:46:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.70/3.98 ============================== Prover9 ===============================
% 3.70/3.98 Prover9 (32) version 2009-11A, November 2009.
% 3.70/3.98 Process 6825 was started by sandbox2 on n023.cluster.edu,
% 3.70/3.98 Mon May 30 20:46:57 2022
% 3.70/3.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6672_n023.cluster.edu".
% 3.70/3.98 ============================== end of head ===========================
% 3.70/3.98
% 3.70/3.98 ============================== INPUT =================================
% 3.70/3.98
% 3.70/3.98 % Reading from file /tmp/Prover9_6672_n023.cluster.edu
% 3.70/3.98
% 3.70/3.98 set(prolog_style_variables).
% 3.70/3.98 set(auto2).
% 3.70/3.98 % set(auto2) -> set(auto).
% 3.70/3.98 % set(auto) -> set(auto_inference).
% 3.70/3.98 % set(auto) -> set(auto_setup).
% 3.70/3.98 % set(auto_setup) -> set(predicate_elim).
% 3.70/3.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.70/3.98 % set(auto) -> set(auto_limits).
% 3.70/3.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.70/3.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.70/3.98 % set(auto) -> set(auto_denials).
% 3.70/3.98 % set(auto) -> set(auto_process).
% 3.70/3.98 % set(auto2) -> assign(new_constants, 1).
% 3.70/3.98 % set(auto2) -> assign(fold_denial_max, 3).
% 3.70/3.98 % set(auto2) -> assign(max_weight, "200.000").
% 3.70/3.98 % set(auto2) -> assign(max_hours, 1).
% 3.70/3.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.70/3.98 % set(auto2) -> assign(max_seconds, 0).
% 3.70/3.98 % set(auto2) -> assign(max_minutes, 5).
% 3.70/3.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.70/3.98 % set(auto2) -> set(sort_initial_sos).
% 3.70/3.98 % set(auto2) -> assign(sos_limit, -1).
% 3.70/3.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.70/3.98 % set(auto2) -> assign(max_megs, 400).
% 3.70/3.98 % set(auto2) -> assign(stats, some).
% 3.70/3.98 % set(auto2) -> clear(echo_input).
% 3.70/3.98 % set(auto2) -> set(quiet).
% 3.70/3.98 % set(auto2) -> clear(print_initial_clauses).
% 3.70/3.98 % set(auto2) -> clear(print_given).
% 3.70/3.98 assign(lrs_ticks,-1).
% 3.70/3.98 assign(sos_limit,10000).
% 3.70/3.98 assign(order,kbo).
% 3.70/3.98 set(lex_order_vars).
% 3.70/3.98 clear(print_given).
% 3.70/3.98
% 3.70/3.98 % formulas(sos). % not echoed (12 formulas)
% 3.70/3.98
% 3.70/3.98 ============================== end of input ==========================
% 3.70/3.98
% 3.70/3.98 % From the command line: assign(max_seconds, 300).
% 3.70/3.98
% 3.70/3.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.70/3.98
% 3.70/3.98 % Formulas that are not ordinary clauses:
% 3.70/3.98
% 3.70/3.98 ============================== end of process non-clausal formulas ===
% 3.70/3.98
% 3.70/3.98 ============================== PROCESS INITIAL CLAUSES ===============
% 3.70/3.98
% 3.70/3.98 ============================== PREDICATE ELIMINATION =================
% 3.70/3.98
% 3.70/3.98 ============================== end predicate elimination =============
% 3.70/3.98
% 3.70/3.98 Auto_denials:
% 3.70/3.98 % copying label prove_commutativity to answer in negative clause
% 3.70/3.98
% 3.70/3.98 Term ordering decisions:
% 3.70/3.98
% 3.70/3.98 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (8).
% 3.70/3.98 Function symbol KB weights: additive_identity=1. a=1. b=1. c=1. add=1. multiply=1. additive_inverse=0.
% 3.70/3.98
% 3.70/3.98 ============================== end of process initial clauses ========
% 3.70/3.98
% 3.70/3.98 ============================== CLAUSES FOR SEARCH ====================
% 3.70/3.98
% 3.70/3.98 ============================== end of clauses for search =============
% 3.70/3.98
% 3.70/3.98 ============================== SEARCH ================================
% 3.70/3.98
% 3.70/3.98 % Starting search at 0.01 seconds.
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=57.000, iters=3411
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=53.000, iters=3360
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=47.000, iters=3365
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=44.000, iters=3408
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=43.000, iters=3413
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=41.000, iters=3413
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=39.000, iters=3488
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=37.000, iters=3381
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=35.000, iters=3350
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=33.000, iters=3367
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=32.000, iters=3341
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=31.000, iters=3339
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=30.000, iters=3366
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=29.000, iters=3373
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=28.000, iters=3363
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=27.000, iters=3361
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=26.000, iters=3337
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=25.000, iters=3336
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=24.000, iters=3376
% 3.70/3.98
% 3.70/3.98 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 69 (0.00 of 2.42 sec).
% 3.70/3.98
% 3.70/3.98 Low Water (keep): wt=23.000, iters=3336
% 3.70/3.98
% 3.70/3.98 Low Water (displace): id=6184, wt=93.000
% 3.70/3.98
% 3.70/3.98 Low Water (displace): id=5714, wt=89.000
% 3.70/3.98
% 3.70/3.98 Low Water (displace): id=4323, wt=85.000
% 3.70/3.98
% 3.70/3.98 Low Water (displace): id=4749, wt=79.000
% 4.67/4.95
% 4.67/4.95 Low Water (displace): id=4338, wt=77.000
% 4.67/4.95
% 4.67/4.95 Low Water (displace): id=12374, wt=19.000
% 4.67/4.95
% 4.67/4.95 Low Water (displace): id=12385, wt=18.000
% 4.67/4.95
% 4.67/4.95 Low Water (displace): id=12425, wt=17.000
% 4.67/4.95
% 4.67/4.95 Low Water (keep): wt=22.000, iters=3339
% 4.67/4.95
% 4.67/4.95 Low Water (displace): id=13283, wt=16.000
% 4.67/4.95
% 4.67/4.95 Low Water (displace): id=13306, wt=15.000
% 4.67/4.95
% 4.67/4.95 ============================== PROOF =================================
% 4.67/4.95 % SZS status Unsatisfiable
% 4.67/4.95 % SZS output start Refutation
% 4.67/4.95
% 4.67/4.95 % Proof 1 at 3.87 (+ 0.08) seconds: prove_commutativity.
% 4.67/4.95 % Length of proof is 162.
% 4.67/4.95 % Level of proof is 41.
% 4.67/4.95 % Maximum clause weight is 24.000.
% 4.67/4.95 % Given clauses 658.
% 4.67/4.95
% 4.67/4.95 2 add(A,additive_identity) = A # label(right_additive_identity) # label(axiom). [assumption].
% 4.67/4.95 3 multiply(a,b) = c # label(a_times_b_is_c) # label(negated_conjecture). [assumption].
% 4.67/4.95 4 c = multiply(a,b). [copy(3),flip(a)].
% 4.67/4.95 6 add(A,additive_inverse(A)) = additive_identity # label(right_additive_inverse) # label(axiom). [assumption].
% 4.67/4.95 7 add(A,B) = add(B,A) # label(commutativity_for_addition) # label(axiom). [assumption].
% 4.67/4.95 8 multiply(A,multiply(A,A)) = A # label(x_cubed_is_x) # label(hypothesis). [assumption].
% 4.67/4.95 9 add(A,add(B,C)) = add(add(A,B),C) # label(associativity_for_addition) # label(axiom). [assumption].
% 4.67/4.95 10 add(A,add(B,C)) = add(C,add(A,B)). [copy(9),rewrite([7(4)])].
% 4.67/4.95 11 multiply(A,multiply(B,C)) = multiply(multiply(A,B),C) # label(associativity_for_multiplication) # label(axiom). [assumption].
% 4.67/4.95 12 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [copy(11),flip(a)].
% 4.67/4.95 13 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distribute1) # label(axiom). [assumption].
% 4.67/4.95 14 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(13),flip(a)].
% 4.67/4.95 15 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distribute2) # label(axiom). [assumption].
% 4.67/4.95 16 add(multiply(A,B),multiply(C,B)) = multiply(add(A,C),B). [copy(15),flip(a)].
% 4.67/4.95 17 multiply(b,a) != c # label(prove_commutativity) # label(negated_conjecture) # answer(prove_commutativity). [assumption].
% 4.67/4.95 18 multiply(b,a) != multiply(a,b) # answer(prove_commutativity). [copy(17),rewrite([4(4)])].
% 4.67/4.95 19 multiply(b,a) = c_0. [new_symbol(18)].
% 4.67/4.95 20 multiply(a,b) != c_0 # answer(prove_commutativity). [back_rewrite(18),rewrite([19(3)]),flip(a)].
% 4.67/4.95 22 multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B))))) = multiply(A,B). [para(12(a,1),8(a,1,2)),rewrite([12(5)])].
% 4.67/4.95 23 multiply(A,multiply(A,multiply(A,B))) = multiply(A,B). [para(8(a,1),12(a,1,1)),rewrite([12(3)]),flip(a)].
% 4.67/4.95 24 multiply(A,add(B,multiply(A,A))) = add(A,multiply(A,B)). [para(8(a,1),14(a,1,1)),rewrite([7(4)]),flip(a)].
% 4.67/4.95 25 multiply(add(A,B),multiply(A,A)) = add(A,multiply(B,multiply(A,A))). [para(8(a,1),16(a,1,1)),flip(a)].
% 4.67/4.95 26 multiply(add(A,B),multiply(B,B)) = add(B,multiply(A,multiply(B,B))). [para(8(a,1),16(a,1,2)),rewrite([7(3)]),flip(a)].
% 4.67/4.95 27 add(multiply(A,multiply(B,C)),multiply(D,C)) = multiply(add(D,multiply(A,B)),C). [para(12(a,1),16(a,1,1)),rewrite([7(6)])].
% 4.67/4.95 28 add(multiply(A,B),multiply(C,multiply(D,B))) = multiply(add(A,multiply(C,D)),B). [para(12(a,1),16(a,1,2))].
% 4.67/4.95 29 multiply(add(A,A),B) = multiply(A,add(B,B)). [para(16(a,1),14(a,1))].
% 4.67/4.95 30 multiply(b,multiply(a,A)) = multiply(c_0,A). [para(19(a,1),12(a,1,1)),flip(a)].
% 4.67/4.95 32 multiply(add(A,b),a) = add(c_0,multiply(A,a)). [para(19(a,1),16(a,1,1)),rewrite([7(6)]),flip(a)].
% 4.67/4.95 35 multiply(b,add(A,multiply(a,B))) = add(multiply(c_0,B),multiply(b,A)). [para(30(a,1),14(a,1,1)),rewrite([7(9)]),flip(a)].
% 4.67/4.95 40 multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,multiply(B,C)))))) = multiply(A,multiply(B,C)). [para(23(a,1),12(a,1)),rewrite([12(2),12(5),12(6)]),flip(a)].
% 4.67/4.95 41 multiply(A,add(B,multiply(A,multiply(A,C)))) = multiply(A,add(C,B)). [para(23(a,1),14(a,1,1)),rewrite([14(3),7(5)]),flip(a)].
% 4.67/4.95 43 multiply(b,multiply(b,c_0)) = c_0. [para(19(a,1),23(a,1,2,2)),rewrite([19(8)])].
% 4.67/4.95 44 multiply(b,multiply(b,multiply(c_0,A))) = multiply(c_0,A). [para(30(a,1),23(a,1,2,2)),rewrite([30(10)])].
% 4.67/4.95 47 multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,C)))))))) = multiply(A,multiply(B,C)). [para(22(a,1),12(a,1)),rewrite([12(2),12(5),12(7)]),flip(a)].
% 4.67/4.95 48 multiply(A,add(B,multiply(C,multiply(A,multiply(C,multiply(A,C)))))) = multiply(A,add(C,B)). [para(22(a,1),14(a,1,1)),rewrite([14(3),7(7)]),flip(a)].
% 4.67/4.95 52 multiply(additive_identity,add(A,A)) = multiply(additive_identity,A). [para(2(a,1),29(a,1,1)),flip(a)].
% 4.67/4.95 64 multiply(A,add(B,add(B,C))) = add(multiply(add(A,A),B),multiply(A,C)). [para(29(a,2),14(a,1,1)),rewrite([7(6),10(6),7(5)]),flip(a)].
% 4.67/4.95 66 multiply(add(A,add(A,B)),C) = add(multiply(A,add(C,C)),multiply(B,C)). [para(29(a,1),16(a,1,1)),rewrite([7(6),10(6),7(5)]),flip(a)].
% 4.67/4.95 84 multiply(additive_identity,add(A,add(A,B))) = multiply(additive_identity,add(A,B)). [para(52(a,1),14(a,1,1)),rewrite([14(5),7(6),10(6),7(5)]),flip(a)].
% 4.67/4.95 105 multiply(A,multiply(add(B,multiply(A,A)),C)) = multiply(add(A,multiply(A,B)),C). [para(24(a,1),12(a,1,1)),flip(a)].
% 4.67/4.95 107 multiply(A,add(B,add(C,multiply(A,A)))) = add(add(A,multiply(A,B)),multiply(A,C)). [para(24(a,1),14(a,1,1)),rewrite([7(7),10(7,R),7(6)]),flip(a)].
% 4.67/4.95 108 add(add(A,multiply(A,B)),multiply(A,C)) = add(A,multiply(A,add(B,C))). [para(24(a,1),14(a,1,2)),rewrite([10(4,R),14(3),7(1),107(7)]),flip(a)].
% 4.67/4.95 109 multiply(A,multiply(A,add(A,B))) = add(A,multiply(A,multiply(A,B))). [para(14(a,1),24(a,1,2)),rewrite([7(1)])].
% 4.67/4.95 111 multiply(A,multiply(add(A,B),A)) = add(A,multiply(A,multiply(B,A))). [para(16(a,1),24(a,1,2)),rewrite([7(1)])].
% 4.67/4.95 119 multiply(A,add(B,add(C,multiply(A,A)))) = add(A,multiply(A,add(B,C))). [back_rewrite(107),rewrite([108(8)])].
% 4.67/4.95 120 multiply(add(b,multiply(A,B)),a) = add(c_0,multiply(A,multiply(B,a))). [para(12(a,1),32(a,2,2)),rewrite([7(3)])].
% 4.67/4.95 141 add(A,multiply(additive_identity,multiply(A,A))) = A. [para(2(a,1),25(a,1,1)),rewrite([8(2)]),flip(a)].
% 4.67/4.95 142 add(A,multiply(additive_inverse(A),multiply(A,A))) = multiply(additive_identity,multiply(A,A)). [para(6(a,1),25(a,1,1)),flip(a)].
% 4.67/4.95 150 add(add(A,multiply(B,multiply(A,A))),multiply(C,multiply(A,A))) = add(A,multiply(add(B,C),multiply(A,A))). [para(25(a,1),16(a,1,1)),rewrite([7(8),10(8),7(7),10(8,R),7(7),25(10)])].
% 4.67/4.95 174 add(additive_inverse(A),multiply(A,multiply(additive_inverse(A),additive_inverse(A)))) = multiply(additive_identity,multiply(additive_inverse(A),additive_inverse(A))). [para(6(a,1),26(a,1,1)),flip(a)].
% 4.67/4.95 240 multiply(additive_identity,additive_identity) = multiply(additive_identity,A). [para(6(a,1),84(a,1,2,2)),rewrite([2(3),6(5)]),flip(a)].
% 4.67/4.95 242 add(additive_identity,multiply(additive_identity,additive_identity)) = add(additive_identity,multiply(additive_identity,A)). [para(24(a,1),84(a,2)),rewrite([119(7),240(4,R)])].
% 4.67/4.95 243 add(additive_identity,multiply(additive_identity,A)) = multiply(additive_identity,additive_identity). [para(141(a,1),84(a,1,2,2)),rewrite([240(3,R),240(7,R),24(9)]),flip(a)].
% 4.67/4.95 247 add(additive_inverse(A),multiply(A,multiply(additive_inverse(A),additive_inverse(A)))) = multiply(additive_identity,additive_identity). [back_rewrite(174),rewrite([240(11,R)])].
% 4.67/4.95 250 add(A,multiply(additive_inverse(A),multiply(A,A))) = multiply(additive_identity,additive_identity). [back_rewrite(142),rewrite([240(7,R)])].
% 4.67/4.95 251 add(A,multiply(additive_identity,additive_identity)) = A. [back_rewrite(141),rewrite([240(3,R)])].
% 4.67/4.95 252 multiply(additive_identity,additive_identity) = additive_identity. [back_rewrite(242),rewrite([251(5),243(5)]),flip(a)].
% 4.67/4.95 253 add(A,multiply(additive_inverse(A),multiply(A,A))) = additive_identity. [back_rewrite(250),rewrite([252(7)])].
% 4.67/4.95 254 add(additive_inverse(A),multiply(A,multiply(additive_inverse(A),additive_inverse(A)))) = additive_identity. [back_rewrite(247),rewrite([252(9)])].
% 4.67/4.95 259 multiply(additive_identity,A) = additive_identity. [back_rewrite(240),rewrite([252(3)]),flip(a)].
% 4.67/4.95 262 multiply(add(A,multiply(B,C)),multiply(C,C)) = multiply(add(B,multiply(A,C)),C). [para(8(a,1),27(a,1,1,2)),rewrite([28(4)]),flip(a)].
% 4.67/4.95 263 multiply(add(A,multiply(B,B)),B) = add(B,multiply(A,B)). [para(8(a,1),27(a,1,1)),flip(a)].
% 4.67/4.95 265 add(multiply(A,multiply(B,C)),multiply(D,multiply(E,C))) = multiply(add(multiply(D,E),multiply(A,B)),C). [para(12(a,1),27(a,1,2))].
% 4.67/4.95 267 multiply(add(A,multiply(B,b)),a) = add(multiply(B,c_0),multiply(A,a)). [para(19(a,1),27(a,1,1,2)),flip(a)].
% 4.67/4.95 268 multiply(add(multiply(A,a),multiply(B,c_0)),C) = multiply(add(A,multiply(B,b)),multiply(a,C)). [para(30(a,1),27(a,1,1,2)),rewrite([265(7)])].
% 4.67/4.95 273 multiply(add(A,multiply(B,C)),multiply(C,multiply(C,D))) = multiply(add(B,multiply(A,C)),multiply(C,D)). [para(23(a,1),27(a,1,1,2)),rewrite([28(6)]),flip(a)].
% 4.67/4.95 278 multiply(add(b,multiply(A,B)),multiply(b,c_0)) = add(c_0,multiply(A,multiply(B,multiply(b,c_0)))). [para(43(a,1),27(a,1,2)),rewrite([7(7)]),flip(a)].
% 4.67/4.95 321 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(259(a,1),16(a,1,1)),rewrite([7(5),2(5)])].
% 4.67/4.95 322 add(additive_identity,c_0) = c_0. [para(19(a,1),321(a,1,2)),rewrite([19(6)])].
% 4.67/4.95 324 add(A,multiply(A,additive_identity)) = A. [para(321(a,1),24(a,1,2)),rewrite([8(2)]),flip(a)].
% 4.67/4.95 328 add(A,add(B,multiply(A,additive_identity))) = add(A,B). [para(324(a,1),10(a,2,2)),rewrite([7(3),7(5)])].
% 4.67/4.95 358 add(A,add(B,multiply(additive_inverse(A),multiply(A,A)))) = B. [para(253(a,1),10(a,2,2)),rewrite([7(4),2(7)])].
% 4.67/4.95 390 multiply(A,additive_identity) = additive_identity. [para(253(a,1),328(a,2)),rewrite([7(6),358(7)])].
% 4.67/4.95 394 multiply(add(b,multiply(c_0,additive_inverse(a))),additive_inverse(a)) = additive_identity. [para(254(a,1),35(a,1,2)),rewrite([390(3),7(13),28(13)]),flip(a)].
% 4.67/4.95 395 multiply(add(b,multiply(c_0,additive_inverse(a))),multiply(additive_inverse(a),A)) = additive_identity. [para(394(a,1),12(a,1,1)),rewrite([259(2)]),flip(a)].
% 4.67/4.95 426 add(A,multiply(add(B,multiply(additive_inverse(A),A)),A)) = multiply(B,A). [para(28(a,1),358(a,1,2))].
% 4.67/4.95 440 multiply(add(A,multiply(B,multiply(C,multiply(B,C)))),multiply(B,C)) = multiply(add(B,multiply(A,B)),C). [para(263(a,1),12(a,2)),rewrite([12(3),12(6),28(10)])].
% 4.67/4.95 582 multiply(A,multiply(add(multiply(A,A),multiply(additive_inverse(B),B)),B)) = additive_identity. [para(253(a,1),41(a,2,2)),rewrite([265(6),390(8)])].
% 4.67/4.95 594 multiply(additive_inverse(a),add(b,multiply(c_0,additive_inverse(a)))) = additive_identity. [para(395(a,1),22(a,1,2,2,2)),rewrite([390(12),390(10),390(4)]),flip(a)].
% 4.67/4.95 603 multiply(add(A,multiply(B,additive_inverse(a))),add(b,multiply(c_0,additive_inverse(a)))) = multiply(A,add(b,multiply(c_0,additive_inverse(a)))). [para(594(a,1),27(a,1,1,2)),rewrite([390(2),321(9)]),flip(a)].
% 4.67/4.95 604 multiply(add(additive_inverse(a),multiply(A,B)),add(b,multiply(c_0,additive_inverse(a)))) = multiply(A,multiply(B,add(b,multiply(c_0,additive_inverse(a))))). [para(594(a,1),27(a,1,2)),rewrite([7(10),321(10)]),flip(a)].
% 4.67/4.95 605 add(additive_identity,add(b,multiply(c_0,additive_inverse(a)))) = add(b,multiply(c_0,additive_inverse(a))). [para(594(a,1),263(a,2,2)),rewrite([603(15),604(18),603(14),109(10),44(9),7(14)]),flip(a)].
% 4.67/4.95 695 multiply(additive_inverse(a),multiply(A,add(b,multiply(c_0,additive_inverse(a))))) = additive_identity. [para(395(a,1),47(a,1,2,2,2,2,2)),rewrite([390(12),390(12),390(10),390(4),390(4)]),flip(a)].
% 4.67/4.95 782 add(A,multiply(additive_inverse(A),multiply(add(A,B),A))) = multiply(additive_inverse(A),multiply(B,A)). [para(14(a,1),426(a,1,2,1)),rewrite([7(2),12(4),12(8)])].
% 4.67/4.95 798 multiply(add(A,multiply(A,multiply(additive_inverse(B),B))),B) = additive_identity. [para(7(a,1),582(a,1,2,1)),rewrite([105(6)])].
% 4.67/4.95 803 multiply(c_0,multiply(add(multiply(a,a),multiply(additive_inverse(A),A)),A)) = additive_identity. [para(582(a,1),30(a,1,2)),rewrite([390(3)]),flip(a)].
% 4.67/4.95 819 multiply(add(A,multiply(A,multiply(additive_inverse(B),B))),multiply(B,C)) = additive_identity. [para(798(a,1),12(a,1,1)),rewrite([259(2)]),flip(a)].
% 4.67/4.95 834 add(c_0,multiply(c_0,multiply(additive_inverse(a),a))) = additive_identity. [para(395(a,1),798(a,1,1,2)),rewrite([7(8),605(8),120(8)])].
% 4.67/4.95 838 multiply(c_0,add(A,multiply(additive_inverse(a),multiply(a,A)))) = additive_identity. [para(834(a,1),16(a,2,1)),rewrite([12(9),12(8),14(10),259(10)])].
% 4.67/4.95 898 multiply(c_0,multiply(add(A,multiply(additive_inverse(a),multiply(a,A))),B)) = additive_identity. [para(838(a,1),12(a,1,1)),rewrite([259(2)]),flip(a)].
% 4.67/4.95 916 multiply(c_0,add(b,multiply(c_0,additive_inverse(a)))) = additive_identity. [para(695(a,1),838(a,1,2,2)),rewrite([7(9),605(9)])].
% 4.67/4.95 918 multiply(c_0,multiply(add(b,multiply(c_0,additive_inverse(a))),A)) = additive_identity. [para(916(a,1),12(a,1,1)),rewrite([259(2)]),flip(a)].
% 4.67/4.95 919 multiply(c_0,add(A,add(b,multiply(c_0,additive_inverse(a))))) = multiply(c_0,A). [para(916(a,1),14(a,1,1)),rewrite([321(4),7(10)]),flip(a)].
% 4.67/4.95 935 multiply(add(b,multiply(c_0,additive_inverse(a))),multiply(A,c_0)) = additive_identity. [para(918(a,1),47(a,1,2,2,2,2,2)),rewrite([390(15),390(15),390(9),390(8),390(8)]),flip(a)].
% 4.67/4.95 1136 multiply(add(a,multiply(additive_inverse(c_0),b)),multiply(a,c_0)) = additive_identity. [para(803(a,1),22(a,1,2,2,2)),rewrite([390(19),390(11),390(10),268(11)]),flip(a)].
% 4.67/4.95 1144 multiply(add(a,multiply(additive_inverse(c_0),b)),multiply(a,multiply(c_0,A))) = additive_identity. [para(1136(a,1),12(a,1,1)),rewrite([259(2),12(11)]),flip(a)].
% 4.67/4.95 1167 multiply(A,add(B,multiply(B,multiply(additive_inverse(A),A)))) = additive_identity. [para(819(a,1),22(a,1,2,2,2)),rewrite([390(6),390(6),390(2)]),flip(a)].
% 4.67/4.95 1172 add(A,multiply(A,multiply(additive_inverse(A),A))) = additive_identity. [para(819(a,1),25(a,1)),rewrite([12(6),12(5),8(4)]),flip(a)].
% 4.67/4.95 1188 multiply(add(b,multiply(c_0,additive_inverse(a))),multiply(a,A)) = additive_identity. [para(395(a,1),819(a,1,1,2)),rewrite([7(8),605(8)])].
% 4.67/4.95 1346 multiply(A,add(B,multiply(additive_inverse(A),multiply(A,B)))) = additive_identity. [para(1172(a,1),16(a,2,1)),rewrite([12(5),12(4),14(6),259(7)])].
% 4.67/4.95 1381 add(c_0,multiply(c_0,multiply(additive_inverse(b),b))) = additive_identity. [para(1167(a,1),35(a,1)),rewrite([19(10),7(9)]),flip(a)].
% 4.67/4.95 1386 multiply(a,add(b,multiply(c_0,additive_inverse(a)))) = additive_identity. [para(395(a,1),1167(a,1,2,2)),rewrite([7(9),605(9)])].
% 4.67/4.95 1393 multiply(c_0,add(A,multiply(additive_inverse(b),multiply(b,A)))) = additive_identity. [para(1381(a,1),16(a,2,1)),rewrite([12(9),12(8),14(10),259(10)])].
% 4.67/4.95 1507 multiply(a,add(A,add(b,multiply(c_0,additive_inverse(a))))) = multiply(a,A). [para(1386(a,1),14(a,1,1)),rewrite([321(4),7(10)]),flip(a)].
% 4.67/4.95 1512 multiply(a,multiply(c_0,add(additive_inverse(a),multiply(c_0,b)))) = additive_identity. [para(1386(a,1),48(a,2)),rewrite([30(12),30(12),14(11)])].
% 4.67/4.95 1519 multiply(add(additive_identity,a),A) = multiply(a,A). [para(1188(a,1),263(a,2,2)),rewrite([12(11),440(15),120(9),834(9),7(3),7(8),321(8)])].
% 4.67/4.95 1524 add(additive_identity,a) = a. [para(8(a,1),1519(a,2)),rewrite([26(7),259(6),7(3)])].
% 4.67/4.95 1771 multiply(b,multiply(add(a,multiply(additive_inverse(b),c_0)),A)) = additive_identity. [para(30(a,1),1346(a,1,2,2,2)),rewrite([28(9)])].
% 4.67/4.95 1914 multiply(c_0,multiply(add(a,multiply(additive_inverse(b),c_0)),A)) = additive_identity. [para(30(a,1),1393(a,1,2,2,2)),rewrite([28(9)])].
% 4.67/4.95 2107 multiply(add(a,multiply(additive_inverse(b),c_0)),b) = additive_identity. [para(1771(a,1),22(a,1,2,2,2)),rewrite([390(15),390(9),390(8)]),flip(a)].
% 4.67/4.95 2114 multiply(add(a,multiply(additive_inverse(b),c_0)),multiply(b,A)) = additive_identity. [para(1771(a,1),40(a,1,2,2,2)),rewrite([390(15),390(9),390(8)]),flip(a)].
% 4.67/4.95 2173 multiply(add(a,multiply(additive_inverse(b),c_0)),multiply(c_0,A)) = additive_identity. [para(1914(a,1),40(a,1,2,2,2)),rewrite([390(15),390(9),390(8)]),flip(a)].
% 4.67/4.95 2266 multiply(add(additive_identity,b),A) = multiply(b,A). [para(2114(a,1),263(a,2,2)),rewrite([12(11),440(15),2107(9),7(3),7(8),321(8)])].
% 4.67/4.95 2273 add(additive_identity,b) = b. [para(8(a,1),2266(a,2)),rewrite([26(7),259(6),7(3)])].
% 4.67/4.95 2274 add(c_0,multiply(c_0,multiply(additive_inverse(a),multiply(b,c_0)))) = additive_identity. [para(2266(a,1),935(a,1,2)),rewrite([278(10)])].
% 4.67/4.95 2501 multiply(c_0,multiply(A,add(a,multiply(additive_inverse(b),c_0)))) = additive_identity. [para(2173(a,1),47(a,1,2,2,2,2,2)),rewrite([390(10),390(10),390(9),390(3),390(3)]),flip(a)].
% 4.67/4.95 3717 multiply(add(A,multiply(additive_inverse(a),multiply(a,A))),c_0) = additive_identity. [para(898(a,1),22(a,1,2,2,2)),rewrite([390(15),390(9),390(8)]),flip(a)].
% 4.67/4.95 3766 multiply(c_0,multiply(add(additive_inverse(a),multiply(c_0,b)),c_0)) = additive_identity. [para(1512(a,1),3717(a,1,1,2,2)),rewrite([390(12),7(10),321(10),12(10)])].
% 4.67/4.96 3860 multiply(add(additive_inverse(a),multiply(c_0,b)),c_0) = additive_identity. [para(3766(a,1),22(a,1,2,2,2)),rewrite([390(15),390(9),390(8)]),flip(a)].
% 4.67/4.96 3863 multiply(add(additive_inverse(a),multiply(c_0,b)),multiply(c_0,A)) = additive_identity. [para(3860(a,1),12(a,1,1)),rewrite([259(2)]),flip(a)].
% 4.67/4.96 3962 multiply(c_0,add(additive_inverse(a),multiply(c_0,b))) = additive_identity. [para(3863(a,1),22(a,1,2,2,2)),rewrite([390(10),390(9),390(3)]),flip(a)].
% 4.67/4.96 3967 multiply(c_0,multiply(add(additive_inverse(a),multiply(c_0,b)),A)) = additive_identity. [para(3863(a,1),40(a,1,2,2,2)),rewrite([390(10),390(9),390(3)]),flip(a)].
% 4.67/4.96 3968 multiply(c_0,multiply(A,add(additive_inverse(a),multiply(c_0,b)))) = additive_identity. [para(3863(a,1),47(a,1,2,2,2,2,2)),rewrite([390(10),390(10),390(9),390(3),390(3)]),flip(a)].
% 4.67/4.96 4084 multiply(add(additive_identity,add(additive_inverse(a),multiply(c_0,b))),A) = multiply(add(additive_inverse(a),multiply(c_0,b)),A). [para(3967(a,1),263(a,2,2)),rewrite([12(16),440(25),3962(14),7(8),7(18),321(18)])].
% 4.67/4.96 5015 multiply(a,multiply(c_0,add(a,multiply(additive_inverse(c_0),b)))) = additive_identity. [para(1144(a,1),47(a,1,2,2,2,2,2)),rewrite([390(12),390(11),390(10),390(4),390(3)]),flip(a)].
% 4.67/4.96 5096 multiply(c_0,multiply(c_0,add(a,multiply(additive_inverse(c_0),b)))) = additive_identity. [para(5015(a,1),30(a,1,2)),rewrite([390(3)]),flip(a)].
% 4.67/4.96 5189 multiply(c_0,add(a,multiply(additive_inverse(c_0),b))) = additive_identity. [para(5096(a,1),23(a,1,2)),rewrite([390(3)]),flip(a)].
% 4.67/4.96 5193 multiply(c_0,multiply(add(a,multiply(additive_inverse(c_0),b)),A)) = additive_identity. [para(5189(a,1),12(a,1,1)),rewrite([259(2)]),flip(a)].
% 4.67/4.96 5265 multiply(add(a,multiply(additive_inverse(c_0),b)),multiply(A,c_0)) = additive_identity. [para(5193(a,1),47(a,1,2,2,2,2,2)),rewrite([390(15),390(15),390(9),390(8),390(8)]),flip(a)].
% 4.67/4.96 7329 add(additive_inverse(A),multiply(additive_inverse(A),multiply(A,additive_inverse(A)))) = additive_identity. [para(254(a,1),111(a,1,2,1)),rewrite([259(4),390(3),12(9),12(8),8(8)]),flip(a)].
% 4.67/4.96 7604 multiply(additive_inverse(A),add(B,multiply(A,multiply(additive_inverse(A),B)))) = additive_identity. [para(7329(a,1),16(a,2,1)),rewrite([12(7),12(6),14(8),259(8)])].
% 4.67/4.96 7715 multiply(additive_inverse(c_0),add(additive_identity,add(a,multiply(additive_inverse(b),c_0)))) = additive_identity. [para(2501(a,1),7604(a,1,2,2)),rewrite([7(10)])].
% 4.67/4.96 7718 multiply(additive_inverse(c_0),add(additive_identity,add(additive_inverse(a),multiply(c_0,b)))) = additive_identity. [para(3968(a,1),7604(a,1,2,2)),rewrite([7(10)])].
% 4.67/4.96 8509 multiply(additive_inverse(c_0),add(a,multiply(additive_inverse(b),c_0))) = additive_identity. [para(10(a,1),7715(a,1,2)),rewrite([1524(9),7(8)])].
% 4.67/4.96 8519 add(additive_identity,add(additive_identity,additive_inverse(c_0))) = add(additive_identity,additive_inverse(c_0)). [para(7715(a,1),108(a,2,2)),rewrite([390(6),7(4),8509(13),7(6),7(10)])].
% 4.67/4.96 8546 multiply(A,add(additive_identity,additive_inverse(c_0))) = multiply(A,additive_inverse(c_0)). [para(8519(a,1),64(a,1,2)),rewrite([390(8),321(10)])].
% 4.67/4.96 8547 multiply(add(additive_identity,additive_inverse(c_0)),A) = multiply(additive_inverse(c_0),A). [para(8519(a,1),66(a,1,1)),rewrite([259(8),321(10)])].
% 4.67/4.96 8615 add(additive_identity,additive_inverse(c_0)) = additive_inverse(c_0). [para(8547(a,1),8(a,1)),rewrite([8546(11),8547(9),8(8)]),flip(a)].
% 4.67/4.96 8821 multiply(additive_inverse(c_0),multiply(add(additive_inverse(a),multiply(c_0,b)),A)) = additive_identity. [para(7718(a,1),12(a,1,1)),rewrite([259(2),4084(12)]),flip(a)].
% 4.67/4.96 12222 multiply(additive_inverse(c_0),multiply(add(c_0,multiply(additive_inverse(a),b)),b)) = additive_identity. [para(262(a,1),8821(a,1,2))].
% 4.67/4.96 12436 multiply(additive_inverse(c_0),multiply(additive_inverse(a),multiply(b,c_0))) = c_0. [para(12222(a,1),120(a,1,1,2)),rewrite([7(3),2273(3),19(3),12(14),19(13),782(14),12(9)]),flip(a)].
% 4.67/4.96 12551 multiply(additive_inverse(c_0),multiply(add(c_0,multiply(additive_inverse(a),b)),c_0)) = additive_identity. [para(12436(a,1),7604(a,1,2,2,2)),rewrite([7(12),28(12)])].
% 4.67/4.96 12568 multiply(add(c_0,multiply(additive_inverse(a),b)),c_0) = additive_identity. [para(12551(a,1),263(a,2,2)),rewrite([12(19),111(18),12(16),2274(18),390(10),7(4),8615(4),12551(11),7(11),321(11)]),flip(a)].
% 4.67/4.96 12571 multiply(add(c_0,multiply(additive_inverse(a),b)),multiply(c_0,A)) = additive_identity. [para(12568(a,1),12(a,1,1)),rewrite([259(2)]),flip(a)].
% 4.67/4.96 12826 multiply(c_0,multiply(add(c_0,multiply(additive_inverse(a),b)),A)) = additive_identity. [para(12571(a,1),40(a,1,2,2,2)),rewrite([390(10),390(9),390(3)]),flip(a)].
% 4.67/4.96 12928 multiply(c_0,add(multiply(c_0,a),multiply(additive_inverse(a),c_0))) = additive_identity. [para(267(a,1),12826(a,1,2)),rewrite([7(9)])].
% 4.67/4.96 13012 multiply(c_0,add(b,multiply(additive_inverse(a),c_0))) = additive_identity. [para(12928(a,1),919(a,2)),rewrite([7(16),10(16),7(15),10(15,R),7(14),14(14),6(11),390(9),7(8),2273(8),7(7)])].
% 4.67/4.96 13017 multiply(c_0,multiply(add(b,multiply(additive_inverse(a),c_0)),A)) = additive_identity. [para(13012(a,1),12(a,1,1)),rewrite([259(2)]),flip(a)].
% 4.67/4.96 13089 multiply(add(b,multiply(additive_inverse(a),c_0)),multiply(c_0,A)) = additive_identity. [para(13017(a,1),40(a,1,2,2,2)),rewrite([390(15),390(9),390(8)]),flip(a)].
% 4.67/4.96 13139 multiply(add(additive_inverse(c_0),multiply(a,b)),c_0) = additive_identity. [para(5265(a,1),273(a,2)),rewrite([43(11)])].
% 4.67/4.96 13146 multiply(add(additive_inverse(c_0),multiply(a,b)),multiply(c_0,A)) = additive_identity. [para(13139(a,1),12(a,1,1)),rewrite([259(2)]),flip(a)].
% 4.67/4.96 13355 multiply(add(additive_inverse(a),multiply(b,c_0)),multiply(c_0,A)) = additive_identity. [para(13089(a,1),273(a,1)),flip(a)].
% 4.67/4.96 13454 multiply(a,multiply(b,multiply(c_0,c_0))) = c_0. [para(13146(a,1),150(a,2,2)),rewrite([253(8),12(8),321(9),7(10),322(10)])].
% 4.67/4.96 13459 multiply(a,multiply(a,c_0)) = c_0. [para(13454(a,1),23(a,1,2,2)),rewrite([13454(12)])].
% 4.67/4.96 13466 multiply(a,multiply(c_0,multiply(b,c_0))) = c_0. [para(13454(a,1),40(a,1,2,2,2,2)),rewrite([30(8),13454(14)])].
% 4.67/4.96 13501 multiply(a,multiply(a,multiply(c_0,A))) = multiply(c_0,A). [para(13459(a,1),12(a,1,1)),rewrite([12(7)]),flip(a)].
% 4.67/4.96 13510 multiply(a,add(b,add(multiply(a,c_0),multiply(c_0,additive_inverse(a))))) = c_0. [para(13459(a,1),1507(a,2)),rewrite([10(11,R),7(10)])].
% 4.67/4.96 13795 multiply(c_0,multiply(b,c_0)) = multiply(a,c_0). [para(13466(a,1),13501(a,1,2)),flip(a)].
% 4.67/4.96 13899 multiply(c_0,add(A,multiply(b,c_0))) = add(multiply(a,c_0),multiply(c_0,A)). [para(13795(a,1),14(a,1,1)),rewrite([7(11)]),flip(a)].
% 4.67/4.96 14192 add(multiply(a,c_0),multiply(c_0,additive_inverse(a))) = additive_identity. [para(13355(a,1),22(a,1,2,2,2)),rewrite([390(10),390(9),390(3),13899(9)]),flip(a)].
% 4.67/4.96 14208 multiply(a,b) = c_0. [back_rewrite(13510),rewrite([14192(10),7(4),2273(4)])].
% 4.67/4.96 14209 $F # answer(prove_commutativity). [resolve(14208,a,20,a)].
% 4.67/4.96
% 4.67/4.96 % SZS output end Refutation
% 4.67/4.96 ============================== end of proof ==========================
% 4.67/4.96
% 4.67/4.96 ============================== STATISTICS ============================
% 4.67/4.96
% 4.67/4.96 Given=658. Generated=109693. Kept=14202. proofs=1.
% 4.67/4.96 Usable=543. Sos=9998. Demods=9212. Limbo=16, Disabled=3656. Hints=0.
% 4.67/4.96 Megabytes=19.04.
% 4.67/4.96 User_CPU=3.87, System_CPU=0.08, Wall_clock=4.
% 4.67/4.96
% 4.67/4.96 ============================== end of statistics =====================
% 4.67/4.96
% 4.67/4.96 ============================== end of search =========================
% 4.67/4.96
% 4.67/4.96 THEOREM PROVED
% 4.67/4.96 % SZS status Unsatisfiable
% 4.67/4.96
% 4.67/4.96 Exiting with 1 proof.
% 4.67/4.96
% 4.67/4.96 Process 6825 exit (max_proofs) Mon May 30 20:47:01 2022
% 4.67/4.96 Prover9 interrupted
%------------------------------------------------------------------------------