TSTP Solution File: RNG009-5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG009-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 20:39:10 EDT 2022
% Result : Unsatisfiable 4.34s 4.65s
% Output : Refutation 4.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.07 % Problem : RNG009-5 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.07 % Command : tptp2X_and_run_prover9 %d %s
% 0.07/0.26 % Computer : n020.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Mon May 30 16:43:38 EDT 2022
% 0.07/0.26 % CPUTime :
% 3.43/3.74 ============================== Prover9 ===============================
% 3.43/3.74 Prover9 (32) version 2009-11A, November 2009.
% 3.43/3.74 Process 32070 was started by sandbox on n020.cluster.edu,
% 3.43/3.74 Mon May 30 16:43:39 2022
% 3.43/3.74 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31915_n020.cluster.edu".
% 3.43/3.74 ============================== end of head ===========================
% 3.43/3.74
% 3.43/3.74 ============================== INPUT =================================
% 3.43/3.74
% 3.43/3.74 % Reading from file /tmp/Prover9_31915_n020.cluster.edu
% 3.43/3.74
% 3.43/3.74 set(prolog_style_variables).
% 3.43/3.74 set(auto2).
% 3.43/3.74 % set(auto2) -> set(auto).
% 3.43/3.74 % set(auto) -> set(auto_inference).
% 3.43/3.74 % set(auto) -> set(auto_setup).
% 3.43/3.74 % set(auto_setup) -> set(predicate_elim).
% 3.43/3.74 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.43/3.74 % set(auto) -> set(auto_limits).
% 3.43/3.74 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.43/3.74 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.43/3.74 % set(auto) -> set(auto_denials).
% 3.43/3.74 % set(auto) -> set(auto_process).
% 3.43/3.74 % set(auto2) -> assign(new_constants, 1).
% 3.43/3.74 % set(auto2) -> assign(fold_denial_max, 3).
% 3.43/3.74 % set(auto2) -> assign(max_weight, "200.000").
% 3.43/3.74 % set(auto2) -> assign(max_hours, 1).
% 3.43/3.74 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.43/3.74 % set(auto2) -> assign(max_seconds, 0).
% 3.43/3.74 % set(auto2) -> assign(max_minutes, 5).
% 3.43/3.74 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.43/3.74 % set(auto2) -> set(sort_initial_sos).
% 3.43/3.74 % set(auto2) -> assign(sos_limit, -1).
% 3.43/3.74 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.43/3.74 % set(auto2) -> assign(max_megs, 400).
% 3.43/3.74 % set(auto2) -> assign(stats, some).
% 3.43/3.74 % set(auto2) -> clear(echo_input).
% 3.43/3.74 % set(auto2) -> set(quiet).
% 3.43/3.74 % set(auto2) -> clear(print_initial_clauses).
% 3.43/3.74 % set(auto2) -> clear(print_given).
% 3.43/3.74 assign(lrs_ticks,-1).
% 3.43/3.74 assign(sos_limit,10000).
% 3.43/3.74 assign(order,kbo).
% 3.43/3.74 set(lex_order_vars).
% 3.43/3.74 clear(print_given).
% 3.43/3.74
% 3.43/3.74 % formulas(sos). % not echoed (9 formulas)
% 3.43/3.74
% 3.43/3.74 ============================== end of input ==========================
% 3.43/3.74
% 3.43/3.74 % From the command line: assign(max_seconds, 300).
% 3.43/3.74
% 3.43/3.74 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.43/3.74
% 3.43/3.74 % Formulas that are not ordinary clauses:
% 3.43/3.74
% 3.43/3.74 ============================== end of process non-clausal formulas ===
% 3.43/3.74
% 3.43/3.74 ============================== PROCESS INITIAL CLAUSES ===============
% 3.43/3.74
% 3.43/3.74 ============================== PREDICATE ELIMINATION =================
% 3.43/3.74
% 3.43/3.74 ============================== end predicate elimination =============
% 3.43/3.74
% 3.43/3.74 Auto_denials:
% 3.43/3.74 % copying label prove_commutativity to answer in negative clause
% 3.43/3.74
% 3.43/3.74 Term ordering decisions:
% 3.43/3.74
% 3.43/3.74 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (7).
% 3.43/3.74 Function symbol KB weights: additive_identity=1. a=1. b=1. add=1. multiply=1. additive_inverse=0.
% 3.43/3.74
% 3.43/3.74 ============================== end of process initial clauses ========
% 3.43/3.74
% 3.43/3.74 ============================== CLAUSES FOR SEARCH ====================
% 3.43/3.74
% 3.43/3.74 ============================== end of clauses for search =============
% 3.43/3.74
% 3.43/3.74 ============================== SEARCH ================================
% 3.43/3.74
% 3.43/3.74 % Starting search at 0.01 seconds.
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=57.000, iters=3411
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=53.000, iters=3360
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=47.000, iters=3365
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=44.000, iters=3408
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=43.000, iters=3413
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=41.000, iters=3413
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=39.000, iters=3488
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=37.000, iters=3381
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=35.000, iters=3350
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=33.000, iters=3367
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=32.000, iters=3341
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=31.000, iters=3339
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=30.000, iters=3366
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=29.000, iters=3373
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=28.000, iters=3363
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=27.000, iters=3361
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=26.000, iters=3337
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=25.000, iters=3336
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=24.000, iters=3376
% 3.43/3.74
% 3.43/3.74 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 69 (0.00 of 2.34 sec).
% 3.43/3.74
% 3.43/3.74 Low Water (keep): wt=23.000, iters=3336
% 3.43/3.74
% 3.43/3.74 Low Water (displace): id=6179, wt=93.000
% 3.43/3.74
% 3.43/3.74 Low Water (displace): id=5709, wt=89.000
% 3.43/3.74
% 3.43/3.74 Low Water (displace): id=4318, wt=85.000
% 3.43/3.74
% 3.43/3.74 Low Water (displace): id=4744, wt=79.000
% 4.34/4.65
% 4.34/4.65 Low Water (displace): id=4333, wt=77.000
% 4.34/4.65
% 4.34/4.65 Low Water (displace): id=12369, wt=19.000
% 4.34/4.65
% 4.34/4.65 Low Water (displace): id=12380, wt=18.000
% 4.34/4.65
% 4.34/4.65 Low Water (displace): id=12420, wt=17.000
% 4.34/4.65
% 4.34/4.65 Low Water (keep): wt=22.000, iters=3339
% 4.34/4.65
% 4.34/4.65 Low Water (displace): id=13278, wt=16.000
% 4.34/4.65
% 4.34/4.65 Low Water (displace): id=13301, wt=15.000
% 4.34/4.65
% 4.34/4.65 ============================== PROOF =================================
% 4.34/4.65 % SZS status Unsatisfiable
% 4.34/4.65 % SZS output start Refutation
% 4.34/4.65
% 4.34/4.65 % Proof 1 at 3.68 (+ 0.08) seconds: prove_commutativity.
% 4.34/4.65 % Length of proof is 159.
% 4.34/4.65 % Level of proof is 41.
% 4.34/4.65 % Maximum clause weight is 24.000.
% 4.34/4.65 % Given clauses 657.
% 4.34/4.65
% 4.34/4.65 1 add(A,additive_identity) = A # label(right_identity) # label(axiom). [assumption].
% 4.34/4.65 2 add(A,additive_inverse(A)) = additive_identity # label(right_additive_inverse) # label(axiom). [assumption].
% 4.34/4.65 3 add(A,B) = add(B,A) # label(commutative_addition) # label(axiom). [assumption].
% 4.34/4.65 4 multiply(A,multiply(A,A)) = A # label(x_cubed_is_x) # label(hypothesis). [assumption].
% 4.34/4.65 5 add(add(A,B),C) = add(A,add(B,C)) # label(associative_addition) # label(axiom). [assumption].
% 4.34/4.65 6 add(A,add(B,C)) = add(C,add(A,B)). [copy(5),rewrite([3(2)]),flip(a)].
% 4.34/4.65 7 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associative_multiplication) # label(axiom). [assumption].
% 4.34/4.65 8 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distribute1) # label(axiom). [assumption].
% 4.34/4.65 9 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(8),flip(a)].
% 4.34/4.65 10 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distribute2) # label(axiom). [assumption].
% 4.34/4.65 11 add(multiply(A,B),multiply(C,B)) = multiply(add(A,C),B). [copy(10),flip(a)].
% 4.34/4.65 12 multiply(a,b) != multiply(b,a) # label(prove_commutativity) # label(negated_conjecture) # answer(prove_commutativity). [assumption].
% 4.34/4.65 13 multiply(b,a) != multiply(a,b) # answer(prove_commutativity). [copy(12),flip(a)].
% 4.34/4.65 14 multiply(b,a) = c_0. [new_symbol(13)].
% 4.34/4.65 15 multiply(a,b) != c_0 # answer(prove_commutativity). [back_rewrite(13),rewrite([14(3)]),flip(a)].
% 4.34/4.65 17 multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B))))) = multiply(A,B). [para(7(a,1),4(a,1,2)),rewrite([7(5)])].
% 4.34/4.65 18 multiply(A,multiply(A,multiply(A,B))) = multiply(A,B). [para(4(a,1),7(a,1,1)),rewrite([7(3)]),flip(a)].
% 4.34/4.65 19 multiply(A,add(B,multiply(A,A))) = add(A,multiply(A,B)). [para(4(a,1),9(a,1,1)),rewrite([3(4)]),flip(a)].
% 4.34/4.65 20 multiply(add(A,B),multiply(A,A)) = add(A,multiply(B,multiply(A,A))). [para(4(a,1),11(a,1,1)),flip(a)].
% 4.34/4.65 21 multiply(add(A,B),multiply(B,B)) = add(B,multiply(A,multiply(B,B))). [para(4(a,1),11(a,1,2)),rewrite([3(3)]),flip(a)].
% 4.34/4.65 22 add(multiply(A,multiply(B,C)),multiply(D,C)) = multiply(add(D,multiply(A,B)),C). [para(7(a,1),11(a,1,1)),rewrite([3(6)])].
% 4.34/4.65 23 add(multiply(A,B),multiply(C,multiply(D,B))) = multiply(add(A,multiply(C,D)),B). [para(7(a,1),11(a,1,2))].
% 4.34/4.65 24 multiply(add(A,A),B) = multiply(A,add(B,B)). [para(11(a,1),9(a,1))].
% 4.34/4.65 25 multiply(b,multiply(a,A)) = multiply(c_0,A). [para(14(a,1),7(a,1,1)),flip(a)].
% 4.34/4.65 27 multiply(add(A,b),a) = add(c_0,multiply(A,a)). [para(14(a,1),11(a,1,1)),rewrite([3(6)]),flip(a)].
% 4.34/4.65 30 multiply(b,add(A,multiply(a,B))) = add(multiply(c_0,B),multiply(b,A)). [para(25(a,1),9(a,1,1)),rewrite([3(9)]),flip(a)].
% 4.34/4.65 35 multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,multiply(B,C)))))) = multiply(A,multiply(B,C)). [para(18(a,1),7(a,1)),rewrite([7(2),7(5),7(6)]),flip(a)].
% 4.34/4.65 36 multiply(A,add(B,multiply(A,multiply(A,C)))) = multiply(A,add(C,B)). [para(18(a,1),9(a,1,1)),rewrite([9(3),3(5)]),flip(a)].
% 4.34/4.65 38 multiply(b,multiply(b,c_0)) = c_0. [para(14(a,1),18(a,1,2,2)),rewrite([14(8)])].
% 4.34/4.65 39 multiply(b,multiply(b,multiply(c_0,A))) = multiply(c_0,A). [para(25(a,1),18(a,1,2,2)),rewrite([25(10)])].
% 4.34/4.65 42 multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,C)))))))) = multiply(A,multiply(B,C)). [para(17(a,1),7(a,1)),rewrite([7(2),7(5),7(7)]),flip(a)].
% 4.34/4.65 43 multiply(A,add(B,multiply(C,multiply(A,multiply(C,multiply(A,C)))))) = multiply(A,add(C,B)). [para(17(a,1),9(a,1,1)),rewrite([9(3),3(7)]),flip(a)].
% 4.34/4.65 47 multiply(additive_identity,add(A,A)) = multiply(additive_identity,A). [para(1(a,1),24(a,1,1)),flip(a)].
% 4.34/4.65 59 multiply(A,add(B,add(B,C))) = add(multiply(add(A,A),B),multiply(A,C)). [para(24(a,2),9(a,1,1)),rewrite([3(6),6(6),3(5)]),flip(a)].
% 4.34/4.65 61 multiply(add(A,add(A,B)),C) = add(multiply(A,add(C,C)),multiply(B,C)). [para(24(a,1),11(a,1,1)),rewrite([3(6),6(6),3(5)]),flip(a)].
% 4.34/4.65 79 multiply(additive_identity,add(A,add(A,B))) = multiply(additive_identity,add(A,B)). [para(47(a,1),9(a,1,1)),rewrite([9(5),3(6),6(6),3(5)]),flip(a)].
% 4.34/4.65 100 multiply(A,multiply(add(B,multiply(A,A)),C)) = multiply(add(A,multiply(A,B)),C). [para(19(a,1),7(a,1,1)),flip(a)].
% 4.34/4.65 102 multiply(A,add(B,add(C,multiply(A,A)))) = add(add(A,multiply(A,B)),multiply(A,C)). [para(19(a,1),9(a,1,1)),rewrite([3(7),6(7,R),3(6)]),flip(a)].
% 4.34/4.65 103 add(add(A,multiply(A,B)),multiply(A,C)) = add(A,multiply(A,add(B,C))). [para(19(a,1),9(a,1,2)),rewrite([6(4,R),9(3),3(1),102(7)]),flip(a)].
% 4.34/4.65 104 multiply(A,multiply(A,add(A,B))) = add(A,multiply(A,multiply(A,B))). [para(9(a,1),19(a,1,2)),rewrite([3(1)])].
% 4.34/4.65 106 multiply(A,multiply(add(A,B),A)) = add(A,multiply(A,multiply(B,A))). [para(11(a,1),19(a,1,2)),rewrite([3(1)])].
% 4.34/4.65 114 multiply(A,add(B,add(C,multiply(A,A)))) = add(A,multiply(A,add(B,C))). [back_rewrite(102),rewrite([103(8)])].
% 4.34/4.65 115 multiply(add(b,multiply(A,B)),a) = add(c_0,multiply(A,multiply(B,a))). [para(7(a,1),27(a,2,2)),rewrite([3(3)])].
% 4.34/4.65 136 add(A,multiply(additive_identity,multiply(A,A))) = A. [para(1(a,1),20(a,1,1)),rewrite([4(2)]),flip(a)].
% 4.34/4.65 137 add(A,multiply(additive_inverse(A),multiply(A,A))) = multiply(additive_identity,multiply(A,A)). [para(2(a,1),20(a,1,1)),flip(a)].
% 4.34/4.65 145 add(add(A,multiply(B,multiply(A,A))),multiply(C,multiply(A,A))) = add(A,multiply(add(B,C),multiply(A,A))). [para(20(a,1),11(a,1,1)),rewrite([3(8),6(8),3(7),6(8,R),3(7),20(10)])].
% 4.34/4.65 169 add(additive_inverse(A),multiply(A,multiply(additive_inverse(A),additive_inverse(A)))) = multiply(additive_identity,multiply(additive_inverse(A),additive_inverse(A))). [para(2(a,1),21(a,1,1)),flip(a)].
% 4.34/4.65 235 multiply(additive_identity,additive_identity) = multiply(additive_identity,A). [para(2(a,1),79(a,1,2,2)),rewrite([1(3),2(5)]),flip(a)].
% 4.34/4.65 237 add(additive_identity,multiply(additive_identity,additive_identity)) = add(additive_identity,multiply(additive_identity,A)). [para(19(a,1),79(a,2)),rewrite([114(7),235(4,R)])].
% 4.34/4.65 238 add(additive_identity,multiply(additive_identity,A)) = multiply(additive_identity,additive_identity). [para(136(a,1),79(a,1,2,2)),rewrite([235(3,R),235(7,R),19(9)]),flip(a)].
% 4.34/4.65 242 add(additive_inverse(A),multiply(A,multiply(additive_inverse(A),additive_inverse(A)))) = multiply(additive_identity,additive_identity). [back_rewrite(169),rewrite([235(11,R)])].
% 4.34/4.65 245 add(A,multiply(additive_inverse(A),multiply(A,A))) = multiply(additive_identity,additive_identity). [back_rewrite(137),rewrite([235(7,R)])].
% 4.34/4.65 246 add(A,multiply(additive_identity,additive_identity)) = A. [back_rewrite(136),rewrite([235(3,R)])].
% 4.34/4.65 247 multiply(additive_identity,additive_identity) = additive_identity. [back_rewrite(237),rewrite([246(5),238(5)]),flip(a)].
% 4.34/4.65 248 add(A,multiply(additive_inverse(A),multiply(A,A))) = additive_identity. [back_rewrite(245),rewrite([247(7)])].
% 4.34/4.65 249 add(additive_inverse(A),multiply(A,multiply(additive_inverse(A),additive_inverse(A)))) = additive_identity. [back_rewrite(242),rewrite([247(9)])].
% 4.34/4.65 254 multiply(additive_identity,A) = additive_identity. [back_rewrite(235),rewrite([247(3)]),flip(a)].
% 4.34/4.65 257 multiply(add(A,multiply(B,C)),multiply(C,C)) = multiply(add(B,multiply(A,C)),C). [para(4(a,1),22(a,1,1,2)),rewrite([23(4)]),flip(a)].
% 4.34/4.65 258 multiply(add(A,multiply(B,B)),B) = add(B,multiply(A,B)). [para(4(a,1),22(a,1,1)),flip(a)].
% 4.34/4.65 260 add(multiply(A,multiply(B,C)),multiply(D,multiply(E,C))) = multiply(add(multiply(D,E),multiply(A,B)),C). [para(7(a,1),22(a,1,2))].
% 4.34/4.65 262 multiply(add(A,multiply(B,b)),a) = add(multiply(B,c_0),multiply(A,a)). [para(14(a,1),22(a,1,1,2)),flip(a)].
% 4.34/4.65 263 multiply(add(multiply(A,a),multiply(B,c_0)),C) = multiply(add(A,multiply(B,b)),multiply(a,C)). [para(25(a,1),22(a,1,1,2)),rewrite([260(7)])].
% 4.34/4.65 268 multiply(add(A,multiply(B,C)),multiply(C,multiply(C,D))) = multiply(add(B,multiply(A,C)),multiply(C,D)). [para(18(a,1),22(a,1,1,2)),rewrite([23(6)]),flip(a)].
% 4.34/4.65 273 multiply(add(b,multiply(A,B)),multiply(b,c_0)) = add(c_0,multiply(A,multiply(B,multiply(b,c_0)))). [para(38(a,1),22(a,1,2)),rewrite([3(7)]),flip(a)].
% 4.34/4.65 316 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(254(a,1),11(a,1,1)),rewrite([3(5),1(5)])].
% 4.34/4.65 317 add(additive_identity,c_0) = c_0. [para(14(a,1),316(a,1,2)),rewrite([14(6)])].
% 4.34/4.65 319 add(A,multiply(A,additive_identity)) = A. [para(316(a,1),19(a,1,2)),rewrite([4(2)]),flip(a)].
% 4.34/4.65 323 add(A,add(B,multiply(A,additive_identity))) = add(A,B). [para(319(a,1),6(a,2,2)),rewrite([3(3),3(5)])].
% 4.34/4.65 353 add(A,add(B,multiply(additive_inverse(A),multiply(A,A)))) = B. [para(248(a,1),6(a,2,2)),rewrite([3(4),1(7)])].
% 4.34/4.65 385 multiply(A,additive_identity) = additive_identity. [para(248(a,1),323(a,2)),rewrite([3(6),353(7)])].
% 4.34/4.65 389 multiply(add(b,multiply(c_0,additive_inverse(a))),additive_inverse(a)) = additive_identity. [para(249(a,1),30(a,1,2)),rewrite([385(3),3(13),23(13)]),flip(a)].
% 4.34/4.65 390 multiply(add(b,multiply(c_0,additive_inverse(a))),multiply(additive_inverse(a),A)) = additive_identity. [para(389(a,1),7(a,1,1)),rewrite([254(2)]),flip(a)].
% 4.34/4.65 421 add(A,multiply(add(B,multiply(additive_inverse(A),A)),A)) = multiply(B,A). [para(23(a,1),353(a,1,2))].
% 4.34/4.65 435 multiply(add(A,multiply(B,multiply(C,multiply(B,C)))),multiply(B,C)) = multiply(add(B,multiply(A,B)),C). [para(258(a,1),7(a,2)),rewrite([7(3),7(6),23(10)])].
% 4.34/4.65 577 multiply(A,multiply(add(multiply(A,A),multiply(additive_inverse(B),B)),B)) = additive_identity. [para(248(a,1),36(a,2,2)),rewrite([260(6),385(8)])].
% 4.34/4.65 589 multiply(additive_inverse(a),add(b,multiply(c_0,additive_inverse(a)))) = additive_identity. [para(390(a,1),17(a,1,2,2,2)),rewrite([385(12),385(10),385(4)]),flip(a)].
% 4.34/4.65 598 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(589(a,1),22(a,1,1,2)),rewrite([385(2),316(9)]),flip(a)].
% 4.34/4.65 599 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(589(a,1),22(a,1,2)),rewrite([3(10),316(10)]),flip(a)].
% 4.34/4.65 600 add(additive_identity,add(b,multiply(c_0,additive_inverse(a)))) = add(b,multiply(c_0,additive_inverse(a))). [para(589(a,1),258(a,2,2)),rewrite([598(15),599(18),598(14),104(10),39(9),3(14)]),flip(a)].
% 4.34/4.65 690 multiply(additive_inverse(a),multiply(A,add(b,multiply(c_0,additive_inverse(a))))) = additive_identity. [para(390(a,1),42(a,1,2,2,2,2,2)),rewrite([385(12),385(12),385(10),385(4),385(4)]),flip(a)].
% 4.34/4.65 777 add(A,multiply(additive_inverse(A),multiply(add(A,B),A))) = multiply(additive_inverse(A),multiply(B,A)). [para(9(a,1),421(a,1,2,1)),rewrite([3(2),7(4),7(8)])].
% 4.34/4.65 793 multiply(add(A,multiply(A,multiply(additive_inverse(B),B))),B) = additive_identity. [para(3(a,1),577(a,1,2,1)),rewrite([100(6)])].
% 4.34/4.65 798 multiply(c_0,multiply(add(multiply(a,a),multiply(additive_inverse(A),A)),A)) = additive_identity. [para(577(a,1),25(a,1,2)),rewrite([385(3)]),flip(a)].
% 4.34/4.65 814 multiply(add(A,multiply(A,multiply(additive_inverse(B),B))),multiply(B,C)) = additive_identity. [para(793(a,1),7(a,1,1)),rewrite([254(2)]),flip(a)].
% 4.34/4.65 829 add(c_0,multiply(c_0,multiply(additive_inverse(a),a))) = additive_identity. [para(390(a,1),793(a,1,1,2)),rewrite([3(8),600(8),115(8)])].
% 4.34/4.65 833 multiply(c_0,add(A,multiply(additive_inverse(a),multiply(a,A)))) = additive_identity. [para(829(a,1),11(a,2,1)),rewrite([7(9),7(8),9(10),254(10)])].
% 4.34/4.65 893 multiply(c_0,multiply(add(A,multiply(additive_inverse(a),multiply(a,A))),B)) = additive_identity. [para(833(a,1),7(a,1,1)),rewrite([254(2)]),flip(a)].
% 4.34/4.65 911 multiply(c_0,add(b,multiply(c_0,additive_inverse(a)))) = additive_identity. [para(690(a,1),833(a,1,2,2)),rewrite([3(9),600(9)])].
% 4.34/4.65 913 multiply(c_0,multiply(add(b,multiply(c_0,additive_inverse(a))),A)) = additive_identity. [para(911(a,1),7(a,1,1)),rewrite([254(2)]),flip(a)].
% 4.34/4.65 914 multiply(c_0,add(A,add(b,multiply(c_0,additive_inverse(a))))) = multiply(c_0,A). [para(911(a,1),9(a,1,1)),rewrite([316(4),3(10)]),flip(a)].
% 4.34/4.65 930 multiply(add(b,multiply(c_0,additive_inverse(a))),multiply(A,c_0)) = additive_identity. [para(913(a,1),42(a,1,2,2,2,2,2)),rewrite([385(15),385(15),385(9),385(8),385(8)]),flip(a)].
% 4.34/4.65 1131 multiply(add(a,multiply(additive_inverse(c_0),b)),multiply(a,c_0)) = additive_identity. [para(798(a,1),17(a,1,2,2,2)),rewrite([385(19),385(11),385(10),263(11)]),flip(a)].
% 4.34/4.65 1139 multiply(add(a,multiply(additive_inverse(c_0),b)),multiply(a,multiply(c_0,A))) = additive_identity. [para(1131(a,1),7(a,1,1)),rewrite([254(2),7(11)]),flip(a)].
% 4.34/4.65 1162 multiply(A,add(B,multiply(B,multiply(additive_inverse(A),A)))) = additive_identity. [para(814(a,1),17(a,1,2,2,2)),rewrite([385(6),385(6),385(2)]),flip(a)].
% 4.34/4.65 1167 add(A,multiply(A,multiply(additive_inverse(A),A))) = additive_identity. [para(814(a,1),20(a,1)),rewrite([7(6),7(5),4(4)]),flip(a)].
% 4.34/4.65 1183 multiply(add(b,multiply(c_0,additive_inverse(a))),multiply(a,A)) = additive_identity. [para(390(a,1),814(a,1,1,2)),rewrite([3(8),600(8)])].
% 4.34/4.65 1341 multiply(A,add(B,multiply(additive_inverse(A),multiply(A,B)))) = additive_identity. [para(1167(a,1),11(a,2,1)),rewrite([7(5),7(4),9(6),254(7)])].
% 4.34/4.65 1376 add(c_0,multiply(c_0,multiply(additive_inverse(b),b))) = additive_identity. [para(1162(a,1),30(a,1)),rewrite([14(10),3(9)]),flip(a)].
% 4.34/4.65 1381 multiply(a,add(b,multiply(c_0,additive_inverse(a)))) = additive_identity. [para(390(a,1),1162(a,1,2,2)),rewrite([3(9),600(9)])].
% 4.34/4.65 1388 multiply(c_0,add(A,multiply(additive_inverse(b),multiply(b,A)))) = additive_identity. [para(1376(a,1),11(a,2,1)),rewrite([7(9),7(8),9(10),254(10)])].
% 4.34/4.65 1502 multiply(a,add(A,add(b,multiply(c_0,additive_inverse(a))))) = multiply(a,A). [para(1381(a,1),9(a,1,1)),rewrite([316(4),3(10)]),flip(a)].
% 4.34/4.65 1507 multiply(a,multiply(c_0,add(additive_inverse(a),multiply(c_0,b)))) = additive_identity. [para(1381(a,1),43(a,2)),rewrite([25(12),25(12),9(11)])].
% 4.34/4.65 1514 multiply(add(additive_identity,a),A) = multiply(a,A). [para(1183(a,1),258(a,2,2)),rewrite([7(11),435(15),115(9),829(9),3(3),3(8),316(8)])].
% 4.34/4.65 1519 add(additive_identity,a) = a. [para(4(a,1),1514(a,2)),rewrite([21(7),254(6),3(3)])].
% 4.34/4.65 1766 multiply(b,multiply(add(a,multiply(additive_inverse(b),c_0)),A)) = additive_identity. [para(25(a,1),1341(a,1,2,2,2)),rewrite([23(9)])].
% 4.34/4.65 1909 multiply(c_0,multiply(add(a,multiply(additive_inverse(b),c_0)),A)) = additive_identity. [para(25(a,1),1388(a,1,2,2,2)),rewrite([23(9)])].
% 4.34/4.65 2102 multiply(add(a,multiply(additive_inverse(b),c_0)),b) = additive_identity. [para(1766(a,1),17(a,1,2,2,2)),rewrite([385(15),385(9),385(8)]),flip(a)].
% 4.34/4.65 2109 multiply(add(a,multiply(additive_inverse(b),c_0)),multiply(b,A)) = additive_identity. [para(1766(a,1),35(a,1,2,2,2)),rewrite([385(15),385(9),385(8)]),flip(a)].
% 4.34/4.65 2168 multiply(add(a,multiply(additive_inverse(b),c_0)),multiply(c_0,A)) = additive_identity. [para(1909(a,1),35(a,1,2,2,2)),rewrite([385(15),385(9),385(8)]),flip(a)].
% 4.34/4.65 2261 multiply(add(additive_identity,b),A) = multiply(b,A). [para(2109(a,1),258(a,2,2)),rewrite([7(11),435(15),2102(9),3(3),3(8),316(8)])].
% 4.34/4.65 2268 add(additive_identity,b) = b. [para(4(a,1),2261(a,2)),rewrite([21(7),254(6),3(3)])].
% 4.34/4.65 2269 add(c_0,multiply(c_0,multiply(additive_inverse(a),multiply(b,c_0)))) = additive_identity. [para(2261(a,1),930(a,1,2)),rewrite([273(10)])].
% 4.34/4.65 2496 multiply(c_0,multiply(A,add(a,multiply(additive_inverse(b),c_0)))) = additive_identity. [para(2168(a,1),42(a,1,2,2,2,2,2)),rewrite([385(10),385(10),385(9),385(3),385(3)]),flip(a)].
% 4.34/4.65 3712 multiply(add(A,multiply(additive_inverse(a),multiply(a,A))),c_0) = additive_identity. [para(893(a,1),17(a,1,2,2,2)),rewrite([385(15),385(9),385(8)]),flip(a)].
% 4.34/4.65 3761 multiply(c_0,multiply(add(additive_inverse(a),multiply(c_0,b)),c_0)) = additive_identity. [para(1507(a,1),3712(a,1,1,2,2)),rewrite([385(12),3(10),316(10),7(10)])].
% 4.34/4.65 3855 multiply(add(additive_inverse(a),multiply(c_0,b)),c_0) = additive_identity. [para(3761(a,1),17(a,1,2,2,2)),rewrite([385(15),385(9),385(8)]),flip(a)].
% 4.34/4.65 3858 multiply(add(additive_inverse(a),multiply(c_0,b)),multiply(c_0,A)) = additive_identity. [para(3855(a,1),7(a,1,1)),rewrite([254(2)]),flip(a)].
% 4.34/4.65 3957 multiply(c_0,add(additive_inverse(a),multiply(c_0,b))) = additive_identity. [para(3858(a,1),17(a,1,2,2,2)),rewrite([385(10),385(9),385(3)]),flip(a)].
% 4.34/4.65 3962 multiply(c_0,multiply(add(additive_inverse(a),multiply(c_0,b)),A)) = additive_identity. [para(3858(a,1),35(a,1,2,2,2)),rewrite([385(10),385(9),385(3)]),flip(a)].
% 4.34/4.65 3963 multiply(c_0,multiply(A,add(additive_inverse(a),multiply(c_0,b)))) = additive_identity. [para(3858(a,1),42(a,1,2,2,2,2,2)),rewrite([385(10),385(10),385(9),385(3),385(3)]),flip(a)].
% 4.34/4.65 4079 multiply(add(additive_identity,add(additive_inverse(a),multiply(c_0,b))),A) = multiply(add(additive_inverse(a),multiply(c_0,b)),A). [para(3962(a,1),258(a,2,2)),rewrite([7(16),435(25),3957(14),3(8),3(18),316(18)])].
% 4.34/4.65 5010 multiply(a,multiply(c_0,add(a,multiply(additive_inverse(c_0),b)))) = additive_identity. [para(1139(a,1),42(a,1,2,2,2,2,2)),rewrite([385(12),385(11),385(10),385(4),385(3)]),flip(a)].
% 4.34/4.65 5091 multiply(c_0,multiply(c_0,add(a,multiply(additive_inverse(c_0),b)))) = additive_identity. [para(5010(a,1),25(a,1,2)),rewrite([385(3)]),flip(a)].
% 4.34/4.65 5184 multiply(c_0,add(a,multiply(additive_inverse(c_0),b))) = additive_identity. [para(5091(a,1),18(a,1,2)),rewrite([385(3)]),flip(a)].
% 4.34/4.65 5188 multiply(c_0,multiply(add(a,multiply(additive_inverse(c_0),b)),A)) = additive_identity. [para(5184(a,1),7(a,1,1)),rewrite([254(2)]),flip(a)].
% 4.34/4.65 5260 multiply(add(a,multiply(additive_inverse(c_0),b)),multiply(A,c_0)) = additive_identity. [para(5188(a,1),42(a,1,2,2,2,2,2)),rewrite([385(15),385(15),385(9),385(8),385(8)]),flip(a)].
% 4.34/4.65 7324 add(additive_inverse(A),multiply(additive_inverse(A),multiply(A,additive_inverse(A)))) = additive_identity. [para(249(a,1),106(a,1,2,1)),rewrite([254(4),385(3),7(9),7(8),4(8)]),flip(a)].
% 4.34/4.65 7599 multiply(additive_inverse(A),add(B,multiply(A,multiply(additive_inverse(A),B)))) = additive_identity. [para(7324(a,1),11(a,2,1)),rewrite([7(7),7(6),9(8),254(8)])].
% 4.34/4.65 7710 multiply(additive_inverse(c_0),add(additive_identity,add(a,multiply(additive_inverse(b),c_0)))) = additive_identity. [para(2496(a,1),7599(a,1,2,2)),rewrite([3(10)])].
% 4.34/4.65 7713 multiply(additive_inverse(c_0),add(additive_identity,add(additive_inverse(a),multiply(c_0,b)))) = additive_identity. [para(3963(a,1),7599(a,1,2,2)),rewrite([3(10)])].
% 4.34/4.65 8504 multiply(additive_inverse(c_0),add(a,multiply(additive_inverse(b),c_0))) = additive_identity. [para(6(a,1),7710(a,1,2)),rewrite([1519(9),3(8)])].
% 4.34/4.65 8514 add(additive_identity,add(additive_identity,additive_inverse(c_0))) = add(additive_identity,additive_inverse(c_0)). [para(7710(a,1),103(a,2,2)),rewrite([385(6),3(4),8504(13),3(6),3(10)])].
% 4.34/4.65 8541 multiply(A,add(additive_identity,additive_inverse(c_0))) = multiply(A,additive_inverse(c_0)). [para(8514(a,1),59(a,1,2)),rewrite([385(8),316(10)])].
% 4.34/4.65 8542 multiply(add(additive_identity,additive_inverse(c_0)),A) = multiply(additive_inverse(c_0),A). [para(8514(a,1),61(a,1,1)),rewrite([254(8),316(10)])].
% 4.34/4.65 8610 add(additive_identity,additive_inverse(c_0)) = additive_inverse(c_0). [para(8542(a,1),4(a,1)),rewrite([8541(11),8542(9),4(8)]),flip(a)].
% 4.34/4.65 8816 multiply(additive_inverse(c_0),multiply(add(additive_inverse(a),multiply(c_0,b)),A)) = additive_identity. [para(7713(a,1),7(a,1,1)),rewrite([254(2),4079(12)]),flip(a)].
% 4.34/4.65 12217 multiply(additive_inverse(c_0),multiply(add(c_0,multiply(additive_inverse(a),b)),b)) = additive_identity. [para(257(a,1),8816(a,1,2))].
% 4.34/4.65 12431 multiply(additive_inverse(c_0),multiply(additive_inverse(a),multiply(b,c_0))) = c_0. [para(12217(a,1),115(a,1,1,2)),rewrite([3(3),2268(3),14(3),7(14),14(13),777(14),7(9)]),flip(a)].
% 4.34/4.65 12546 multiply(additive_inverse(c_0),multiply(add(c_0,multiply(additive_inverse(a),b)),c_0)) = additive_identity. [para(12431(a,1),7599(a,1,2,2,2)),rewrite([3(12),23(12)])].
% 4.34/4.65 12563 multiply(add(c_0,multiply(additive_inverse(a),b)),c_0) = additive_identity. [para(12546(a,1),258(a,2,2)),rewrite([7(19),106(18),7(16),2269(18),385(10),3(4),8610(4),12546(11),3(11),316(11)]),flip(a)].
% 4.34/4.65 12566 multiply(add(c_0,multiply(additive_inverse(a),b)),multiply(c_0,A)) = additive_identity. [para(12563(a,1),7(a,1,1)),rewrite([254(2)]),flip(a)].
% 4.37/4.65 12821 multiply(c_0,multiply(add(c_0,multiply(additive_inverse(a),b)),A)) = additive_identity. [para(12566(a,1),35(a,1,2,2,2)),rewrite([385(10),385(9),385(3)]),flip(a)].
% 4.37/4.65 12923 multiply(c_0,add(multiply(c_0,a),multiply(additive_inverse(a),c_0))) = additive_identity. [para(262(a,1),12821(a,1,2)),rewrite([3(9)])].
% 4.37/4.65 13007 multiply(c_0,add(b,multiply(additive_inverse(a),c_0))) = additive_identity. [para(12923(a,1),914(a,2)),rewrite([3(16),6(16),3(15),6(15,R),3(14),9(14),2(11),385(9),3(8),2268(8),3(7)])].
% 4.37/4.65 13012 multiply(c_0,multiply(add(b,multiply(additive_inverse(a),c_0)),A)) = additive_identity. [para(13007(a,1),7(a,1,1)),rewrite([254(2)]),flip(a)].
% 4.37/4.65 13084 multiply(add(b,multiply(additive_inverse(a),c_0)),multiply(c_0,A)) = additive_identity. [para(13012(a,1),35(a,1,2,2,2)),rewrite([385(15),385(9),385(8)]),flip(a)].
% 4.37/4.65 13134 multiply(add(additive_inverse(c_0),multiply(a,b)),c_0) = additive_identity. [para(5260(a,1),268(a,2)),rewrite([38(11)])].
% 4.37/4.65 13141 multiply(add(additive_inverse(c_0),multiply(a,b)),multiply(c_0,A)) = additive_identity. [para(13134(a,1),7(a,1,1)),rewrite([254(2)]),flip(a)].
% 4.37/4.65 13350 multiply(add(additive_inverse(a),multiply(b,c_0)),multiply(c_0,A)) = additive_identity. [para(13084(a,1),268(a,1)),flip(a)].
% 4.37/4.65 13449 multiply(a,multiply(b,multiply(c_0,c_0))) = c_0. [para(13141(a,1),145(a,2,2)),rewrite([248(8),7(8),316(9),3(10),317(10)])].
% 4.37/4.65 13454 multiply(a,multiply(a,c_0)) = c_0. [para(13449(a,1),18(a,1,2,2)),rewrite([13449(12)])].
% 4.37/4.65 13461 multiply(a,multiply(c_0,multiply(b,c_0))) = c_0. [para(13449(a,1),35(a,1,2,2,2,2)),rewrite([25(8),13449(14)])].
% 4.37/4.65 13496 multiply(a,multiply(a,multiply(c_0,A))) = multiply(c_0,A). [para(13454(a,1),7(a,1,1)),rewrite([7(7)]),flip(a)].
% 4.37/4.65 13505 multiply(a,add(b,add(multiply(a,c_0),multiply(c_0,additive_inverse(a))))) = c_0. [para(13454(a,1),1502(a,2)),rewrite([6(11,R),3(10)])].
% 4.37/4.65 13790 multiply(c_0,multiply(b,c_0)) = multiply(a,c_0). [para(13461(a,1),13496(a,1,2)),flip(a)].
% 4.37/4.65 13894 multiply(c_0,add(A,multiply(b,c_0))) = add(multiply(a,c_0),multiply(c_0,A)). [para(13790(a,1),9(a,1,1)),rewrite([3(11)]),flip(a)].
% 4.37/4.65 14187 add(multiply(a,c_0),multiply(c_0,additive_inverse(a))) = additive_identity. [para(13350(a,1),17(a,1,2,2,2)),rewrite([385(10),385(9),385(3),13894(9)]),flip(a)].
% 4.37/4.65 14203 multiply(a,b) = c_0. [back_rewrite(13505),rewrite([14187(10),3(4),2268(4)])].
% 4.37/4.65 14204 $F # answer(prove_commutativity). [resolve(14203,a,15,a)].
% 4.37/4.65
% 4.37/4.65 % SZS output end Refutation
% 4.37/4.65 ============================== end of proof ==========================
% 4.37/4.65
% 4.37/4.65 ============================== STATISTICS ============================
% 4.37/4.65
% 4.37/4.65 Given=657. Generated=109687. Kept=14199. proofs=1.
% 4.37/4.65 Usable=542. Sos=9998. Demods=9211. Limbo=16, Disabled=3651. Hints=0.
% 4.37/4.65 Megabytes=19.04.
% 4.37/4.65 User_CPU=3.68, System_CPU=0.08, Wall_clock=4.
% 4.37/4.65
% 4.37/4.65 ============================== end of statistics =====================
% 4.37/4.65
% 4.37/4.65 ============================== end of search =========================
% 4.37/4.65
% 4.37/4.65 THEOREM PROVED
% 4.37/4.65 % SZS status Unsatisfiable
% 4.37/4.65
% 4.37/4.65 Exiting with 1 proof.
% 4.37/4.65
% 4.37/4.65 Process 32070 exit (max_proofs) Mon May 30 16:43:43 2022
% 4.37/4.65 Prover9 interrupted
%------------------------------------------------------------------------------