TSTP Solution File: TOP050-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : TOP050-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 21 21:33:55 EDT 2022
% Result : Unsatisfiable 0.82s 1.31s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : TOP050-1 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun May 29 03:52:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.82/1.31 ============================== Prover9 ===============================
% 0.82/1.31 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.31 Process 25573 was started by sandbox on n029.cluster.edu,
% 0.82/1.31 Sun May 29 03:52:13 2022
% 0.82/1.31 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25409_n029.cluster.edu".
% 0.82/1.31 ============================== end of head ===========================
% 0.82/1.31
% 0.82/1.31 ============================== INPUT =================================
% 0.82/1.31
% 0.82/1.31 % Reading from file /tmp/Prover9_25409_n029.cluster.edu
% 0.82/1.31
% 0.82/1.31 set(prolog_style_variables).
% 0.82/1.31 set(auto2).
% 0.82/1.31 % set(auto2) -> set(auto).
% 0.82/1.31 % set(auto) -> set(auto_inference).
% 0.82/1.31 % set(auto) -> set(auto_setup).
% 0.82/1.31 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.31 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.31 % set(auto) -> set(auto_limits).
% 0.82/1.31 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.31 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.31 % set(auto) -> set(auto_denials).
% 0.82/1.31 % set(auto) -> set(auto_process).
% 0.82/1.31 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.31 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.31 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.31 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.31 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.31 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.31 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.31 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.31 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.31 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.31 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.31 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.31 % set(auto2) -> assign(stats, some).
% 0.82/1.31 % set(auto2) -> clear(echo_input).
% 0.82/1.31 % set(auto2) -> set(quiet).
% 0.82/1.31 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.31 % set(auto2) -> clear(print_given).
% 0.82/1.31 assign(lrs_ticks,-1).
% 0.82/1.31 assign(sos_limit,10000).
% 0.82/1.31 assign(order,kbo).
% 0.82/1.31 set(lex_order_vars).
% 0.82/1.31 clear(print_given).
% 0.82/1.31
% 0.82/1.31 % formulas(sos). % not echoed (35 formulas)
% 0.82/1.31
% 0.82/1.31 ============================== end of input ==========================
% 0.82/1.31
% 0.82/1.31 % From the command line: assign(max_seconds, 300).
% 0.82/1.31
% 0.82/1.31 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.31
% 0.82/1.31 % Formulas that are not ordinary clauses:
% 0.82/1.31
% 0.82/1.31 ============================== end of process non-clausal formulas ===
% 0.82/1.31
% 0.82/1.31 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.31
% 0.82/1.31 ============================== PREDICATE ELIMINATION =================
% 0.82/1.31
% 0.82/1.31 ============================== end predicate elimination =============
% 0.82/1.31
% 0.82/1.31 Auto_denials:
% 0.82/1.31 % copying label goal to answer in negative clause
% 0.82/1.31
% 0.82/1.31 Term ordering decisions:
% 0.82/1.31 Function symbol KB weights: a19=1. a21=1. a3=1. a5=1. a1=1. a11=1. a15=1. a17=1. a23=1. a25=1. a29=1. a31=1. a7=1. a9=1. a10=1. a12=1. a13=1. a14=1. a16=1. a18=1. a2=1. a20=1. a22=1. a24=1. a26=1. a27=1. a28=1. a30=1. a32=1. a4=1. a8=1. a6=1. product=1. tuple=1.
% 0.82/1.31
% 0.82/1.31 ============================== end of process initial clauses ========
% 0.82/1.31
% 0.82/1.31 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.31
% 0.82/1.31 ============================== end of clauses for search =============
% 0.82/1.31
% 0.82/1.31 ============================== SEARCH ================================
% 0.82/1.31
% 0.82/1.31 % Starting search at 0.01 seconds.
% 0.82/1.31
% 0.82/1.31 ============================== PROOF =================================
% 0.82/1.31 % SZS status Unsatisfiable
% 0.82/1.31 % SZS output start Refutation
% 0.82/1.31
% 0.82/1.31 % Proof 1 at 0.22 (+ 0.01) seconds: goal.
% 0.82/1.31 % Length of proof is 296.
% 0.82/1.31 % Level of proof is 34.
% 0.82/1.31 % Maximum clause weight is 65.000.
% 0.82/1.31 % Given clauses 275.
% 0.82/1.31
% 0.82/1.31 1 product(A,A) = A # label(involutory_quandle) # label(axiom). [assumption].
% 0.82/1.31 2 product(a1,a31) = a2 # label(knot) # label(axiom). [assumption].
% 0.82/1.31 3 product(a2,a25) = a3 # label(knot_03) # label(axiom). [assumption].
% 0.82/1.31 4 product(a3,a29) = a4 # label(knot_04) # label(axiom). [assumption].
% 0.82/1.31 5 product(a4,a11) = a5 # label(knot_05) # label(axiom). [assumption].
% 0.82/1.31 6 product(a5,a15) = a6 # label(knot_06) # label(axiom). [assumption].
% 0.82/1.31 7 product(a7,a19) = a8 # label(knot_07) # label(axiom). [assumption].
% 0.82/1.31 8 product(a8,a5) = a9 # label(knot_08) # label(axiom). [assumption].
% 0.82/1.31 9 product(a9,a17) = a10 # label(knot_09) # label(axiom). [assumption].
% 0.82/1.31 10 product(a10,a7) = a11 # label(knot_10) # label(axiom). [assumption].
% 0.82/1.31 11 product(a11,a5) = a12 # label(knot_11) # label(axiom). [assumption].
% 0.82/1.31 12 product(a12,a19) = a13 # label(knot_12) # label(axiom). [assumption].
% 0.82/1.31 13 product(a13,a7) = a14 # label(knot_13) # label(axiom). [assumption].
% 0.82/1.31 14 product(a14,a17) = a15 # label(knot_14) # label(axiom). [assumption].
% 0.82/1.31 15 product(a15,a5) = a16 # label(knot_15) # label(axiom). [assumption].
% 0.82/1.31 16 product(a16,a19) = a17 # label(knot_16) # label(axiom). [assumption].
% 0.82/1.31 17 product(a17,a9) = a18 # label(knot_17) # label(axiom). [assumption].
% 0.82/1.31 18 product(a18,a15) = a19 # label(knot_18) # label(axiom). [assumption].
% 0.82/1.31 19 product(a19,a11) = a20 # label(knot_19) # label(axiom). [assumption].
% 0.82/1.31 20 product(a20,a29) = a21 # label(knot_20) # label(axiom). [assumption].
% 0.82/1.31 21 product(a21,a25) = a22 # label(knot_21) # label(axiom). [assumption].
% 0.82/1.31 22 product(a22,a31) = a23 # label(knot_22) # label(axiom). [assumption].
% 0.82/1.31 23 product(a23,a21) = a24 # label(knot_23) # label(axiom). [assumption].
% 0.82/1.31 24 product(a24,a3) = a25 # label(knot_24) # label(axiom). [assumption].
% 0.82/1.31 25 product(a25,a23) = a26 # label(knot_25) # label(axiom). [assumption].
% 0.82/1.31 26 product(a26,a1) = a27 # label(knot_26) # label(axiom). [assumption].
% 0.82/1.31 27 product(a27,a21) = a28 # label(knot_27) # label(axiom). [assumption].
% 0.82/1.31 28 product(a28,a3) = a29 # label(knot_28) # label(axiom). [assumption].
% 0.82/1.31 29 product(a29,a1) = a30 # label(knot_29) # label(axiom). [assumption].
% 0.82/1.31 30 product(a30,a23) = a31 # label(knot_30) # label(axiom). [assumption].
% 0.82/1.31 31 product(a31,a3) = a32 # label(knot_31) # label(axiom). [assumption].
% 0.82/1.31 32 product(a32,a21) = a1 # label(knot_32) # label(axiom). [assumption].
% 0.82/1.31 33 product(product(A,B),B) = A # label(involutory_quandle_01) # label(axiom). [assumption].
% 0.82/1.31 34 product(product(A,B),C) = product(product(A,C),product(B,C)) # label(involutory_quandle_02) # label(axiom). [assumption].
% 0.82/1.31 35 product(product(A,B),product(C,B)) = product(product(A,C),B). [copy(34),flip(a)].
% 0.82/1.31 36 tuple(a1,a30,a31,a2,a24,a25,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a23,a26,a27) != tuple(a2,a31,a32,a3,a25,a26,a4,a29,a30,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a23,a24,a27,a28) # label(goal) # label(negated_conjecture) # answer(goal). [assumption].
% 0.82/1.31 37 tuple(a2,a31,a32,a3,a25,a26,a4,a29,a30,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a23,a24,a27,a28) != tuple(a1,a30,a31,a2,a24,a25,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a23,a26,a27) # answer(goal). [copy(36),flip(a)].
% 0.82/1.31 38 product(a2,a31) = a1. [para(2(a,1),33(a,1,1))].
% 0.82/1.31 39 product(a3,a25) = a2. [para(3(a,1),33(a,1,1))].
% 0.82/1.31 40 product(a4,a29) = a3. [para(4(a,1),33(a,1,1))].
% 0.82/1.31 43 product(a8,a19) = a7. [para(7(a,1),33(a,1,1))].
% 0.82/1.31 45 product(a10,a17) = a9. [para(9(a,1),33(a,1,1))].
% 0.82/1.31 46 product(a11,a7) = a10. [para(10(a,1),33(a,1,1))].
% 0.82/1.31 47 product(a12,a5) = a11. [para(11(a,1),33(a,1,1))].
% 0.82/1.31 48 product(a13,a19) = a12. [para(12(a,1),33(a,1,1))].
% 0.82/1.31 50 product(a15,a17) = a14. [para(14(a,1),33(a,1,1))].
% 0.82/1.31 51 product(a16,a5) = a15. [para(15(a,1),33(a,1,1))].
% 0.82/1.31 52 product(a17,a19) = a16. [para(16(a,1),33(a,1,1))].
% 0.82/1.31 53 product(a18,a9) = a17. [para(17(a,1),33(a,1,1))].
% 0.82/1.31 54 product(a19,a15) = a18. [para(18(a,1),33(a,1,1))].
% 0.82/1.31 55 product(a20,a11) = a19. [para(19(a,1),33(a,1,1))].
% 0.82/1.31 56 product(a21,a29) = a20. [para(20(a,1),33(a,1,1))].
% 0.82/1.31 57 product(a22,a25) = a21. [para(21(a,1),33(a,1,1))].
% 0.82/1.31 58 product(a23,a31) = a22. [para(22(a,1),33(a,1,1))].
% 0.82/1.31 59 product(a24,a21) = a23. [para(23(a,1),33(a,1,1))].
% 0.82/1.31 60 product(a25,a3) = a24. [para(24(a,1),33(a,1,1))].
% 0.82/1.31 61 product(a26,a23) = a25. [para(25(a,1),33(a,1,1))].
% 0.82/1.31 62 product(a27,a1) = a26. [para(26(a,1),33(a,1,1))].
% 0.82/1.31 64 product(a29,a3) = a28. [para(28(a,1),33(a,1,1))].
% 0.82/1.31 65 product(a30,a1) = a29. [para(29(a,1),33(a,1,1))].
% 0.82/1.31 66 product(a31,a23) = a30. [para(30(a,1),33(a,1,1))].
% 0.82/1.31 67 product(a32,a3) = a31. [para(31(a,1),33(a,1,1))].
% 0.82/1.31 68 product(a1,a21) = a32. [para(32(a,1),33(a,1,1))].
% 0.82/1.31 69 product(product(A,B),A) = product(A,product(B,A)). [para(1(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 70 product(product(a1,A),a31) = product(a2,product(A,a31)). [para(2(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 71 product(product(A,a31),a2) = product(product(A,a1),a31). [para(2(a,1),35(a,1,2))].
% 0.82/1.31 72 product(product(a2,A),a25) = product(a3,product(A,a25)). [para(3(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 77 product(product(A,a4),a11) = product(product(A,a11),a5). [para(5(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 80 product(product(a7,A),a19) = product(a8,product(A,a19)). [para(7(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 81 product(product(A,a7),a19) = product(product(A,a19),a8). [para(7(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 82 product(product(a8,A),a5) = product(a9,product(A,a5)). [para(8(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 83 product(product(A,a8),a5) = product(product(A,a5),a9). [para(8(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 84 product(product(a9,A),a17) = product(a10,product(A,a17)). [para(9(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 88 product(product(a11,A),a5) = product(a12,product(A,a5)). [para(11(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 89 product(product(A,a11),a5) = product(product(A,a5),a12). [para(11(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 90 product(product(a12,A),a19) = product(a13,product(A,a19)). [para(12(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 92 product(product(a13,A),a7) = product(a14,product(A,a7)). [para(13(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 93 product(product(A,a13),a7) = product(product(A,a7),a14). [para(13(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 96 product(product(a15,A),a5) = product(a16,product(A,a5)). [para(15(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 98 product(product(a16,A),a19) = product(a17,product(A,a19)). [para(16(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 101 product(product(A,a9),a18) = product(product(A,a17),a9). [para(17(a,1),35(a,1,2))].
% 0.82/1.31 102 product(product(a18,A),a15) = product(a19,product(A,a15)). [para(18(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 103 product(product(A,a18),a15) = product(product(A,a15),a19). [para(18(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 104 product(product(a19,A),a11) = product(a20,product(A,a11)). [para(19(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 106 product(product(a20,A),a29) = product(a21,product(A,a29)). [para(20(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 108 product(product(a21,A),a25) = product(a22,product(A,a25)). [para(21(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 109 product(product(A,a25),a22) = product(product(A,a21),a25). [para(21(a,1),35(a,1,2))].
% 0.82/1.31 110 product(product(a22,A),a31) = product(a23,product(A,a31)). [para(22(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 111 product(product(A,a22),a31) = product(product(A,a31),a23). [para(22(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 112 product(product(a23,A),a21) = product(a24,product(A,a21)). [para(23(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 113 product(product(A,a23),a21) = product(product(A,a21),a24). [para(23(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 115 product(product(A,a24),a3) = product(product(A,a3),a25). [para(24(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 116 product(product(a25,A),a23) = product(a26,product(A,a23)). [para(25(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 117 product(product(A,a25),a23) = product(product(A,a23),a26). [para(25(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 118 product(product(a26,A),a1) = product(a27,product(A,a1)). [para(26(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 120 product(product(a27,A),a21) = product(a28,product(A,a21)). [para(27(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 122 product(product(a28,A),a3) = product(a29,product(A,a3)). [para(28(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 124 product(product(a29,A),a1) = product(a30,product(A,a1)). [para(29(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 125 product(product(A,a29),a1) = product(product(A,a1),a30). [para(29(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 127 product(product(A,a30),a23) = product(product(A,a23),a31). [para(30(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 129 product(product(A,a31),a3) = product(product(A,a3),a32). [para(31(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 130 product(product(a32,A),a21) = product(a1,product(A,a21)). [para(32(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 131 product(product(A,a32),a21) = product(product(A,a21),a1). [para(32(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 132 product(product(product(A,B),C),B) = product(A,product(C,B)). [para(33(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 133 product(product(A,product(B,C)),C) = product(product(A,C),B). [para(33(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 136 product(product(A,a4),a11) = product(product(A,a5),a12). [back_rewrite(77),rewrite([89(8)])].
% 0.82/1.31 137 product(product(a2,A),a31) = product(a1,product(A,a31)). [para(38(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 138 product(product(A,a2),a31) = product(product(A,a31),a1). [para(38(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 139 product(product(a3,A),a25) = product(a2,product(A,a25)). [para(39(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 140 product(product(A,a25),a2) = product(product(A,a3),a25). [para(39(a,1),35(a,1,2))].
% 0.82/1.31 148 product(product(A,a8),a19) = product(product(A,a19),a7). [para(43(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 151 product(product(a10,A),a17) = product(a9,product(A,a17)). [para(45(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 158 product(product(A,a13),a19) = product(product(A,a19),a12). [para(48(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 165 product(product(a17,A),a19) = product(a16,product(A,a19)). [para(52(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 172 product(product(A,a20),a11) = product(product(A,a11),a19). [para(55(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 178 product(product(A,a31),a22) = product(product(A,a23),a31). [para(58(a,1),35(a,1,2))].
% 0.82/1.31 180 product(product(A,a24),a21) = product(product(A,a21),a23). [para(59(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 181 product(product(a25,A),a3) = product(a24,product(A,a3)). [para(60(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 182 product(product(A,a25),a3) = product(product(A,a3),a24). [para(60(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 187 product(product(A,a27),a1) = product(product(A,a1),a26). [para(62(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 194 product(product(A,a30),a1) = product(product(A,a1),a29). [para(65(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 196 product(product(A,a31),a23) = product(product(A,a23),a30). [para(66(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 197 product(product(A,a22),a31) = product(product(A,a23),a30). [back_rewrite(111),rewrite([196(8)])].
% 0.82/1.31 200 product(product(a1,A),a21) = product(a32,product(A,a21)). [para(68(a,1),35(a,1,1)),flip(a)].
% 0.82/1.31 201 product(product(A,a1),a21) = product(product(A,a21),a32). [para(68(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 204 product(a4,a3) = product(a3,a28). [para(4(a,1),69(a,1,1)),rewrite([64(7)])].
% 0.82/1.31 211 product(a10,a9) = product(a9,a18). [para(9(a,1),69(a,1,1)),rewrite([17(7)])].
% 0.82/1.31 212 product(a18,a17) = product(a17,a10). [para(9(a,1),69(a,2,2)),rewrite([17(3)])].
% 0.82/1.31 220 product(a18,product(a15,a18)) = product(a19,a18). [para(18(a,1),69(a,1,1)),flip(a)].
% 0.82/1.31 223 product(a21,product(a25,a21)) = product(a22,a21). [para(21(a,1),69(a,1,1)),flip(a)].
% 0.82/1.31 224 product(a22,product(a31,a22)) = product(a23,a22). [para(22(a,1),69(a,1,1)),flip(a)].
% 0.82/1.31 240 product(a2,a3) = product(a3,a24). [para(39(a,1),69(a,1,1)),rewrite([60(7)])].
% 0.82/1.31 246 product(a10,product(a17,a10)) = product(a9,a10). [para(45(a,1),69(a,1,1)),flip(a)].
% 0.82/1.31 249 product(a13,product(a19,a13)) = product(a12,a13). [para(48(a,1),69(a,1,1)),flip(a)].
% 0.82/1.31 254 product(a18,product(a9,a18)) = product(a17,a18). [para(53(a,1),69(a,1,1)),flip(a)].
% 0.82/1.31 255 product(a19,product(a15,a19)) = product(a18,a19). [para(54(a,1),69(a,1,1)),flip(a)].
% 0.82/1.31 256 product(a20,product(a11,a20)) = product(a19,a20). [para(55(a,1),69(a,1,1)),flip(a)].
% 0.82/1.31 258 product(a22,product(a25,a22)) = product(a21,a22). [para(57(a,1),69(a,1,1)),flip(a)].
% 0.82/1.31 260 product(a30,a31) = product(a31,a22). [para(58(a,1),69(a,2,2)),rewrite([66(3)])].
% 0.82/1.31 263 product(a27,product(a1,a27)) = product(a26,a27). [para(62(a,1),69(a,1,1)),flip(a)].
% 0.82/1.31 281 product(a2,product(a21,a31)) = product(a32,a31). [para(68(a,1),70(a,1,1)),flip(a)].
% 0.82/1.31 288 product(product(a9,a18),a10) = product(a10,product(a9,a10)). [para(211(a,1),69(a,1,1))].
% 0.82/1.31 358 product(product(a15,a19),a18) = product(a15,product(a15,a18)). [para(220(a,1),69(a,2,2)),rewrite([33(5),35(12)]),flip(a)].
% 0.82/1.31 374 product(product(A,product(a31,a22)),product(a23,a22)) = product(product(A,a23),a31). [para(224(a,1),35(a,1,2)),rewrite([35(14),178(12)])].
% 0.82/1.31 425 product(product(a10,a19),a8) = product(a11,a19). [para(10(a,1),81(a,1,1)),flip(a)].
% 0.82/1.31 426 product(a14,a19) = product(a12,a8). [para(13(a,1),81(a,1,1)),rewrite([48(6)])].
% 0.82/1.31 445 product(a9,product(a19,a5)) = product(a7,a5). [para(43(a,1),82(a,1,1)),flip(a)].
% 0.82/1.31 482 product(a9,product(a9,a18)) = product(a10,a18). [para(254(a,1),69(a,2,2)),rewrite([33(5),35(12),9(8)])].
% 0.82/1.31 497 product(product(A,product(a25,a22)),product(a21,a22)) = product(product(A,a21),a25). [para(258(a,1),35(a,1,2)),rewrite([35(14),109(12)])].
% 0.82/1.31 536 product(product(a32,a31),product(A,product(a21,a31))) = product(product(a2,A),product(a21,a31)). [para(281(a,1),35(a,1,1))].
% 0.82/1.31 538 product(a3,product(a22,product(a31,a25))) = product(product(a32,a31),a25). [para(281(a,1),72(a,1,1)),rewrite([108(11)]),flip(a)].
% 0.82/1.31 548 product(a12,product(a7,a5)) = product(a10,a5). [para(46(a,1),88(a,1,1)),flip(a)].
% 0.82/1.31 566 product(product(a19,a5),a12) = product(a20,a5). [para(19(a,1),89(a,1,1)),flip(a)].
% 0.82/1.31 589 product(a13,product(a5,a19)) = product(a11,a19). [para(47(a,1),90(a,1,1)),flip(a)].
% 0.82/1.31 601 product(product(product(a10,a19),a5),a9) = product(a12,product(a19,a5)). [para(425(a,1),83(a,1,1)),rewrite([88(5)]),flip(a)].
% 0.82/1.31 626 product(a14,product(product(a19,a7),a14)) = product(product(a12,a7),a14). [para(249(a,1),92(a,1,1)),rewrite([93(5),93(11)]),flip(a)].
% 0.82/1.31 638 product(a10,product(a9,a10)) = product(a9,product(a17,a10)). [para(482(a,1),84(a,1,1)),rewrite([151(5),212(4),84(11),212(10),246(11)]),flip(a)].
% 0.82/1.31 639 product(product(a9,a18),a10) = product(a9,product(a17,a10)). [back_rewrite(288),rewrite([638(10)])].
% 0.82/1.31 652 product(a13,product(a8,product(a5,a19))) = product(product(a10,a5),a19). [para(548(a,1),90(a,1,1)),rewrite([80(11)]),flip(a)].
% 0.82/1.31 666 product(product(A,product(a5,a19)),product(a11,a19)) = product(product(A,a13),product(a5,a19)). [para(589(a,1),35(a,1,2))].
% 0.82/1.31 678 product(a16,product(a17,a5)) = product(a14,a5). [para(50(a,1),96(a,1,1)),flip(a)].
% 0.82/1.31 702 product(a17,product(a16,product(a5,a19))) = product(product(a14,a5),a19). [para(678(a,1),98(a,1,1)),rewrite([165(11)]),flip(a)].
% 0.82/1.31 728 product(product(a17,a10),a15) = product(a19,product(a17,a15)). [para(212(a,1),102(a,1,1))].
% 0.82/1.31 740 product(product(product(A,a9),a15),a19) = product(product(product(A,a17),a9),a15). [para(101(a,1),103(a,1,1)),flip(a)].
% 0.82/1.31 745 product(a20,product(product(a15,a19),a11)) = product(product(a18,a19),a11). [para(255(a,1),104(a,1,1)),flip(a)].
% 0.82/1.31 761 product(a21,product(a11,a29)) = product(a19,a29). [para(55(a,1),106(a,1,1)),flip(a)].
% 0.82/1.31 784 product(a22,product(a29,a25)) = product(a20,a25). [para(56(a,1),108(a,1,1)),flip(a)].
% 0.82/1.31 787 product(a22,product(product(a11,a29),a25)) = product(product(a19,a29),a25). [para(761(a,1),108(a,1,1)),flip(a)].
% 0.82/1.31 807 product(a23,product(a25,a31)) = product(a21,a31). [para(57(a,1),110(a,1,1)),flip(a)].
% 0.82/1.31 811 product(a23,product(product(a29,a25),a31)) = product(product(a20,a25),a31). [para(784(a,1),110(a,1,1)),flip(a)].
% 0.82/1.31 814 product(a24,product(a31,a21)) = product(a22,a21). [para(58(a,1),112(a,1,1)),flip(a)].
% 0.82/1.31 824 product(product(a25,a21),a24) = product(a26,a21). [para(25(a,1),113(a,1,1)),flip(a)].
% 0.82/1.31 829 product(product(a31,a21),a24) = product(a30,a21). [para(66(a,1),113(a,1,1)),flip(a)].
% 0.82/1.31 833 product(product(A,product(a25,a21)),a24) = product(product(A,a24),product(a26,a21)). [para(824(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 845 product(product(A,product(a31,a21)),a24) = product(product(A,a24),product(a30,a21)). [para(829(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 852 product(product(a24,product(a21,a3)),a25) = product(product(a26,a21),a3). [para(824(a,1),115(a,1,1)),rewrite([181(10)]),flip(a)].
% 0.82/1.31 858 product(a26,product(a3,a23)) = product(a24,a23). [para(60(a,1),116(a,1,1)),flip(a)].
% 0.82/1.31 884 product(a27,product(product(a3,a23),a1)) = product(product(a24,a23),a1). [para(858(a,1),118(a,1,1)),flip(a)].
% 0.82/1.31 903 product(a28,a32) = product(a26,a21). [para(62(a,1),120(a,1,1)),rewrite([68(7)]),flip(a)].
% 0.82/1.31 919 product(product(a26,a21),a3) = product(a29,a31). [para(67(a,1),122(a,2,2)),rewrite([903(3)])].
% 0.82/1.31 923 product(product(a24,product(a21,a3)),a25) = product(a29,a31). [back_rewrite(852),rewrite([919(12)])].
% 0.82/1.31 935 product(a30,product(a3,a1)) = product(a28,a1). [para(64(a,1),124(a,1,1)),flip(a)].
% 0.82/1.31 939 product(product(a3,a1),a30) = product(a4,a1). [para(4(a,1),125(a,1,1)),flip(a)].
% 0.82/1.31 943 product(product(a4,a1),a30) = product(a3,a1). [para(40(a,1),125(a,1,1)),flip(a)].
% 0.82/1.31 953 product(product(A,product(a3,a1)),a30) = product(product(A,a30),product(a4,a1)). [para(939(a,1),35(a,1,2)),flip(a)].
% 0.82/1.31 976 product(product(product(a4,a1),a23),a31) = product(product(a3,a1),a23). [para(943(a,1),127(a,1,1)),flip(a)].
% 0.82/1.31 984 product(product(a1,a3),a32) = product(a3,a24). [para(2(a,1),129(a,1,1)),rewrite([240(3)]),flip(a)].
% 0.82/1.31 988 product(product(a3,a24),a32) = product(a1,a3). [para(38(a,1),129(a,1,1)),rewrite([240(6)]),flip(a)].
% 0.82/1.31 1005 product(a1,product(a3,a21)) = product(a31,a21). [para(67(a,1),130(a,1,1)),flip(a)].
% 0.82/1.31 1012 product(product(A,product(a3,a21)),product(a31,a21)) = product(product(A,a1),product(a3,a21)). [para(1005(a,1),35(a,1,2))].
% 0.82/1.31 1017 product(product(a32,product(a3,a21)),a1) = product(product(a3,a21),a23). [para(984(a,1),131(a,1,1)),rewrite([180(5),200(10)]),flip(a)].
% 0.82/1.31 1019 product(product(product(a3,a21),a23),a1) = product(a32,product(a3,a21)). [para(988(a,1),131(a,1,1)),rewrite([200(5),180(10)]),flip(a)].
% 0.82/1.31 1021 product(product(product(A,a5),a12),a11) = product(A,a4). [para(136(a,1),33(a,1,1))].
% 0.82/1.31 1033 product(product(product(A,a23),a30),a31) = product(A,a22). [para(58(a,1),132(a,2,2)),rewrite([196(4)])].
% 0.82/1.31 1170 product(product(product(A,a1),a26),product(a1,a27)) = product(A,product(a26,a27)). [para(263(a,1),132(a,2,2)),rewrite([133(6),187(4)])].
% 0.82/1.31 1258 product(product(product(A,a15),a19),a18) = product(A,product(a15,a18)). [para(103(a,1),132(a,1,1))].
% 0.82/1.31 1298 product(product(product(A,a23),a26),a25) = product(A,product(a23,a25)). [para(117(a,1),132(a,1,1))].
% 0.82/1.31 1323 product(product(product(A,a30),product(a4,a1)),product(a3,a1)) = product(A,product(a28,a1)). [para(935(a,1),132(a,2,2)),rewrite([953(6)])].
% 0.82/1.31 1348 product(a1,product(a25,a31)) = product(a3,a31). [para(3(a,1),137(a,1,1)),flip(a)].
% 0.82/1.31 1355 product(product(product(a2,A),a3),a32) = product(product(a1,product(A,a31)),a3). [para(137(a,1),129(a,1,1)),flip(a)].
% 0.82/1.31 1359 product(product(product(a3,a31),A),product(a25,a31)) = product(a1,product(A,product(a25,a31))). [para(1348(a,1),132(a,1,1,1))].
% 0.82/1.31 1366 product(a2,product(a29,a25)) = product(a4,a25). [para(4(a,1),139(a,1,1)),flip(a)].
% 0.82/1.31 1406 product(product(A,product(a22,a21)),product(a25,a21)) = product(product(A,a21),a25). [para(223(a,1),133(a,1,1,2)),rewrite([133(14)])].
% 0.82/1.31 1437 product(product(A,product(a19,a20)),product(a11,a20)) = product(product(A,a11),a19). [para(256(a,1),133(a,1,1,2)),rewrite([133(14),172(12)])].
% 0.82/1.31 1490 product(product(A,product(a19,a29)),product(a11,a29)) = product(product(A,product(a11,a29)),a21). [para(761(a,1),133(a,1,1,2))].
% 0.82/1.31 1495 product(product(A,product(a22,a21)),product(a31,a21)) = product(product(A,a24),product(a30,a21)). [para(814(a,1),133(a,1,1,2)),rewrite([845(14)])].
% 0.82/1.31 1522 product(a1,product(product(a29,a25),a31)) = product(product(a4,a25),a31). [para(1366(a,1),137(a,1,1)),flip(a)].
% 0.82/1.31 1526 product(product(a24,product(A,a3)),a25) = product(product(a25,product(A,a25)),a2). [para(69(a,1),140(a,1,1)),rewrite([181(10)]),flip(a)].
% 0.82/1.31 1533 product(product(a25,a22),a2) = product(a29,a31). [back_rewrite(923),rewrite([1526(7),21(4)])].
% 0.82/1.31 1534 product(a31,a22) = product(a25,a22). [para(1533(a,1),33(a,1,1)),rewrite([71(5),29(3),260(3)])].
% 0.82/1.31 1539 product(a27,a29) = a29. [para(1533(a,1),138(a,1,1)),rewrite([33(5),197(6),25(4),194(6),26(4)]),flip(a)].
% 0.82/1.31 1555 product(product(A,product(a25,a22)),product(a23,a22)) = product(product(A,a23),a31). [back_rewrite(374),rewrite([1534(3)])].
% 0.82/1.31 1561 product(a23,a22) = product(a21,a22). [back_rewrite(224),rewrite([1534(4),258(5)]),flip(a)].
% 0.82/1.31 1564 product(product(A,a23),a31) = product(product(A,a21),a25). [back_rewrite(1555),rewrite([1561(7),497(8)]),flip(a)].
% 0.82/1.31 1576 product(product(product(a4,a21),a32),a25) = product(product(a3,a1),a23). [back_rewrite(976),rewrite([1564(7),201(5)])].
% 0.82/1.31 1590 a27 = a29. [para(1539(a,1),33(a,1,1)),rewrite([1(3)]),flip(a)].
% 0.82/1.31 1612 product(product(product(A,a1),a26),product(a1,a29)) = product(A,product(a26,a29)). [back_rewrite(1170),rewrite([1590(6),1590(10)])].
% 0.82/1.31 1637 product(a29,product(product(a3,a23),a1)) = product(product(a24,a23),a1). [back_rewrite(884),rewrite([1590(1)])].
% 0.82/1.31 1669 a30 = a26. [back_rewrite(62),rewrite([1590(1),29(3)])].
% 0.82/1.31 1670 tuple(a2,a31,a32,a3,a25,a26,a4,a29,a26,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a23,a24,a29,a28) != tuple(a1,a26,a31,a2,a24,a25,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a23,a26,a29) # answer(goal). [back_rewrite(37),rewrite([1669(9),1590(30),1669(34),1590(63)])].
% 0.82/1.31 1671 product(a29,a21) = a28. [back_rewrite(27),rewrite([1590(1)])].
% 0.82/1.31 1672 product(a26,a1) = a29. [back_rewrite(26),rewrite([1590(4)])].
% 0.82/1.31 1711 product(product(a3,a1),a26) = product(a4,a1). [back_rewrite(939),rewrite([1669(4)])].
% 0.82/1.31 1769 product(product(A,product(a22,a21)),product(a31,a21)) = product(product(A,a24),product(a26,a21)). [back_rewrite(1495),rewrite([1669(11)])].
% 0.82/1.31 1775 product(product(product(A,a26),product(a4,a1)),product(a3,a1)) = product(A,product(a28,a1)). [back_rewrite(1323),rewrite([1669(1)])].
% 0.82/1.31 1782 product(product(product(A,a23),a26),a31) = product(A,a22). [back_rewrite(1033),rewrite([1669(3)])].
% 0.82/1.31 1841 a31 = a25. [back_rewrite(30),rewrite([1669(1),61(3)]),flip(a)].
% 0.82/1.31 1842 product(a29,a1) = a26. [back_rewrite(29),rewrite([1669(4)])].
% 0.82/1.31 1866 product(product(A,a24),product(a26,a21)) = product(product(A,a21),a25). [back_rewrite(1769),rewrite([1841(5),1406(8)]),flip(a)].
% 0.82/1.31 1871 product(product(A,product(a3,a21)),product(a25,a21)) = product(product(A,a1),product(a3,a21)). [back_rewrite(1012),rewrite([1841(5)])].
% 0.82/1.31 1896 product(A,product(a23,a25)) = product(A,a22). [back_rewrite(1782),rewrite([1841(5),1298(6)])].
% 0.82/1.31 1908 tuple(a2,a25,a32,a3,a25,a26,a4,a29,a26,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a23,a24,a29,a28) != tuple(a1,a26,a25,a2,a24,a25,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a23,a26,a29) # answer(goal). [back_rewrite(1670),rewrite([1841(2),1841(35)])].
% 0.82/1.31 1916 product(a1,a29) = a4. [back_rewrite(1522),rewrite([1841(5),33(6),1841(7),33(8)])].
% 0.82/1.31 1930 product(a1,product(A,a25)) = product(a3,product(A,a25)). [back_rewrite(1359),rewrite([1841(2),39(3),1841(4),1(5),72(4),1841(7),1(8)]),flip(a)].
% 0.82/1.31 1932 product(product(product(a2,A),a3),a32) = product(a3,product(product(A,a3),a24)). [back_rewrite(1355),rewrite([1841(8),1930(10),69(12),182(11)])].
% 0.82/1.31 1935 product(a1,a25) = a2. [back_rewrite(1348),rewrite([1841(3),1(4),1841(5),39(6)])].
% 0.82/1.31 1965 product(a23,a29) = a20. [back_rewrite(811),rewrite([1841(5),33(6),1841(7),33(8)])].
% 0.82/1.31 1968 product(a23,a25) = a22. [back_rewrite(807),rewrite([1841(3),1(4),1841(5),21(6)])].
% 0.82/1.31 1972 product(a3,a21) = a32. [back_rewrite(538),rewrite([1841(3),1(5),57(4),1841(5),33(8)])].
% 0.82/1.31 1974 product(product(a32,a25),product(A,a22)) = product(product(a2,A),a22). [back_rewrite(536),rewrite([1841(2),1841(5),21(6),1841(10),21(11)])].
% 0.82/1.31 1994 a1 = a3. [back_rewrite(38),rewrite([1841(2),3(3)]),flip(a)].
% 0.82/1.31 1995 a32 = a24. [back_rewrite(31),rewrite([1841(1),60(3)]),flip(a)].
% 0.82/1.31 1996 a23 = a21. [back_rewrite(22),rewrite([1841(2),57(3)]),flip(a)].
% 0.82/1.31 2010 product(a21,a3) = a24. [back_rewrite(1019),rewrite([1972(3),1995(1),1996(2),59(3),1996(1),1994(2),1995(4),1972(7),1995(5),1(6)])].
% 0.82/1.31 2011 a25 = a21. [back_rewrite(1017),rewrite([1995(1),1972(4),1995(2),1(3),1994(2),24(3),1972(4),1995(2),1996(3),59(4),1996(2)])].
% 0.82/1.31 2012 product(product(A,a24),a21) = A. [back_rewrite(180),rewrite([1996(7),33(8)])].
% 0.82/1.31 2014 a28 = a24. [back_rewrite(1637),rewrite([1996(3),1972(4),1995(2),1994(3),24(4),2011(2),1671(3),1996(3),59(4),1996(2),1994(3),2010(4)])].
% 0.82/1.31 2021 product(product(A,a21),a24) = A. [back_rewrite(833),rewrite([2011(1),1(3),1866(10),2011(7),33(8)])].
% 0.82/1.31 2032 product(product(A,a3),a24) = A. [back_rewrite(1871),rewrite([1972(3),1995(1),2011(3),1(5),2012(4),1994(1),1972(5),1995(3)]),flip(a)].
% 0.82/1.31 2034 a26 = a24. [back_rewrite(1842),rewrite([1994(2),64(3),2014(1)]),flip(a)].
% 0.82/1.31 2040 product(A,a3) = product(A,a21). [back_rewrite(1775),rewrite([2034(1),1994(4),204(5),2014(4),35(6),2032(4),1994(2),1(3),2014(3),1994(4),24(5),2011(3)])].
% 0.82/1.31 2046 product(a4,a21) = product(a3,a24). [back_rewrite(1711),rewrite([1994(2),1(3),2034(2),1994(5),2040(6)]),flip(a)].
% 0.82/1.31 2055 a29 = a21. [back_rewrite(1672),rewrite([2034(1),1994(2),2040(3),59(3),1996(1)]),flip(a)].
% 0.82/1.31 2065 product(A,a24) = product(A,a21). [back_rewrite(1612),rewrite([1994(1),2040(2),2034(3),2021(4),1994(1),2055(2),1972(3),1995(1),2034(3),2055(4),59(5),1996(3)])].
% 0.82/1.31 2067 a24 = a21. [back_rewrite(1576),rewrite([2046(3),2065(3),1972(3),1995(1),1995(2),1(3),2011(2),59(3),1996(1),1994(3),1(4),1996(3),1972(4),1995(2)]),flip(a)].
% 0.82/1.31 2074 product(A,a22) = product(A,a21). [back_rewrite(1896),rewrite([1996(1),2011(2),1(3)]),flip(a)].
% 0.82/1.31 2080 product(product(a2,A),a21) = product(a21,product(A,a21)). [back_rewrite(1974),rewrite([1995(1),2067(1),2011(2),1(3),2074(3),2074(8)]),flip(a)].
% 0.82/1.31 2085 product(a3,A) = product(a21,A). [back_rewrite(1932),rewrite([2040(4),2080(4),1995(5),2067(5),69(6),33(5),2040(5),2067(6),33(7)]),flip(a)].
% 0.82/1.31 2086 a2 = a21. [back_rewrite(1935),rewrite([1994(1),2011(2),2085(3),1(3)]),flip(a)].
% 0.82/1.31 2087 a4 = a21. [back_rewrite(1916),rewrite([1994(1),2055(2),2085(3),1(3)]),flip(a)].
% 0.82/1.31 2088 tuple(a3,a21,a21,a21,a21,a21,a3,a21,a21,a21,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a21,a21,a21) != tuple(a21,a21,a21,a3,a21,a21,a21,a21,a21,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a21,a21,a21,a21) # answer(goal). [back_rewrite(1908),rewrite([2086(1),2011(2),1995(3),2067(3),2011(5),2034(6),2067(6),2087(7),2055(8),2034(9),2067(9),1996(28),2067(29),2055(30),2014(31),2067(31),1994(33),2034(34),2067(34),2011(35),2086(36),2067(37),2011(38),2014(40),2067(40),2055(41),2087(42),1996(61),2034(62),2067(62),2055(63)]),flip(a)].
% 0.82/1.31 2089 a3 = a21. [back_rewrite(988),rewrite([2067(2),2085(3),1(3),1995(2),2067(2),1(3),1994(2),1(4)]),flip(a)].
% 0.82/1.31 2090 a22 = a21. [back_rewrite(1968),rewrite([1996(1),2011(2),1(3)]),flip(a)].
% 0.82/1.31 2091 a20 = a21. [back_rewrite(1965),rewrite([1996(1),2055(2),1(3)]),flip(a)].
% 0.82/1.31 2093 product(a21,a11) = a19. [back_rewrite(787),rewrite([2090(1),2055(3),2011(5),33(6),2055(5),2011(7),33(8)])].
% 0.82/1.31 2099 product(product(A,product(a19,a21)),product(a11,a21)) = product(product(A,a21),a11). [back_rewrite(1490),rewrite([2055(2),2055(6),2055(10),133(14)])].
% 0.82/1.31 2110 product(a21,product(product(a15,a19),a11)) = product(product(a18,a19),a11). [back_rewrite(745),rewrite([2091(1)])].
% 0.82/1.31 2122 product(product(a19,a5),a12) = product(a21,a5). [back_rewrite(566),rewrite([2091(6)])].
% 0.82/1.31 2133 product(product(A,a11),a19) = product(product(A,a21),a11). [back_rewrite(1437),rewrite([2091(2),2091(6),2099(8)]),flip(a)].
% 0.82/1.31 2183 product(product(product(A,a5),a12),a11) = product(A,a21). [back_rewrite(1021),rewrite([2087(7)])].
% 0.82/1.31 2218 a5 = a19. [back_rewrite(5),rewrite([2087(1),2093(3)]),flip(a)].
% 0.82/1.31 2219 tuple(a21,a21,a21,a21,a21,a21,a21,a21,a21,a21,a10,a11,a19,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a21,a21,a21,a21,a21,a21) != tuple(a21,a21,a21,a21,a21,a21,a21,a21,a21,a19,a11,a12,a6,a15,a16,a7,a8,a19,a21,a9,a10,a17,a18,a13,a14,a21,a21,a21,a21,a21,a21) # answer(goal). [back_rewrite(2088),rewrite([2089(1),2089(7),2218(13),2091(26),2090(28),2089(36),2218(42),2091(51),2090(59)])].
% 0.82/1.31 2231 a14 = a17. [back_rewrite(702),rewrite([2218(3),1(5),16(4),1(3),2218(3),426(4),148(6),12(4),13(4)]),flip(a)].
% 0.82/1.31 2234 product(product(A,a21),a11) = product(product(A,a19),a12). [back_rewrite(666),rewrite([2218(1),1(3),35(6),2133(4),2218(7),1(9),158(8)])].
% 0.82/1.31 2236 a10 = a17. [back_rewrite(652),rewrite([2218(3),1(5),43(4),13(3),2231(1),2218(3),33(6)]),flip(a)].
% 0.82/1.31 2238 product(a11,a19) = a12. [back_rewrite(589),rewrite([2218(2),1(4),48(3)]),flip(a)].
% 0.82/1.31 2245 a18 = a13. [back_rewrite(601),rewrite([2236(1),52(3),2218(2),16(3),17(3),2218(4),1(5),12(4)])].
% 0.82/1.31 2270 product(product(product(A,a19),a12),a11) = product(A,a21). [back_rewrite(2183),rewrite([2218(1)])].
% 0.82/1.31 2279 product(a21,a19) = product(a19,a12). [back_rewrite(2122),rewrite([2218(2),1(3),2218(5)]),flip(a)].
% 0.82/1.31 2373 product(a9,a19) = a8. [back_rewrite(445),rewrite([2218(3),1(4),2218(5),7(6)])].
% 0.82/1.31 2400 a17 = a15. [back_rewrite(51),rewrite([2218(2),16(3)])].
% 0.82/1.31 2401 a13 = a11. [back_rewrite(47),rewrite([2218(2),12(3)])].
% 0.82/1.31 2403 a9 = a7. [back_rewrite(8),rewrite([2218(2),43(3)]),flip(a)].
% 0.82/1.31 2404 a6 = a11. [back_rewrite(6),rewrite([2218(1),54(3),2245(1),2401(1)]),flip(a)].
% 0.82/1.31 2440 a15 = a11. [back_rewrite(728),rewrite([2400(1),2236(2),2400(2),1(3),1(3),2400(3),1(5),54(4),2245(2),2401(2)])].
% 0.82/1.31 2441 product(a7,a11) = a7. [back_rewrite(639),rewrite([2403(1),2245(2),2401(2),2236(4),2400(4),2440(4),33(5),2403(2),2400(3),2440(3),2236(4),2400(4),2440(4),1(5)]),flip(a)].
% 0.82/1.31 2442 a7 = a11. [back_rewrite(638),rewrite([2236(1),2400(1),2440(1),2403(2),2236(3),2400(3),2440(3),2441(4),46(3),2236(1),2400(1),2440(1),2403(2),2400(3),2440(3),2236(4),2400(4),2440(4),1(5),2441(4)]),flip(a)].
% 0.82/1.31 2444 product(A,a11) = product(A,a21). [back_rewrite(1258),rewrite([2440(1),2133(4),2234(4),2245(5),2401(5),2270(6),2440(3),2245(4),2401(4),1(5)]),flip(a)].
% 0.82/1.31 2446 product(A,a21) = product(A,a19). [back_rewrite(740),rewrite([2403(1),2442(1),2444(2),2440(3),2444(4),33(4),2400(3),2440(3),2444(4),2403(5),2442(5),2444(6),33(6),2440(3),2444(4)]),flip(a)].
% 0.82/1.31 2449 tuple(a21,a21,a21,a21,a21,a21,a21,a21,a21,a21,a11,a11,a19,a11,a11,a11,a11,a11,a19,a8,a11,a16,a11,a12,a11,a21,a21,a21,a21,a21,a21) != tuple(a21,a21,a21,a21,a21,a21,a21,a21,a21,a19,a11,a12,a11,a11,a16,a11,a8,a19,a21,a11,a11,a11,a11,a11,a11,a21,a21,a21,a21,a21,a21) # answer(goal). [back_rewrite(2219),rewrite([2236(11),2400(11),2440(11),2231(14),2400(14),2440(14),2440(15),2404(16),2442(17),2245(18),2401(18),2403(21),2442(21),2400(23),2440(23),2401(25),2404(45),2440(46),2442(48),2403(52),2442(52),2236(53),2400(53),2440(53),2400(54),2440(54),2245(55),2401(55),2401(56),2231(57),2400(57),2440(57)])].
% 0.82/1.31 2456 a12 = a11. [back_rewrite(626),rewrite([2231(1),2400(1),2440(1),2442(3),2444(4),2446(4),1(4),2231(3),2400(3),2440(3),2444(4),2446(4),1(4),2238(3),2442(3),2444(4),2446(4),12(4),2401(2),2231(3),2400(3),2440(3),1(4)])].
% 0.82/1.31 2461 a11 = a21. [back_rewrite(2110),rewrite([2440(2),2238(4),2456(2),1(4),2444(3),1(3),2245(2),2401(2),2238(4),2456(2),1(4)]),flip(a)].
% 0.82/1.31 2462 a21 = a19. [back_rewrite(358),rewrite([2440(1),2461(1),2279(3),2456(2),2461(2),2446(3),1(3),2245(2),2401(2),2461(2),2446(3),1(3),2440(2),2461(2),2440(3),2461(3),2245(4),2401(4),2461(4),1(5),1(4)]),flip(a)].
% 0.82/1.31 2472 a16 = a19. [back_rewrite(52),rewrite([2400(1),2440(1),2461(1),2462(1),1(3)]),flip(a)].
% 0.82/1.31 2474 a8 = a19. [back_rewrite(2373),rewrite([2403(1),2442(1),2461(1),2462(1),1(3)]),flip(a)].
% 0.82/1.31 2477 $F # answer(goal). [back_rewrite(2449),rewrite([2462(1),2462(2),2462(3),2462(4),2462(5),2462(6),2462(7),2462(8),2462(9),2462(10),2461(11),2462(11),2461(12),2462(12),2461(14),2462(14),2461(15),2462(15),2461(16),2462(16),2461(17),2462(17),2461(18),2462(18),2474(20),2461(21),2462(21),2472(22),2461(23),2462(23),2456(24),2461(24),2462(24),2461(25),2462(25),2462(26),2462(27),2462(28),2462(29),2462(30),2462(31),2462(33),2462(34),2462(35),2462(36),2462(37),2462(38),2462(39),2462(40),2462(41),2461(43),2462(43),2456(44),2461(44),2462(44),2461(45),2462(45),2461(46),2462(46),2472(47),2461(48),2462(48),2474(49),2462(51),2461(52),2462(52),2461(53),2462(53),2461(54),2462(54),2461(55),2462(55),2461(56),2462(56),2461(57),2462(57),2462(58),2462(59),2462(60),2462(61),2462(62),2462(63)]),xx(a)].
% 0.82/1.31
% 0.82/1.31 % SZS output end Refutation
% 0.82/1.31 ============================== end of proof ==========================
% 0.82/1.31
% 0.82/1.31 ============================== STATISTICS ============================
% 0.82/1.31
% 0.82/1.31 Given=275. Generated=7942. Kept=2474. proofs=1.
% 0.82/1.31 Usable=6. Sos=63. Demods=89. Limbo=21, Disabled=2419. Hints=0.
% 0.82/1.31 Megabytes=1.75.
% 0.82/1.31 User_CPU=0.22, System_CPU=0.01, Wall_clock=1.
% 0.82/1.31
% 0.82/1.31 ============================== end of statistics =====================
% 0.82/1.31
% 0.82/1.31 ============================== end of search =========================
% 0.82/1.31
% 0.82/1.31 THEOREM PROVED
% 0.82/1.31 % SZS status Unsatisfiable
% 0.82/1.31
% 0.82/1.31 Exiting with 1 proof.
% 0.82/1.31
% 0.82/1.31 Process 25573 exit (max_proofs) Sun May 29 03:52:14 2022
% 0.82/1.31 Prover9 interrupted
%------------------------------------------------------------------------------